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CONSTRUCTION AND VERIFICATION OF A LARGE PHYLOGENY OF MARSUPIALS F RANÇOIS -JOSEPH LAPOINTE AND JOHN A. W. K IRSCH Lapointe F-J and Kirsch JAW, 2001. Construction and verification of a large phylogeny of marsupials. Australian Mammalogy 23: 9-22. Much of the controversy over marsupial phylogeny at higher-categorical levels stems from the piecemeal nature of the contributing studies or the paucity of taxonomic representation in many of them. Yet the problems of constructing large phylogenies are manyfold, involving the initial generation of the data as well as their efficient analysis. Often unaddressed, also, is the need to validate extremely large data sets and trees. Many of these problems can be ameliorated by treating the data as distances (or generating distances directly). We show that, contrary to the assertions of many protagonists in the total-evidence versus consensus debate, the validated data and pathlength (tree) matrices usually give very similar results, although a few additional unstable nodes may be found when the results of internal and external validations are themselves combined in a global-congruence test. Here we illustrate our protocols with a 109-taxon data set, representing combination of marsupial DNA-hybridisation data with similar information on a series of outgroups. Phylogenetically, the results affirm the marsupial groupings we have previously found, and suggest but do not unambiguously support a nearer relationship of monotremes than placentals to marsupials. This paper represents the first attempt to validate the tree of 101 marsupials presented earlier. Key words: congruence, data combination, Marsupialia, Monotremata, supertrees, validation. F.-J. Lapointe*, Département de sciences biologiques, Université de Montréal, Montréal, C.P. 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada. Email : Francois- [email protected] J.A.W. Kirsch, The University of Wisconsin Zoological Museum, Madison, Wisconsin, USA. Manuscript received 23 June 2000; accepted 12 March 2001. * Corresponding author ISSUES of the higher-level phylogeny of marsupials have often been discussed of late (e.g., Luckett 1994; Springer et al. 1994). There is general agreement about the monophyly of most marsupial families and orders (see Kirsch et al. 1997 for discussion), but there is, in contrast, little consensus on supraordinal associations - in stark contrast to the situation for placentals, where molecular studies are at last yielding several groupings among the orders (Stanhope et al. 1998). Indeed, and particularly as the molecular database on marsupials has grown, the obvious, traditional geographic division among them has become less tenable. The position of bandicoots especially remains completely uncertain as a result of the DNA studies, as earlier "firm" but conflicting conclusions from anatomy or serology placing Peramelina with Diprotodontia or Dasyuromorphia would now seem unsupportable; and while an unresolved tree (such as most of those based on DNA evidence) can be considered consistent with a resolved one, it cannot simultaneously be reconciled with all conflicting arrangements. Similarly, special relationship between Didelphimorphia and Paucituberculata continues to be poorly if at all supported by any molecular study, and by few anatomical characters (Springer et al. 1997). On the other hand, with the exception of Hershkovitz' (1992) idiosyncratic placement of Microbiotheria outside all other marsupials, there seems little doubt that the South American Dromiciops gliroides is associated with the non- peramelinan Australasian orders, either generally or specifically with diprotodontians. Likewise, pairing of Dasyuromorphia and Notoryctemorphia seems almost certain, and a diminished Australasian grouping of these and Diprotodontia with Microbiotheria (but excluding Peramelina) is likely. One serious problem with many of the existing data sets purporting to address interordinal relationships is that the sampling of taxa is quite limited, in contrast to the now comparatively thorough examinations of some families (e.g., Dasyuridae, Didelphidae, and Peramelidae); and no doubt some of the uncertainty about supraordinal

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CONSTRUCTION AND VERIFICATION OF A LARGE PHYLOGENY OF MARSUPIALS

FRANÇOIS -JOSEPH LAPOINTE AND JOHN A. W. KIRSCH

Lapointe F-J and Kirsch JAW, 2001. Construction and verification of a large phylogeny of marsupials. Australian Mammalogy 23: 9-22.

