Hard Polytomy Research Articles

Molecular phylogeny and plumage signal evolution in a trans Andean and circum Amazonian avian species complex

Species with fragmented distributions are particularly useful models for investigating processes underlying biological diversification in the Neotropics. The Phaeothlypis wood-warbler complex (Aves: Parulidae) is comprised of six disjunct or parapatric populations. The geographic distribution of these six populations mirrors the classic map of Neotropical areas of endemism that were originally proposed as putative Pleistocene forest refugia, but the magnitude of mitochondrial DNA divergence between these populations suggests that they are each substantially older, with origins in the late Pliocene. Phylogenetic reconstructions based on long mtDNA coding sequences show that the Guiana Shield and Atlantic Forest populations are sister lineages, and group this combined lineage and the remaining four population-specific lineages in a five-way hard polytomy. MtDNA-based phylogenetic reconstructions provide no evidence that the three populations with conspicuous yellow rump and tail feathers currently grouped as the Buff-rumped Warbler ( P. fulvicauda) form a monophyletic group. Furthermore, there is a broad discordance between mtDNA and plumage along a transect just east of the Andes, where the contact zone between highly divergent mtDNA clades is more than 1000 km north of the phenotypic hybrid zone between the bright and dark plumage forms. This discordance between mtDNA genotype and plumage phenotype is similar to patterns seen on a finer geographic scale in other avian hybrid zones and may result from asymmetric introgression of the bright plumage trait.

Tempo of speciation in a butterfly genus from the Southeast Asian tropics, inferred from mitochondrial and nuclear DNA sequence data

Molecular systematics is frequently beset with phylogenetic results that are not fully resolved. Researchers either state that the absence of resolution is due to character conflict, explosive speciation, or some combination of the two, but seldom do they carefully examine their data to distinguish between these causes. In this study, we exhaustively analyze a set of nuclear and mitochondrial nucleotide data for the Asian tropical butterfly genus Arhopala so as to highlight the causes of polytomies in the phylogenetic trees, and, as a result, to infer important biological events in the history of this genus. We began by using non-parametric statistical methods to determine whether the ambiguously resolved regions in these trees represent hard or soft polytomies. In addition we determined how this correlated to number of inferred changes on branches, using parametric maximum likelihood estimations. Based on congruent patterns in both mitochondrial and nuclear DNA sequences, we concluded that at two stages in the history of Arhopala there have been accelerated instances of speciation. One event, at the base of the phylogeny, generated many of the groups and subgroups currently recognized in this genus, while a later event generated another major clade consisting of both Oriental and Papuan species groups. Based on comparisons of closely related taxa, the ratio of instantaneous rate of evolution between mitochondrial and nuclear DNA evolution is established at approximately 3:1. The earliest radiation is dated between 7 and 11 Ma by a molecular clock analysis, setting the events generating much of the diversity of Arhopala at well before the Pleistocene. Periodical flooding of the Sunda plateau during interglacial periods was, therefore, not responsible for generating the major divisions in the genus Arhopala. Instead, we hypothesize that large-scale climatic changes taking place in the Miocene have induced the early acceleration in speciation.

Speciation and anagenesis in the genus Cyprinella of Mexico (Teleostei: Cyprinidae): a case study of Model III allopatric speciation

Allozyme variation at 42 presumptive gene lociis presented for members of the C. formosa species group. This group iscorroborated as a monophyletic assemblage whosecommon ancestor occupied pluvial Lake Palomasof the Guzman Basin. With increasingaridity during the Pleistocene this basin andassociated populations of this commonancestor were fragmented into several lineagesthat diverged independently of oneanother. The pattern of relationships andlevels of anagenetic change observed inindependent lineages for this clade are notconsistent with expectations of the mostcommon modes of speciation, Model I large-scalevicariance or Model II peripheralisolation. Rather, divergence in these fishlineages is consistent with the rarely observedModel III allopatric speciation. Consistentwith predictions of this model, thephylogenetic pattern recovered revealspolychotomous relationships (a hard polytomy)and varied rates of anagenetic change acrossexamined lineages.

Phylogeny and biogeography of wood-feeding cockroaches, genus Salganea Stål (Blaberidae: Panesthiinae), in Southeast Asia based on mitochondrial DNA sequences.

Molecular phylogenetic relationships among 25 species of the wood-feeding cockroach belonging to the genus Salganea Stål (Panesthiinae; Blaberidae) in Southeast Asia were analyzed based on the DNA sequence of the complete mitochondrial cytochrome oxidase II (COII) gene. Most basal relationships among species of Salganea are poorly resolved by both neighbor-joining and nonweighted parsimony analyses, suggesting the possibility of a hard polytomy due to a rapid and potentially simultaneous radiation early in the history of the genus. For more apical relationships, however, some interesting phylogenetic relationships were recognized. The monophyly of the two species groups, morio and foveolata, the former of which is distributed mainly in the Sunda lands (containing the Malay Peninsula, Sumatra, Java, and Borneo), whereas the latter is Sulawesi endemic, was strongly supported. Based on the inferred phylogenetic patterns and recent palaeogeographic scenario for Southeast Asia, it is suggested that a radiation of Salganea species occurred in Southeast Asia presumably in the early Tertiary, and several barriers against dispersal and gene flow, such as the formation of straits or high mountains, have arisen from the middle Tertiary.

