Three-taxon statement analysis and its relation with primary data: Implications for cladistics and biogeography

Transcription

1 Implications of three-taxon statement analysis for cladistics and biogeography 171 Three-taxon statement analysis and its relation with primary data: Implications for cladistics and biogeography Three-taxon statement analysis (3ts) has been heavily discussed in the last ten years. The procedure was established by Nelson and Platnick (1991), following some papers on biogeography (Nelson and Ladiges, 1991a,b), and subsequently developed or defended by several authors (Nelson and Ladiges, 1992, 1993, 1994; Nelson, 1992, 1993, 1994, 1996; Platnick, 1993; Platnick et al., 1996; Siebert and Williams, 1998; Carine and Scotland, 1999; Scotland, 2000). Contemporary with these developments, several other authors have made criticisms to 3ts (Harvey, 1992; Kluge, 1993, 1994; Farris et al., 1995; Deleporte, 1996; Farris, 1997; Laet and Smets, 1998; Farris and Kluge, 1998; Farris, 2000). These discussions generated some interesting points to be analyzed. First, the acceptance of 3ts by the cladists appears to be quite difficult (cf. examples of exception in Scotland, 2000) and the reason why this occurs can help understand the procedure. Second, it seems that 3ts was treated as a procedure somewhat separated from biology, sometimes charged of being merely operational (e.g., Kluge, 1994) or having no theoretical basis at all (Farris, 1997). In this regard, de Pinna (1996: 10) attempts to synthesize the astonishment concerning 3ts: The most interesting idea in mainstream theoretical systematics in recent years is the so-called three-item analysis [...] Three-item analysis has undergone some debate and has attracted few proponents so far. The method is a profoundly different way of seeing the relationship between characters and their derivative hypothesis of relationships. Most of the criticisms addressed to 3ts concern its relationship with cladistics itself, and possibly this is the main reason why it is not widely accepted nowadays. In fact, Nelson and Platnick (1991) created 3ts within the context of cladistic theory, publishing 3ts in a cladistics bulletin (Cladistics). Besides, Cladistics has been the forum for most of the discussion concerning 3ts, and even Willi Hennig meetings were taken as opportunities to discuss the subject. This unavoidably renders criticisms of 3ts and comparisons between it and cladistics, as Kluge (1994: 404) stated: Several important cladistic concepts and practices are identified in these references, and these justify the bases for most of my previous (Kluge, 1993) and present criticisms of the three-taxon transformation. Although Nelson and Platnick (1991), Nelson (1993) and Platnick (1993) have not always consistently stated or employed those concepts and practices (see below), there can be no doubt that they intended three-taxon analysis to be an improvement to cladistics, not a competing or alternative form of phylogenetic inference (emphasis is mine). Perhaps Nelson and Platnick created and still believe that 3ts is really an improvement of cladistics; however, what if 3ts is not cladistics? Which biological perspectives and problems would be enlightened and how would evolutionary theory gain with that? The insistence in comparing standard cladistic parsimony analysis with 3ts is worthless: 3ts has exclusive issues that cannot be compared to those of cladistics. The possibility that 3ts is apart from cladistics and at the same time has been generated in the heart of the latter is not a new event in evolutionary biology and epistemology. In a historical perspective, other systematic schools were created in the heart of previous theories, but they were generally marked with abrupt landmarks in which the rising theories were extensively discussed and exposed, sometimes with the creation of a proper jargon for them. Moreover, these theories were generally assumed to be different ways to focus similar problems (e.g., Hennig, 1966 for phylogenetic systematics and Sokal and Sneath, 1963 for numerical taxonomy). This independence facilitates the identity of the rising theory and perhaps its wider acceptance (see comparisons in Hull,

2 , criticisms to the book by Farris and Platnick, 1989). The rise of 3ts was definitely not such case, because it first appeared as a simple study published in a very cladistic bulletin. This certainly makes 3ts more difficult to be understood, because some cladists already have biased ideas of evolution and systematic approaches (cf. Nulius in Verba passage quoted by Nelson, 1996: 151). Part of the issues discussing homology either in relation to cladistics as well as 3ts were addressed in Scotland (2000), but much more can be discussed. In this essay, I will try to discuss some of the remaining 3ts issues, bringing it closer to biological reasoning, and trying to clarify in which issues 3ts should be set aside from Cladistics. In the same way as de Pinna (1996), I prefer to refer to 3ts as an interesting idea in mainstream of theoretical systematics, not cladistics properly. Comparisons between 3ts and cladistics A point by