Much of the controversy over marsupial phylogeny at higher-categorical levels stems from the piecemeal nature of the contributing studies or the paucity of taxonomic representation in many of them. Yet the problems of constructing large phylogenies are manyfold, involving the initial generation of the data as well as their efficient analysis. Often unaddressed, also, is the need to validate extremely large data sets and trees. Many of these problems can be ameliorated by treating the data as distances (or generating distances directly). We show that, contrary to the assertions of many protagonists in the total-evidence versus consensus debate, the validated data and pathlength (tree) matrices usually give very similar results, although a few additional unstable nodes may be found when the results of internal and external validations are themselves combined in a global-congruence test. Here we illustrate our protocols with a 109-taxon data set, representing combination of marsupial DNA-hybridisation data with similar information on a series of outgroups. Phylogenetically, the results affirm the marsupial groupings we have previously found, and suggest but do not unambiguously support a nearer relationship of monotremes than placentals to marsupials. This paper represents the first attempt to validate the tree of 101 marsupials presented earlier.

Key words: congruence, data combination, Marsupialia, Monotremata, supertrees, validation.

F.-J. Lapointe*, Département de sciences biologiques, Université de Montréal, Montréal, C.P. 6128, Succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada. Email : [email protected] J.A.W. Kirsch, The University of Wisconsin Zoological Museum, Madison, Wisconsin, USA. Manuscript received 23 June 2000; accepted 12 March 2001.

* Corresponding author

ISSUES of the higher-level phylogeny of marsupials have often been discussed of late (e.g., Luckett 1994; Springer et al. 1994). There is general agreement about the monophyly of most marsupial families and orders (see Kirsch et al. 1997 for discussion), but there is, in contrast, little consensus on supraordinal associations - in stark contrast to the situation for placentals, where molecular studies are at last yielding several groupings among the orders (Stanhope et al. 1998). Indeed, and particularly as the molecular database on marsupials has grown, the obvious, traditional geographic division among them has become less tenable. The position of bandicoots especially remains completely uncertain as a result of the DNA studies, as earlier "firm" but conflicting conclusions from anatomy or serology placing Peramelina with Diprotodontia or Dasyuromorphia would now seem unsupportable; and while an unresolved tree (such as most of those based on DNA evidence) can be considered consistent with a resolved one, it cannot simultaneously be reconciled with all conflicting arrangements. Similarly, special relationship between Didelphimorphia and Paucituberculata continues to

be poorly if at all supported by any molecular study, and by few anatomical characters (Springer et al. 1997).

On the other hand, with the exception of Hershkovitz' (1992) idiosyncratic placement of Microbiotheria outside all other marsupials, there seems little doubt that the South American Dromiciops gliroides i s associated with the non-peramelinan Australasian orders, either generally or specifically with diprotodontians. Likewise, pairing of Dasyuromorphia and Notoryctemorphia seems almost certain, and a diminished Australasian grouping of these and Diprotodontia with Microbiotheria (but excluding Peramelina) is likely.

One serious problem with many of the existing data sets purporting to address interordinal relationships is that the sampling of taxa is quite limited, in contrast to the now comparatively thorough examinations of some families (e.g., Dasyuridae, Didelphidae, and Peramelidae); and no doubt some of the uncertainty about supraordinal

AUSTRALIAN MAMMALOGY 10

phylogeny results from long-branch attraction or some other algorithmic or biochemical anomaly. Long-branch attraction is a problem that cannot easily be addressed, given that several marsupial orders (such as Paucituberculata, Notoryctemorphia, and Microbiotheria) lack many extant representatives or diversified only relatively recently (e.g., Peramelina); so it may be impossible to resolve relationships by subdividing these branches through inclusion of more representatives. Still, the species-density of many molecular studies could certainly be improved, at least by combination of the different studies. Yet systematists, molecular or otherwise, face a serious dilemma in that algorithms for exact solutions for large data sets do not, and indeed cannot, exist: a large phylogeny, desirable as it may be, presents its own problems.

