Richard H. Zander
Missouri Botanical Garden
St. Louis, MO 63166-0299
November 26, 2003


When Classifications Conflict

Richard H. Zander



Three criteria are proposed for identifying the best of competing classifications based on scientific value. Morphologically based classifications are expected to continue to be important because molecularly based classifications are not generally demonstrable as reliable in detail, and the former may include identifiable biological hypotheses or theories that integrate with other fields.


A problem common to all of systematics is exactly how and when is a new classification better than a previous one? This paper rebuts several recent treatments of the Pottiaceae (Musci) that go back to generic classifications popular prior to my new proposals (Zander 1993), which taxonomically emphasize gametophyte characters.


A reason sometimes given for rejection of new classifications and retention of largely traditional generic concepts is that a natural classification is to be preferred, generally meaning giving equal weight to characters of the sporophyte and gametophyte. This is opposed to my rationale which consists of basically two ideas: First, that new concepts are warranted by the fact that several separate series of cleistocarpous and stegocarpous peristomes (including the eperistomate and all levels of peristome length and twist from rudimentary, to short and straight, to medium length and weakly twisted with a short basal membrane, to long and well twisted from a high basal membrane), with the peristome teeth grading from flattened to filamentous, are all or mostly present in species with quite similar gametophytes previously placed in Phascum, Pottia, Desmatodon, Stegonia, Tortella and Tortula. Because there are more gametophytic characters than sporophytic characters, a natural classification thus requires emphasis on gametophytic characters. Second, when gametophytic characters are used to organize the sporophytic characters (instead of vice versa or some combination), the variation in morphology of the sporophytes in the various newly emended genera (especially the large genera Henediella, Microbryum, and Tortula) may be explained as nearly identical transformation series involving reduction (parallel elaboration of a peristome is improbable unless genes are turned off and on controlling expression of several complex characters, for which there is presently no evidence).


Mayr (1982: 275) defined a natural system as a classification “based on the degree of similarity of their morphological or anatomical systems…,” noting that its overall success is ultimately explained by shared ancestry. Similarly, Stuessy (1990) pointed out that a natural system “is one based upon states of several to many characters selected a posteriori for their value in positively correlating with states of other characters to form a hierarchical structure of groups in ranks containing high information content and predictive value.” A taxonomist may choose intuitively as major characters those relatively stable features that best organize or maximize the similarity of other, possibly more variable characters; e.g. using flower morphology for higher categories of angiosperms, or may use numerical taxonomy to identify such organizing characters, and the resultant similarity among taxonomic units is informative and predictive. This is not the same as simply giving equal weight to all characters. Stuessy (1990: 60) pointed out that equal weighting is simply a preliminary part of the method of phenetics (numerical taxonomy), while natural classification differentially weights characters after evaluation of perceived utility in maximizing similarity. The result is the same, but a numerical analysis is needed to maximize similarity among species of recognized genera.


An emphasis on the utility of gametophytic characters is based on two synergic rationales: (1) a natural system choosing certain gametophytic characters (primarily leaf shape, costal anatomy, and areolation features) to maximize similarity of other characters among the genera, especially the sporophytic characters which self-organize into neatly parallel transition series, and (2) interpretation of the sporophyte transition series as evolutionary adaptations that hypothetically involve selected fine control of diaspore dispersal in different environments, as with reduced sporophytes and larger spores or late-rupturing capsules (Carlquist 1966; Van der Pijl 1972; Zander 1993: 14), similar transition series in sexual condition (dioicy to autoicy to synoicy in Weissia s.lat.) that may have been selected for control of degree of outbreeding. There is good evidence that reduction also occurs in the gametophyte, e.g. see my (1993) treatment of Trichostomum.


So which classification is better for others to use, old one(s) or new ones (e.g. mine)? The only proper judgement must be on the basis of the proposals themselves.


Although we may all subscribe to a dictionary-style definition of science as “gathering, organization and analysis of information about the natural world and inference of general principles therefrom,” when scientific methods compete, such as in systematics, a judicious perspective on the question “which produces the better model of reality?” is a way to approach the dilemma. “Reality” or that which is “out there” can attain a metaphysical substance in all fields but a self-correcting science, which assumes that all theories are only approximations. Most scientists at least implicitly subscribe to “critical realism,” in which the immediate world is very real (predictions or manipulations are easy and reliable), but realities that are non-immediate, being distant in time and space, are in a way “less real” and are usually dealt with probabilistically (either as empiric extensions of long-run frequency observations or as psychological expectation based on logic), or at least in an instrumentalist fashion (are the theories useful?). Science attempts to make non-immediate reality almost as easily dealt with as the immediate by creating models based on facts (i.e., well documented observations). Systematics is a “quasi-experimental” field (Cook & Campbell 1979) where patterns in nature are discerned in much the same way that scientific laws or regularities in nature (Carnap 1966) are established in experimental sciences. The basis null hypothesis for systematics is that there are no species, for biogeography is that there are no discrete ranges, for evolution is that there is no evidence that it did occur. Thus, one expects, in both experimental science and systematics, testable theories to disprove or support.


