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A PHYLOGRAMMATIC EVOLUTIONARY
ANALYSIS OF THE MOSS GENUS DIDYMODON IN NORTH AMERICA NORTH OF |
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Originally published in Bulletin
of the Buffalo Society of Natural Sciences 36: 81–115. 1998. A PHYLOGRAMMATIC
EVOLUTIONARY ANALYSIS OF THE MOSS GENUS DIDYMODON IN NORTH AMERICA NORTH OF Richard H. Zander Division of Botany, Abstract: A key is
presented for the 22 known species of Didymodon
(Musci) in North America north of The moss genus Didymodon as expanded by Saito (1975) has proven
large and complex in 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. TAXONOMY DIDYMODON Hedw., Sp.
Musc. 104, 1801. Sections of the genus
previously recognized for North America north of 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). KEY TO DIDYMODON IN NORTH AMERICA NORTH OF 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. KEY TO VARIETIES OF DIDYMODON RIGIDULUS 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 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 1d. Didymodon rigidulus var. gracilis (Hook. & Grev.) Zand., Cryptogamie, Bryol. Lichénol.
2: 393. 1981. Tortula gracilis Hook. & Grev., 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. 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., 4. Didymodon
australasiae (Hook. & Grev.) Zand., Phytologia 41: 21. 1978. Tortula australasiae Hook. & Grev., 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 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 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 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. KEY TO VARIETIES OF DIDYMODON VINEALIS 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., 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 ( 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 This species was
originally reported (Zander 1978b) from specimens on bark of living or fallen
trees at low elevations in southern 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 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, 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 20. Didymodon
giganteus (Funck) Jur., Laubm. Fl. Oest. Ungarn. 102. 1882. Geheebia gigantea (Funck) Boul., Musc. Only one specimen,
collected in 21. Didymodon
tophaceus (Brid.) Lisa, Elenco Muschi 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 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. EVOLUTIONARY EVALUATION 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 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. CONVERGENCE 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. RECOVERY OF TRUE TREES:
PHENETICS VS. CLADISTICS 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. CONVERGENCE AND HABITAT 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 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 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. STATISTICS, THEORY AND
RECONSTRUCTION: A CRITIQUE 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. THE BAYESIAN BET 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.” STATISTICAL RELEVANCE 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; 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 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 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). EXAMPLES 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 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 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 ANALYSIS 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. ADDITIONAL ASSUMPTIONS 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. RELATIVE CERTAINTY 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. A MORE STRINGENT
REQUIREMENT 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 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. CONCLUSIONS 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. TAXONOMIC RESULTS 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. ACKNOWLEDGEMENTS 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
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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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