What, in fact, is a large phylogeny? This is a moving target: ten years ago, the algorithms for phylogenetic reconstruction were limited to the analysis of a mere handful of taxa. Since then, computers have evolved, new heuristics have been developed, and larger problems (i.e., n > 100) have been addressed by phylogeneticists (e.g., Rice et al. 1997, and references therein). But the problem remains the same as before; namely, that no algorithm can be optimal in every possible case (but see Hillis 1996). The reconstruction of a phylogeny still represents an NP-complete problem (Penny et al. 1992), but there might be some ways to make it less difficult. For instance, it might be simpler to reconstruct a phylogeny representing 20 species on which 200 characters were scored, or one bearing 200 species but based on only 20 characters. In both cases, the rationale is to subdivide the larger problem into smaller ones, by reducing the number of characters and/or taxa. The results of these smaller problems would need to be put back together to see the big picture, however. Given a set of phylogenies obtained from different data sets and/or representing different taxa, how should one assemble them to obtain a larger (and more accurate) phylogeny? Would it be better to treat these different data sets independently before combining the resulting trees or should all data be combined prior to phylogenetic reconstruction? Proponents of either side of the so-called total-evidence versus consensus debate have raised a series of philosophical and empirical arguments to demonstrate the superiority of their approach (Kluge 1989; Barrett et al. 1991; de Queiroz 1993; Eernisse and Kluge 1993; Kluge and Wolf 1993; Chippindale and Wiens 1994; Huelsenbeck et al. 1994; Wiens and Chippindale 1994; de Queiroz et al. 1995; Miyamoto and Fitch 1995; Huelsenbeck et al. 1996; Nixon and Carpenter 1996; Page 1996a; Lapointe et al. 1999). A third position has emerged

recently which claims that data should sometimes be combined, and sometimes not, depending on the outcome of tests for compatibility (Bull et al. 1993; Rodrigo et al. 1993; Farris et al. 1995; Huelsenbeck and Bull 1996). Interestingly, Lapointe et al. (1999) have shown that data and trees (bearing identical, inclusive, or overlapping sets of taxa) can be combined in a coherent fashion, when treated as distances. Thus, the debate on whether one should combine or not combine data becomes one about how to combine the ever-increasing amount of data and their corresponding phylogenies.

In a recent paper, Kirsch et al. (1997) were able to generate a large phylogeny of 101 marsupials plus an outgroup eutherian by combining the matrices from 13 independent DNA-hybridisation studies. That tree was never validated, however. In the present study, we take this tree a further step by combining the underlying data with an outgroup matrix to generate a phylogeny of 109 species. Then, we will show, once again, that a coherent validation procedure can be used at every step of the combination protocol, on trees and data likewise. We will demonstrate that the validated phylogeny is in agreement with previous groupings of the included taxa, and that it confirms the relationships inferred from the smaller analyses. The present effort thus represents validation, as well as extension, of the final tree presented in Kirsch et al. (1997), and so completes our summary of DNA-hybridisation studies on marsupials. The contentious issue of "Marsupionta" is also briefly addressed herein.

MATERIALS AND METHODS

Data and Total-Evidence Analysis

We used the two completed marsupial "supermatrices" and the notoryctid matrix of ?T50H DNA-hybridisation distances examined in Kirsch et al. (1997), and a similar set of data including non-mammalian amniotes abstracted from those used in Kirsch and Mayer (1998) but there presented as ?NPHs. The 48- and 58-taxon supermatrices from Kirsch et al.'s paper had each been concatenated from several data sets and validated at each step by taxonomic jackknifing; Kirsch et al. (1997) should be consulted for details. Here, we treated the supermatrices as primary data sets and validated them using SUPERMAT (see Fig. 1 for details of the validation procedure), performing 500 deletions of half the taxa in each case, chosen equiprobably from among the putatively monophyletic higher-category taxa represented in each (8 in the case of the 48-taxon matrix and 9 in that of the 58-taxon set). Membership of species in each of these and two

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Fig. 1. Flowchart illustrating the various steps of the validation procedure using the taxonomic jackknife (Lapoin te et al. 1994). SUPERMAT is a computer program that creates a series of jackknife (JK) replicates by deleting species at random from an input distance matrix according to user-defined parameters. Once trees are obtained from the JK matrices, TRANSLAT is then used to compute pathlength (PL) matrices from the corresponding treefiles. NONSENSE reads in the various pathlength matrices of different sizes and returns the minimum, average, and maximum pathlength distance matrices. CONSENSE is a program from the PHYLIP package (Felsenstein 1993) which is used to compute the range consensus from the minimum and maximum consensus trees. In the present application, the KITSCH program (Felsenstein 1993) was used as a TREE BUILDING ALGORITHM, but any other distance algorithm would do. All programs are available upon request from the authors.

AUSTRALIAN MAMMALOGY 12

Fig. 2. Flowchart illustrating the various steps of the combination procedure for distance and pathlength matrices (Lapointe et al. 1999). Given a series of input distance matrices, SUTALL is used to combine them. In the case of overlapping matrices, some cells need to be estimated and RECALL is used to fill the missing values with either the ultrametric (Lapointe and Kirsch 1995) or four -point condition (Landry et al. 1996). When trees are combined, TRANSLAT is called to compute pathlength matrices from the corresponding treefiles. The global-congruence tree is a strict consensus of the total-evidence and total-consensus trees. In the present application, the KITSCH program (Felsenstein 1993) was used as a TREE BUILDING method, but any other distance algorithm would do. The validation part is as in Fig. 1. All programs are available upon request from the authors.

