Modelling phylogenetic relationships using reticulated networks

Makarenkov, V., Legendre, P. & Desdevises, Y. (2004). Modelling phylogenetic relationships using reticulated networks. —  Zoologica Scripta , 33 , 89–96.
Most traditional methods of phylogenetic analysis assume that species evolution can be represented by means of a bifurcating tree model. In many phylogenetic situations, however, some of the evolutionary links between species are due to reticulate evolution. For instance, reticulate models can adequately describe such complicated mechanisms as lateral gene transfer in bacteria or species hybridization. The theoretical concepts of reticulate evolution developed in the 1980s and 1990s need to be supported by appropriate analytical tools and software. In this paper, we present the main features of a new distance-based method for modelling phylogenetic relationships among species by means of reticulated networks (RNs). The method uses the least-squares model to build a RN by gradually improving upon the solution provided by a phylogenetic tree. A computer program facilitating the reconstruction and visualization of reticulate phylogenies is made available to researchers. In the application section, we illustrate the usefulness of the method by studying the evolution of honeybees (genus Apis ). The method for reconstructing RNs has been included in the T-Rex ( Tree and Reticulogram Reconstruction ) package recently developed by the first-named author.     

From a phylogenetic tree to a reticulated network.

In many phylogenetic problems, assuming that species have evolved from a common ancestor by a simple branching process is unrealistic. Reticulate phylogenetic models, however, have been largely neglected because the concept of reticulate evolution have not been supported by using appropriate analytical tools and software. The reticulate model can adequately describe such complicated mechanisms as hybridization between species or lateral gene transfer in bacteria. In this paper, we describe a new algorithm for inferring reticulate phylogenies from evolutionary distances among species. The algorithm is capable of detecting contradictory signals encompassed in a phylogenetic tree and identifying possible reticulate events that may have occurred during evolution. The algorithm produces a reticulate phylogeny by gradually improving upon the initial solution provided by a phylogenetic tree model. The new algorithm is compared to the popular SplitsGraph method in a reanalysis of the evolution of photosynthetic organisms. A computer program to construct and visualize reticulate phylogenies, called T-Rex (Tree and Reticulogram Reconstruction), is available to researchers at the following URL: www.fas.umontreal.ca/biol/casgrain/en/labo/t-rex.     

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent

The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.     

Distinguishing terminal monophyletic groups from reticulate taxa: performance of phenetic, tree-based, and network procedures

Hybridization is a well-documented, natural phenomenon that is common at low taxonomic levels in the higher plants and other groups. In spite of the obvious potential for gene flow via hybridization to cause reticulation in an evolutionary tree, analytical methods based on a strictly bifurcating model of evolution have frequently been applied to data sets containing taxa known to hybridize in nature. Using simulated data, we evaluated the relative performance of phenetic, tree-based, and network approaches for distinguishing between taxa with known reticulate history and taxa that were true terminal monophyletic groups. In all methods examined, type I error (the erroneous rejection of the null hypothesis that a taxon of interest is not monophyletic) was likely during the early stages of introgressive hybridization. We used the gradual erosion of type I error with continued gene flow as a metric for assessing relative performance. Bifurcating tree-based methods performed poorly, with highly supported, incorrect topologies appearing during some phases of the simulation. Based on our model, we estimate that many thousands of gene flow events may be required in natural systems before reticulate taxa will be reliably detected using tree-based methods of phylogeny reconstruction. We conclude that the use of standard bifurcating tree-based methods to identify terminal monophyletic groups for the purposes of defining or delimiting phylogenetic species, or for prioritizing populations for conservation purposes, is difficult to justify when gene flow between sampled taxa is possible. As an alternative, we explored the use of two network methods. Minimum spanning networks performed worse than most tree-based methods and did not yield topologies that were easily interpretable as phylogenies. The performance of NeighborNet was comparable to parsimony bootstrap analysis. NeighborNet and reverse successive weighting were capable of identifying an ephemeral signature of reticulate evolution during the early stages of introgression by revealing conflicting phylogenetic signal. However, when gene flow was topologically complex, the conflicting phylogenetic signal revealed by these methods resulted in a high probability of type II error (inferring that a monophyletic taxon has a reticulate history). Lastly, we present a novel application of an existing nonparametric clustering procedure that, when used against a density landscape derived from principal coordinate data, showed superior performance to the tree-based and network procedures tested.     