Comparative methods for the analysis of continuous variables: geometric interpretations.

This study is concerned with statistical methods used for the analysis of comparative data (in which observations are not expected to be independent because they are sampled across phylogenetically related species). The phylogenetically independent contrasts (PIC), phylogenetic generalized least-squares (PGLS), and phylogenetic autocorrelation (PA) methods are compared. Although the independent contrasts are not orthogonal, they are independent if the data conform to the Brownian motion model of evolution on which they are based. It is shown that uncentered correlations and regressions through the origin using the PIC method are identical to those obtained using PGLS with an intercept included in the model. The PIC method is a special case of PGLS. Corrected standard errors are given for estimates of the ancestral states based on the PGLS approach. The treatment of trees with hard polytomies is discussed and is shown to be an algorithmic rather than a statistical problem. Some of the relationships among the methods are shown graphically using the multivariate space in which variables are represented as vectors with respect to OTUs used as coordinate axes. The maximum-likelihood estimate of the autoregressive parameter, p, has not been computed correctly in previous studies (an appendix with MATLAB code provides a corrected algorithm). The importance of the eigenvalues and eigenvectors of the connection matrix, W, for the distribution of p is discussed. The PA method is shown to have several problems that limit its usefulness in comparative studies. Although the PA method is a generalized least-squares procedure, it cannot be made equivalent to the PGLS method using a phylogenetic model.

Polytomies, the power of phylogenetic inference, and the stochastic nature of molecular evolution: a comment on Walsh et al. (1999).

Walsh et al. (1999) recently suggested an innovative application of power analysis (Cohen 1977) to explore the nature of polytomies (multifurcating rather than bifurcating relationships) in phylogenetic inference. The frequent recovery of polytomies in phylogenetic analyses has prompted substantial interest in the underlying biological nature of these inferred polytomies. Many authors assume that polytomies simply reflect the inability to resolve bifurcating relationships (soft polytomies) and suggest that additional data or improved analyses will allow the recovery of the underlying relationships (e.g., Maddison 1989; DeSalle et al. 1994). In contrast, other researchers consider polytomous relationships to be valid phylogenetic hypotheses reflecting multiple simultaneous speciation events (a polytomy; Hoelzer and Melnick 1994a,b). Examining the differences between these alternative viewpoints is extremely difficult, because soft polytomies do not exhibit clear differences from hard polytomies in phylogenetic analyses. Specifically, Walsh et al. (1999) sought to determine whether internal branch lengths which were not significantly different from zero simply reflect an insufficient sample size (amount of sequence data). The example developed by Walsh et al. (1999) involved the polytomous relationships among auklets (Charadriiformes: Alcidae) inferred using mitochondrial DNA sequences. Since this inferred polytomy might reflect a soft polytomy (defined by Walsh et al. [1999] as speciation during successive glacial/interglacial periods during the late Pliocene and early Pleistocene) or a hard polytomy (defined as multiple speciations during the same period of climatic oscillation), Walsh et al. (1999) used power analysis to determine whether the number of base pairs (sites) of sequence data obtained was sufficiently large to detect substitutions along the internal branches if the speciation was not simultaneous (a soft polytomy). We found this an innovative application of classical power analysis and an excellent alternative to Monte Carlo simulation (e.g., Saitou and Nei 1986; Hillis et al. 1994; Huelsenbeck et al. 1996). We believe that an extremely important aspect of the work by Walsh et al. (1999) is their clear statement of the alternative and null hypotheses concerning the differentiation between hard and soft polytomies. As they point out, of the biological reality of polytomies is complicated by the fact that a polytomy represents the null hypothesis for phylogenetic reconstruction-all taxa are equally relatedand therefore cannot be proven. By restating the problem in the context of the power necessary to detect short internal branches, Walsh et al. (1999) place the hypothesis of a hard polytomy in a much more testable context. However, we were surprised to find that power analysis suggests only 215 to 1237 base pairs of mitochondrial sequence data are required for resolution of a soft polytomy in the auklets, as defined by Walsh et al. (1999). To further explore the study of polytomies in a statistical context, we examined the implications of the inherent variance exhibited by the nucleotide substitution process. It is clear that molecular evolution is a stochastic process with the number, type, and position of fixed sequence differences being determined by the processes of mutation, selection, and genetic drift. The stochastic nature of molecular evolution may have a profound impact upon the number of differences observed during a specific time period and it is possible that many fewer (or many more) mutations will be fixed during a particular period of time than one expects based upon the total number of substitutions in the phylogenetic tree. Nucleotide substitution can be modeled as a Poisson process (e.g., Wilson et al. 1987), with the probability (P) of N nucleotide substitutions occurring during a given period of time given by:

POWER AND STOCHASTICITY IN THE RESOLUTION OF SOFT POLYTOMIES: A REPLY TO BRAUN ET AL

POWER AND STOCHASTICITY IN THE RESOLUTION OF SOFT POLYTOMIES: A REPLY TO BRAUN ET AL

COMPARATIVE METHODS FOR THE ANALYSIS OF CONTINUOUS VARIABLES: GEOMETRIC INTERPRETATIONS

This study is concerned with statistical methods used for the analysis of comparative data (in which observations are not expected to be independent because they are sampled across phylogenetically related species). The phylogenetically independent contrasts (PIC), phylogenetic generalized least-squares (PGLS), and phylogenetic autocorrelation (PA) methods are compared. Although the independent contrasts are not orthogonal, they are independent if the data conform to the Brownian motion model of evolution on which they are based. It is shown that uncentered correlations and regressions through the origin using the PIC method are identical to those obtained using PGLS with an intercept included in the model. The PIC method is a special case of PGLS. Corrected standard errors are given for estimates of the ancestral states based on the PGLS approach. The treatment of trees with hard polytomies is discussed and is shown to be an algorithmic rather than a statistical problem. Some of the relationships among the methods are shown graphically using the multivariate space in which variables are represented as vectors with respect to OTUs used as coordinate axes. The maximum-likelihood estimate of the autoregressive parameter, ρ, has not been computed correctly in previous studies (an appendix with MATLAB code provides a corrected algorithm). The importance of the eigenvalues and eigenvectors of the connection matrix, W, for the distribution of ρ is discussed. The PA method is shown to have several problems that limit its usefulness in comparative studies. Although the PA method is a generalized least-squares procedure, it cannot be made equivalent to the PGLS method using a phylogenetic model.Corresponding Editor: T. Garland Jr.

POLYTOMIES AND THE POWER OF PHYLOGENETIC INFERENCE.

Although phylogenetic hypotheses can provide insights into mechanisms of evolution, their utility is limited by our inability to differentiate simultaneous speciation events (hard polytomies) from rapid cladogenesis (soft polytomies). In the present paper, we tested the potential for statistical power analysis to differentiate between hard and soft polytomies in molecular phytogenies. Classical power analysis typically is used a priori to determine the sample size required to detect a particular effect size at a particular level of significance (a) with a certain power (1 - β). A posteriori, power analysis is used to infer whether failure to reject a null hypothesis results from lack of an effect or from insufficient data (i.e., low power). We adapted this approach to molecular data to infer whether polytomies result from simultaneous branching events or from insufficient sequence information. We then used this approach to determine the amount of sequence data (sample size) required to detect a positive branch length (effect size). A worked example is provided based on the auklets (Charadriiformes: Alcidae), a group of seabirds among which relationships are represented by a polytomy, despite analyses of over 3000 bp of sequence data. We demonstrate the calculation of effect sizes and sample sizes from sequence data using a normal curve test for difference of a proportion from an expected value and a t-test for a difference of a mean from an expected value. Power analyses indicated that the data for the auklets should be sufficient to differentiate speciation events that occurred at least 100,000 yr apart (the duration of the shortest glacial and interglacial events of the Pleistocene), 2.6 million years ago.

Phylogenetic Relationships and Tempo of Early Diversification in Anolis Lizards

We examine phylogenetic relationships among anoles using mitochondrial DNA se- quences from the NADH dehydrogenase subunit 2 gene (ND2) andve transfer-RNA genes repre- senting 1,455 alignable base positions and 866 phylogenetically informative characters (parsimony criterion). We also present 16 morphological characters for phylogenetic analysis. Our analyses yielded poorly-supported nodes deep in the anole tree but many well-supported nodes for more recent phylogenetic divergences. We test the hypothesis that the major clades of anoles form a hard polytomy and present a general statistical framework for testing hypotheses of simultaneous branching of lineages by using molecular sequence data. Our results suggest that rapid diversi- �cation early in the evolutionary history of anoles explains why numerous researchers have had difculty reconstructing well-supported dichotomous phylogenetic trees for anoles. ( Anolis; mito- chondrial DNA; parametric bootstrap; permutation test; phylogeny; polytomy.)