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other groups represented only in the Kirsch and Mayer matrix is indicated on Fig. 5. KITSCH trees (Felsenstein, 1993) were then generated from each matrix, and the pathlengths on each were assembled using TRANSLAT. NONSENSE was then employed to summarize these pathlengths as three new matrices representing the average, minimum, and maximum observed for all pairwise comparisons. For the two smaller matrices, we carried out exhaustive jackknifes (i.e., all possible deletions leaving a minimum of four taxa), and again compiled the average, minimum, and maximum pathlengths. Then, ultrametric trees were calculated for the three pathlength matrices corresponding to each of the jackknifes on the four matrices.

The combination of the four distance matrices (using SUTALL) resulted in a 109-taxon data set, which was subsequently filled by the methods of Lapointe and Kirsch (1995), i.e., using the ultrametric De Soete (1984) algorithm implemented in RECALL (see Fig. 2 for details of the combination procedure). This large matrix was then jackknifed in the same manner as were the two supermatrices (55 taxa were deleted in each of 500 replicates), and new trees were calculated from the resulting average, minimum, and maximum pathlength matrices.

Consensus Analysis

The average-consensus (Lapointe and Cucumel 1997) pathlength matrices were taken as the best representations of trees generated from each of the constituent data matrices, and so were combined, completed, and validated similarly to the 109-taxon data matrix. Because the pathlengths from each component tree represent a single matrix and are ultrametric, they show no instabilities when jackknifed.

Global Congruence

Two strict-consensus trees were computed, using Felsenstein's (1993) CONSENSE program: first, between the average-consensus trees of the data and pathlengths jackknifes on 109 taxa; and second, between the range-consensus trees of the same jackknife sets (the range consensus is defined as the strict consensus of trees calculated from the minimum and maximum pathlengths observed over all jackknife trees). The second is therefore a more severe test of matrix-stability, because a collapsed node in any range consensus depends only on outliers.

RESULTS

Fig. 3 shows the validated trees (i.e., average-consensus KITSCH jackknife trees) for each of the four contributing data matrices. Dotted lines on three of these represent nodes which were not supported in

the range consensus. Fig. 3A thus has five uncertain nodes, while 3B has four, 3C none, and 3D a single uncertainty.

Fig. 4 represents the jackknife results from (A) combining the data matrices and (B) pathlength matrices corresponding to the trees of Fig. 3, again showing the average-consensus trees based on 500 deletions of about half the taxa (55) with dotted lines used to indicate nodes that collapse in the range-consensus of each. Thus, there are ten uncertainties generated by combining, completing, and validating the combination of data (Fig. 4A); but only three in the case of combined trees (Fig. 4B).

Fig. 5 is the strict-consensus of the trees in Fig. 4. Eight nodes are in disagreement between the two average-consensus trees, and are therefore shown as polytomies; four of these are also implied by the range consensus of Fig. 4A and another two by that of Fig. 4B. However, a further seven nodes collapse when a strict consensus of the range-consensus trees of Figs 4A and 4B is calculated, and these are once more shown with dotted lines. Thus, in the most severe consensus of the combined-data and combined-tree analyses, 14% of the potential dichotomies (15 out of 108) remain unresolved, and include two polytomies not implied separately by either the validated data or trees. Therefore, while some irresolution is unique to each half of the analysis (combined evidence versus combined trees), further uncertainty is introduced by the final combination.

DISCUSSION

Methodological Considerations

As long as the algorithms for phylogeny-reconstruction were not evolving as fast as the taxa, or as rapidly as data accumulate, treating large phylogenies could only be addressed with sub-optimal methods (heuristics), with the hope that there exist some optimal sub-optimal methods. When dealing with large phylogenies, validation then becomes even more important than when smaller phylogenies are considered, because heuristics can be less efficient as the number of taxa increases. Different resampling and randomisation methods are currently available to validate phylogenies (Lapointe 1998a), but do not always apply to very large trees. For instance, bootstrapping or jackknifing on characters produces a series of large data matrices which need to be analysed with the same heuristic methods as the original data set (a multiplication of uncertainties can thus be created). For this reason, the taxonomic jackknife (Lanyon 1985; Lapointe et al. 1994) is probably the best validation method to use with very large phylogenies. Because it creates a series of smaller data matrices by sampling from the

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AUSTRALIAN MAMMALOGY 14

larger data set, taxonomic jackknifing reduces the size of the algorithmic problem, and heuristics are thus more likely to converge to the optimal tree in each case (which is not true with the bootstrap and jackknife on characters). Then, the only problem remaining is how to combine the subtrees representing each jackknife replicate.