point comparison between 3ts and cladistics has never been made, simply because they were assumed (even if it was only implicitly assumed) to belong to the same reasoning (cf. Siebert and Williams, 1998, replied by Farris and Kluge, 1998). Possibly because of this, Kluge (1994) has pointed out so many incoherences for 3ts views. In fact, trying to understand 3ts under a mainstream cladistic viewpoint may indeed show these incoherences ; however, although partially related to cladistics, 3ts has some particular issues that must be addressed separately, making the understanding of the procedure easier. Observation, primary homologies, and characters There is not much question about what observations are. Observations, the first step in a systematic study, are the same for any comparative analysis, be they traditional, phenetic or cladistic. There is nothing more than crude information in each observation, not necessarily related to evolution of the groups or to a given hierarchical pattern. Observations that are different can be considered products of something (evolution, for instance), however, they can be false clues of phylogenetic relationships. Whether or not an observation is truly phylogenetically informative cannot be predicted a priori, simply considering empiricism. Several definitions of characters and homology were already proposed, part of them by cladists. Operationally, I will take two widely accepted definitions: the one of character by Platnick (1979) and the homology definitions by de Pinna (1991). After some individual interpretation and understanding, the observations are linked to one another in small groups. There are no rules for this linkage of the observations, although similarity and congruence criteria can help in the procedure (Patterson, 1982; de Pinna, 1991). Once linked, observations are arranged in a matrix of characters x taxa, what can be called a character matrix. All data in this matrix are primary homologies (de Pinna, 1991). In the same way as observations, it is not possible to know whether or not these data are good indicators of relationships (some randomization tests have been proposed to check the cladistic structure of the matrix, e.g., Archie, 1989a,b; Faith and Cranston, 1991, but I will not comment on them, for criticisms see Peres-Neto and Marques, Thus: conventional analysis indicates that a character consists of two or more different attributes (character states) found in two or more specimens that, despite their differences, can be considered alternate forms of the same thing (the character). A character is thus a theory, a theory that two attributes which appear different in some way are nonetheless the same (or homologous). As such, a character is not empirically observable; hence any (misguided) hope to reduce taxonomy to mere empirical observation is futile (Platnick, 1979: 542). Empiricism is connected to observations, and theories (= characters) are a further step that demands interpretation. During a study, one can make mistakes at both stages, as I shall demonstrate. What if this theory is not correct? What if the facts that lead us to propose this theory are obscured to us? What if an observation does not reflect the evolutionary history of a given group? There are many ways that one can be led to suggest a mistaken theory. For instance, one can mistakenly put together two attributes in a given theory (character) that actually are not the same, specially because the transformation itself is not observable (Sattler, 1984; cf. Scot-

3 Implications of three-taxon statement analysis for cladistics and biogeography 173 land, 2000 commenting on taxic homology by Patterson, 1982), exception made to ontogenetical characters or those that include two actual synapomorphies in different theories (characters) because of incorrect interpretation of observations. Besides, sometimes the observation could not reflect actual evolution (Weston, 2000), because it may be supposed that observation is only the final eventual product of evolution, and it does not tell us the whole evolutionary history (i.e., it is not indisputable evidence). Every observation can comprise eventual failure, e.g., actual homoplasies considered under the same code (i.e., observation considered as putative synapomorphies when they are not), actual reversals considered together with plesiomorphies (i.e., observation considered a plesiomorphy when it is not). Marques and Gnaspini (2001) provide a biological example of incorrect theories that are impossible to be predicted based only on observations. Studying troglomorphisms (animal characters adapted for cave environments), they considered the problem of recognizing if adaptive characters (observations) are either homoplasies or synapomorphies. For this, they proposed a method in which missing entries were added in a re-coding procedure to express their doubts in relation to the primary homology of the troglomorphic characters. Their consideration that troglomorphisms are the only adaptive characters in the data matrix, however, is a simplified and anthropic view of the problem. Nobody can know whether a character is good or not for a