The Molecular Phylogenetics of Tuco-Tucos (genusCtenomys,Rodentia: Octodontidae) Suggests an Early Burst of Speciation

Variation in the nucleotide sequence of the entire mitochondrial cytochrome b gene (1140 bp) was examined for 27 individuals representing 13 species of South American rodents of the generaCtenomys, Octodontomys, Tympanoctomys,andSpalacopus.Representatives of the family Echimyidae,EuryzygomatomysandMesomys,were used as outgroups to test the monophyly of the Octodontinae and Ctenomyinae. Relationships among species of tuco-tucos (genusCtenomys) were also examined including representatives of the three described subgenera and the two sperm morphs. Reciprocal monophyly of the Octodontinae and Ctenomyinae is strongly supported. Several basal relationships among species of the genusCtenomysare poorly resolved, suggesting the possibility of a hard polytomy due to a rapid and potentially simultaneous radiation early in the history of the genus. In other cases, clades within the Ctenomyinae previously identified on the basis of allozymes, chromosomes, parasites, or skull morphology were supported. Calibrations based on the fossil record suggest that the mitochondrial cytochrome b of these caviomorphs has evolved at a rapid rate, comparable to those proposed forMus-Rattus,and three to four times higher than ungulate rates.

Mitochondrial DNA Sequence Variation among the Subspecies of Sarus Crane (Grus antigone)

We examined DNA sequence variation in an 1,831 base-pair segment of the mitochondrial DNA genome from representatives of the three subspecies of Sarus Crane (Grus antigone). The sequences include the entire cytochrome-b, tRNAThr, tRNAPr?, and ND6 genes, as well as three short intergenic spacer regions. Nine distinct haplotypes were iden- tified in a sample of nine individuals, three each from the Indian (G. a. antigone), Burmese (G. a. sharpei), and Australian (G. a. gillae) subspecies. Phylogenetic analysis revealed that although Sarus Crane haplotypes form a monophyletic assemblage relative to Brolga (G. rubicunda) and White-naped Crane (G. vipio) outgroups, they cannot be resolved onto a di- chotomously branching tree. A minimum-length network for the Sarus Crane haplotypes reveals at least one instance of direct ancestry and one hard polytomy, but shows no phy- logeographic partitioning of haplotypes among subspecies. Net sequence divergence among subspecies is not significantly different from zero. Estimated sequence divergence times, neutral coalescent times, and data on the Quaternary geology of Australasia suggest that Sarus Cranes colonized Australia during the late Pleistocene. Received 25 October 1995, accepted 10 December 1995. SARUS CRANES (Grus antigone) are among the

Polytomies in Comparative Analyses of Continuous Characters

ple species. One requirement of the meth? od is that the true phylogeny linking the species in the data set be known in full, including the lengths of the branches in units of expected variance of change for the character(s) being studied (see Harvey and Pagel, 1991; Martins and Garland, 1991; Garland et al., 1992). In practice, we cannot be certain of the true phylogeny for any set of species. Instead, we must use an es? timate of it. This working phylogeny (sensu Graf en, 1989) might differ from the real phylogeny in three ways: (1) taxa depicted as sister groups in the working phylogeny might not be so in reality, causing the wrong taxa to be compared when comput? ing contrasts; (2) the working phylogeny might not depict all of the real sister-group relationships, i.e., a series of bifurcations in the true phylogeny might be repre? sented as a polytomy in the working phy? logeny; and (3) the lengths of branches be? tween nodes (including tips) of the working phylogeny might be incorrect. Differences of the first type clearly must be minimized because they violate the as? sumptions of Felsenstein's method to an unknown and possibly very serious de? gree. Differences of the third type also weaken the method, but apparently not fatally (see Graf en, 1989; Martins and Gar? land, 1991). However, we still want the branch lengths on the working phylogeny to reflect the truth as accurately as possible (Garland et al., 1992). Differences of the second type?incomplete resolution of the working phylogeny?raise some interest? ing conceptual and analytical issues. Un? less we are prepared to assume that spe? ciation is always a strictly dichotomous process, then we must recognize that some polytomies in working phylogenies will represent true cases of multiway speciation events; these are termed polyto? mies (Maddison, 1989). In the original de? scription of the comparative method of phylogenetically independent contrasts, Felsenstein (1985:10) alluded to the correct way to analyze hard polytomies. However, other polytomies in working phylogenies simply reflect our ignorance of the true dichotomous branching pattern (soft po? lytomies, Maddison, 1989). Felsenstein's suggestion to set some internode branch lengths to zero when computing standard? ized independent contrasts leads to unbi? ased estimates of correlations and slopes for both hard and soft polytomies but does not indicate how many degrees of freedom are available for hypothesis testing with the latter. Grafen (1989), Harvey and Pagel (1991), and Pagel (1992) have offered other more complicated ways of dealing with soft polytomies that allow only one degree of freedom per node. Table 1 presents the differences between the two positions. We want to recognize any hard polytomies as such to claim the maximum degrees of freedom associated with them.