When different data matrices bearing nonidentical sets of taxa are to be combined, what are the options? The total-evidence approach was initially developed to allow combination of identical taxonomic sets. When overlapping sets of taxa (or inclusive sets) are treated simultaneously, one has then to deal with missing information. The potential problems associated with these missing data outweigh by far the merits of data-combination. In the case of character-state data (including gene-sequence data) a parallel problem obtains when different characters have been scored for a suite of taxa, resulting in extensive missing entries (e.g., “no comparison” or “state unknown”) into the data matrix. The problem of calculating a plausible tree is compounded when both missing characters and non-identical taxa are involved, and it is then practically impossible to combine matrices when different characters represent different sets of taxa (there is overlap among neither rows, nor columns!). Similarly, partition-homogeneity tests (Farris et al. 1995) cannot be computed when nonidentical sets of taxa are considered. These problems are not as important when data are treated as distances, however. Because the entries in a distance matrix are not independent from one another, it is possible to estimate the missing values among taxa which were not all included in the same study (or were treated independently as taxon-jackknife replicates). In the present case, the final phylogeny bearing 109 taxa was obtained from less than 12% of the data which would be present in a complete 109-by-109 matrix, by estimating the missing comparisons (see Kirsch et al., 1997 for details of how the supermatrices were assembled).

The problem of missing data in total-evidence studies is somewhat related to the supertree problem arising when computing consensus trees for phylogenies bearing overlapping sets of taxa. What are the options in that case? The hopeful agenda of constructing supertrees from character data has not yet been given a firm foundation (Sanderson et al. 1998). Such methods as do exist rely on different

additive coding schemes for trees, and thus the results obtained vary depending on the coding method selected (Baum 1992; Ragan 1992; Baum and Ragan 1993; Rodrigo 1993; Purvis 1995; Ronquist 1996; Steel et al. 2000). Also, these consensus methods do not take branch lengths (see Lapointe 1998b), nor branch support, into account. The approach selected in this paper relies on the bijection between additive trees and their corresponding pathlength matrices (Buneman 1974). For this reason, trees and data (both depicted as distance matrices) can be combined in a coherent fashion. Just like distance data, overlapping pathlength matrices can be sutured and missing cells estimated. Similarly, pathlength matrices can be validated in the same manner as data matrices.

The parallel treatment of both data and trees is very important because data-validation can lead to different results from tree-validation (see Fig. 5). Contrary to some potential criticisms of our approach, this fact clearly shows that a coherent treatment of data and trees is not tautological. The more structured the data (i.e., the greater the tree-like structure), the less discrepant the results will be, however. Consequently, the global-congruence tree becomes a more conservative estimate of phylogenetic relationships than either the "total-evidence" or "total-consensus" side of the parallel analyses. In the present study, the resolution of the global tree is considerable, given the size of the phylogeny and the amount of data that were estimated.

In our application of the distance-based approach, DNA-hybridisation matrices were validated and combined (see also Kirsch et al. 1997; Lapointe 1998a; Lapointe et al. 1999). These pairwise comparisons (like serological data) are readily available in the form of distance matrices and can be directly treated as such. However, it is worth repeating once more that any other data can be treated as distances and thus be combined in a coherent fashion. In previous papers, we have shown that matrices of character-state data converted to distances can be combined with each other, or with other distance matrices (Lapointe et al. 1999). When this is done, the results of total-evidence and consensus analyses seldom differ much, as we found here.