Phylogenomics of Fargesia and Yushania reveals a history of reticulate evolution

Reticulate evolution is a common and important driving force in angiosperm evolution. In this study, we analyzed the phylogenetic signals of genomic regions with different inheritance patterns to understand the evolutionary process of organisms using species-rich Himalaya–Hengduan taxa of bamboos (Fargesia Franchet and Yushania Keng). We constructed phylogenetic trees using different sampling strategies and reconstruction methods based on genome skimming and double digest restriction-site-associated DNA sequencing data. We assessed the congruence of topologies generated from different datasets and employed several approaches to reveal the causes of phylogenetic incongruence, including the detection of hybridization and introgression using PhyloNetworks and the D-statistic test (ABBA-BABA test). We found that, in the plastome-based phylogeny, Fargesia bamboos can be clustered into three groups and Yushania was nested within one of them, which contradicts the nuclear–double digest restriction-site-associated DNA sequencing-based phylogeny. Moreover, the genetic variation of chloroplast DNA is significantly correlated with geographical distribution. The strong signal of incomplete lineage sorting, hybridization, introgression, and cytoplasmic gene flow found among genera and species suggests that reticulate evolution is the main cause for the phylogenetic incongruence between nuclear and chloroplast datasets. Our results add evidence that genomes with different inheritance patterns can reveal distinct evolutionary histories of species and suggest that reticulate evolution is prevalent in rapidly diversifying groups.     

Reticulate evolution on a global scale: a nuclear phylogeny for New World Dryopteris (Dryopteridaceae)

Reticulate, or non-bifurcating, evolution is now recognized as an important phenomenon shaping the histories of many organisms. It appears to be particularly common in plants, especially in ferns, which have relatively few barriers to intra- and interspecific hybridization. Reticulate evolutionary patterns have been recognized in many fern groups, though very few have been studied rigorously using modern molecular phylogenetic techniques in order to determine the causes of the reticulate patterns. In the current study, we examine patterns of branching and reticulate evolution in the genus Dryopteris, the woodferns. The North American members of this group have long been recognized as a classic example of reticulate evolution in plants, and we extend analysis of the genus to all 30 species in the New World, as well as numerous taxa from other regions. We employ sequence data from the plastid and nuclear genomes and use maximum parsimony (MP), maximum likelihood (ML), Bayesian inference (BI), and divergence time analyses to explore the relationships of New World Dryopteris to other regions and to reconstruct the timing and events which may have led to taxa displaying reticulate rather than strictly branching histories. We find evidence for reticulation among both the North and Central/South American groups of species, and our data support a classic hypothesis for reticulate evolution via allopolyploid speciation in the North America taxa, including an extinct diploid progenitor in this group. In the Central and South American species, we find evidence of extensive reticulation involving unknown ancestors from Asia, and we reject deep coalescent processes such as incomplete lineage sorting in favor of more recent intercontinental hybridization and chloroplast capture as an explanation for the origin of the Latin American reticulate taxa.     

Using Haplotype Trees for Phylogeographic and Species Inference in Fish Populations