phylogenetic inference. Hence, their method could be extended to all characters of the data matrix in order to do the same recoding. Besides, they proposed a minimal number of combinations to recode the characters in question and this could be extended to all possible combinations of two terminals with one state against a third terminal with a another state. Therefore, if Marques and Gnaspini s (2001) procedure is taken to its extreme, the recoding would reach similar procedures to that of 3ts. In another example, Nelson (1993: 261) suggested hints for the same problems of incorrect theories, when discussing that homology of mammary glands as diagnostic of the taxon Mammalia was the result of several three taxon statements, i.e. comparison among taxa with / without the character. Perhaps Nelson should have stressed the importance of noticing that the observation of the mammary gland does not guarantee that the organism is a mammal, but it also does not say the contrary, and propositions of groups can only be made after comparison with other organisms included as terminals in the analysis. The simplest and necessary comparison to be made is the three taxon comparison, two against one. For instance, the comparison of the mammary glands could be made among a flounder, a frog, a zebra, and a horse (see possible combinations in Platnick et al., 1996: 243). The observation of the frog proves that it does not have mammary glands, and those of zebras and horses say they have; however, other hypotheses, related to the errors in the proposal of theories listed above, still occur: (1) the frog had mammary glands during its evolution and the character was posteriorly reversed (let s forget our imprinting about ontogeny for the example), and (2) mammary glands of zebras and horses, although apparently primary homologues, are not. The insertion of missing entries in this case only embraces these two historical possibilities (inclusion of missing entries would also prevent errors in the composition of the theory, i.e., linking of two attributes in the same character when they should be considered apart). It is important to notice that, in both cases, the missing entry does not forbid the homology to occur and it also does not imply in the non-homology. Hence, the adoption of this kind of coding is more relaxed concerning evolutionary assumptions and tends to prevent eventual unavoidable interpretative mistakes. It is unnecessary to stress that, once included in a primary homology matrix, the observation (carrying all its eventual errors) assumes the condition of total truth, and will determine the topological results after parsimony analysis (see Scotland, 2000; Marques and Gnaspini, 2001). Hence, parsimony itself cannot find the incorrect theories included in the primary homology matrix because the coding adopted will never allow parsimony to do that. At best, in cladistics, parsimony could be viewed as a way to minimize wrong and correct theories in a given topology, and the best topology would be that with the minimum number of wrong and correct constraints allowed by the coding procedure. Besides, coding procedures can vary from the classical linking of unor-

4 174 dered plesiomorphy-apomorphy to the ignored assumption of homology between the attributes (as in Pleijel, 1995; see Scotland, 2000). Missing entries, transformed matrices, and primary-and-a-half homologies Up to now, it was shown that observations are empiric and included as primary homologies in the matrix. This procedure results in an original data matrix. As already stated, a subsequent step would be to consider the uncertainty on the equivalence of the primary homologies. From the example above, this would be achieved considering relationships of the mammary glands of any two taxa in relation to a third taxon without mammary glands, and uncertainty is included with the addition of missing entries (the very expression of uncertainty) to all other terminals. Different combinations (three taxon statements) would guarantee the doubtfulness spread all over the matrix. In the 3ts procedure, the missing entries work in two ways (taking the same example): (1) allowing that the observation of absence of mammary glands in some taxa is wrong because they actually had that and reversed, and (2) allowing that the supposed homology among two taxa with mammary glands is false in relation to a third taxon. It is quite clear from thousands of cladograms already published by classical parsimony methods that this doubtfulness is not impossible or even unlikely in evolutionary terms. Actually it is quite common, since the acceptance of reversals and homoplasies is widespread among cladistic analyses. This is a pattern observation. Obviously, some characters like mammary glands have great appeal, and are considered most probably as certain synapomorphies (whatever sentimental appeal this has for researchers) by some people; but the procedure is never saying anything against that evidence. However, some other characters, like a setae present in the terminalia of individuals of an insect group, may not have this appeal. In both cases, the procedure works in the same