This method is not perfect, however. Because it relies on an estimation procedure to fill missing cells, some may argue that we are inventing data. This is not true. In a series of papers (Lapointe and Kirsch 1995; Landry et al. 1996; Landry and Lapointe 1997), in which known distances were deleted and then estimated, we have clearly established that such estimates are accurate representations of the true distances. "Taxonomic hyperspace" is demonstrably Euclidean, and distances in it are at least additive; thus, given the accuracy of distances which are

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known, estimating those which have not been measured becomes a matter of simple arithmetic. For

this reason, the ultrametric inequality can be used to fill missing cells (Lapointe and Kirsch 1995) when

Fig. 4. Ultrametric trees based on the combination of (A) all four data matrices used to generate the trees of Fig. 3 or (B) pathlengths read from those trees. Topologies shown are based on the average-consensus pathlengths

AUSTRALIAN MAMMALOGY 16

obtained by taxon-jackknifing, with discrepancies from the depicted topology in the range consensus of minimum and maximum pathlengths

indicated with dotted lines. Note that bandicoots occupy quite different positions in the two trees and that their names are not opposite each other in (A) and (B). Other taxa whose inconsistent placements similarly could not be

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reconciled by rotation around nodes are boldfaced. Scale bar equals a ? T50H of 1ºC. See text for details of analysis.

Fig. 5. The "global-congruence" cladogram representing the conclusions of this study, being a strict -consensus of the two average-consensus jackknife trees shown in Fig. 4, with additional discrepancies between the corresponding range-consensus trees depicted with dotted lines. Numbers between or at horizontal lines at right of figure indicate

AUSTRALIAN MAMMALOGY 18

the 16 groups used to constrain deletions in the jackknife samples. See text for further details of analysis.

ultrametric trees are considered, whereas the more general four-point condition can be called to estimate missing distances (Landry et al. 1996) in nonultrametric additive trees. For the sake of demonstration (and to speed up the computations), we relied on the ultrametric approach in the present case. However, similar results have been obtained with the four-point condition in other studies (see Kirsch et al. 1997: 215), because DNA-hybridisation distances are not far from ultrametric. Whatever approach is selected, one caveat remains: it is impossible for our or any other method to recover a missing distance between terminal sister-taxa if neither pairwise distance between them has been measured (at best, the sister-pair will collapse to a tritomy with their next -nearest relative). However, this special case certainly does not obtain here, as we have combined complete (or previously completed) data-matrices and only estimated distances among distant relatives.

Phylogeny

Figs 3A, 3B, and 3C respectively correspond to figs. 6, 11, and 12 in Kirsch et al. (1997), the latter being FITCH trees which were validated by random multiple-deletion taxon-jackknifing (uncertain nodes shown in the Kirsch et al. trees represent discrepancies between the depicted average-consensus diagrams and equivalent jackknife results on KITSCH computations, and so incorporate analyses similar to those presented here). It is of interest that there are very few differences between the ultrametric (KITSCH) and additive (FITCH) trees considered in Kirsch et al.; one reason is that DNA-hybridisation matrices usually imply rather little rate variation. However, there are some exceptions to that generalisation:

New information presented here is represented by Fig. 3D, derived from an "outgroup" matrix which was sutured with the data underlying Figs 3A, 3B, and 3C to provide the basis for the 109-taxon topologies (Figs 4 and 5). Unlike for the other three component matrices, a FITCH computation and exhaustive FITCH jackknife on Fig. 3D data (not shown) gave different answers from the KITSCH analysis. Specifically, the marsupial Didelphis virginiana and monotreme Tachyglossus aculeatus were always joined apart from the other six taxa in the FITCH trees, this result is, however, consistent with the irresolution in the range consensus of Fig. 3D. The KITSCH/FITCH discrepancies are echoed in the data- (but not pathlengths-) based tree of Fig. 4, where in addition the placental Procyon lotor is sister to a combined marsupial-monotreme group. This association among the major mammalian groups is of some interest in view of the recent revival of Gregory's (1947) Marsupionta hypothesis (of a

special marsupial-monotreme relationship), based on both complete mitochondrial coding sequences (Janke et al. 1996, 1997) and DNA-hybridisation distances (Kirsch and Mayer 1998). Yet, the difference in placement of Tachyglossus in Fig. 3D and its FITCH equivalent can, in this instance, most likely be traced to rate-nonuniformity among the taxa examined. Indeed, several authors have remarked on the apparently slow rate of molecular change in monotremes (Westerman and Edwards 1992; Gemmell and Westerman 1994; Messer et al. 1998), and this slowdown may be a sufficient reason for the surprising pairing of marsupials and monotremes in additive but not all ultrametric trees. Significantly, Tachyglossus is removed from proximity to any other mammals in the pathlengths-based 109-taxon tree (Fig. 4B), and hence becomes part of a basal multitomy in the final global-congruence cladogram (Fig. 5). Thus we would recommend caution concerning conclusions about the interrelationships of the major mammalian groups, despite the apparently clear indications of considerable molecular information: Marsupionta may well prove to be an artefact traceable to just a few short monotreme branch lengths. Two newer molecular studies, one of LDH amino-acid sequences (Messer et al., 1998) and another of haemoglobin gene-sequences (Lee et al. 1999), fail to support Marsupionta. However, both studies necessarily relied on comparisons among known or suspected paralogous genes (or their protein products) to root the trees, and thus the associations among mammals indicated require verification based on orthologous sequences.

