Richard H. Zander
Res Botanica
February 19, 2003

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Originally published in Bulletin of the Buffalo Society of Natural Sciences 36: 81–115. 1998.





Richard H. Zander

Division of Botany, Buffalo Museum of Science, 1020 Humboldt Parkway,

Buffalo, New York 14211


Abstract: A key is presented for the 22 known species of Didymodon (Musci) in North America north of Mexico, with taxonomic commentaries for each. A phylogram combining PCA ordination and a cladogram shows evident morphological convergence between five pairs of species. Six species are interpreted as surviving ancestors. Phylogenetic analysis is an assumption-laden and belief-oriented attempt at reconstructing a past unique conditional chain of events. Through misapplication of the theory of statistical relevance, the fine structure of trees of maximum synapomorphy is generally artificial and antiparsimonious; also, trees of maximum likelihood are often not probabilistic estimations. Cladistic analysis, however, may be useful under certain conditions in devising general classifications and in phylo­grammatic analysis.


The moss genus Didymodon as expanded by Saito (1975) has proven large and complex in North America (e.g., studies by Zander 1978a, 1981, 1994). Work on the genus Didymodon for the bryophyte volume of the Flora of North America (FNA Editorial Committee 1993) is sufficiently advanced that an annotated key to the 22 known species might be profitably presented in advance of FNA final publication four or five years from now. A phyletic evolutionary study addresses apparent morphological convergence, while the statistical assumptions and methods used for obtaining modern detailed classifications are reviewed.


Many species of the genus are common and often difficult to distinguish. The present study updates the above-cited previous work. The key below should aid considerably the floristic and ecological studies by other botanists that have been given impetus by the FNA project. Descriptions and details of geographic ranges, habitats and sporo­phyte maturation dates will be given in that work.




DIDYMODON Hedw., Sp. Musc. 104, 1801.

Sections of the genus previously recognized for North America north of Mexico are: Didymodon Hedw. sect. Didymodon, type: Didymodon rigidulus Hedw.; Didymodon sect. Asteriscium (C. Müll.) Zand., type: Didymodon umbrosus (C. Müll.) Zand.; Didymodon sect. Fallaces (De Not.) Zand., type: Didymodon fallax (Hedw.) Zand.; and Didymodon sect. Vineales (Steere) Zand., type: Didymodon vinealis (Brid.) Zand. Sectional synonyms and descriptions were given and species were assigned to the sections by Zander (1978a, 1993). Many species, however, remain problematic in assignment to sections.


There are about 122 species of Didymodon worldwide (Zander 1993), growing on a variety of substrates, mostly soil and rock. It is a large genus widely diversified in temperate and montane areas worldwide.


The genus Didymodon is distinguished from a similarly widely distributed relative Barbula Hedw., with which it is often confused, by its usually lanceolate to long-lanceolate leaves, axillary hairs with one or more brown basal cells, basal laminal cells less strongly differentiated from the upper, ventral costal cells usually quadrate (six species have elongate ventral costal cells), laminal papillae absent or simple or only occasionally multiplex, gemmae composed of only 1–10 cells, and peristome teeth seldom long and twisted (see also Saito 1975).




1. Leaf apices caducous or very fragile.

2. Leaf apices not swollen, usually evenly narrowing.

3. Cells of leaf apex smooth...... 1. Didymodon rigidulus (var. icmadophilus)

3. Cells of leaf apex weakly conic-mamillose.......... 14. Didymodon sinuosus

2. Leaf apices apically swollen as a propagulum.

4. Upper laminal cells 13–15 mm wide................... 3. Didymodon johansenii

4. Upper laminal cells 8–10 mm wide............. 2. Didymodon anserinocapitatus

1. Leaf apices intact or only occasionally broken.

5. Plants in nature red- to black-brown, leaves not keeled, not highly recurved, margins finely crenulate by bulging cell walls, usually plane above midleaf, costa thin, 2–3 cells wide above midleaf, laminal papillae absent or low, massive and lens-shaped.

6. Leaves dimorphic: cochleariform, epapillose leaves present on fragile branchlets or portions of some stems................................ 9. Didymodon subandreaeoides

6. Leaves monomorphic.

7. Plants often fruiting, leaf apices acute, propagula absent 7. Didymodon nigrescens

7. Plants sterile, leaf apices obtuse, clusters of unicellular propagula in the leaf axils.................................... 8. Didymodon perobtusus

5. Plants without the above exact combination of characters, usually green, orange or red, sometimes keeled or highly recurved, margins usually entire or dentate, often recurved above midleaf, costa usually broad, of 2–4 or more cells wide above midleaf, laminal papillae seldom absent or massive and lens-shape.

8. Costa with elongate superficial ventral cells.

9. Leaf base auriculate or weakly winged at insertion, apex often whip-like, very long-acuminate...................................... 18. Didymodon leskeoides

9. Leaf base gradually or quickly narrowed to the insertion, not flaring, apex obtuse to acuminate.

10. Leaves ovate to long-elliptical, apex often obtuse, costa often ending before the apex........................... 21. Didymodon tophaceus

10. Leaves short- to long-lanceolate, apex always acute, costa subpercurrent to short-excurrent.

11. Plants with axillary gemmae, leaves mostly 0.9–1.1 mm long, catenulate when dry........................................... 17. Didymodon michiganensis

11. Plants lacking gemmae in leaf axils, leaves usually 1.2–5.0 mm long, appressed-incurved to weakly spreading when dry.

12. Leaves when moist spreading to weakly recurved, usually lying flat, costa usually distinctly widened at base.

13. Leaves 0.8–1.7(–2.5) mm, acuminate, upper cell walls little thickened or irregularly thickened and lumens angular, trigones absent or weakly developed................. 15. Didymodon fallax

13. Leaves usually 2.0(–3.5) mm, upper cell walls irregularly thickened and trigonous, trigones as large as the lumens or nearly so...................................... 20. Didymodon giganteus

12. Leaves when moist strongly recurved and keeled, lying on their sides, costa little widened at base.

14. Stems to 2.5 cm, leaves usually 0.8–2.0 mm long 16. Didymodon ferrugineus

14. Stems usually more than 3 cm, leaves mostly 2.0–2.5 mm long 19. Didymodon maximus

8. Costa with quadrate or occasionally short-rectangular superficial ventral cells, or, if elongate, then upper laminal cells bistratose.

15. Leaves ventrally with a narrow medial channel about the width of the costa at least at leaf apex, apex mostly apiculate by one or more conical cells, costa usually percurrent, margins usually recurved, often to near the apex, laminal color reaction to KOH usually brick-red, occasionally orange.

16. Entire leaf strongly both reflexed backwards and strongly keeled when moist, papillae when present simple, stem central strand usually absent 22. Didymodon asperifolius

16. Entire leaf spreading to weakly reflexed backwards and weakly keeled when moist, papillae when present bifid to multiplex, stem central strand present.

17. Leaves deltoid to short-lanceolate, to 1.5 or rarely to 2.0 mm long, margins recurved or revolute to near apex, propagula sometimes present.

18. Costa often with an apical conical cell, costa gradually narrowing distally, ventral surface nearly flat and not forming a wide pad of cells (but costa occasionally thickened and bulging ventrally), guide cells in 1 layer, leaf margins recurved to tightly revolute, gemmae often present in leaf axils

......................................... 12. Didymodon brachyphyllus

18. Costa usually lacking an apical conical cell, costa wider at midleaf than below, with bulging ventral surface forming a long-elliptical unistratose pad of cells, guide cells in 2(–3)  layers, leaf margins loosely revolute, tubers occasional on basal rhizoids .................................. 13. Didymodon nevadensis

17. Leaves short- to long-lanceolate or long-triangular, to 4.0 mm long, margins recurved near base or up to lower 2/3 of leaf, propagula rare.

19. Leaves long-ovate to broadly lanceolate, apex blunt to broadly acute, upper marginal cells bistratose marginally, throughout or or occasionally in patches, laminal color reaction to KOH deep yellow or orange-brown to red-brown  ................ 11. Didymodon nicholsonii

19. Leaves triangular to narrowly lanceolate, apex narrowly acute, upper marginal cells unistratose or occasionally bistratose in patches, laminal color reaction to KOH deep red to red-brown ............................................. 10. Didymodon vinealis

15. Leaves ventrally very widely channeled medially or merely slightly concave across leaf, apex seldom apiculate by a conical cell, costa percurrent or excurrent as a multicellular, stout mucro, margins plane to recurved below midleaf, laminal color reaction to KOH usually negative, yellow or orange, seldom brick-red.

20. Axillary gemmae present.

21. Propagula all multicellular, leaf apex acute 1. Didymodon rigidulus (var. rigidulus)

21. Propagula mostly unicellular, leaf apex broadly obtuse.

22. Costa narrow, usually 2 cells wide at midleaf, not strongly spurred ................................... 8. Didymodon perobtusus

22. Costa broad, 4–6 cells wide at midleaf and often strongly spurred by rows of lateral cells ending abruptly in the lamina 6. Didymodon revolutus

20. Axillary gemmae absent.

23. Upper lamina unistratose or occasionally bistratose in small patches.

24. Plants flagellate, leaves strongly appressed when dry, linear-lanceolate, costa long-excurrent

.......................... 1. Didymodon rigidulus (var. ditrichoides)

24. Plants not flagellate, leaves appressed-incurved to weakly twisted and weakly spreading when dry, short- to long-lanceolate, costa short- to long-excurrent.

25. Leaf base rectangular and gradually widened, costa short-excurrent, unbroken, basal leaf cells short-rectangular 1. Didymodon rigidulus (var. gracilis)

25. Leaf base ovate and often abruptly widened, costa long-excurrent, often fragile, basal leaf cells quadrate 1. Didymodon rigidulus (var. icmadophilus)

23. Upper lamina bistratose totally or just along margins.

25. Upper lamina entirely bistratose 1. Didymodon rigidulus (var. subulatus)

25. Upper lamina bistratose along margins.

26. Basal laminal cells with firm, weakly to strongly thickened walls, differentiated usually only medially.

27. Leaves long-ligulate to lanceolate 1. D. rigidulus (var. rigidulus)

27. Leaves short-ovate........................... 6. D. revolutus

26. Basal laminal cells thin-walled and usually somewhat inflated,  often bulging-rectangular, differentiated across leaf base.

28. Leaves long-lanceolate, usually smooth or weakly papillose, marginal basal cells narrowly rectangular in 2–4 rows, ventral superficial cells of costa usually elongate, stem with hyalodermis............................. 5. Didymodon umbrosus

28. Leaves short-lanceolate, smooth to strongly papillose, marginal basal cells not or weakly differentiated from the medial, ventral superficial cells of costa quadrate, stem lacking hyalodermis or this weakly differentiated.. 4. D. australasiae


1. Didymodon rigidulus Hedw., Sp. Musc. 104. 1801.


Barbula acuta var. bescherellei (Sauerb. ex Jaeg. & Sauerb.) Crum; Barbula bescherellei Sauerb. in Jaeg.; Barbula rigidula (Hedw.) Mild.; Barbula valida (Limpr.) Möll.; Barbula waghornei Kindb.; Didymodon fuscoviridis Card.; Didymodon mexicanus Besch.; Didymodon rigidulus subsp. validus (Limpr.) Loeske; Didymodon rigidulus var. validus (Limpr.) R. Düll; Tortula rigidula (Hedw.) Lindb.; Tricho­stomum rigidulum (Hedw.) Turn.


The species s. lat., as emended by Zander (1981) is polymorphic, with several varieties distinguished by fairly good correlations of combinations of characters. Speci­mens of intermediate morphology that are not clearly assignable to any one variety may be identified as D. rigidulus s. lat. Although some authors use the presence of axillary gemmae as diagnostic of the typical variety, the other varieties, notably var. gracilis, may occasionally have such. These gemmae are also found in other species, especially those of the D. vinealis complex, which may likewise have a bistratose upper lamina, e.g., D. vinealis itself may have bistratose upper laminal cells, and should be carefully distinguished. From D. vinealis, this species may be distinguished by the combination of long-triangular or oblong-lanceolate leaf shape, usual presence of many gemmae in the leaf axils and the commonly yellow-green color in nature (sometimes blackish green, rarely reddish below) and yellow or yellow-orange color in KOH.




1. Upper lamina entirely bistratose...1b. Didymodon rigidulus var. subulatus

1. Upper lamina unistratose or bistratose only at the extreme leaf apex or on the margins.

2. Leaves oblong-lanceolate to long-triangular; costa usually short-excurrent and blunt; apex and upper margins generally bistratose; gemmae often present .............

1a. Didymodon rigidulus var. rigidulus

2. Leaves lanceolate; costa percurrent to long-excurrent, usually sharp; upper margins unistratose or less commonly bistratose in patches; gemmae usually absent.

3. Plants flagellate, leaves strongly appressed when dry, linear-lanceolate, costa long-excurrent................... 1c. Didymodon rigidulus var. ditrichoides

3. Plants thickly leaves, leaves appressed to spreading when dry, short-lanceolate to long-lanceolate; costa percurrent to long-excurrent.

4. Leaves short- to long-lanceolate; base evenly broadened, square or rectangular; costa percurrent to long-excurrent as a rigid subula; upper cells generally papillose, oval or rounded-quadrate; basal cells short-rect­angular; gemmae occasionally present........... 1d. Didymodon rigidulus var. gracilis

4. Leaves long-lanceolate; base abruptly broadened, ovate; costa long-excurrent as a straight or flexuose, often fragile subula; upper cells usually smooth, lumens usually angular, basal cells usually quadrate; gemmae very rare 1e. Didymodon rigidulus var. icmadophilus


1a. Didymodon rigidulus Hedw. var. rigidulus


Didymodon rigidulus var. rigidulus is relatively uniform in eastern North America, with slightly spreading, oblong-lanceolate to long-triangular leaves with thickened upper margins, percurrent or short-excurrent costa, thick-walled cells, gemmae usually present, and the peristome straight or only weakly twisted (var. gracilis and var. icmadophilus sometimes have long peristomes which are somewhat twisted). When the upper margins are not bistratose or are only slightly so, it can be difficult to identify, especially as it may occasionally have the costal groove of D. vinealis. It intergrades in the West with the other varieties, and propagula are less common. The typical variety, with distinctive oblong-lanceolate leaf shape and propagula, is rare in the Arctic.


1b. Didymodon rigidulus var. subulatus (Thér. & Bartr.) Zand., Cryptogamie, Bryol. Lichénol. 2: 395. 1981.


Didymodon mexicanus var. subulatus Thér. & Bartr. ex Bartr., Bryologist 29: 1. 1926.


This variety is similar to var. icmadophilus in leaf shape and most other characters, and intergrades occur. It may be regarded as a somewhat distinctive geographical variant.


1c. Didymodon rigidulus var. ditrichoides (Broth.) Zand., Phytologia 41: 20. 1978.


Barbula ditrichoides Broth., Sitzungsb. Akad. Wiss. Wien Math. Nat. Kl. 133: 566. 1924; Didymodon acutus var. ditrichoides (Broth.) Zand.


The var. ditrichoides is a highly reduced, flagellate form of the var. icmadophilus but has a distinctive appearance. It is disjunct from montane China (Chen 1941). The olive coloration and general appearance is similar to that of D. leskeoides but the plant is somewhat smaller and the alar auricles are lacking.


1d. Didymodon rigidulus var. gracilis (Hook. & Grev.) Zand., Cryptogamie, Bryol. Lichénol. 2: 393. 1981.


Tortula gracilis Hook. & Grev., Edinburgh J. Sci. 1:300. 1824; Barbula acuta (Brid.) Brid.; Didymodon acutus (Brid.) Saito; Tortula acuta Brid.