way. Hence, it seems possible that a matrix containing primary homologies has less evidence than a transformed matrix of 3ts, because the latter includes the former plus the eventual errors impossible to be determined through simple observation. This fact is also commonly observed in biogeography. When studying the historical distribution of taxa, assumed to be due to vicariance, it is common to see incongruence in their distribution. This is interpreted with other than historical reasons to explain taxomic distribution, namely extinction and dispersal. This was already predicted in the biogeographic literature (Nelson and Platnick, 1981) and was more precisely interpreted as the use of assumptions 1 and 2 (van Veller et al., 1999). Anyhow, acceptance that the present distribution of taxa is imperfect appears to be completely accepted by biogeographers, even if the unique evidence for this is a secondary interpretation of area cladograms (it is not the observation per se). Apparently, 3ts may be of benefit to biogeography (Kluge, 1993: 246; Morrone, 1993; Morrone and Carpenter, 1994; see Siebert and Williams, 1998: 346). Hence, if biogeographers have doubts about the observed distribution of taxa because they know that extinction and dispersal can occur, why do the systematists so truly believe in their observations if they know that reversals (equivalent to assumption 1) and homoplasies (equivalent to assumption 2) also occur? For 3ts, this can be considered the interpretation 1 and 2 (Platnick et al., 1996; Siebert and Williams, 1998; criticisms by Farris and Kluge, 1998) and the way to correct this is the 3ts coding (for biogeography as well). One of the main criticisms addressed to 3ts is that the method distorts and adds ambiguity to the original observations, as hypothesis of homology (Kluge, 1993: 255; 1994: 404). This ambiguity is added where none existed before (Kluge, 1993, 1994: 407: [t]hat the operation adds ambiguity to the evidence where none existed before). However, in a certain way, in any matrix with incongruence there is already an implied ambiguity of results (G. Nelson, pers. comm.). Besides, ambiguity was always there, in the form of doubtfulness implicit in the data, as exposed above. Considering this, 3ts could also be understood as a way to remove eventual ambiguities from the original matrix, because it has the property to minimize errors in the empirical data (= observations) due to unknown effects of evolution or wrong theories. Or, if one prefers, 3ts indeed adds ambiguity (missing entries) to the matrix to describe the ambiguity that was already there before.

5 Implications of three-taxon statement analysis for cladistics and biogeography 175 Most possibly, one could consider it naive to accept raw observations as indicative of relationships, especially assuming that evolution is a complex process (we do not know that for sure, but the majority of the patterns found by cladograms seem to indicate that, because they frequently contain incongruences shown as homoplasies and reversals; besides, there are also non-sense illogical optimizations from the anthropic viewpoint, which can have some appeal for some researchers). We should expect that the potential to be false is incorporated in each observation (i.e., product of homoplasy or reversal). This potential is not considered in the classical coding and because of that the relationships suggested by evidence can be obscured. In this sense, there is no synapomorphy precisely because synapomorphy is constrained into naive models of character evolution (see below). These values plotted in the re-coded matrix of 3ts could be considered primary-and-a-half homologies, a way to synthesize evidence of better quality and, therefore, more suitable to be tested in the congruence test (i.e. ready for parsimony analysis). Hence, primary-and-a-half homologies are considered to be the observations+ interpretation (primary homologies) plus the eventuality of misleading in these observations. In this sense, much of the discussion of what indeed are the data (e.g., Platnick, 1993; Kluge, 1994), loses its relevance. For instance, Kluge (1994) accused Platnick (1993) to have people understand that the problem of interpretation lies in Kluge s treatment of: a matrix of three-taxon statements as if it were an ordinary character matrix and continued it is not an ordinary character matrix; for every character the entries for only three taxa are relevant (two 1 entries and one 0 entry). The remaining entries (all question marks) are neither indicators nor place holders for any conceivable character state assignments, and cannot be optimized as if they were. Using a standard parsimony program to optimize them is simply a misuse of the program (Platnick, 1993: 267). Platnick was partially right, because the matrix is indeed different from an ordinary character matrix because it includes more information than simply those included in a primary homology matrix. He was not entirely right, however, when he stated that the addition of missing entries was a consequence of filling the blanks of the matrix left by the three taxon statements (also Platnick in