Given that systematics is a science, when is one theory better than another? There is a vast literature on evaluating scientific theories, and directly pertinent, though often philosophically conflicting treatments include Carnap (1966), Glymour (1980), Hemple (1963), Hull (1974), Pap (1962), and Popper (1962). One might advance the following three traits of a better theory: (1) It should explain or make fit in a reasonable manner additional relevant facts. (2) It should be simpler, more elegant, and make understanding nature easier. (3) It should be congruent with other generally accepted theories and suggest new studies. (4) It should have more testable elements.


A system that emphasizes the taxonomical importance of gametophytic characters (1993) matches these criteria in the following respects: (1) More characters are used, and more species examined. (2) It simplifies dealing with sporophytic characters in that a rather standard transformation series may be assumed unless there are particular anomalous characters (e.g. the combination of a short seta but elongate, stegocarpous capsule in Willia). That is, there are fewer ad hoc explanations. (3) It fits in well with other theories in that Weissia is now commonly acknowledged to include past segregates Astomum and Hymenostomum, these genera apparently being artifactually discontinuous perceptions of a single transformation series in sporophytic characters (Stoneburner 1985). (4) The transformation series in sporophytes reflects theories of environmental patterning, atelochory and r- and K-selection, and is a good hypothesis that may be tested. With such embedded theories, my system also matches the “more bold” criterion of Popper (1962). Thus, although some classifications may differ largely according to “taste” or whether the author is a lumper or a splitter, in this case there are clear methodological and biological reasons why taxonomic emphasis on the gametophyte is to be preferred. The next advance in classification of the Pottiaceae will doubtless be made at the species level using modern methods of phylogenetic analysis, but there remain major problems with that technique.


An expectation that DNA data will provide ultimate solutions to intractable systematic problems is shared by many recent authors. This, however, cannot be expected to be the case, at least in the next very many years. There are major problems with reliability on the results of molecular (and morphological) phylogenetic analyses. This is because the best answer is not necessarily much better supported than the second best, or the third best, which may be quite different (Zander 1998). This applies to maximum parsimony in that bootstrapping cannot evaluate confidence levels for branches not in the shortest tree, and the gene pool is coarsely heterogeneous due to lineage sorting (different “speciation” times for genes and species). Also, Bremer support is a poor measure of branch support in data sets of very many characters because a branch of length n and Bremer support of x may have an alternative branch length of n–x, which could be large. Likelihood ratios, the standard measure of support in maximum likelihood studies cannot be used in phylogenetic analysis because the likelihoods are already optimizations. Full Bayesian studies such as Markov chain Monte Carlo analysis yield posterior probabilities of different alternative trees that appear to add to 100%, yet these are relative to the sum of the probabilities of the myriad trees with likelihoods too small to be calculated. Steel & Penny (2000) summarize additional problems. Non-parametric tests of reliability that evaluate the whole tree, such as the Kishino-Hasagawa test, may demonstrate that the best tree is much better than the next best, but many branches of that best tree may be poorly supported.


I have introduced, for measuring reliability of internal cladogram branches, a new non-parametric test of reliability (Zander, 2001) called the Conditional Probability of Reconstruction (CPR), which uses chi-squared analysis after nearest neighbor interchange under constraint. It tests whether the best choice of the three possible alternative arrangements for any four nearest neighbor branches is distinguishable from a random distribution at some chosen level of confidence (for small data sets, Bayes’ Theorem with uniform priors are used instead of chi-squared). Analysis of two published data sets (Didymodon morphology and primate mtDNA) indicated that many of the optimal internal branches of both morphological and molecular trees can be indistinguishable from a random distribution at a reasonable confidence level vis-a-vis the lengths of the two immediate alternative branches. Although some lineages are well supported probabilistically, probabilities of individual branch reconstruction when multiplied give rather low summary probabilities to the whole tree. Thus, cladistic analysis, when recouched in terms of statistical analysis (probability) rather than an optimality criterion (parsimony) is no longer as promising. To bring this home, consider a coin flipped 100 times, coming up tails 57 times and heads 43 times. Under parsimony, the hypothesis that the coin is unfairly loaded to come up more often as tails is valid, though poorly supported; statistically, however, there is no reasonable degree of confidence that the result was not due to chance, and no hypothesis is reasonably considered (although the null of random generation of data is not proven).


