METHODS

The phylogenetic inference method used was that of parsimony; this method has been successful in reconstructing a complex, known, real phylogeny, and predicts ancestral character states (Atchley & Fitch 1991, Hillis et al. 1992). This obtains apparently in spite of problems of present computerized techniques of phylogenetic inference via parsimony, for example, in dealing with treatment of missing entries representing “unknown data, inapplicable data, and polymorphic taxa. Each of those potential sources of ambiguity is logically (if not computationally) different¼” (Platnick et al. 1991; also see Doyle 1993, Faith 1991 and Robinson 1986a). Although, ideally, is it best to analyze the limits of genera from a cladogram in which species are the terminal taxa (Funk 1985), this was unachievable with the large number of species involved. The relationships of the genera reflected in the cladograms produced in this study deal with traditional generic concepts derived from overall similarity of the species (see above) and apprehension of morphological “gaps” between genera. Inasmuch as only 75 morphological characters were used, a data set with more than a thousand species would produce a very poorly resolved cladogram. It may be hoped that the present study has resolved the family into smaller groups related by shared apomorphic characters; these groups may be studied separately in the future.

Maximally parsimonious trees were generated using the program Hennig86 (Farris 1988, 1989) with an extended branch-swapping algorithm, that is, the preliminary multiple tree-generating command “mhennig*” followed by an extended branch-breaking command, “bb*”. The full data set consists of 75 characters and 86 taxa including ten genera not in the Pottiaceae; the “Pottiaceae” data set consists of a subset of 76 taxa. All multistate characters were treated as additive (ordered) in that all such characters could be viewed as having transitional character states; character states that were not viewed as transitional (e.g. shape of propagula) and which were therefore probably governed by different genetic systems were treated as states of different characters. A character that is variable in state (polymorphic in the sense of Mishler 1990) is scored with a dash (“–”)as “unknown, undefined, or missing” (Farris 1988). The particular algorithm used in Hennig86, because of the large data set, apparently produces only a “heuristic approximation,” not a guaranteed minimal tree or trees; exact algorithms are, apparently, impossibly time-consuming for data sets larger than 15 to 25 taxa (Sanderson 1990). On the other hand, phylogenetic analysis of this large data set offers a window on evolution in a large and complex taxonomic group.

The order in which data is presented to the computer program affects, according to Maddison (1991), the length of the tree when heuristic tree-searching algorithms are used and retention index is less than .67 and number of terminal taxa is greater than 20. So, to find a short tree for each different outgroup used, the data set was subjected to a minimum of 30 computer runs based on random orderings of the rows of taxon data. A relentless search for the “shortest tree” was deemed useless, however, because of abundant homoplasy, and because the general concurrence of critical groupings between the short trees obtained with different outgroups was considered contributing at least sufficient resolution of patterns for purposes of suprageneric classification.

The number of equally parsimonious trees represented in most strict consensus cladograms is only a fraction of the number possible because of limitations in computer memory; however, the loss of resolution in the consensus trees based on the first 1000 or more trees is very small compared to consensus trees based on only the first 100 trees, and Cladograms 11 and 12 support the fine structure of the rest of the trees, being consensus trees based on smaller data subsets and a definite, much smaller number of equally parsimonious trees.

An Homoplasy-Excess-Ratio analysis (Archie 1989 a,b), which demonstrates the difference between the length of trees generated by the data set and that of those created by randomized data, was not performed. This is because the data set is certainly non-random since it reflects considerable sorting in past studies. A data randomization study is appropriate for studies that require identification of possibly random initial data sets (as in gene studies, cf. Waters et al. 1992), or to compare two or more data sets to judge which is more non-random.

The particular polarization of character states of the outgroups used here supports in large part Miller's (1979) list of commonly accepted polarizations or “principles for moss systematics” (Miller warned of occasional reversals in these generalizations in particular families). These polarizations were presumably derived from non-rigorous evaluations but akin to the outgroup criterion. Some of the 26 polarizations listed by Miller are relevant to the present study of the Pottiaceae. Presumed primitive traits are summarized as follows: large size, well-developed stem central strand, distinct stem sclerodermis (vs. an undifferentiated cortex), strong costa, epapillose laminal cells; while advanced traits include excurrent costa, very thin- or very thick-walled laminal cells, presence of propagula (“specialized diaspores”), axillary hairs with brownish basal cells (vs. all hyaline hairs), monoicy, sporophyte with short seta and immersed capsule, stomata absent, cleistocarpy, and peristome reduced or absent. These intuitive ideas, when compared (1) with the polarizations indicated in the list of characters below and (2) with the character states of the various outgroups contributing to the classification used in this study (Polytrichum, Ptychomitrium, Timmia and Timmiella in the Data Set) are largely acceptable at least as they apply to the present study.

Advanced traits may be convergent across family lines. For instance, Frahm (1991b) found the following traits to be apomorphic in the Campylopodioideae of the Dicranaceae, many of which are likewise apomorphic in the Pottiaceae: “presence of alar cells, leaf-borne rhizoids, incrassate laminal cells, hyaline leaf tips and strongly differentiated perichaetial leaves, hyalocysts in transverse section of costa¼in the gametophyte and presence of an annulus, fringed calyptra, filiform peristome teeth, long lid, stomata and large spore size¼” in the sporophyte. Vitt (1984) described an hypothetical ancestor to the Bryales as intolerant of desiccation; perennial; acrocarpous; essentially branchless; stems with hydroids and leptoids; leaves entire, strongly costate, spiralled, little spreading, unistratose; laminal cells thin-walled, rectangular, mostly homogeneous, alar cells not different; laminal papillae absent; dioicous; perigonial paraphyses numerous, thin-walled, apical cell enlarged; seta elongate, with hydroids and leptoids; capsule cutinized, with superficial stomates, photosynthetic, annulus and operculum present, exostome inwardly thickened, endostome segments oppositely placed and partly fused to a membrane, cilia absent; spores numerous and homogeneous in size; calyptra mitrate, hairless and epapillose. Eddy (1991) postulated as an “archetype” for the Pottiaceae “an erect, tufted or gregarious moss, 0.5–2 cm tall, with lanceolate, rather opaque leaves that lack either a border, teeth or specialized basal cells”; the present study has managed to clothe this simple pro-pottiaceous structure with many additional plesiomorphic character states.