The var. gracilis may sometimes have gemmae and the upper lamina is sometimes bistratose in patches, but it differs from var. rigidulus most clearly its the short- to long-lanceolate leaves. The upper laminal cells are commonly papillose, and their lumens are oval or rounded-quadrate. Because of intergradation, some collections must be assigned to this variety only on the basis of a majority of the characters given in the key. Problems involving synonymy of heterotypic type specimens that cannot be confidently assigned to any infraspecific taxon are discussed by Zander (1981). Although leaves in this variety are short in dry habitats—in the lower range for the species, which commonly causes the stems to appear filiform—leaf length in collections from moist environments may be in the upper range.


1e. Didymodon rigidulus var. icmadophilus (C. Müll.) Zand., Cryptogamie, Bryol. Lichénol. 2: 394. 1981.


Barbula icmadophila C. Müll., Syn. Musc. 1: 614. 1849; Barbula acuta subsp. icmadophila (C. Müll.) Amann; Barbula acuta var. icmadophila (C. Müll.) Crum; Barbula acuta ssp. icmadophila (C. Müll.) Podp.; Barbula gracilis ssp. icmadophila (C. Müll.) Amann; Barbula grailis var. icmadophila (C. Müll.) Moenk.; Didymodon acutus var. icmadophilus (C. Müll.) Zand.; Didymodon icmadophilus C. Müll.) Saito as “icmadophyllus”; Tortula icmadophila (C. Müll.) Lindb.


This taxon is similar to var. gracilis in general aspect but the leaf apices are usually hairlike, the upper laminal cells are usually smooth and their lumens usually angular. Var. icmadophilus is common on the North American Plains, where it may occur in association with D. fallax. The var. icmadophilus is dark green, sometimes with a blue-black cast, and has boat-shaped, elon­gate, erect leaves that are only slightly incurved when dry, laminal cells smooth and costa excurrent and often flexuose. Didymodon fallax has light green to reddish green color and triangular leaves that are often incurved or even catenulate when dry, costa percurrent and leaves papillose.


2. Didymodon anserinocapitatus (X.-j. Li) Zand., Bull. Buffalo Soc. Nat. Sci. 32: 162. 1993.


Barbula anserinocapitata X.-j. Li, Acta Bot. Yunnan. 3: 103, 1981.


This rare Asian species is known from only two sites in the New World: Colorado (Freemont Co., 4.5 km up lower portion of Phantom Canyon, 1500–2200 m elev., red-sandstone cliff, Weber, Herman & Feddema, 1 June 1971, herb. no. B-37528, COLO), and New Mexico (San Miguel Co., Pecos, along Pecos River, 2100 m elev., Richards & Drouet 456, 21 Oct. 1939, DUKE). It differs from D. johansenii mainly by the smaller upper laminal cells and the double layer of guide cells, with the appearance of a robust D. rigidulus var. icmadophilus, which differs, however, by leaf apices never swollen though sometimes fragile. Details were reported by Zander and Weber (1997).


3. Didymodon johansenii (Williams) Crum, Canad. Field-Nat. 83: 157. 1969.


Barbula johansenii Williams, Rep. Canad. Arctic Exped. 1913–18, Bot. 4E: 4. 1921.


Distinctive characters of this Arctic species are the striate peristome teeth, deciduous, clavate leaf apex and large, trigonous laminal cells. Most collections of D. johansenii have truncate leaves, with the propaguliform apex fallen in all but the most immature leaves; the leaves are oblong-lanceolate. Some specimens (e.g., Northwest Territories, Scotter 22404, MICH) of this species, however, approach D. ridigulus var. icmadophilus in the green color, ovate leaf base, not much widened or tapering and apparently non-deciduous leaf apices. These collections can be rightly placed by the presence of claviform apices in at least some leaves (especially those near an inflorescence) and the large upper laminal cells, which often have trigones. Didymodon nigrescens has fragile, clavate tips to its perichaetial leaves, but the crenulate upper leaf margins and very thin costa will distinguish it.


4. Didymodon australasiae (Hook. & Grev.) Zand., Phytologia 41: 21. 1978.


Tortula australasiae Hook. & Grev., Edinburgh J. Sci. 1: 301. 1824; Didymodon diaphanobasis Card.; Didymodon diaphanobasis var. angustifolius Thér. in Bartr.; Didymodon torquescens Card.; Husnotiella torquescens (Card.) Bartr.; Tricho­stomopsis australasiae (Hook & Grev.) Robins.; Tricho­stomopsis brevifolia Bartr.; Tricho­stomopsis crispifolia Card.; Tricho­stomopsis diaphanobasis (Card.) Grout; Tricho­stomopsis fayae Grout


In Didymodon, hydroids are found only in the costae of D. australasiae, D. umbrosus, D. revolutus and D. vinealis. The ventral stereid band usually absent in well developed specimens of the first three species, and is often absent in the fourth. Intergrades exist between D. australasiae and D. umbrosus, but the extreme forms are common and quite distinctive.


5. Didymodon umbrosus (C. Müll.) Zand., Phytologia 41: 22. 1978.


Barbula umbrosa C. Müll., Linnaea 42: 340. 1879; Didymodon australasiae var. umbrosus (C. Müll.) Zand.; Tricho­stomopsis crispifolia Card.; Tricho­stomopsis umbrosa (C. Müll.) Robins.


This species is one of a number of mundivagant taxa the distribution of which is associated with human activities (e.g., Eckel 1986). The transversely slit basal cells are distinctive in many specimens though also found in taxa of the Dicranaceae (Zander & Cleef 1982).


6. Didymodon revolutus (Card.) Williams, Bryologist 16: 25. 1922.


Husnotiella revoluta Card., Rev. Bryol. 36:71. 1909; Husnotiella revoluta var. palmeri (Card.) Thér.


Distinctive characters in combination are: arid habitat, ovate leaves with often revolute margins, subpercurrent, strongly spurred costa (with one or more lateral costal cells wending into the lamina), one layer of guide cells, and a rudimentary or absent peristome. Like D. perobtusus and Bryoerythrophyllum calcareum (Thér.) Zand., D. revolutus has unicellular gemmae occasionally present in the leaf axils.


7. Didymodon nigrescens (Mitt.) Saito, J. Hattori Bot. Lab. 39: 510. 1975.


Barbula nigrescens Mitt., J. Linn. Soc. Bot. Suppl. 1: 36. 1859; Barbula rufofusca Lawt. & Herm.


The specimens cited from the Firth River Basin by Steere (1978), det. R. Zander, are actually D. subandreaeoides. The distinguishing characters of D. nigrescens are the blackish coloration when dry (red in KOH), thin costa, and upper laminal margins minutely crenulate by the small, bulging marginal cells. This and the following two species appear to be closely related. Didymodon asperifolius is similar but may be distinguished by its longer leaves, straight or reflexed to strongly recurved when wet, upper margins recurved, upper laminal cells larger, 10–13 mm wide, epapillose or papillae simple, and costa usually comparatively wide.


8. Didymodon perobtusus Broth., Rev. Bryol. n. ser. 2: 1. 1929.


Barbula perobtusa (Broth.) Chen.


Didymodon perobtusus has several characters in common with D. revolutus (Card.) Williams of the southwestern U.S.A. and Mexico, including leaf and laminal papillae shape and unicellular gemmae borne in dense axillary clusters; however, D. revolutus differs by the strongly recurved to revolute margins, leaf cells with thin, light yellow walls, and gemmiferous plants uncommon. Both North American collections seen were from stations in which D. subandreaeoides is also present, growing in separate or occasionally confluent cushions. The taxonomic position of D. perobtusus is not clear. It is placed near D. subandreaeoides because of dark, reddish color, and similarity of areolation and laminal papillae. It may, however, turn out to be related to D. tophaceus, with which it has a certain resemblance.


9. Didymodon subandreaeoides (Kindb.) Zand., Phytologia 41: 23. 1978.


Barbula subandreaeoides Kindb., Rev. Bryol. 32: 36. 1909; Barbula andreaeoides Kindb.


The distribution of D. subandreaeoides is through inland mountain ranges from the North Slope of Alaska south along the Cordillera into Colorado. It is commonly associated with Molendoa sendtneriana (BSG) Limpr. with which it is often mixed in collections, and which apparently has a similar distribution in northwestern North America. The fragile, cochleariform-leaved branchlets may possibly figure in asexual reproduction. Andreaea rothii Web. & Mohr lacking sporophytes may be confused with D. subandreaeoides, but may be distinguished by the former's autoicous inflorescence, its ecostate, oblong perichaetial leaves, leaves monomorphic, cauline leaves plane, cells with bulging but epapillose bright orange walls, bistratose along the upper margins, middle lamellae often evident between basal cells, and costa not sharply distinguished from laminal cells above midleaf.


10. Didymodon vinealis (Brid.) Zand., Phytologia 41: 25. 1978.


Barbula vinealis Brid., Bryol. Univ. 1: 830. 1827; Barbula bakeri Card. & Thér.; Barbula circinnulata C. Müll. & Kindb; Barbula cylindrica (Tayl.) Schimp. in Boul.; Barbula fallax var. vinealis (Brid.) Hüb.; Barbula flexifolia Hampe; Barbula horridifolia C. Müll. & Kindb.; Barbula laterita Kindb.; Barbula pseudorigidula C. Müll. & Kindb.; Barbula robustifolia C. Müll. & Kindb.; Barbula semitorta Sull.; Barbula subcylindrica Broth.; Barbula subfallax C. Müll.; Barbula subgracilis C. Müll. & Kindb. in Macoun (syn. nov.); Barbula tortellifolia C. Müll. & Kindb.; Barbula treleasei Card. & Thér.; Barbula vinealis subsp. cylindrica (Tayl.) Podp.; Barbula vinealis subsp. cylindrica (Tayl.) Podp.; Barbula vinealis var. flaccida BSG; Barbula vinealis var. flaccida BSG; Barbula virescens Lesq.; Didymodon vinealis var. flaccidus (BSG) Zand.; Didymodon vinealis var. flaccidus (BSG) Zand.


This species is often difficult to distinguish from sterile forms of D. rigidulus, but the red color in nature, the often strongly papillose laminal cells, and the distinct groove down the ventral surface of the leaf along the costa are characteristic features. Some but not all specimens may be quickly assigned to this taxon by the unique deep slit floored by elongate cells on the ventral surface of the costal apex (the ventral epidermis being absent), which is visible as a white window dorsally. Bryoerythrophyllum recurvirostrum (Hedw.) Chen, though equally bright red in KOH solution, is immediately distinguished by the clear, enlarged basal cells. Like Bellibarbula recurva (Griff.) Zand., small forms of D. vinealis may have quadrate or very short-rectangular basal cells and a sinuose costa, but the former has thick-walled basal cells and the costa twists laterally (not vertically as in the concave upper portion of the leaf of D. vinealis), and the ventral cells of the costa are commonly elongate, 2:1 or more. Two specimens of the new synonym D. subgracilis: Canadian Musci, B.C, Yale, on rocks, Coll. Macoun, May 18, 1889, isotype, CANM, and “Canadian Mosses, Collected by John Macoun. Determined by Dr. N. C. Kindberg. 58a. Barbula subgracilis Kindb. On rocks, [Casrartne?] Bay, [V.I.?], June 24, 1908,” CANM, are both Didymodon vinealis with typical long, twisted peristomes.



1. Peristome present, well developed, cells of operculum twisted 10a. Didymodon vinealis var. vinealis

1. Peristome absent, cells of operculum straight or nearly so 10b. Didymodon vinealis var. rubiginosus


10a. Didymodon vinealis var. vinealis


Some collections have elongate, very fragile leaf apices that are sometimes bistratose, but are not clavate as in D. anserinocapitatus. The var. flaccidus was synonymized by Sollman (1983), but may be distinguished if needed by the leaves long, often 2.5 mm or longer, crisped when dry, and the upper margins plane. The peristome commonly falls with the operculum in many specimens seen, and may appear to be absent, but the operculum has twisted cells and is thin-walled.


10b. Didymodon vinealis var. rubiginosus (Mitt.) Zand., Cryptogamie Bryol. Lichénol. 2: 379–422. 1981.


Barbula rubiginosa Mitt., J. Linn. Soc. Bot. 8: 27. 1864; Didymodon occidentalis Zand.


Although the gametophyte of var. rubiginosus varies little morphologically, having short-lanceolate to triangular leaves, it is well within the range of variation of the typical variety. It has been reputed (e.g., Zander 1981) to differ in a very narrow upper lamina that is often fragile or notched, or by large upper laminal cells, or by quadrate basal cells, but these characters are insufficient to distinguish sterile specimens. Although the eperistomate sporophyte is required for accurate identification, var. rubiginosus fruits abundantly. The spores are slightly smaller, 8–11 mm, than those of the typical variety. Forms of var. vinealis with weakly twisted opercular cells and weak, very fragile peristomes (e.g., California, Flowers 6561, COLO) may be taken as intermediates.


11. Didymodon nicholsonii Culm., Rev. Bryol. 34: 100. 1907.


Barbula nicholsonii Culm.; Barbula rigidula ssp. nicholsonii (Culm.) Dix.; Didymodon rigidulus var. nicholsonii (Culm.) Roth; Didymodon luridus ssp. nicholsonii (Culm.) Loeske; Didymodon luridus var. nicholsonii (Culm.) Loeske; Didymodon vinealis var. nicholsonii (Culm.) Zand.


This species intergrades somewhat with D. vinealis but the ovate-lanceolate leaf with a rather broad apex usually is distinctive, as is the tendency toward a partially or completely bistratose upper lamina. The western species Grimmia cinclidontea C. Müll. is disconcertingly similar and grows in the same wet habitats, but is autoicous, has smooth leaf cells and a homogeneous costal section.


12. Didymodon brachyphyllus (Sull.) Zand., Phytologia 41: 24. 1978.


Barbula brachyphylla Sull. in Whipple, Rept. Pacific R. R. Surv., Bot. 4: 186. 1856; Barbula olivacea (Mitt.) Besch.; Didymodon reedii Robins.; Didymodon vinealis var. brachyphyllus (Sull.) Zand.; Tortula olivacea Mitt.


One robust collection of D. brachyphyllus (New Mexico: Bartram 99, US), in its stout costa matches European material of D. cordatus Jur., while two other collections (Colorado: Hermann 23431, MICH, and the type of D. reedii) are similar to the weaker nerved but otherwise identical Asian D. tectorum (C. Müll.) Saito. Given the variation seen, all American collections are referred to D. brachyphyllus, which is conveniently the earlier epithet. When reduced in size, this largely aridland species has a more ovate leaf shape, margins less strongly recurved, and costa ends before the apex, which may terminate in a small conical cell or apiculus.


Didymodon luridus Spreng. (see Zander 1978a) does not occur in the range of the flora, though reported by many authors (often as D. trifarius, see discussion of Zander 1981). It differs in the triangular leaves and the smooth, more homogeneous and tiny upper laminal cells, 6–9 mm. American collections identified as this are commonly actually D. brachyphyllus, D. nicholsonii, D. tophaceus or D. vinealis. Small forms of D. nicholsonii have the leaf shape of D. brachyphyllus but the lamina is bistratose. Sterile Grimmia Hedw. species may be confused with this species, but a small hyaline apex is commonly found on at least some leaves of those. Small forms of D. vinealis may be confused with D. brachyphyllus but the latter never has lanceolate leaves, and its perichaetial leaves are also short and rather deltoid.