Platnick et al., 1996). In my view, missing entries adopted in 3ts have a completely new meaning, different from all other understandings of missing entries (cf. Platnick et al., 1991; Kitching et al., 1998). In the 3ts case, missing entries incorporate inherent doubtfulness to the observation, something totally plausible when one observes the results of most of the traditional parsimony analysis. Although it is implemented as any other missing entries by software packages, the very meaning of the missing entry is: as I do know that ambiguity can exist in the data, which it is quite common in phylogenetic inferences, and as I do not know exactly which entry(ies) of the matrix is(are) incorrect (i.e., misled observation), why don t I doubt each value of the matrix, but not prevent it from being a true observation and, consequently, valid primary evidence? In this sense, a missing entry of 3ts represents a doubt if that 0 is really a 0 (since all the possible combinations are considered, it is equivalent to considering also a doubt if each 1 is really a 1). Parsimony analysis, parsimony reasoning and models In a contextualization of methodologies and science, Platnick (1979: 538) wrote: It may seem paradoxical to suggest that systematics (or any science) must adopt methods without itself being able to attest to their efficacy. But the fact is that we use our methods in an attempt to solve problems. If we already knew the correct solutions to those problems, we could easily evaluate and choose among various competing theories: those methods which consistently provide the correct solutions would obviously be preferred. But of course, if we already knew the correct solutions, we would have no need of the methods. Evaluations of scientific methodology, then, typically involve questions that are philosophical rather than scientific, from which we can conclude that one s general philosophy of science may greatly influence methodological discussions and decisions. Hence, comparisons between cladistics and 3ts are influenced by beliefs; however, we should not forget that several times (including in Kluge, 1994), meth-

6 176 odologies derived from parsimony were defended for phylogenetic systematics. Parsimony has been proposed as an underlying principle related to models (e.g., Kluge, 1993 justified its use considering inheritance; and even Hennig, 1965, 1966, in his auxiliary principle, linked parsimony to evolutionary models). In fact, Kluge (1993) criticized operationalist procedures based on no models (referring to 3ts), exactly because he believes that parsimony is necessarily related to inheritance (for other views of parsimony see Sober, 1988), and he added (Kluge, 1994: 405) that: Nelson and Platnick (1991) could avoid the controversy surrounding a parsimony analysis of question marks by employing some other grouping technique, such as character compatibility / clique analysis, but then the three-taxon operation could not be presented as a possible improvement to the use of parsimony in cladistics. Platnick (1979: 538) established the basis of pattern cladistics considering that: Hennig presented his methods by referring to one particular model of evolutionary process, whereas contemporary cladists recognize that neither the value nor the success of the methods is limited by the value or success of Hennig s particular evolutionary model. Indeed, it seems that the more constraints the underlying model imposes, the weaker is the related methodology when it is applied to real situations, simply because variables can be different from the suggested (narrow) model. In this way, models accepting fewer constraints should be preferred because they allow a wider range of possible solutions under quite different situations. This was brilliantly pinpointed by Farris (1983: 35) when justifying parsimony for phylogenetic inferences: To a devotee of supposition, to be sure, parsimony seems to presume very much indeed: that evolution is not irreversible, that rates of evolution are not constant, that all characters do not evolve according to identical stochastic processes, that one conclusion of homoplasy does not imply others. But parsimony does not suppose in advance that those possibilities are false only that they are not already established. The use of parsimony depends just on the view that the truth of those -and any other- theories of evolution is an open question, subject to empirical investigation. Resolution by parsimony for 3ts matrices is still philosophically adequate because of the same reasons listed for parsimony (cf. Farris, 1983) applied to cladistics. Using a complementation of Farris (1983: 35) to justify parsimony, one could say the same for 3ts (parts in italics and in brackets are mine): [3ts and] [p]arsimony seems to presume very much indeed: that evolution is not irreversible, that rates of evolution are not constant, that all characters do not evolve according to identical stochastic processes, that one conclusion of homoplasy does not imply in others [,that character evolution does not assume linearity, that there is no need of classical homology and synapomorphy to express evidence of