The CPR method can also be used to evaluate the problem of conflicting gene lineages in molecular phylogenetic analysis, which is also entirely relevant here. For example, there has long been controversy over the relationships of humans, chimpanzees and gorillas. A meta-analysis of the Homo-Pan-Gorilla data sets was recently done by Satta et al. (2000) who surveyed data from the literature for 45 loci consisting of 46,855 bp. There was conflict between data sets, with 23 loci supporting the ((Homo Pan) Gorilla) gene tree, 8 that support ((Homo Gorilla) Pan), 8 that support ((Gorilla Pan) Homo), while 6 support a (Homo Gorilla Pan) trichotomy. This incongruence was attributed by them to different gene and species phylogenies associated with the different loci. A CPR analysis (Zander 2001) treating each gene as a character, with alternative branch lengths of 23, 8 and 8, provided a probability of reconstruction of the species tree of .997. A similar high probability (.999) is obtained when only data sets with bootstrap values greater than 80% are used. Thus, species evolution can indeed be probabilistically reconstructed using molecular techniques. It also implies, however, that, absent this way of probabilistically identifying genes that actually track species evolution, the prior probability that the absolute order of an internal branch of any molecular tree really reflects species evolution rather than a contrary gene lineage may be on the order of 23/(23+8+8) or 59%.


Additional papers that reflect on the use, particularly the successful versus the unsuccessful use, of statistics in evaluating the reliability of individual branch arrangements in a cladogram were published recently (Zander in press).


Given the perspective that (1) many cladograms, though presented as fully resolved in the literature, may be poorly supported, and (2) that genes may be expected to provide significantly conflicting (through differential lineage sorting) but sometimes well supported trees, one cannot expect present phylogenetic techniques to result in a reliable evaluation of the evolution of the Pottiaceae in the immediate future. It is therefore more, not less, important to produce morphologically based, predictively useful, fruitful, illuminating and broadly applicable classifications that may have embedded biological theories relevant to other fields.



Carlquist, S. 1966. The biota of long-distance dispersal. III. Loss of dispersibility in the Hawaiian flora. Brittonia 18: 310-335.

Carnap, R. 1966. An Introduction to the Philosophy of Science. Basic Books, New York.

Glymour, C. 1980. Theory and Evidence. Princeton University Press, Princeton, New Jersey.

Hemple, C. G. 1963. Aspects of Scientific Explanation. Free Press, Collier-Macmillan, New York.

Hull, D. L.  1974.  Philosophy of Biological Sciences.  Prentice Hall, Englewood Cliffs, New Jersey.

Mayr, E. 1982. Systematics and the Origin of Species. Introduction by N. Eldredge. Columbia University Press., New York.

Pap, A. 1962. An Introduction to the Philosophy of Science. Macmillan Co., New York.

Popper, K. R. 1962. Conjectures and Refutations: The Growth of Scientific Knowledge. Harper Torchbooks, Harper & Row, New York. 1965 Edition.

Steel, M. & D. Penny. 2000. Parsimony, likelihood and the role of models in molecular phylogenetics. Mol. Biol. Evol. 17: 839-850.

Stoneburner, A. 1985 [1986]. Variation and taxonomy of Weissia in the southwestern United States. II. Taxonomic treatment. Bryologist 88: 293-314.

Stuessy, T. 1990. Plant Taxonomy: The Systematic Evaluation of Comparative Data. Columbia University Press, New York.

Van der Pijl, L. 1972. Principles of Dispersal in Higher Plants. 2nd. Ed. Springer-Verlag, New York.

Zander, R. H. 1989. Seven new genera in Pottiaceae (Musci) and a lectotype for Syntrichia. Phytologia 65: 424-436.

Zander, R. H. 1993. Genera of the Pottiaceae: Mosses of Harsh Environments. Bull. Buffalo Soc. Nat. Sci. 32: i-vi, 1-378.

Zander, R. H. 1998. Phylogenetic reconstruction, a critique. Taxon 47: 681-693.

Zander, R. H. 2001. A conditional probability of reconstruction measure for internal cladogram branches. Syst. Biol.

Zander, R. H. 2001. Reliable phylogenetic resolution of morphological data can be better than that of molecular data. Taxon 52: 109-112. 2003.

Zander, R. H. (in press) Minimal values for reliability of bootstrap and jackknife proportions, decay index, and Bayesian posterior probability. Phyloinformatics