13. Didymodon nevadensis Zand. in Zand., Stark & Marrs-Smith, Bryologist 98: 590.


Didymodon nevadensis is similar to Pseudocrossidium crinitum (Schultz) Zand. and has much the same appearance under the dissecting microscope. It differs by the somewhat cucullate, acute leaf apex, the costa percurrent (not excurrent as a short awn), smaller upper laminal cells (13–15 mm for P. crinitum), and occasional presence of tubers on the basal rhizoids. Like P. crinitum, D. nevadensis in KOH has blotches of red coloration at midleaf and above, and this irregular red coloration distinguishes it from Bryoerythrophyllum Chen species, which are evenly colored red. This species has two layers of guide cells (occasionally to three near the leaf base), while P. crinitum is nearly constant in a single layer of guide cells. Unlike Bryoerythrophyllum columbianum (Herm. & Lawt.) Zand., which has somewhat the same appearance and rather broad upper costa, the leaf apices of D. nevadensis are not fragile and asexual reproduction is by (1–)2(–4)-celled spherical propagula born on rhizoids in the lower leaf axils. Didymodon australasiae is similar to B. nevadensis but its leaves differ in the thin-walled basal cells and bistratose upper margins. Tortula atrovirens (Sm.) Lindb. is very similar in its ventral costal pad but differs in its short oblong leaf shape, broadly channeled leaf apex and strong, rounded stereid band; Flowers (1973, pl. 31) treated and illustrated both species under the name Desmatodon convolutus (Brid.) Grout.


14. Didymodon sinuosus (Mitt.) Delogn., Bull. Soc. R. Bot. Belg. 12: 423. 1873.


Tortula sinuosa Mitt., J. Bot. 5: 327. 1867; Barbula sinuosa (Mitt.) Grav.


On bark of living or fallen trees; low elevations; known from only two stations in southern Alaska.


This species was originally reported (Zander 1978b) from specimens on bark of living or fallen trees at low elevations in southern Alaska. It differs from European material by the smaller leaves, elongate ventral costal cells and deciduous (as opposed to merely fragile) leaf apex, and may prove to be a distinct species. Small, reddish plants of Tricho­stomum tenuirostre (Hook. & Tayl.) Lindb. may occasionally have similar sequentially constricted, fragile leaves, but the leaf cells are papillose and the plane leaf margins are crenulate by projecting walls.


15. Didymodon fallax (Hedw.) Zand., Phytologia 41: 28. 1978.


Barbula fallax Hedw., Sp. Musc. 120. 1801.


The elongate cells on the ventral surface of the costa and the usually rounded lumens of the upper laminal cells are characteristic. Hymenostylium recurvirostrum (Hedw.) Dix. is similar in these respects and could be mistaken for D. fallax when sterile, but that species lacks a stem central strand and the median laminal cells are usually larger than those of the margin. Ditrichum flexicaule (Schwaegr.) Hampe may be mistaken for this species but has rather strongly serrulate upper margins, no laminal papillae, and is always clear yellow in KOH, never with an orangish cast. Didymodon asperifolius is similar in general morphology but has quadrate or short-rectangular ventral costal cells, and is not hygric in habitat. Didymodon fallax intergrades to some extent with D. ferrugineus and D. maximus. Thick laminal cell walls are correlated with lack of papillae in these species. Robust collections from Newfoundland with long (to 2.5 mm) leaves and basally very broad costae (to 150 mm) have much the appearance of the European D. spadiceus (Mitt.) Limpr., but differ by the long (to 800 mm) twisted peristome and margins recurved commonly to near the apex. The leaves of D. fallax, being somewhat keeled though not strongly recurved, have the grooved costa of D. vinealis but plants may be placed correctly by the elongate ventral costal cells.


16. Didymodon ferrugineus (Schimp. ex Besch.) Hill, J. Bryol. 11: 599. 1981 (1982).


Barbula ferruginea Schimp. ex Besch., Mem. Soc. Sci. Nat. Cherbourg 16: 181. 1872; Barbula fallax var. recurvifolia (Wils.) Husn.; Barbula reflexa (Brid.) Brid.; Didymodon fallax var. reflexus (Brid.) Zand.; Didymodon rigidicaulis (C. Müll.) Saito; Tortula recurvifolia (Schimp.) Aust., hom. illeg.; Triquetrella ferruginea (Besch.) Thér.


The sporophyte is rare and similar to, but often smaller than, that of D. fallax. This species is easily mistaken for Triquetrella californica (Lesq.) Grout, which, however, is quickly distinguished by its triangular stem section, upper leaf margins sharply crenulate by projecting papillae (but not by projecting cell walls as in D. nigrescens), and upper medial laminal papillae tall, branching from the base and centered over each lumen. Didymodon ferrugineus intergrades with D. fallax to some extent but is usually larger, with broader, ovate-lanceolate leaves that are commonly strongly reflexed, and the papillae may be large and strongly evident. The peristome is very fragile and often appears to be missing.


17. Didymodon michiganensis (Steere) Saito, J. Hattori Bot. Lab. 39: 517. 1975.


Barbula michiganensis Steere in Grout, Moss Fl. N. Am. 1: 180. 1938; Barbula catentulata Dix.; Barbula catenulata Dix.


The significant characters are the small size of the leaves, which are catenulate when dry, and the presence of propagula. The laminal cells are arranged in distinct rows but this trait cannot distinguish this species from many congeners.


18. Didymodon leskeoides Saito, J. Hattori Bot. Lab. 39: 508. 1975.


Differs from D. rigidulus var. ditrichoides by the distinctive short and broadly decurrent alar leaf margins (the former has long and narrowly decurrent margins). It is easily distinguished from Hymenostylium recurvirostrum, with which it commonly occurs, by its usually olive or orange-brown tinge, as opposed to the green to yellow color of the former. One collection, Canada, N.W.T., Scotter 22277, BUF, has unusually long stems, to 6 cm.


19. Didymodon maximus (Syed & Crundw.) Hill, J. Bryol. 11: 599. 1981 [1982].


Barbula maxima Syed & Crundw., J. Bryol. 7: 527. 1973 [1974] nom. nov. for Barbula reflexa var. robusta Braithw.


This western Arctic taxon is rare and apparently disjunctive to the western British Isles. Is it essentially a very large version of D. ferrugineus.


20. Didymodon giganteus (Funck) Jur., Laubm. Fl. Oest. Ungarn. 102. 1882.


Geheebia gigantea (Funck) Boul., Musc. France 395. 1884.


Only one specimen, collected in Alaska, has been seen with the combination of characters implied by the above key, being identical with European specimens: Alaska. North slope of DeLong Mts., headwaters of Utukok R., Driftwood Camp, 68° 53'N, 161° 10'W, 1951, Steere 16830 (CANM). Other collections seen that had been previously identified as this are either D. ferrugineus or D. maximus. Also reported from Europe, the Himalayas of India, China, arctic East Asia, and Japan.


21. Didymodon tophaceus (Brid.) Lisa, Elenco Muschi Torino 31. 1837.


Tricho­stomum tophaceum Brid., Mant. Musc. 84. 1819; Barbula pringlei (Card.) Hilp.; Barbula tophacea (Brid.) Mitt.; Dactylhymenium pringlei Card.; Desmatodon hendersonii (Ren. & Card.) Williams in Millsp. & Nutt.; Husnotiella pringlei (Card.) Grout.


Although long leaf decurrencies are often considered characteristic of this species, they are not present in a large percentage of specimens. Being rather variable, this species is sometimes difficult to distinguish from D. fallax, a species that is seldom found in very hygric habitats. Didymodon tophaceus is absent from the Arctic. Like its fellow calciphilic hygrophiles Hymenostylium recurvirostrum and Eucladium verticillatum (Brid.) BSG, D. tophaceus is often encrusted with calcium carbonate; the broad, obtuse leaves and often red costa help distinguish the last. Barbula ehrenbergii (Lor.) Fleisch. is quite like D. tophaceus but can be immediately distinguished by its large size, 20–30 even rows of thin-walled, often papillose upper laminal cells with quadrate to short-rectangular lumens, and peristome when present long and twisted, while D. tophaceus has 10–15 often irregular rows of usually thick-walled, usually smooth upper laminal cells with usually oval lumens, and a short peristome or this occasionally absent.


22. Didymodon asperifolius (Mitt.) Crum, Steere & Anders., Bryologist 67: 163. 1964.


Barbula asperifolia Mitt., J. Linn. Soc. London Bot. 1(Supp7l.): 34. 1859; Barbula rufa (Lor.) Jur., hom. illeg.; Didymodon rufus Lor.


The ventral surface of the costa may have quadrate or short-rectangular cells. The KOH reaction, as well as the natural color of the lamina, is sometimes light orange, but usually a clear red. This species is quite similar to D. ferrugineus but the ventral costal cells are quadrate to short-rectangular.




A phyletic study (combining cladistics, phenetics and patristics—see Stuessy 1990: 135) was undertaken. This can demonstrate convergence in combining a hypothetical evolutionary tree with a phenetic distance ordination. A cladistic analysis was done with the data set (Table 1) of 23 morphological characters (Table 2) with Barbula unguiculata Hedw. as outgroup. Barbula Hedw. is a very closely related genus with a large number of shared morphological characters (Zander 1993); other related genera lack as many comparable characters, possibly through reduction. The parsimony software Hennig86 (Farris 1988) was used to generate the most synapomorphous tree or trees using the commands “mh*;bb*” for heuristic branch-swapping. The data was treated as non-additive (non-ordered) and equal (no) weighting was used. Multiple runs using randomized data sequences found no multiple islands (Maddison, D. 1991) of most-synapomorphous trees. Character state changes were mapped to the strict consensus tree (command “nelson”). The work was exactly dupli­cated with PAUP (Swofford 1985) using the settings “mulpars,” and likewise no weights or additivity. The relative robustness of the subclades was evaluated by Bremer support (“decay”) analysis in PAUP with the command “bbsave”, where multiple trees were saved with synapo­morphy relaxed one, two, three and four steps with note of which clades collapsed at each analysis. This procedure indicates “the number of steps that must be added before each clade present in the minimum length trees is no longer unequi­vocally supported” (Donoghue et al. 1992).


The study found three equally most-synapomorphous trees, with ambiguity only over which taxon was more basal, D. nicholsonii or D. sinuosus. Characters were mapped on the consensus tree (Fig. 1), which may be taken as the estimated phylo­genetic tree since the polytomy may be seen as modeling evolutionary events that do not greatly affect topology. Character state changes are shown for all branches. Unique and homoplastic synapomorphies are indicated by “u” and “h”, respectively. Salient charac­ter states unique to single terminal taxa and also not included in the data set are appended to the listed aut­apo­morphies.


In the phylo­genetic tree (Fig. 1) branches ending in D. perobtusus and D. subandreaoides, and in D. australasiae and D. umbrosus, had strong Bremer support values (Bremer 1988; Davis 1995), each only collapsing at 4 extra steps, while the remaining branches collapse with one extra step each. The tree is divided into two large branches, with one branch comprised of sect. Fallaces with the D. nigrescens group terminal to that lineage, and the species of the other three previously recognized sections (see above) variously combined in the other branch. The D. australasiae group and the D. nigrescens group, the latter possibly related to Didymodon sect.­ Rufidulus (Chen) Zand. of Asia, may well prove misplaced due to long-branch attraction or are different at the genus level or both, and more extensive study including species of other sections and genera should address these possibilities.


To the extent that a phylo­genetic tree of nested sister groups (Fig. 1) actually models ancestor-descendent relationships, it may be termed an evolutionary tree (as in Fig. 5, cf. discussion of Lamboy 1996). Information from interior branches, especially of the more deep ones, has been used to analyze ancestral areas (e.g. Bremer 1995), though Goldman (1990) felt that nodal values at least in maximum likelihood analysis are only “particular reali­zations of parts of the [analytic] process,” and are unpredictable because in the absence of a model known to be correct they are not inferentially consistent, that is, “it is not possible to increase indefinitely the number of obser­vations (data) pertinent to each.” Although some interior branches of Fig. 1 are based on only one or two homo­plastic synapomorphies, there is no reason that the nodes do not model the evolu­tionarily signi­fi­cant traits of hypothetical, mostly extinct, shared ances­tral species. This conclusion is supported in that most extant taxa of Di­dy­modon differ little from each other—by only one or two aut­apo­mor­phies. This implies no large numbers of unmodeled intervening and confounding evolutionary events in the past. According to Mayr (1982: 234), “When­ever a clade (a phyletic lineage) has entered a new adaptive zone, resulting in a drastic reorgani­zation, the transformation may have to be given greater taxonomic weight than the proximity of joint ancestry. The particular importance of the autapomorphies is that they reflect the occupation of new niches and new adaptive zones, which often are of far greater biological significance than the cladistic synapo­morphies.” The aut­apo­morphies of ancestors become the synapomorphies of future taxa, and species evolve, not characters (except in an  analytic sense). One might then expect uniformi­tarianism to be a useful guide to modeling ancestor-descendent relationships. The most dubious “synapo­species” are the immediate ancestral node of D. giganteus and the next most distal node, each based on a single homoplastic, variable (intraspecifically in the terminal taxa of the lineage) shared character state (numbers 10 and 2, respectively). These nodes would not model acceptable ancestors if their patristically close terminal taxa each had more autapomorphies. But, even if these two nodes were collapsed into a hard polytomy (D. giganteus, D. ferrugineus and D. maximus do intergrade to some extent), no great violence would be done to the evolutionary tree of Fig. 5.


Four terminal taxa showed no aut­apo­morphies: D. australasiae, D. fallax, D. ferrugineus and D. johansenii. Two other species, D. rigidulus and D. vinealis, include their respective nearest ancestral node in aut­apomorphic charac­ter variation. These six taxa are proposed as surviving ancestors and are rendered as intercalated, not terminal, in the simplified evolutionary tree that is overlain in the phylogram (Fig. 5). According to Grant (1985) “living fossils” show slow evolution. This is correlated with high adaptation to stable environments, as opposed to such habitats as “imper­manent lakes, high mountains, volcanic deposits, active tundra, etc.” The above six species are commonly sexual and are widespread globally. One, D. johansenii, is characteristic of northern montane and arctic localities, but the species is apparently quite mobile: collections show little biomass devoted to morphology associated with vegetative growth (perhaps allowed by copious sunlight during long northern days) and much biomass is given to both sexual and asexual reproduction in the same turfs. Sister group species to the first four of the six taxa either occur rarely and apparently reproduce asexually (D. anserinocapitatus, D. giganteus and D. maximus), or are probably recently widely distributed through inad­ver­tent human agency (D. umbrosus).


A cluster dendrogram (Fig. 2) of overall phenetic relationships was produced by a standardized UPGMA analysis (unweighted pair group method using arithmetic averaging) using the software package MVSP (Kovach 1995). The characters and data set are given in Tables 1 and 2. This analysis is sensitive to the distances among the data and leads to grouping closest pairs (Hair et al. 1987). The data set (Table 2) was the same as that used for the clad­istic analysis above (thus restricting the phenetic analysis to phylo­genetically informative characters) but the entries labeled in that study as “variable” were perforce given an exact character state, in this case the commonest state in very well developed “typical” plants. Two species groups (D. australasiae, D. revolutus and D. umbrosus, and D. nigrescens, D. perobtusus and D. subandreaeoides) that were clearly isolated as terminal to phylo­genetic lineages (Fig. 1) are also isolated in the cluster analysis with the exception of D. revolutus. Didymodon asperi­folius was shown in the cluster analysis to be overall phenetically similar to D. ferrugineus and D. maximus, this apparently through convergence: note the large patristic distance (sum of steps in character state changes across intervening nodes) of the first species from the last two in Fig. 1.


A standardized principal component analysis (PCA, Kovach 1995; Sneath & Sokol 1973: 245) was done with the same data set to show similarities in two-dimensional ordination (Fig. 4). There was no variation in results with different data orderings. Other ordination methods, with different optimizations, have also been used in study of patterns in homoplasy, such as detrended correspondence analysis and hybrid multi­dimensional scaling (Faith 1989; Faith 1997). Axes 1 and 3 were chosen to avoid the dis­tortion of the unusually high score for propagula type on axis 2. Axes 1 and 3 reflect 45 percent of the variation, unrotated to preserve the usual multiple-variable representation of axis 1. Figure 5 is an overlay of the PCA and the evolu­tionary tree (the terminal taxa are represented by single capital letters, see Table 2). Plots of axes 1 and 2, and of 2 and 3, supported the phylogrammatic analysis below, though individually they were somewhat different.