relationships]. But [3ts and parsimony] does not suppose in advance that those possibilities are false - only that they are not already established. The use of [3ts and parsimony] depends just on the view that the truth of those - and any other - theories of evolution is an open question, subject to empirical investigation. Concluding, it seems that information content (see below) is the very same goal of 3ts, and parsimony is as well justifiable to be adopted for the procedure as it is for cladistic analysis. The point is not the application of parsimony, but how cladistics and 3ts see the data. The fact that 3ts accepts evolutionary events (homoplasies and reversals) that most likely have occurred and cannot be catalogued in the observations (although not denying the potential of the observations to be real), and its intermediary re-coding of a matrix of primary-and-a-half homologies before parsimony analysis, allows 3ts to encompass more evolutionary possibilities. If the problem of 3ts being considered operationalist is the lack of a model (and here I disagree with the idea of model by Siebert and Williams, 1998), the complementation of Farris (1983) reasoning is a model too, more tolerant and, in this sense, perhaps indeed a more precise use of parsimony (cf. Nelson and Platnick, 1991), not because of parsimony per se, but because of the recoding made by 3ts and its implications. Synapomorphies and secondary homologies Synapomorphies are of paramount importance for cladistics. Actually, Platnick (1979: 538) explicitly considered them as the main principle of cladistics: Indeed, to the extent that there might be said to be a

7 Implications of three-taxon statement analysis for cladistics and biogeography 177 single main principle of the Hennigian system, it would be none mentioned by Simpson but rather the idea that the taxa which we recognize in our classifications should be based on synapomorphies (emphasis is mine). Still, synapomorphies are considered equivalent to homologies by many authors (Patterson, 1982; Rieppel, 1988; de Pinna, 1991). In his remarks about the subject, de Pinna (1991) established that synapomorphies are equivalent to secondary homologies and these are obtained after parsimony analysis leading to the optimal congruence of primary homologies. In this sense, synapomorphies are derived from congruence of primary homologies. Hence, the maximum explanatory power of an hypothesis is the one with the minimum length. Kluge (1994: 406) assumed that a matrix: analyzed cladistically with parsimony involves assessing the synapomorphy-homology relation as the basis for delimiting natural groups (see e.g., Nelson and Platnick, 1991). As already stated, 3ts does not deal directly with primary homologies, but with statements ( primary-and-a-half homologies ). Carrying out a parsimony analysis for a matrix of homology statements will generate hypotheses in which the largest number of statements can be accommodated. Statements, as already exposed, are primary homologies (common to any comparative analysis) plus doubtfulness over observations (particular to 3ts analysis). This means that statements constitute a broader acceptance of evidence than the simple acceptance of primary homologies. In this sense, the best hypothesis from parsimony analysis of 3ts matrices is that with the minimum amount of primaryand-a-half homologies, or that in which these primary evidences are most congruent (still, in the parsimony implemented by computer programs, the best hypotheses are the ones with minimum length for 3ts as well). Primary evidence (= primary-and-ahalf homology) is hierarchically nested to constitute what we could call secondary evidence. Secondary evidences are not synapomorphies; they are something different because they incorporate uncertainties inherent to observations. Hence, the best hypothesis might not include synapomorphies. Following Platnick s (1979) definition, the groups defined by this procedure are not Hennigian, consequently the analysis is also not cladistic. Besides, the suggestion that taxon and homology represent the same relationship for terminals and character states, respectively (Nelson, 1994) and, consequently, accepting that no taxon necessarily gave rise to another, makes it obvious that no character state necessarily (in a model) gave risen to any other character state. Again, in this sense, there is no possible acceptance of synapomorphies because there is no such need in the model for an unlinked rise of character state (Nelson, 1992, 1996). Last, but not least, the basis of 3ts is evidence, not synapomorphy. Synapomorphies are somewhat circumvented in 3ts, sometimes they may be included in eventual congruence of primary-and-a-half homologies and sometimes they can even be coincidental with those found in traditional cladistics. However, as already demonstrated, it is important to notice that 3ts does not deny synapomorphies; it is simply not necessary to assume them to find evidence and they are not necessary in the proposed 3ts model, although 3ts accepts them (simply does not use them because it can have evidences without synapomorphies). Concluding, 3ts is