The differing placement of the other outgroups between the two parts of Fig. 4, and hence the basal irresolution in Fig. 5, are of some analytical interest. Most such uncertainties, and also the irresolution among the major marsupial clades, result less from discrepancies within either the data- or pathlengths-based trees than from differences between them, and these differences are concentrated (for the most part) on basal rather than distal nodes. Moreover, all three uncertainties in the validated pathlengths-tree of Fig. 4B are also relatively basal, in contrast to most of the unresolved nodes in the data-tree (Fig. 4A). Why the validations of concatenated data and pathlengths should give such characteristically different results, and whether these might prove to be general rather than specific to the present case, are questions for future empirical and analytical work.

However, the greater interest of Fig. 5 is phylogenetic, as it represents our first attempt to validate the 102-taxon tree in Kirsch et al. (1997: fig. 13), which showed the accumulated uncertainties within and among thirteen component analyses based on both FITCH and KITSCH computations. Of the 101 possible dichotomies, 30 were shown as

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uncertain, more than twice the number found in the work reported here, even with an additional seven outgroups added. Once again, our new phylogeny and the previous one are almost entirely consistent, when irresolution uncovered by the validation procedures is considered; that consistency is especially noteworthy when it is remembered that Fig. 5 is merely a strict-consensus cladogram, which does not take branch lengths into account. Even though, for practical reasons, the Fig. 5 tree is based strictly on ultrametric computations, it should be noted that only a small percentage of the 30% irresolution in the Kirsch et al. fig. 13 tree resulted from rate differences affecting the KITSCH vs. FITCH topologies. Furthermore, a critical aspect of judging our results is that the families of marsupials are uniformly supported here, as are the majority of superfamilial and all ordinal distinctions.

The major differences between Fig. 5 and Kirsch et al.'s fig. 13 are that Fig. 5 gives stronger support to the outgroup status of caenolestids relative to other marsupials, and to the sister-relation of Dromiciops gliroides with respect to diprotodontians (caenolestids and Dromiciops were each differently or uncertainly placed in at least one of the validated trees determining the depicted uncertainties in fig. 13). Otherwise the composition of and irresolution among some marsupial orders - here represented by opossums (group 11 on Fig. 5), dasyurids (group 10), the marsupial mole (Notoryctes typhlops; group 9), bandicoots (group 12), and Dromiciops (group 8) plus Diprotodontia (the order including kangaroos, phalangers, the koala, and wombats; groups 1-7) - but apparently not among these and caenolestids (group 13), are much as concluded in Kirsch et al. (1997) and other papers assessing the import of molecular data for marsupial phylogeny (e.g., Springer et al. 1997, 1998; Burk et al. 1999). That is to say, the pairwise relationships among (or more inclusive groupings of) the seven extant marsupial orders are here largely unresolved, except for the association of Dromiciops with Diprotodontia and the sister-group status of caenolestids with respect to the other six orders. Certainly, there is no clear division into "American" versus "Australasian" marsupials.

Similarly, and as implied above, our results do not unambiguously resolve pairwise relationships among the three major mammalian lineages represented (marsupials, the placental, and the monotreme) or among the non-mammalian outgroups included (birds, turtles, the snake, and the alligator). But, the average-consensus trees do agree on the surprising sister-group relationship between turtles and the archosaurs demonstrated by Kirsch and Mayer (1998), Hedges and Poling (1999), and Kumazawa and Nishida (1999), among others.

ACKNOWLEDGEMENTS

An earlier version of this paper was originally presented at the DIMACS Symposium "Estimating Large Scale Phylogenies: Biological, Statistical, and Computational Problems", Princeton University, 26 June 1998. This work was partially supported by NSERC grant OGP0155251to FJL. Trees were produced by Rod Page's (1996b) TreeView program and finished by William Feeny.

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