There were no gaps separating the clusters in the PCA ordination (Fig. 4), confirming that Didymodon is, after all, a difficult genus taxonomically. The PCA shows that the same data used for the cluster analysis of distance, giving Fig. 2, a neat dendrogram, does not necessarily produce well-isolated clusters in the ordination, based on a correlation matrix. On the other hand, species of the two main subclades are well distinguished in the PCA. Both the phenetic and cladistic analyses demonstrate a close relationship between D. ridigulus and D. vinealis, previously placed in different sections. The sect. Didymodon and sect. Fallaces subclades (Fig. 1 and 5) are fairly well distinguished phenetically in the PCA ordination (Fig. 4) as clusters though there is some interpenetration.




The phylogram (Fig. 5) shows D. nigrescens being strongly morphologically convergent towards D. brachy­phyllus of sect. Didymodon, and D. leskeoides convergent towards D. rigidulus and D. vinealis of that same section. Although D. sinuosus is phenetically close to D. anserino­capitatus and D. johansenii, the phylo­genetic tree (Fig. 1) shows it to be patristically rather distant. In the phylogram, Didymodon revolutus is seen to tend morphologically towards the somewhat patristically distant but cladistically related D. nevadensis in the same lineage, with overall convergence supported by the cluster dendrogram.


Although in different major subclades and thus different taxonomic sections, D. tophaceus and D. asperifolius converge morphologically but they are also patristically somewhat near each other at the base of the two subclades. Given certain arguments made below, these two are only doubtfully convergent and may just as well be near each other on the same lineage. The phylo­genetically widely divergent species D. gigan­teus and D. nicholsonii are shown to be morph­o­logically convergent in the phylogram, and are very closely associated in overall phenetic traits in the cluster dendrogram (Fig. 2). Particular previously suggested (Zander 1978a) parallel trends in speciation in Didymodon were supported in this study to some extent where the single shared traits were also reflected in convergence in the phylogram (Fig. 5). For instance, rather distantly related species with pro­pagula present in leaf axils (D. rigidulus, D. brachy­phyllus, and D. michiganensis) showed convergence in the phylogram, and two of three species with long-lanceolate leaves (D. gigan­teus, D. nicholsonii, D. vinealis formae) were also convergent but the other (D. umbrosus) was rather isolated in the PCA. Other pairs and trios of unrelated species that shared single salient traits showed less convergence.


Cladistics is here accepted as an adequate basis for general classification, assuming sufficient resolution of the phylo­genetic tree, but the major thrust of this evolutionary study is to see if additional relationships may be hypo­the­sized through a phenetic analysis presenting the homo­plastic convergence in a cladogram as an evolutionary model. This is acceptable as theory even if maximum parsimony is simply another clustering method, a misnomer when taken to its mathematical limit, and the most likely tree is doubtfully probabilistically the true tree, see discussion below. The conjectures derived from Fig. 5 are logical assuming the methods provide best models of phenetic and phylo­­genetic relation­ships assuming maximum synapomorphy. Swofford and W. Maddison (1992) discuss methods using the tree of maximum synapomorphy alone in analysis of paralellisms due to habitat shifts.




It is evident that much information about phylo­genetic relationships (e.g. that subject to evolutionary selection or over­written through saturation) is lost and we are left only with the ability to do approximations. Given the carefully selected small number of characters used in this study (although the consistency index at 0.44 is low), however, it might be expected that the difference between the standard phenetic (Fig. 2) and phylo­genetic (Fig. 1) analyses reflects convergence (or divergence) between the taxonomic elements belonging to two clades. This remains problematic.


Using artificial phylo­genies based on computer-gener­ated data sets, Lamboy (1994, 1996) found that for sets with consistency indexes in the range commonly reported in the literature, maximum parsimony techniques retrieved the true tree only 0.7–27.8% of the time, while overall, for 85.2% of the simulations accurate retrieval was less than 75%, and for the remainder was much less accurate.


With differently generated artificial phylo­genies, Heijer­man (1997) demonstrated that certain clustering methods are better at retrieving true trees than parsimony methods of phylo­genetic estimation when homoplasy is relatively high. Neither clustering nor parsimony, however, achieved better than 74% similarity with the true tree. In another study using artificial phylogenies (Heijerman 1990), parsimony methods were found to be more accurate than clustering methods when the consistency index is above 0.8, and are fully accurate when CI = 1.0 (no homoplasy) though this is not a commendation since the absence of homoplasy must be known beforehand. Usually, however, parsimony methods found shorter trees than true trees.


Moss species usually differ by few, apparently simple, commonly reversed and re-elaborated character states. One might wonder if the differences between the PCA and the parsimony derived tree—that are here attri­buted to convergence—might be due to artifacts generated by two different and, given the low consistency index, inadequate methods of analyzing complex evolutionary relationships. One could, of course, simply eliminate from the cladistic analysis those states that contribute to homoplasy (see discussion of this by Philippe et al. 1996); but, as Mickevich (1982) indicated, convergent characters contributing to homoplasy provide important evolutionary information. As Doyle (1992) pointed out, some characters (e.g. inverted-repeat deletions) may be locally informative and globally have occurred in more than one plant group. With relatively small numbers of character states or relatively large numbers of terminal taxa, a low consistency index is inevitable, and poor retrieval or poor resolution of the true tree must be expected in phenetic and cladistic analyses at least when working at the species level.


In any case, a cluster dendrogram is given in Fig. 3, which reflects the results of one of methods Heijerman found most effective in retrieving at least an approximation of artificial phylo­genies with significant homo­plasy: UPGMA using unstan­dardized Pearson product moment correlation coefficient, a similarity measure for linear correlations between all character values of O.T.U.'s, but which is insensitive to variation in character magnitudes (Abbott et al. 1985), and should be robust to outliers. It is much the same as Fig. 2, but reflects the cladogram better in positioning together D. anser­ino­capitatus, D. johansenii and D. sinuosus, and in a better integration of D. australasiae and D. umbrosus. Didy­modon michiganensis is, however, oddly placed in Fig. 3, and D. revolutus continues to be removed (as in Fig. 2) from association with D. australasiae and D. umbrosus. If Heijerman's conclusions are applicable to this data set, then Fig. 3 would be a better reflection of the phylo­geny than the estimation procedure using Hennig86 and PAUP (Fig. 1), given the low consistency index.


Because the differences between phylo­genetic and phenetic analyses cannot be well evaluated by these techniques when the consistency index is less than about 0.8 according to Heijerman (1990), consilience with other data is needed to decide whether the differences logically attri­butable to convergence (or divergence) are meaningful.




One might assume that species that converge morpho­logically would tend to occupy the same habitats. This is at least true for a demonstrated phenocopy phenomena between Molendoa sendtneriana (BSG) Limpr. and Gymno­stomum aeruginosum Sm. in Colorado (Zander 1977). However, none of the five pairs of apparently converging species in this study are known to occur in the same habitats, and often are not found in the same areas of the world. Didymodon anserino­capitatus grows on sandstone cliffs in the Ameri­can southwest while the convergent D. sinuosus (or what­ever this name represents in the New World) is found on the bark of trees in the Arctic; D. asperifolius is found on calcareous or acid rock, peatland and soil, at high eleva­tions in northern areas while D. tophaceus is a hygro­phytic calciphile of temperate areas; D. giganteus is found on moist soil in the Arctic while D. nicholsonii occurs on soil and rock in western temperate areas; D. leskeoides is a northern species of waterfall spray zones and wet alpine tundra while D. vinealis is a common


ly western-temperate climate species of soil and rock; and D. nigrescens is an arctic and far northwestern species of rocky substrates at streams and waterfalls while D. brachyphyllus is found on soil and lava in dry areas, especially western steppes but scattered in the North Temperate Zone. Aside from the species shown as conver­gent in Fig. 5, species with the rare unicellular gemmae, D. per­obtusus and D. revolutus, are found in disparate habitats and different areas of the world, while those with multi­cellular gemmae, D. brachyphyllus, D. michi­ganensis, and D. rigidulus var. rigidulus, are also of rather different habitats.


Overall, however, there is no doubt that the species shown as apparently convergent in Fig. 5 indeed share more characters between each pair than they do with other species. If the species are evolutionarily convergent, then the characteristics of their habitats as described above are insufficient to explain their similarities of form.


In spite of this study being up against the limits of numerical evolutionary analysis with morphological charac­ters, similar species of North American Didymodon, whether or not distantly related, are apparently not evolved to clearly similar niches. Possibly this is because we have not yet done the microhabitat analyses that would clearly define the presumably similar niches, or because other comb­ina­tions of characters simply are less advantageous in any environment and are now extinct.




A word about cladistics. It has been assumed that phylo­genetic classification must reflect an interpretation of derivation from common stock, but apparent synapomorphy in the shortest tree may include convergence (Lyons-Weiler et al. 1996). A phylo­geny based on descent from shared ancestors is not logically consistent (Nagel & Newman 1974) as effectuated in maximum synapomorphy tech­niques in that it is valid parsimoniously only in eliminating grossly unreasonable trees, as discussed below. I am also uncomfortable with the fact that a hypothetical tree derived through phylo­genetic analysis may have a low probability that it is the same as the true tree, whether the former is a tree of so-called maximum parsi­mony or of maximum likeli­hood (or both). I reassure the reader that the clado­gram in Fig. 1 is not intended as a proba­bilistic “recon­struction” or “discovery” of the phylo­genetic history of Didymodon, but, as theory, is yet scientifically valuable. The word probable originally meant ready to be tested (proofable) or “to try the goodness” of one's best efforts (Skeat 1993). Another meaningful defini­tion was “having more evidence for than against” (Harris 1915), but now probable can mean anything from “com­monly true” to “possible” (Gove 1976). Harper (1979), however, demanded for scientifically plausible models in phylo­genetic analysis that the probability of two taxa sharing closer ancestry to one another than to others in the group, given that the two taxa share one or more uniquely derived advanced character states and the others do not, to be “>.5”, a minimally acceptable definition of probable.


A phylo­genetic hypo­thesis presented, as is common in the liter­a­ture, as a “recon­struction” resulting from a “discov­ery process” by implication should have more probabilistic surety associated with it than merely being not contrary to fact, but this is seldom the case.




Early on in cladistic study it was “generally agreed that the reconstruction of evolutionary trees should ideally be regarded as a problem in statistical inference...” (Farris 1973, see also Yang 1997). According to Sober (1986), “the parsimonious hypo­thesis is the hypo­thesis of maximum likelihood.” Although Disraeli may have railed quotably against the ease with which statistics can be misused, there is a brand of statistics that even statisticians look on askance, and it is that methodo­logy on which numerical phylo­genetic analysis is based. Statistical probability using relative frequency well predicts long-run outcomes of series of instances, but the meaning of “probable” shifts when describing the probabilities involved in a single instance (as discussed by Braithwaite 1953: 118–127, 186–189 and von Mises 1957), and is largely identified with Bayesian analysis techniques in which probability models frequency (Frank & Althoen 1994). Phylo­genetic analysis is, at least implicitly, Bayes­ian.


Many introductory texts emphasize the con­se­quences of the difference between classical frequentist analysis of multiple runs and Bayesian analysis of single instances: Hoel et al. (1971) discuss the former as the “relative frequency interpretation,” while Mosteller et al. (1961) call it the “objective” (as opposed to “personalistic” or “intui­tive”) position. That there is a problem is often debated: Winkler (1972) rightly pointed out that intuitive betting on single instances is “operational” (as opposed to “con­ceptual”) and is the basis for everyday life decisions (though these do not ordinarily involve the special regular­ity constraints and mathematical compounding issues of the concatenated series of conditional probabilities associated with hypo­thetical phylo­genetic trees). According to Salmon (1971: 56) probabilistic methods can deal with single events because these can be usually be referred to a reference class (see also Pap 1962: 175, 216) of known initial probabilities, specifically the largest homogeneous reference class, which provides the highest posterior probability. Bayesian analysis, for it to work, assigns prior and calculates posterior probabilities of appli­cable reference classes. That there is a problem of choice of analytical technique is, of course, nonsense, since scientists generally use Bayesian forms of analysis, formal or informal, in initial stages of examination of a pheno­menon, then classical frequentist methods as more information becomes available and processes are better understood.


To the classical statistician, a phylo­geny, like a single roll of the dice, is a Poincaré system (Braithwaite 1953: 190), in which events that may be assigned equal proba­bilities when generalized as a series of events (as in J. M. Keynes' Principle of Indifference, Pap 1962: 169) are in a single instance actually much affected by unknown, often small differences that make a great difference in final effect—here, in particular, the mani­fold, non-independent (Sanderson 1993: 241) evolutionary mechanisms contri­buting to the true phylo­geny. A phylo­genetic data set is a view of the phylo­geny taken at one instant in time, and Bayesian generaliza­tions and inferences are required for thorough analysis (Harper 1979).


A Bayesian bet, in a simple example, might have to do with two hidden dice, a four-sided (tetrahedric) die and an ordinary six-sided (cubic) die, which are rolled randomly by a second person until a “1” turns up (one pip up—or down in the case of the tetrahedron). One must guess which hidden die was used to generate the data set “1”. The initial probability of getting a 1 with a four-sided die is 1/4, but from a six-sided die it is 1/6—these are regularity assumptions that the dice are not loaded and are fairly cast. The likelihood is proportional (in this case 1:1) to the initial probabilities and thus one may conclude that the four-sided die has the maximum likelihood of being the die that was used to generate the data set (in this case with a single datum). This is the best theory and the best bet. By Bayes' Theorem (Harper 1979; Winkler 1972), the posterior probability that one's tetrahedric die hypo­thesis is correct is 0.6 (while that of a cubic die is 0.4, these adding to “probability 1”). This gives a somewhat better bet than the 0.5 (random) chance one had before knowledge of the additional information (data set). Classical statistics requires multiple throws yielding infor­mation on the proportion of 1's to other results to make a well-supported guess, but Bayesian analysis can deal with incomplete infor­­­mation through regularity assumptions. Such assump­tions may eventually be proved correct or frequencies may be shown to even out in the long run. But before actual frequency data are known, Bayesian analysis remains the best method of dealing with incomplete information.


On the other hand, a purported reconstruction should certainly not be based on belief-oriented Bayesian analysis of unique phenomena when the bet is poor or at long odds, especially when one must build upon the results, which compounds the effects of being wrong.


In a critical paper discussing the Dollo model, Farris (1977) found that “the more parsimonious of two rooted trees differing by only one in total steps would be at least 4 times as probable as the other.” The probability increases to 16, 64 and 256 times for 2, 3 and 4 steps longer, respectively. Although one assumes that Farris is mathematically correct that “preferring a tree with 4 fewer total steps than an alternative tree for the same data is statistically better justified than preferring an alternative to a null hypo­thesis when the latter can be rejected at a = 0.001,” there are, of course, usually many more than one additional possible longer trees at each of 1, 2, 3, 4 or more steps longer than the shortest. The sum of the probabilities of these many trees (if Farris' probability assignments are theoretically acceptable) is generally far greater than that of the shortest tree. Rogers et al. (1967) pointed out much the same problem, to which Kluge and Farris (1969) responded, inadequately (see discussion of the fallacy of irrelevance, Cohen & Nagel 1934: 381), that convergence and parallelism is shown in cladistic homoplasy thus “demon­strating that evolution is not parsimonious.” According to Fischer (1970: 53) “valid empirical proof requires not merely the establishment of possibility, but an estimate of probability. Moreover, it demands a balanced estimate of probabilities pro and con.”