not cladistics in the sense of the exclusive adoption of synapomorphies, because it uses broader evidence. There is no doubt that both are indeed parsimony methods, minimizing something (as pointed out by Farris and Kluge, 1998: 361), and these things were shown to be different: statements of 3ts can be understood as more inclusive than the synapomorphies of cladistics. Final remarks It is possible that at the time Nelson and Platnick created 3ts, they aimed at one target (perhaps an operationalist analysis, only they can say) and hit another (the meaning of homologies in a broader and unexplored perspective for biology). Although I began the text defending this thesis, I do not believe that the relevance of the discussion is necessary to consider 3ts a new school of systematics (e.g., Siebert and Williams, 1998 defended that it is not). If 3ts can be considered a new school, and this makes people happier because they can use another label, somebody could call the school 3tstics and its followers would be 3tsts. As a matter of fact, Gareth Nelson

8 178 does not seem to be worried with that as well. He wrote: As exemplified by the usual cladistic argument, the identification of evidence with an optimization routine is too narrow minded, in my view, to have any general or lasting relevance, even if some persons might believe that the underlying model is true, or true enough. I doubt, however, whether anyone believes it to be true, rather than merely that its exhibition be politically expedient. It is time to be concerned more with truth than with expediency. The routine itself is merely a model a mere formalism, the use of which leaves open entirely the question of its, or the results of its use, corresponding to anything real in the world (G. Nelson, 2000, in litt.). Maybe what is discussed here (and the big deal) could be exactly a broader model serving as a basis for a new procedure of phylogenetic inference. This new procedure is not Martian, but it is derived from the knowledge gathered from decades of phylogenetics / cladistics; however, it may be inadequate try to view this procedure and its eventual advantages with cladistic eyes. An open mind is also desired for the understanding of new perspectives that could, perhaps, even improve cladistics itself. Continuing: The issue is evidence of relationship. Nominally, relationship = homology = synapomorphy. Can there be evidence without homology? Consider matrix 1 [Nelson, 1996: 141] of Nullius in Verba: is there evidence, yes or no? Is there homology, yes or no? Is there synapomorphy, yes or no?... Three-items interests me because, among other reasons, it exposes these questions. Other reasons concern the future and the pathway into it (G. Nelson, 2000, pers. comm.). Whether or not 3ts is a superior method to traditional cladistics is a secondary problem. I expect that neither will the discussion be over soon and the method will be quite perfect from now, nor is the method better than standard parsimony analysis. More important than this competition is the understanding that by bringing 3ts closer to biology new questions can arise, and yet others be enlightened. Concluding with de Pinna s (1996: 11) words: Regardless of the fate of three-item analysis as a method of character analysis, I predict there will be an increased awareness of the problem of ancestor-descendant relationships among character states. Even if threeitem analysis turns out not be an appropriate solution, I think it will have its place in history as the first concrete attempt at terminating ancestor-descendant thinking at the level of character coding. Acknowledgements This study and manuscript was enriched with discussions and/or reviews by D. Meyer, G. Nelson, P. Gnaspini, R.W. Scotland, S.A. Vanin, and my former students C.M.D. Santos, G.C. Ribeiro and M.M. Pavani, however, I am the only responsible for all the ideas expressed in the text and not necessarily any other person that reviewed the text or gave suggestions agrees with them. The study was supported by FAPESP grants 1996/ , 1997/ , 2001/ and CNPq / References Archie, J.W. 1989a. A randomization test for phylogenetic information in systematic data. Syst. Zool., 38: Archie, J.W. 1989b. Phylogenies of plant families: A demonstration of phylogenetic randomness in DNA sequence data derived from proteins. Evolution, 43: Carine, M.A. and R.W. Scotland Taxic and transformational homology: Different ways of seeing. Cladistics, 15: Deleporte, P Three-taxon statements and phylogeny reconstruction. Cladistics, 12: Faith, D.P. and P.S. Cranston Could a cladogram this short arisen by chance alone? On permutation tests for cladistic structure. Cladistics, 7: Farris, J.S The logical basis of phylogenetic analysis, pp In: Advances in Cladistics proceedings of the Second meeting of the Willi Hennig Society Platnick, N.I. and V.A. Funk (eds). Columbia University Press, New York Farris, J.S Cycles. Cladistics, 13: Farris, J.S Diagnostic efficiency of three-taxon analysis. Cladistics, 16: Farris, J.S., M. Källersjö, V.A. Albert, M. Allard, A. Anderberg, B. Bowditch, C. Bult, J.M. Car-

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