W. Maddison (1995) calculated the probabilities of single nodes being correctly reconstructed; in the hypo­thetical case of a binary character with a 0.1 per branch probability of change and a 4-node tree, his calculated probabilities of correct reconstruction of each of the nodes were 0.93, 0.93, 0.90, and 0.79. These values are indivi­dually relatively high and fit Harper's (1979) >0.5 criterion of “probable” for each node. For a tree, however, to be probably the true tree, i.e., that all nodes in practice are correctly reconstructed, requires the product of the probabilities of correct recon­struction at each node; seven nodes each at 0.9 probability (assuming single synapo­morphies) give the structure a total probability of 0.48. The probability of a correct recon­struction of most large trees based on data sets of morphological data should thus be small in practice. This analysis, of course, assumes the belief-oriented Bayesian stance that characters are random variables, not Poincaré systems, and estimates (being mathe­matical expectations of relative frequency, Pap 1962: 205) are calculated from probabilistically modeled sample data. According to Swofford and W. Maddison (1992): “In general, we accept the use of ‘simple' assump­tions—unordered character states and equal costs for all transformations—as a suitable starting point, loosely analogous to neutral (equal) prior probabilities often used in Bayesian statistical analysis.”




Requiring covariance to be interpreted as based on shared ancestral relationships (not convergence) whenever possible  has been hammered into the literature as an equivalence between maximum parsimony and maximum syn­apo­morphy. Though now axiomatic, it is more a convenience for actually obtaining a single tree—­on which to base a classification that might prove generally acceptable—then for tree reconstruction, and as such reflects a confusion between practical classification and reconstruction on the part of cladists. There are several methods of phylogenetic analysis, and the two presently commonly used techniques are reviewed below.


A basic concept shared by maximum likelihood and maximum parsimony techniques of phylogenetic analysis is that of “statistical relevance.” This is only obliquely referred to in the literature, since its application in systematics is faulty. Basically, the more probable one of two or more hypo­theses has higher explana­tory power, dubbed statistical relevance by Salmon (1971: 11). Salmon showed that a demonstration that a unique event has a probability greater than .5 may not be the appropriate goal of predictive statistical analysis in some cases. His example is of a medical test showing an increase of the chance of a disease in a particular person, from the chance of one member of the general population having that disease to a higher probability (but less than .5) of that particular person having the disease. This increase is certainly reason for concern and further testing in this case.


But Salmon (1971: 56) goes on: “According to Hemple [1965], the basic requirement for an inductive explanation is that the posterior weight...must be high, whereas I have been suggesting that the important characteristic is the increase of the posterior weight over the prior weight as a result of incorporating the event into a homogeneous reference class.... When the posterior weight of an event is low, it is tempting to think that we have not fully explained it.... [but] when the reference class is epistemically homogen­eous in terms of our present know­ledge, ...we have provided the most adequate explana­tion possible in view of the knowledge we possess.” Also: “To explain an event is to provide the best possible grounds we could have had for making predictions concerning it. An explanation does not show that the event was to be expected; it shows what sorts of expectations would have been reasonable and under what circumstances it was to be expected. To explain an event is to show to what degree it was to be expected, and this degree may be translated into practical predictive behavior such as wagering on it. In some cases the explanation will show that the explanan­dum event was not to be expected, but that does not destroy the symmetry of explanation and prediction. The symmetry consists in the fact that the expanatory facts constitute the fullest possible basis for making a prediction of whether or not the event would occur...” (1971: 79).


Clearly, if Salmon's criterion is applied to phylogenetic analysis, second best hypotheses (and third best, etc.) must be rejected because they involve somewhat less homo­gen­eous reference classes. It is an argument for accepting, at times, an improbable tree as a best hypo­thesis in phylo­genetic analysis because that tree best explains the data (see also Farris 1983; Hull 1974). There is no concern for how badly it explains the data or for the relative quality of second best, third best, etc., explanations. There is also no concern for whether the best explanation is a good Bayes­ian bet or not in situations where a good bet is necessary. Fischer (1970: 50) pointed out, discussing the fallacy of the circular proof, that the best available proof of a historical event may not be good enough to carry the question. Admitting that a correct hypothesis may be an improbable one once it is known, I find problematic the method for selecting as a “recon­struction” one from many nearly equally impro­b­able hypotheses. The single most-adequate explanation can be scientifically inadequate as a hypo­thesis, and when posterior probability of that one is less than .5, all adequate explanations must be considered.


Maximum likelihood analysis is appropriate in all situations in which loss due to the failure to identify increased risk is very great, and has value in medicine and other critical activities. Statistical relevance in whatever guise has been applied, however, to the results of maximum likeli­hood and maximum parsi­mony evolution­ary analyses as a justifi­cation for presenting the tree of maximum likelihood or maximum posterior probability, or the tree capable of least falsification as the “best” phylo­genetic hypothesis. This is a misrepresentation in context, substituting an attainable goal for one that is presently unattainable or rarely attainable, i.e., accepting a most-adequate hypo­thesis from a number of similar hypotheses instead of an entirely adequate hypothesis that can stand alone. Unless there can be demonstrated more evidence for than against, no one tree can be chosen as a probabilistic hypothesis. In the literature, “best” in the sense of statistically most relevant does not necessarily mean probable, and should not be passed off as probable. All trees with a significant increase in probability or decrease in falsifi­ability in light of information in a data set are candidates for a reasonable phylogenetic hypo­thesis, and a more stringent criterion for a single hypo­thesis is necessary.


These problems are associated with a particular philosophical stance, so-called “realism” whose opposite is “antirealism.” R. Hendry (1996, see also Murphey 1994: 307) compared these opposed scientific world-views as follows: in Realism, truth is a criterion, and “if a theory explains, this is an indication that it is true.... Science is a process of discovery: of truths and entities (electrons, quarks, genes) that were ‘there before' [and proposes] extra-empirical criteria for theory choice: explanatory power, simplicity, unity, elegance....” Also, “Theore­t­i­cal statements, construed literally, make factual claims about the world.... Uses of theoretical terms are attempts to refer to theory-indepen­dent entities.... Theoretical statements can be true or false independently of our ability to know their truth-values.... We can have good reasons to believe that our best theories are (approximately) true, and that their theoretical terms refer (i.e. electrons exist)....”


On the other hand, in Antirealism, “The only truths that could interest us are the observational ones.... Theories help us predict the observed behavior of the world. In order to do this, they need not be true, they could be convenient schemes for summarizing, classifying, ordering and predicting.... Neither scheme nor concept correspond to anything ‘out there in the world.' ...Science is a process of construction: [of] theoretical schemes and concepts that are our creations [and of] prediction: ‘saving the phenomena.'” Also, “Theoretical statements are just tools, instruments or conventions.... Theoretical statements say no more than their observational consequences.... Truth for theoretical statements is to be identified with either: (i) Verification conditions...; or (ii) The theory that is accepted in the ideal limit of enquiry.... We can have good reasons to believe only that our best theories are empirically adequate (i.e. their observational parts are true).”


It may surprise some systematists that they must in fact choose (in an educated manner or by default) between a realist and an antirealist ­­viewpoint, and that this can make a difference in standards of hypothesis construction. The problems associated with statistical relevance are more easily, but not necessarily, acceptable to the realist viewpoint. Donald Davidson (according to Murphy 1990), building on the well-known (to philosophers) “gavagai” argument of W. V. Quine, defines truth-knowledge as the best interpretation possible that a totally independent interpreter can make of an alien statement with available observational information. This view of truth-knowledge can be used in an overly optimistic manner. Murphey (1994), for instance, argued “...for the form of realism in which the existence of a real world is a postulate to explain our experience rather than a presup­position of inquiry. True knowledge of the real world is possible even though complete knowledge of it is not—that is, we are led to postulate the existence of some states of affairs about which many of the propositions we can formulate will be undecidable. Nevertheless, I argue that science will lead to the best theory which is also a true theory, and that our best confirmed theory is our best present theory. Hence, we can have ‘true knowledge'—more strictly, well-con­fir­med theories that are our best estimate of the true knowledge—about the real world.”


Van Fraasen (1980: 64, italics his), on the other hand, formulated a contrary antirealist stance: “To present a theory is to specify a family of structures, its models, and secondly, to specify certain parts of these models (the empirical substructures) as candidates for the direct representation of observable phenomena. The structures which can be described in experimental and measurement reports we can call appearances: the theory is empirically adequate if it has some model such that all appearances are isomorphic to empirical substructures of that model.” This obtains in phylogenetics, in the case of any reasonable tree of a number of reasonable trees obtained after grossly longer trees (those suggesting close relationships between dissimilar terminal taxa) or statistically impro­b­able trees are eliminated.


Perspective on the Platonic realism implicit in mathematical “discovery” is provided by Scott-Ram (1990) and Nagel and Newman (1974), and such belief has long been a problem in human endeavors. John Stuart Mill (s.d.) responded to William Whewell's “Germanic” philosophy with “The notion that truths external to the mind may be known by intuition or consciousness, independently of observation and experience, is, I am persuaded, in these times, the great intellec­tual support of false doctrines and bad institutions.... And the chief strength of this false philo­sophy...lies in the appeal which it is accus­tomed to make to the evidence of mathematics and of the cognate branches of physical science. To expel it from these is to drive it from its stronghold....” Whewell (1847) promoted research into progress and change over time, devised the hypo­thetico-deductive method (conjecture and refutation) though also strongly supporting the inductive method, and coined the term “palae­tiology” for the so-called historical sciences (O'Hara 1997), these being a unified inferential study of antecedent events of present-day phenomena in many intellectual fields with “certain principles, maxims, and rules of procedure in common.” Mill declared that inductive conclusions are capable of complete certainly, but William S. Jevons (in 1874 fide Kiernan 1965) found that scientists' informally devised hypo­theses that were subsequently evaluated through the calculus of probability were never more than “just barely certain.”


More modernly, the empiricist/pragmatist W. V. Quine (1953, 1993) argued that all observational sentences are theory-laden (see also discussion of the Baconian fallacy by Fischer 1970), and (as explained by Murphy 1990: 81) there is no clear difference between statements grounded in fact and those grounded in meaning indepen­dent of fact; while, equally true, ”there is no place for a priori philo­sophy” (in Murphy 1990: 96). It is in inadver­tent or purposeful reification (e.g. that synapo­morphies and phylo­genetic patterns are real) that I see idealism sneaking into realism and thus supporting the misuse of statistical relevance in phylo­genetic analysis. Van Fraasen (1980: 40) has posited a kind of natural selection of theories: “Only the successful theories survive—the ones which in fact latched on to actual regularities in nature.” This implies that the theory (from cladistics, phenetics or maximum likelihood) that predicts best by ongoing external verification (e.g. value in prediction) is the best theory, and this may be a brute force solution to the problems associated with choosing methodologies and with verification of inductive generalizations. The problem of whether the best theory is also an adequate theory may be approached this way: is it predictive enough, by some independent measure, to be scientifically useful? According to Hendry (1996), the “pessimistic meta-induc­tivist” philosophical position cautions that false scientific theories in the past have been pre­dic­tive successes, which is, however, an argument for, not against, antirealism.




Maximum likelihood estimation is often considered superior to parsimony methods. According to Yang (1997): “Under quite general regularity conditions, maximum-likelihood esti­mators have desirable large-sample properties: they are consistent, asymptotically unbiased, and most efficient....” Some cladists, however, find it philosophically anti­thetical to hypothetico-deductivism and corro­bor­­a­tion through congruence alone. Kluge (1997) argued that, as a verificationist methodology, likelihood techniques are opposed to Popperian falsificationism, and cladists (here apparently meaning ­those using parsimony techniques) are “not preoccupied with knowing the absolute truth, unlike verifi­cationists.” Siddall and Wenzel (1997) admonished phylo­geneti­cists “to abandon neojustifi­ca­tionist statistical interpretations.” On the other hand, Yang (1997), a statistical phylogeneticist and partisan of maximum likelihood methods, referred to maximum parsimony and similar methods as studies using “intuitive clustering algorithms for phylo­geny reconstruction, which lack a rigorous statistical basis.” Refreshingly, H. E. Ballard, Jr. (pers. comm.) found that maximum likeli­hood analysis of ITS molecular data may generate more parsi­monious explanations of evolution than do parsimony methods in that for oceanic island groups fewer biogeo­graphic dispersal events or ecological shifts are required. In the present paper, I argue that both methods can produce unacceptable results, at least from an anti­realist viewpoint.


A phylo­genetic tree may be viewed stochas­tic­ally as a martingale (Goldman 1990; Williams l991), consisting of branching Markov chains (Sanderson 1993) of conditional probabilities. Each event is dependent only on the event immediately preceding it in the chain. The abstruse mathematics of maximum likelihood analysis in the literature is a result of having to deal with many parameters. Variables are treated as continuous (just as the bell-shaped curve associated with the Central Limit Theorem may be of use when working with discrete data in frequentist statistics). Maximum likelihood is the point on the curve of probability density where the slope of a tangent line is zero, i.e., the top of the curve, and thus recourse can be made to the infinitesimal calculus. For computational reasons, maximum likelihood analysis has been limited to small data sets until recently. Much of the research in efficiency (computational speed) is in devising ways around having to solve complex, high order (powers) differential equations, such as reducing them to binomials or modeling solutions with Monte Carlo methods. Log likeli­hoods are used as measures, in part, because they are easily distinguished to the left of the decimal point, while actual likelihood values are often very small decimal fractions; also, log likelihoods are conveniently monotonic (the values are unaltered).


Because gene mutations are readily calculated as stochastic events, maximum likelihood is presently a much used method of molecular phylogenetic analysis. The rate of evolutionary change of morphological characters is difficult to estimate (Martins 1994). With maximum synapo­morphy, in addition, all identical character states are considered to have been caused by a single mutation unless forced to be interpreted otherwise in the shortest tree, thus there is no independent measure of mutation rate outside of the method itself. Kluge and Farris (1969) have suggested weighting by the degree of variation of a character within a taxon, a position abandoned by them and most cladists since (though occasion­ally mentioned wistfully in the literature).


Likelihood analysis simulates DNA sequences by calculating probabilities of oligo­nucleotides by correlation between base frequencies in various positions of the sequence (Bralley 1996). Functional gene sequences expressed in the mRNA may also be affected by evolutionary selection (their mutations thus are mainly only base substitutions since functionality may be impaired by other changes) and are commonly related to other genes through duplication, while non-translated intervening spacers and other non-functional genomic elements (Lewin 1985: 333; Suzuki et al. 1981: 524), are better bets for stochastic analysis of changes (deletions, insertions and base substitutions) accumulated through phylogenetic time—assuming rates may be well estimated in speed and vari­abil­ity or if the method is somehow robust to variation in such. Portions of the genome that are (theoretically) most isolated from direct evolutionary selection are, for instance, almost absent from the mtDNA genome though common in chloro­plast DNA, but where there is also a high level of homo­plasy (Avise 1994: 337). The neutralist-selectionist debate continues, however, as to relative isolation from natural selection of different genomic elements (reviewed by Avise 1994), but likelihood analyses generally include no coefficients of selection. Another problem is expected quantity of infor­ma­tion: e.g. the much bally­hooed ITS (internal transcriber spacers) region of the nuclear ribo­somal DNA may have no intra­populational variation and almost no useful phylo­genetic informat_on for morphologically very different species in the same genus (Soltis & Kuzoff 1993).




Markov chains tend toward a steady state or an equilibrium (Rolf & Williams 1991) which allows analysis of long-term trends. A maximum likeli­hood method using a Markov chain Monte Carlo method was used by Mau et al. (1997) to estimate the phylo­geny of nine species of Clarkia Pursh (Onagraceae) on the basis of cpDNA restriction-site data. The tree of maximum likelihood was chosen as the best phylo­genetic hypothesis. This is commonly justified as being a correct method in the Bayesian sense because the more probable one of two or more hypo­theses has higher explana­tory power (or statistical relevance, Salmon 1971: 11). Posterior probabilities (the actual chance that the hypothesis is true) can easily be calculated from likeli­hood values via the Bayes Theorem. Marginalized posterior proba­­bilities of the five most likely phylo­genies were reported as 0.649 (the tree of maximum likelihood as usual has highest posterior probability), 0.179, 0.168, 0.002 and 0.001. This means in classical frequentist terms that if this exact, same data set were to occur many times, the tree of maximum likelihood will also be the true tree in about 13 out of every 20 duplications. Rannala and Yang (1996) used much the same technique with primate pseudo­genes to select a (((human, chimpanzee), gorilla), orangutan) tree with a posterior probability of 0.84. This same paper reported a similar study of 11 mito­chondrial tRNA genes in a slightly larger set of primates giving the ((((common chimpanzee, pygmy chimpanzee), human) gor­illa) orangutan) tree a posterior probability close to one (0.9999). A study of mitochondrial genome segments, being “parts of two protein-coding genes and three tRNA genes,” by Yang and Rannala (1997) found a high posterior probability for nine primates: ((((((human, chim­pan­zee) gorilla) orangutan) gibbon) crab-eating macaque) squirrel monkey)(tarsier, lemur) of between 0.95 to 0.96 depending on the evolutionary model used, all models obtaining the same tree.


The curves of probability density in these studies are high-peaked. These particular Bayesian probablistic bets are, however, for small and thus limited data sets, and assume that no other data (sharing significant numbers of advanced characters) applies. As to this, Yang and Rannala (1997) asserted that posterior proba­bilities did not change much among different analy­tical variations, and their method “is robust to variations in the prior” because “most information concerning phylo­geny derives from the data.” In any case, the analyses appear to have successfully estab­lished good gene tree hypotheses for the primate data sets, given the regul­a­r­ity assumptions, neutralist expectation toward gene selection, the logic of treating character states as independent and uniformly distributed random variables in these particular genes, the amount of sampling for intraspecific variation in traits, and pending congruence with trees based on other, independent genes. There may be eventual selection of a species tree in the pool of reason­able parsimony results as a good phylo­genetic hypothesis of evolution in the group.


In the same Mau et al. (1997) paper above, mito­chon­d­rial DNA for 31 species of African cichlid fish (plus an outgroup) was reported as having been analyzed at 1044 aligned sites. The posterior probabilities of the five most likely phylo­genies were 0.11, 0.07, 0.06, 0.04 and 0.03. Here the curve of probability density is much flattened. The chance, with this larger data set, is about 1 in 10 that the most likely tree is the true tree. This is about the same posterior probability of guessing correctly that the tetra­hedric die generated the data set “1” when one tetra­hedric die and an additional 14 cubic dice are cast randomly until a “1” appears. The very strong Bayesian bet is that the most likely tree is not the true tree—one of the cubic dice (statistics does not tell us which one) most probably generated the “1” because the effect of the number of dice involved outweighed that of the likelihoods. Though the best theory available (of the 15 dice the tetrahedric die has maximum likelihood of gener­ating the data set), this is hardly the kind of probabilistic evaluation from which, say, outgroups should be selected for analyses of taxa higher in the tree of life, unless perhaps the pertinent subclades in the several most likely clades are identical and their trees add to a strong posterior probability (most did not).


Avise (1994: 350) suggested that “In the foreseeable future, it should be possible to assemble molecular (and other) data into a grand phylogenetic encyclopedia—­a universal Tapestry linking all life forms.” Sections could be “stored and referenced as nested series of phylogenies of increasing evolutionary depths.... Different molecules and assay procedures will have to be employed at different levels of the hierarchy, due to the varying windows of resolution provided.” This vision is impressive and possibly eventually achievable in part and in various degrees of confidence. Clearly, one can foresee weak links due to poorly supported maximum syn­apo­­morphy or low pos­terior probability causing false branches in this deeply conditional chain of life. Rice et al. (1997) review problems with analysis of massive data, where “maximum parsimony (at run times within reach of today's hardware) has poor asymptotic performance...” with large data sets, and recommend adding more characters rather than more taxa, and trying new methods, such as parsimony jackknifing and the inferred ancestral states approach (a hypothetical exemplar ancestor replacing a large presumptive clade). They allow that abandoning maximum parsimony and maximum likeli­hood as optimality criteria “requires that we rethink the hypotheticodeductive or probabilistic underpinnings of the discipline...,” as is encouraged in the present paper. A grand cladogram of life is thus limited by analytical techniques for single large data sets and by gradual lowering of probabilities of being correct when separately derived clado­grams are logically concatenated.


There are more than 38 million possible tree arrangements for a mere 10 taxa (according to Doyle 1993). Of course, of these, one could eliminate perhaps 37 million trees as unreason­ably different from dendrograms of phenetic analyses (based on the same data), which cer­tainly reflect natural selection to a considerable extent (Yablokov 1986), but what of the remainder? Although Mau et al. (1997) eliminated in the cichlid study above most of ca. 1040 trees to get the 250 trees that comprised their “95 percent credible zone” (the most likely trees with posterior probabilities adding to 95%), one would have to some­how elimin­ate all but the two most likely trees to make the one most likely tree a good bet to be the true tree. It is this “some­how” that is the proper focus of new research in phylogenetic methodology and is reflected in some papers cited here. Taking a mathematical elimination process to the limit may be wrong if the justification for eliminating the majority of possibilities (phylo­genetically grossly long trees or improbable trees) is different from the justification (mathe­matically projecting theoretical requirements maximally) of eliminating all but one from the pool of credible trees. In maximum likelihood studies this is done perhaps to get a single tree as a result, to match the apparent success of maximum synapomorphy results. On the analogy with reports of radiocarbon dating of anthro­pological artifacts where a measure of plus or minus a number of years is given to reflect different sigma values, a strict or majority-rule consensus tree of how trees in the 95% credible zone actually agree would seem to be the better interpretive result in likelihood analyses.


A comparison of a consensus gene tree from the .5 and .95 credibility zones obtained with statistical methods with the gene tree of maximum synapomorphy (from the same data set) might throw light on what the word “approaches” means when cladists assert that a particular result appro­aches, approximates or converges on the true tree, and on what Bremer support really signifies. Hendry's (1996) account of “con­ver­gence realism” includes a caution that the expectation of science converging on the truth is only applicable to mature sciences—this is hardly a description of phylo­genetic systematics.


It is important to grasp that at least with larger phylo­genetic data sets the most probable tree is not “probably the true tree.” Few papers using maximum likelihood to date discuss relevant posterior proba­bilities: Bohs and Olm­stead (1997) do not mention them, Huelsenbeck and Rannala (1997) promoted the use of likeli­hood ratio tests (e.g. as used by Yang 1996) instead and did not mention posterior probabilities. I agree with Rannala and Yang (1996) that “the posterior probability provides a natural measure of the reliability of the esti­m­ated phylo­geny” given the various assumptions required for it to be calculated, but it must be used relative to the sum of the alternative probabilities, not relative to the next highest value.




Maximum parsimony analyses are parsimonious in elimin­ating myriads of unreasonable trees of overly complex hypotheses. This leaves a pool of tens or hundreds of trees (similar to the “credible zone” above) that are acceptably reasonable under Darwinian theory, thus the phrase “maxi­mum parsimony” as used in the literature is a semantic distortion. The explanation of descent from common stock applies to all plausible trees, whether common descent is maximized or not. Maximum parsimony methods require that all covariance where possible must be inter­preted as due to shared ancestors, something not required by Darwinian theory—­this problem is also discussed by Lyons-Weiler et al. (1996).


In fact, contra Farris (1983) and Kluge (1997), elimi­n­ating longer trees to the mathematical limit from the pool of credible or reasonable trees is based on unjustifiable ad hoc assump­tions about the degree of joint ancestry of terminal taxa. At the point that the method goes beyond elimination of grossly unreason­able trees, and the number of syn­apo­morphies (as assumptions against convergence) is needlessly increased, the method becomes antipar­simonious and overly interpretive. A tree selected as that one with all covar­i­ance possible treated as ancestrally based is not a phylo­genetic recon­struction through parsi­mony, but is the theoretical tree of maximum (interpreted) synapo­morphy or, alter­nately, of minimum convergence, a con­cept not unmen­tioned in the literature but the signi­fi­cance of which is little discussed. The shortest tree may be used for classification if it is understood that all plausible evolu­tionarily convergent alternative trees have been elimin­­ated, to which extent the fine structure is artificial and reflects a too-simple theory of evolution. Those who insist on the original ad hoc argument should consider the second, third, fourth, etc., least falisifiable trees, which compete as reasonable explanations in quantity if not in quality. Here again, philosophical realism can introduce low standards for hypotheses.


The hypotheses of homology and of indepen­dence of traits necessary for phylo­­genetic analysis in practice are (1) almost always to some extent wrong (even if homo­logies are apparently more easily identified in molecular data—­Avise 1994, but according to Philippe et al. 1996 because there are only four nucleotide states, this makes convergence very likely) and (2) evolutionary homoplasy is, as is well known, apparently common and introduces ambi­guities into the data set, both leading to data sets that may be interpreted easily in various ways as different, often slightly longer trees. Like the incorrect assumption that the Winter Solstice must be the coldest moment of the year, the shortest tree is only doubtfully similar to the true tree unless, perhaps, Bremer support (1988) extends through the pool of plausible trees. Though Bremer support for subclades might help with this problem, the charac­ters involved must be shown to be independent variables, because suites of characters that evolve in concert cannot be acceptable as multiple support.


In sum, congruence in the tree of maximum synapo­morphy is not corroborative, it is methodologically based coincidence and based on unjust­i­fied rejection of plausible alternative interpretations on the basis of convergence (including parallelism).




Molecular data may conflict among sources, or between molecular data and morphological data (Avise 1994: 314; Philippe et al. 1996; Seberg et al. 1997); “diverse data sets do not always yield the same estimates of phylo­geny for the same organisms” (Sites et al. 1996). Hasegawa (1997) discussed the differing results of various researchers in mammalian evolution (citing examples in whales and among eutheria, marsupials and monotremes) when using different genes; Hasegawa thought a total evidence (Carnap 1962; Kluge 1989) approach using maximum likelihood techniques might solve this problem. Total evidence means that there should be no more data available whose addition to the data set might change the degree to which a conclusion is supported. Sites et al. (1996) presented a method of approaching a total evidence analysis of discordant mole­cular and morphological data sets using parsimony analysis; they found that deleting homoplastic characters produced a better (more parsimonious than previously published trees) result but part of the tree structure collapsed, being ­“an unacceptable loss of phylo­genetic information.” They instructively discussed several critical problems with molecular phylo­genetic analysis that apparently affected their results. In line with this, Philippe et al. (1996) warned that “A character may contain reliable phylo­­genetic infor­mation what­ever the number of extra steps it requires. As a result, discarding the more variable characters leads to an increase in the number of multifurcations, demonstrating that information was lost.... Thus, the more a character chan­ges the more it is subject to homo­plasy, but also the more information it potentially contributes.... Removal of the sites for which more steps are required in the true tree than in the most parsimonious tree does not result in the true tree....”


Milinkovitch et al. (1996) found that “different phylo­genetic analyses of the same genetic data set can yield conflicting results, depending on the choice of parameter settings and included taxa,” and used a sensi­ti­vity analysis to identify “portions of the multidimensional parameter space where phylo­genetic signal is most reliably recovered.” Naylor and Brown (1997), dealt with the “notion that historical ‘signal' will rise above misleading ‘noise' as more sequence is gathered.” They found that a poor match between a bootstrap consensus parsimony tree based on “the entire protein-coding portion (12,234 base pairs) of the mitochondrial genome of 19 taxa whose interrelation­ships are widely accepted...” with the accepted tree was due to, for instance, among codons, poor fit of nucleotides at third positions (see also Felsenstein & Churchill 1997: 100); among genes, NADH2; and among amino acids, isoleucine, leucine and valine. The reten­tion index was used to deter­mine phylo­genetically reliable functional classes of sites, though it was recognized that using the expected tree to discover resilient sites was not an independent test. On the other hand, they pointed out that molecular data may show a similar covariation due to both shared history and functional requirements as have morphological characters, resulting in a need to ascertain the “relative importance of particular co-varying combinations of residues for protein structure, function and folding.”


Sometimes a single tree may represent the pool of reasonable trees if the terminal taxa are disparate and all have have reference groups of intermediate taxa. Philippe et al. (1996) used an “accepted” tree of 29 Vertebrata as the “true tree” for comparative purposes. With data sets concerning a few taxa for which all but two have have clearly differ­ent traits (say human, chimpanzee, fox, cow, fish), maximum syn­­apo­­morphy yields a reasonable and parsimonious estimate of phylogenetic relationships because there are many shared traits and reference groups of inter­me­diate taxa, contributing patristic distance, are known. This yields a so-called “accep­ted” tree. Inter­mediate lineages contribute as reasonable hypo­theses but may not be resolvable in fine structure. It is the relationships of the intermediate taxa in the data set that should not be blithely considered adequately resolved by maximum synapo­morphy methods because at some point, similarity of the taxa and lack of intermediates allow perfectly reasonable alternative evolutionary hypo­theses; a probabilistic result of an analysis based on multiple independent genes that supports a reasonable species tree seems a necessary requirement for a hypothesis in such cases.




In cladistic analysis, it is, for now, rather improbable that either the shortest tree or the most likely tree is likely to be the same as the true tree, that is, the results of phylo­genetic analysis of substantial groups cannot be expected to have more evidence for than against. Thus, those willing to attempt a statistical analysis of a unique past pheno­menon of concatenated events are given short odds on recovering fine tree structure. There is apparently a pool of trees similar to the so-called most parsimonious, maximally likely, and best phenetic cluster dendro­grams, that include, probabilistically, the true tree, but which can all be almost equally easily explained through Darwinian theory (assuming convergence is an option, and grossly unreason­able trees are eliminated). Swofford and W. Maddison evaluated the effect of underestimation of character state changes, especially in regard to evaluation of parallelism, but only as to the effect on mapping state changes on the tree of maximum synapomorphy.


In a new field, thoroughness in initial broad analyses is often sacrificed in the excitement of discovery, but eventu­ally this must be corrected. Doyle (1992) questioned the present privileged status of molecular systematics studies, which are commonly exempt from testing for variation in gene characters within an OTU; see also discussion of intra­specific cpDNA polymorphism by Rodriguez and Spooner (1997).


Rzhetsky and Sitnikova (1996) found that recognition of a set of unreasonable trees was important—in that selection, reliability and efficiency of the correct complex mathe­matical model of molecular evolution can be facili­tated through “estimation of the prior distribution of phylo­genetic parameters” of alternative tree topologies. They  indicated that it “is rather intuitive that different tree topo­logies and different combinations of parameter values may have very different likelihoods of being encountered in real phylo­genetic analysis and therefore the vast majority of possible tree topo­logies and parameter values should not be considered in the real data analysis....“ Also, they point out that such estimation of “prior probabilities” is done in any case by simply focusing on a particular taxonomic group for study. Milinkovitch et al. (1996) increased efficiency of parsimony analysis by reducing degrees of freedom for “uncontested groups” with a constraint tree based on “reasonable assumptions because of strong support from numerous morphological characters.” Molecularly based “nonsensical” trees that violated the morphologically based constraint were found to be few.


According to Felsenstein and Churchill (1997): “It has long been recognized that the assumption of equal rate of evolution implicit in many methods of analyzing phylo­genies from molecular data is unrealistic.” They offered a method of introducing particular assignments of rates to sites, but relied on maximum likelihood and relative posterior probabilities. Philippe et al. (1996), however, showed that the evolutionary rate of a given position apparently varies throughout time and “substitution models should incorporate variation in evolutionary rate at a given site....”


The consistency argu­ment in maximum likelihood analysis and other probabilistic studies is that the method ensures that the tree of, for instance, maximum likeli­hood must converge probabi­l­isti­cally to 1 as data increase to infinity (Shenton & Bowman 1977), in other words, in Keynes' theory of induction “it can be demonstrated by means of the cal­cu­lus of probability that the probability of a generalization g increases with its confirmations and approaches certainty as the limit...” (Pap 1962: 167). This is merely intuitive and liable to sampling errors according to Yang (1994), and was flatly denied by Sober (1983, 1986) as impractical, echoing an argument (attributed to J. Nicod by Pap 1962: 166) that the resultant certain generalization would be useless because it would be monst­rously complex in having to reflect all confirming instan­ces. Belief-oriented analytical methods require rigid, precise regularity constraints that surely require investigation, e.g. equal prior proba­bilities and selective neutrality of evolutionary events, and whether sup­posedly independent and uniformly distributed random variables do even out in the long run. “Most of the models used in evolutionary analyses describe a gene as a collec­tion of independent sites each being an instance of the same random process, a Markov chain,” according to Rzhetsky and Sitnikova (1996). Also, the numbers of species supplying increasing data are limited (Sanderson 1993).


If data conflict, bias and sample error are negligible, the chance of the maximum tree converging to probability 1 and also of being the true tree is also limited by the chance that the assumed model mirrors the manner of gene modification; “Any model of a process as complicated as evolution will necessarily be a simpli­fication of the true situation” (Goldman 1990). There are several (relatively simple) models (Schöniger & von Haeseler 1995) of gene modifica­tion so the most likely tree is again only the best theory since one must intuitively choose the theoretically best model and apply it across the board (but see Yang 1997). On the other hand, “A method assuming a wrong model may still be consistent and may have smaller sampling errors than one using the right model” (Yang et al. 1995); while, apropos of this problem, Hendry (1996) remarked “App­rox­imate truth is a difficult concept. On any reasonable construal, approximate truth does not explain predictive success....”


Morphological characters, as they change evolu­tion­arily, are of particular value because they are often recognizable as transformation series, but gene sequencing has promise of providing many phylogenetically informative data, with an expected redun­dancy of data among different genes at similar levels of taxonomic resolution that helps cut through “phylo­genetic noise.” (Note, however, that Rice et al. 1997 demonstrated that “branch lengths should not be used as a measure of confidence or robustness....” at least in large data sets.) Such data may have high consistency indexes (showing low esti­m­ated homoplasy on parsimony trees) commonly between 0.45 and 0.85, with many studies at the high end, assuming no inflation of CI by “hidden autapo­mor­phies”—Nixon 1991—in the data). Another reason molecular systematics is very attractive is because morphological character states  of ancestors that are selected against in environments that the terminal taxa no longer inhabit are (at least in part) no longer in the data set. Likewise, morphological character states of ancestral nodes (in other words, the branches below the vertices) in any one lineage that are expressly adaptive to environments in which the extant terminal taxa of the lineage are not found have been elimin­ated (at least in part). This is may occur by anagenetic change, identical reversal(s) in daughter taxa, or identical reversal(s) and an extinction in daughter taxa, as daughter taxa adapt to environments sufficiently different than that of their shared ancestor. Only if the synapomorphy to autapo­morphy ratio (as relative mean numbers of traits per terminal taxon or node) is near 1 can one hope for good retention of morphological ancestral characters.


In molecular systematics, this may be also true to some extent for exons, but apparently non-functional genomic elements are not expected to lose phylogenetic information through selection (eventual saturation, however being a problem). According to Avise (1994: 8), although there is much homoplasy due to apparent parallelism, conver­gence, and reversals in molecular characters, “any wide­spread and intricate similarities [in the genome] that appear are unlikely to have arisen by convergent evolution...” and (Avise 1994: 28) “...nucleotide positions or genic regions that are functionally less constrained are those most likely to harbor neutral variation and to exhibit the most rapid pace of allelic substitution.” If selection has indeed eliminated many important ancestral molecular character states, it is possible that recently evolved traits (essentially autapomorphies) are sometimes incor­rectly resolved as synapomorphies on a random basis. There is no need for such speculation in cases of a general agreement of analyses using apparently adaptive morpho­logical and non-adaptive molecular traits (when grossly unreason­able trees have been eliminated and the trees of maxi­mum likelihood and maximum synapo­morphy which generally represent the credible pools are compared). There are, however, still many additional problems with molecular systematics.


According to Doyle (1992), because a gene tree may be uncoupled from a species tree by introgression, lineage sorting, or mistaken orthology, molecular systematics has many of the faults of one-character taxonomy—unless many genes are tested in a cladogram—and molecular analysis is not alone a better alternative to morphological analysis (this contested by Olmstead & Palmer 1997 for relatively distant relationships they studied in in Solan­aceae); Doyle added: “...additional data for any particular gene, while it may produce a better gene tree, cannot increase confidence in that gene as representative of the species phylo­geny.” Some recent studies have begun to use several genes in analysis for just this reason (e.g. Nei & Take­zaki 1996 who used a genetic distance measure). Also, Avise (1994: 314 ff.) reviewed many cases of apparently successful application of molecular techniques to solution or clarification of intransigent systematic problems, often accomplished with congruent results from analysis of more than one genic element. Avise (1994: 354) recommended multiple lines of evidence as important in addressing such problems as “shared retention of ancestral states by the taxa in question, extreme molecular rate heterogeneities across lineages, convergent evolution to a shared molecular condition, introgressive hybridization, and a mistaken assumption of orthology when the loci in question might truly be para­logous...” and he reviewed apparently well supported evidence for at least occasional horizontal transmission of particular genes, which may be mediated by parasites.




In spite of much discussion in the literature about technical consistency and eliminating ad hoc assumptions, certainty is never attain­able in scien­tific applications even though the method is consistent, or an ideal data set matching an ideal model may ensure it (as in Heijerman's 1990 finding that phylo­genies generated from his artificial data sets are fully retrievable with maximum synapomorphy methods when there is no homoplasy), or in the face of the sanguine enthusiasm over the “virtually infinite number of [gene] characters available” (Doyle 1992). Also, a consistency index even as high as 0.85 means that there is still considerable cladistic homoplasy (CI is essentially the number of observed steps divided by the necessary steps, Kluge & Farris 1969, though it has subsequently been vari­ously calculated), which implies a similar amount of evolu­tionary conver­gence “hidden” among the synapo­morphies of the tree of interpreted maximum synapo­morphy. Patrist­i­cally distant convergence is identi­fiable as cladistic homoplasy, but patristically close conver­gence, in morphological or gene data, is lost among trees a few steps longer than the shortest tree.


Because of the nature of the strongly belief-oriented probabilistic analysis used in phylo­genetics and the poor results in practice, the degree of assurance that frequency-based long-run statistical analyses give to other scientific studies may never be attained. It is paradoxical that some of those using the above intuitive numerical analysis techniques should deprecate previous evolutionary theori­zation (the “New Systematics”) as being intuitive. For instance: “...patterns of functional evolution should be founded on a corroborated set of statements about phylo­genetic patterns of structural features. The emphasis on theories of process and evolutionary transformation, for example, has obfuscated the analysis of tetrapod origins throughout this century...” (Lauder & Liem l983: 187; see also Crowe 1994). (Apparently, the major problem with evolutionary theory ca. 1950–1980 was a mistaken expectation of little genetic variability in species, excepting balanced polymorphism, because of strong selection forces, Avise 1994; the problem was not the fact of theorization itself but a basic assumption later proved mistaken.)


The supposedly “standard evolutionary theory” that is inherent in the synapo­morphy criterion (pointed out by various authors, including Scott-Ram 1990: 175) adduces an expectation that the shortest tree is the best hypothesis of evolutionary relationships explained though derivation by common ances­tral stock­ alone, and thus it cannot contribute to an acceptable theoretical reconstruction even if there were such a thing as a discovery process for Platonic realities.


The shortest or most likely tree may be seen has having a pragmatic (Pap 1962: 228) scientific value in that, if a choice must be made from among very many hypo­theses, even on the basis of a less-than-probabilistic reductionism, the perceived risk is then lowest. In many sciences, one can devise an immediate test of the correctness of the most-likely hypo­thesis, or each of the several most likely. The expectation of the success of post hoc testing for correctness may be the psycho­logical justification of the otherwise illogical (Wittgenstein 1961: 70) idea of simplicity (Sober 1975) or Occam's Razor (Jefferys & Berger 1992). This is not so in systematics, where immediate, clear-cut tests of correctness are unavailable. One rejoices, instead, in the expectation that at least one “least wrong” hypo­thesis is probably truly correct every, say, ten or twenty published papers—which was the breakthrough paper, however, is unknown. Cohen and Nagel (1934) discuss the fallacy of exclusive particularity in science, one example of which is a confusion of a sufficient condition for a necessary one. The best hypothesis as “least wrong” in maximum syn­apo­morphy or maximum likeli­hood analysis is not necessarily a scientifically acceptable result. This reminds one of the casino gambler, who, when asked how luck was holding out, replied: “Fine! I have not won in two hours, but my friend here has not won in four hours.”


Though risk-based losses (incor­rect predictions) may now be greater than gains, with additional information and better methods over time one may begin to probabilistically model the past with Whewellian consilience, but only to the extent it is indeed retrievable. If one has a species trees, with many gene trees congruent to it, and there are many of such examples, the method may be seen to have general value; one requires such overwhelming evidence in the face of presently overwhelming regularity assumptions.


This paper's cladogram (Fig. 1) shows minimum phylo­genetic distance (as summed steps) of the ensemble terminal taxa from a hypothetical shared ancestor (here deter­mined by an outgroup), and as such is valuable as a clustering technique (Barker 1996; Yang 1997: 107) that maximally interprets character covariance as due to shared ancestors. Even if we accept, however, the assumption-laden (summarized well by Farris 1973 and Swofford & W. Maddison 1992) regularity strictures of computerized evolutionary analysis, the clado­gram's explana­tory power (as per Farris 1983; Hull 1974) is restricted to evolutionary theory that eliminates or renders as improb­able the possibility of convergence other than that implied by cladistic homoplasy. My previous cladistic work (Zander 1993, 1995, 1996), along this same line, should be interpreted as cluster analyses (the distance measure summing state changes minimized globally) supportive of the derived general classification alone, given the few steps per node and the simple character states, and the fine structure of the maximum synapomorphy trees remains rather dubious as an estimate of true relationships.


It is possible that molecular systematics can provide data for evolutionary trees of high probability (as at least good Bayesian bets), but there is as yet successful demon­stration for only a few small data sets and the problems involved are immense. Further advancement in evolu­tion­ary analysis must concern ways of distinguishing synapo­morphies in the shortest tree that are due to shared ancestry from those due to evolutionary convergence. An ingenious method of distinguishing at least some apparent synapo­morphy from evolutionary synapomorphy was proposed by Lyons-Weiler et al. (1996), for instance, based on identifying fidelity of phylogenetic signal by “how much unique similarity exists between two taxa with no redun­dant information added.” According to J. Lyons-Weiler (pers. comm.) “...in the absence of fidelity of phylo­genetic signal, a high degree of covariation of character changes along branches in parsi­mony trees is not expected.” Apropos of this, a totally random data set may be used to generate highly resolved cladograms of maximum parsimony.




In my opinion, a probabilistic estimate of species phylo­­geny addressing fine tree structure must (at least) use a model incor­por­ating variable evolutionary rates if possible in Bayesian statistical analysis of data sets of several selectively neutral, independent genes (total evidence is better) resulting in a gene tree with posterior probability greater than .5 (greater than .95 is better if the results are to be used as a basis for analyzing concatenated trees higher in the tree of life) that is congruent to a short tree derived from a morphological data set that passes at least a fidelity of phylo­genetic signal test.


The species tree should be within the pool of reasonable parsimony trees, and may even turn out to be same as the so-called tree of maximum parsimony. A pool of candidate reason­able species trees might be developed through a parsimony analysis of non-gene characters with “accepted” relation­ships constrained (as per Milinkovitch et al. 1996) and then the shortest tree and all trees one step longer (at least) retained. This produces a set of trees with grossly unreasonable trees eliminated. It remains a problem that the only test of such a hypothesis is congruence of the model with information about the past obtained from other sources, since the essentially Bayesian bet on a single (chained) past evolutionary event can have no direct corroboration.


 Ways of estimating confidence sets for cladistics studies have been suggested by, e.g., Sanderson (1989) using bootstrap replicates, and Faith (1991) using random character correlation, but these use the tree of maximum synapomorphy as methodologically central. According to Swofford and W. Maddison (1992): “One way to minimize the impact of incor­rect assumptions regarding the phylo­geny when examining hypotheses of character evolution is to reconstruct the  character(s) on a variety of reasonable trees, ideally a large enough set of trees that the probability of including the true tree is relatively high.” Felsenstein (1985) cautioned, in the case of multiple equally shortest trees, against the assumption of good support for those subclades appearing identically in all trees: “the confidence interval on phylogenies appears to be much larger than the set of all most parsimonious trees.” Bremer (1988) concluded, with protein sequence data, “Not only the shortest cladograms, but also those with an increasing number of steps should be combined into strict-consensus trees.... Only those groups present in the consensus trees may be hypothesized to be monophyletic with any confidence. There is no easy way to determine how many extra steps should be allowed....”


Along the lines of these suggestions, the results of the present analysis were reinterpreted from a set of trees one step longer than the shortest (but including the shortest). First, the two main subclades were constrained as “uncon­tested” by being analyzed separately with PAUP (B. ungui­c­­­ulata as outgroup, unordered, “bbsave” set to one step more than the number of steps in the shortest tree). For a true parsimony analysis, the number of extra steps to include reasonable trees might be estimated as the average number of steps per node (length per branch). Only the sect. Fallaces subclade produced a set of trees that did not overrun computer memory. The 48 resulting trees were analyzed by majority-rule tech­niques (CONSENSE, Felsenstein 1995; MAJORITY, Wilkinson 1995). Clusters of terminal taxa in the following exact topologies appearing in greater than 50 percent of the total number of trees (48) were (D. nigres­cens (D. perobtusus, D. sub­andreae­oides)) 100%; (D. leske­oides, D. tophaceus) 96%; (D. ferruginascens, D. maximus) 88%; and (D. michi­ganensis (D. nigrescens (D. perobtusus, D. subandre­ae­oides))) 63%­. The cluster (D. leske­oides, D. tophaceus) was at the base of the tree in 54% of the trees. Of the 48, there were 22 trees in this pool of reasonable trees that include all three subclades. Thus, even if the tree of maximum synapomorphy is excluded as less parsimonious, true parsimony analysis (given the above assumptions) results in poor resolution at least with this particular data set.


 If the 48 trees examined constitute a confidence interval, the particular majority rule subclades have probabilistic support, but if not, then this is another example of unuseful statistical relevance. Which obtains remains uncertain. The .44 con­sis­tency index of the clado­gram in Fig. 1 is evidence for at least minor conver­gence that affects topology (of course, some minor convergence does not affect tree structure) and is to some extent modeled in the reinterpretation. Major conver­­gence would be, for example, nodes of one of the two subclades (sect. Didymodon and sect. Fallaces) being derived in parallel from several nodes of the other subclade through immediate elaboration of several states of a suite of character states associated with adaptation to a particular, different environment—but no evidence of different environments (plus clear cut envir­on­mentally associated traits) associated with the two subclades is at hand. This exercise, in dealing with an “accepted” subclade, does not challenge the phylo­grammatic results.


A disenchantment with statistics (as improper use of null hypo­thesis testing) has recently developed in the psy­cho­logical sciences where “...more theoretical courage” is called for (J. Kagan in Bower 1997). In modern systematics, accep­tance of maximum synapomorphy trees as provisional “best” reconstructions just because they are least falsified or are best explanations is a philosophically realist too-low standard. Least falsification here is similar to the concept of “power of the test” in classical statistics (Rawlings 1988: 100; Tabachnick & Fidell 1989), which is the probability of rejecting a false null hypothesis (e.g. by large F-ratios). Likelihood ratios with low posterior probabilities are not acceptable simply because no other more probable tree has come to light. Requirements for null hypotheses in phylogenetics are discussed by Wollenberg et al. (1996), among others, especially Faith and Cranston (1992).


That a great deal is presently expected from phylo­genetic analysis is clear from many university positions presently being offered for phylogenetic systematists (especially those using molecular techniques) and from the amount of U.S. National Science Foundation grant support. As to the latter, for the year 1997 (National Science Foundation 1997), more than $14 million was awarded in 96 grants for systematic research. Of these, 55 awards (57%) had the words “phylo­geny” or “cladistic” or “mole­cular systematics” or some variant in their title: these grants totalled about $7.5 million, averaging $135,000 per grant. An additional 16 grants (16%) had the word “evolu­tion” or a variant in their title: these grants totalled about $1.5 million, averaging $97,000 per grant. The 23 remaining systematics research grants (23%) totalled about $5.3 million, averaging $250,000 per grant; for these, any emphasis on phylo­genetics could not be told from their titles. If one combines the phylo­genetic and evolution categories (evo­l­ution in systematics studies being almost certainly used in the sense of phylo­genetics), support for modern computerized evolutionary analysis by NSF in just the one year 1997 is conservatively estimated at about $9 million (of a $14 million pot), taking at least 70% of the awards. Now there are two kinds of phylo­genetic studies presently common in the literature: (1) those that methodo­­­­logically wrongly equate maximum parsimony with maximum syn­apo­morphy, and wrongly substitute ratios of maximum likeli­hood and maxi­mum posterior probabilities for pos­terior probability greater than .5 (i.e. more evidence for than against); and (2) those that treat their results as steps along the way in building a modern method for probabilistically estimating phylo­genetic relation­ships for at least some groups (as do many of the theoretical studies cited in the present paper). Clearly little scientific advance can be expected from support given funded projects like the former, other than the generation of data sets. One might hope that, in view of the well-known world-wide critical status of biological diversity, alpha taxonomic studies (keys, descriptions, nomenclature, typification, discussion of range and variation, illustration, etc.) are part of morphologically based phylo­genetic projects, as is sometimes the case, that are supported by NSF.




There are three major problems with phylo­genetic analysis as currently practiced that are outlined in this paper. (1) A difficulty shared by all phylo­genetic analysis is the exten­sive regularity assumptions neces­sary for modeling frequencies in Bayesian-style analysis of unique events. (2) A second problem is that analysis through maxi­mum syn­apo­morphy is evidently not proba­bilistic at all beyond elimi­nating evolutionary scenarios that appear to be grossly unreasonable, or at least calculation of such probabilities are highly dubious. Also, the posterior probability of a tree of maximum likelihood selected through likelihood ratio (or similar linear rank) techniques may be very low and then does not reflect more evidence for than against when compared with other reasonable trees in the pool or “credible zone.” (3) Third is over-interpretation through computer algorithms of the idea of descent from common stock. A pool of somewhat short trees that are each a reasonable evolutionary hypothesis are impro­perly reduced to one tree by maximum synapo­morphy, thus falsely (in view of consistency indexes seldom higher than .85 and usually much lower) “recon­structing” a phylo­geny by the assumption of no evolutionary convergence unless it is shown in cladistic homoplasy.


Recognizing that the result of parsimony analysis is merely a best theoretical model for classification by common descent alone avoids the idea implied in the literature that such analysis is a statistical method producing concrete, confidence-inspiring recon­structions, but instead reflects the powerful ability of com­puterized ana­ly­sis to interpret large, complex data sets on the basis of a simp­listic theory of common descent. If we do base classification on explanations that are merely best of a number of competing explanations requiring in addition a host of regularity assumptions, then this is the sorry burden of systematics that has not been alleviated to any significant extent by modern computerized evolutionary analysis. A similar problem exists in vicariance biogeography, where scenarios involving long-distance dispersal, except where obvious, are largely ignored, and the results are valuable as heuristic constructions but not as reconstructions.


I justify this phyletic study of North American Didy­modon species in three ways. (1) The cladogram provides an accep­table general classification as there are many terminal taxa of similar morphology intermediate between extreme morphotypes, and the two identified clades are reasonable interpretations for this particular data set. (2) The lineages seem to be good hypotheses in the distal areas of the tree because there are relatively many ancestral nodes that approximate the morphological complexity of the terminal taxa, allowing identification of possible surviving ancestors (which themselves are generalist). Though most nodes do model ancestors, the existence of such ancestors as characterized by the state combinations at the nodes is only theoretical. Most nodes collapse at one additional step (but see majority-rule analysis above), and the fine structure, cer­tainly that deeper in the tree, is thus question­able. (3) The tree of maximum synapo­morphy can be considered in its alternate guise as the tree of theoretically mini­mum convergence in a trait-polarized, phylo­genetic context. The phenetic ordination is related, then, to the broad patristic distances between terminal taxa (not the fine structure in lineages) and the phylogram helps identify species that may be evolution­arily convergent in the genus.


The theoretical phylo­geny (at least as a cluster dendro­gram) suggested by the phylo­genetic estima­tion (Fig. 1) is useful for classification purposes also because it is reasonable, and agrees with intuitive evaluations involving “look and feel” charac­­­ters not easily scored, and of apparent transformation series (the robust species D. giganteus and D. nicholsonii are clearly part of two different stature-gradient series as suggested in figures 1 and 2). Further analytical exploration, given the increased agreement of figures 1 and 3 over that of figures 1 and 2, is warranted, with study of additional species and data.


Phylogrammatic analysis can provide explicit phenetic information as an interpretive classificatory aid for cladis­t­ic­ally poorly resolved groups or poorly supported subclades, though this was not needed in the present study in which the major lineages for these very similar taxa are well resolved in the tree of maximum (interpreted) synapo­morphy. The two relatively least sup­ported nodes or vertices of the phylo­genetic cluster dendro­­gram (discussed above) are, in fact, supported by the PCA analysis. Theoretically, the phylo­gram (Fig. 5) demon­strates that cladistically evinced evolutionary conver­gence in Didymo­don would have adversely affected supra­specific classification by phenetic analysis in only a few species. Principal com­ponent analysis was less affected by apparent con­vergence than cluster analysis when both are compared with the results of cladistic analysis. To the extent that phenogram and cladogram agree, the possibility of poten­tially confounding convergence identified by cladistic homoplasy in classification is minimized.




Based on the results of the evolutionary analysis, species in Didymodon sect. Asteriscium (C. Müll.) Zand. and Didymodon sect. Vineales (Steere) Zand. are better associated with Didymodon sect. Didymodon. Given the high synapo­morphy to autapomorphy ratio and the similarity of the terminal taxa (relatively few autapomorphies per taxon contributing to low patristic distance), at least the sectional classification may be considered a parsimonious hypo­thesis. That this supra­specific arrangement will obtain for the genus world­wide is doubtful, however, especially concerning the distinctive D. nigrescens and D. australasiae groups that terminate long branches, and further study is, of course, needed. But, in any case, based on the available information, the species of Didymodon in North American can be distributed as follows:


Sect. Didymodon: D. anserinocapitatus (L.-j. Li) Zand., D. australasiae (Hook. & Grev.) Zand., D. brachy­phyllus Sull., D. johansenii (Williams) Crum, D. neva­d­ensis Zand., D. nicholsonii Culm., D. perobtusus Broth., D. revolutus (Card.) Williams, D. rigidulus Hedw., D. sinuosus (Mitt.) Delogn., D. umbrosus (C. Müll.) Zand., D. vinealis (Brid.) Zand.


Sect. Fallaces Steere: D. asperifolius (Mitt.) Crum, D. fallax Hedw., D. ferrugineus (Besch.) Hill., D. giganteus (Funck) Jur., D. leskeoides Saito, D. maximus (Syed & Crundw.) Hill., D. michiganensis (Steere) Saito, D. nigrescens (Mitt.) Saito, D. subandreaeoides (Kindb.) Zand., D. tophaceus (Brid.) Lisa.




I thank Patricia M. Eckel, Wayne K. Gall, James Lyons-Weiler, Charles A. May­nard, Gert S. Mogen­sen, Lloyd R. Stark, Kevin P. Smith and Tod Stuessy for helpful comments on early drafts or particular portions of this work, or who have been otherwise helpful. Through the Taxacom listserver (see archives for September through December 1997, http://kaw.keil.ukans.edu/ mail_archives/taxacom) I profited from the shared pers­pec­tives accompanying the illuminating James Lyons-Weiler/Tom DiBene­detto debate, that included Sylvia Hope, Ted Schultz and others. Lyons-Weiler provided especially helpful comments, sug­ges­­tions, and encouragement on proba­bilistic aspects of phylo­genetic analysis. Warren Kovach suggested methods of cluster analysis. For loans of Didymo­don over the years, I thank the curators at many herbaria, especially ALA, BM, C, CANM, COLO, DUKE, F, FH, H, MICH, NY, PC, S, UBC, US, and WTU. Grati­tude is extended to George F. Goodyear for the support he has given the Museum and its scientific divisions over the years.




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Note in Proof: Scotland (1997) recently argued that parsimony algorithms do not necessarily maximize character congruence or minimize homoplasy, through there remain problems with the definition of congruence. Parsimony minimizes the number of interpretations of synapomorphy (as steps per branch) but maximizes the number of terminal taxa affected by each synapomorphy. The phrase “tree of maximum synapomorphy” in the present paper, however, may be replaced with “the shortest tree” with little violence to my arguments against optimality criteria as these are used in phylogenetic inference.


(Scotland, R. W. 1997. Parsimony neither maximizes congruence nor minimizes incongruence or homoplasy. Taxon 46: 743–746).


Note added, December 29, 2008: Pianka (1986) diagrammed a PCA and phylogram combination detailing evolutionary ecomorphology of certain desert lizards. His phylogram is also available in his well-known text book (Pianka 1999: 343).


(Pianka, E. R. 1986. Ecology and Natural History of Desert Lizards. Analyses of the Ecological Niche and Community Structure. Princeton University Press.

Pianka, E. R. 1999. Evolutionary Ecology. Sixth Edition. Addison Wesley Longman, Inc., San Francisco.



 Figure 1. Phylogenetic tree of 22 species of Didymodon. Characters were mapped on the consensus tree of 3 trees of maximum synapomorphy with tree length 63, consistency index 0.44. The outgroup is Barbula unguiculata Hedw. The capital letters correspond to these same species on the PCA diagram and Table 2. R = reversal; u = unique, appearing once in cladogram; h = homoplasy. Bremer support values are indicated above the branches where greater than 1.


Figure 2. Dendrogram of UPGMA cluster analysis of 22 species of Didymodon, using standardized Euclidean distance.


Figure 3. Dendrogram of UPGMA cluster analysis of 22 species of Didymodon, using an unstandardized Pearson product moment correlation coefficient.

Figure 4. Principal component analysis of the data set, axes 1 and 3, Euclidean distance, standardized. D and d = species of Didymodon sect. Didymodon; F and f = species of D. sect. Fallaces. Lower case “d” refers to D. australasiae group, lower case “f” to D. nigrescens group. There is little interpenetration between the two sectional clusters.


Figure 5. Phylogram combining principal component analysis and an evolutionary tree of maximum synapomorphy simplified from Fig. 1. The tree is rooted outside the square at the “ground” symbol. Letters correspond to list of species in Table 2 (see also Fig. 1). Species “C”, “E”, “F”, “H”,“Q” and “V” are possible surviving ancestors. The two main subclades branching from the root are sect. Didymodon and sect Fallaces. The phylogram shows morphological convergence (length of branches are not significant), especially between the species pairs “A” and “R”, “B” and “T”, “G” and “M”, “I” and “V”, “D” and “N”.




Table 1. States of twenty characters scored in the data set of 22 Didymodon species.


1. Leaf stance when moist:

0. spreading to weakly recurved, commonly lying flat when removed.

1. strongly recurved, lying on their sides when removed.

2. Leaf shape:

0. short- to long-lanceolate.

1. deltoid to ovate-lanceolate.

3. Leaf length:

0. 0.9–1.5 mm.

1. 1.2–2.5 mm.

2. 2.0–3.5 mm

3. 3.5–5.0 mm

4. Leaf channeling above midleaf:

0. with a narrow groove along ventral surface of costa.

1. broadly channeled to nearly plane.

5. Leaf apex shape:

0. rounded or obtuse (occasionally broadly acute).

1. broadly to narrowly acute.

2. very long acuminate, whiplike.

3. swollen as a propagulum.

6. Leaf apex cells:

0. of a clear conical cell or mucro:

1. rounded and obscure.

7. Leaf margin flexion:

0. plane or nearly so.

1. recurved in lower 1/2 or 3/4.

2. recurved or revolute to apex.

8. Leaf upper margin ornamentation:

0. minutely crenulate.

1. smooth or papillose.

9. Leaf base:

0. gradually or quickly narrowed to the insertion.

1. winged or auriculate.

10. Costa ending:

0. clearly excurrent, usually as a short mucro.

1. percurrent or ending to 2 cells before

the apex

2. ending more than 2 cells before the apex.

11. Costa width at midleaf:

0. 2–3(–4) cells.

1. 4–5(–6) cells.

2. (5–)6–9 cells.

12. Costa superficial ventral cells:

0. elongate, more than 2:1.

1. quadrate or very short-rectangular (at least near apex).

13. Costa hydroids:

0. present.

1. absent.

14. Cells, upper laminal, layering:

0. unistratose, rarely bistratose in patches.

1. bistratose along margins, at apex, or often bistratose in patches.

15. Upper laminal cell lumens:

0. mostly rounded.

1. mostly angular.

16. Upper laminal papillae:

0. absent or simple, bifid or multifid.

1. low, massive and lens-shaped.

17. Propagula:

0. absent.

1. present, axillary, multicellular.

2. present, axillary, unicellular.

3. tubers present on rhizoids.

18. KOH color reaction of upper laminal cells:

0. yellow or orange, occasionally negative.

1. brick-red, seldom red-orange.

19. Basal cell walls:

0. firm, thin to thickened.

1. very thin, hyaline.

20. Well developed specimens with ventral costal stereid band:

0. present.

1. absent






Table 2. Data set of 20 characters for 22 species of Didymodon and the outgroup Barbula unguiculata. Character states that were scored as variable in the cladistic analysis are underlined, otherwise they are as used in the PCA and cluster analyses. The capital letters map to the PCA ordination.



  unguiculata       00100 01000 10000 00000


A anserinocapitatus 00113 11100 11111 00100


B asperifolius      11101 01101 11101 00100


C australasii       01011 11101 11010 03111


D brachyphyllus     01010 02101 11110 01100


E fallax            01101 11100 00101 00000


F ferrugineus       11101 11101 00101 00100


G giganteus         00301 11101 20101 00100


H johansenii        00013 11100 11111 00100


I leskeoides        00102 11110 10101 00100


J maximus           11201 11101 00101 00100


K michiganensis     01001 11101 10100 01000


L nevadensis        01010 02101 21100 03100


M nicholsonii       00301 01101 11110 00100


N nigresens         00011 11001 00100 10100


O perobtusus        01010 11002 01101 12100


P revolutus         00010 12102 21010 02100


Q rigidulus         00001 11101 11111 01100


R sinuosus          00003 01101 11110 00100


S subandreaeoides   01000 11002 01101 10100


T tophaceus         01101 11111 10100 00100


U umbrosus          00101 10101 10010 13011


V vinealis          00101 01101 11111 01100







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