Genetic variation is now routinely screened at the DNA sequence level in many studies. If the DNA region being screened has not experienced excessive amounts of recombination, it is often possible to reconstruct the evolutionary history of the genetic variation in the form of a haplotype tree. This tree estimates the evolutionary pathway that interconnects all the different haplotypes (sequence variants) observed in the sample. This haplotype tree can be used to define a series of nested branches (clades) that reflects the relative temporal history of the haplotypes and groups of haplotypes. Geographical information can then be overlaid upon this temporal series to test for significant associations between geography and temporal position in the haplotype tree. This allows a reconstruction of how the genetic variation arose and spread in both space and time. Such reconstructions can yield many insights into the joint roles of recurrent events such as gene flow and of historical events such as fragmentation or range expansion. These points are illustrated with studies on the chub, Leuciscus cephalus. There is also a need to extend such nested phylogeographic analyses to a phylo/reticulate geographic analysis that incorporates both assortment and recombination between and within DNA regions. A preliminary phylo/reticulate geographic analysis is presented of the transferrin locus in the brown trout, Salmo trutta, species complex that reveals the importance of hybridization in the recent evolutionary history of this group. This example shows the inadequacy of a strictly phylogenetic approach and illustrates the need to incorporate reticulate evolution. The results of nested clade phylogeographic analysis and the new phylo/reticulate geographic analysis are then used for inferring species status of the marbled trout. The results indicate that an old hybridization event may have played a role in the origin of the marbled trout. Currently the marbled trout is primarily endangered by hybridization with introduced brown trout. These results show both the positive and negative impacts of hybridization upon biodiversity. Such phylo/reticulate geographic studies will challenge both our concepts of species and our conservation management strategies.     

The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection

Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa.     

Rapid maximum likelihood ancestral state reconstruction of continuous characters: A rerooting‐free algorithm

Ancestral state reconstruction is a method used to study the evolutionary trajectories of quantitative characters on phylogenies. Although efficient methods for univariate ancestral state reconstruction under a Brownian motion model have been described for at least 25 years, to date no generalization has been described to allow more complex evolutionary models, such as multivariate trait evolution, non‐Brownian models, missing data, and within‐species variation. Furthermore, even for simple univariate Brownian motion models, most phylogenetic comparative R packages compute ancestral states via inefficient tree rerooting and full tree traversals at each tree node, making ancestral state reconstruction extremely time‐consuming for large phylogenies. Here, a computationally efficient method for fast maximum likelihood ancestral state reconstruction of continuous characters is described. The algorithm has linear complexity relative to the number of species and outperforms the fastest existing R implementations by several orders of magnitude. The described algorithm is capable of performing ancestral state reconstruction on a 1,000,000‐species phylogeny in fewer than 2 s using a standard laptop, whereas the next fastest R implementation would take several days to complete. The method is generalizable to more complex evolutionary models, such as phylogenetic regression, within‐species variation, non‐Brownian evolutionary models, and multivariate trait evolution. Because this method enables fast repeated computations on phylogenies of virtually any size, implementation of the described algorithm can drastically alleviate the computational burden of many otherwise prohibitively time‐consuming tasks requiring reconstruction of ancestral states, such as phylogenetic imputation of missing data, bootstrapping procedures, Expectation‐Maximization algorithms, and Bayesian estimation. The described ancestral state reconstruction algorithm is implemented in the Rphylopars functions anc.recon and phylopars.     

An HMM-Based Comparative Genomic Framework for Detecting Introgression in Eukaryotes

One outcome of interspecific hybridization and subsequent effects of evolutionary forces is introgression, which is the integration of genetic material from one species into the genome of an individual in another species. The evolution of several groups of eukaryotic species has involved hybridization, and cases of adaptation through introgression have been already established. In this work, we report on PhyloNet-HMM—a new comparative genomic framework for detecting introgression in genomes. PhyloNet-HMM combines phylogenetic networks with hidden Markov models (HMMs) to simultaneously capture the (potentially reticulate) evolutionary history of the genomes and dependencies within genomes. A novel aspect of our work is that it also accounts for incomplete lineage sorting and dependence across loci. Application of our model to variation data from chromosome 7 in the mouse (Mus musculus domesticus) genome detected a recently reported adaptive introgression event involving the rodent poison resistance gene Vkorc1, in addition to other newly detected introgressed genomic regions. Based on our analysis, it is estimated that about 9% of all sites within chromosome 7 are of introgressive origin (these cover about 13 Mbp of chromosome 7, and over 300 genes). Further, our model detected no introgression in a negative control data set. We also found that our model accurately detected introgression and other evolutionary processes from synthetic data sets simulated under the coalescent model with recombination, isolation, and migration. Our work provides a powerful framework for systematic analysis of introgression while simultaneously accounting for dependence across sites, point mutations, recombination, and ancestral polymorphism.     

Hybrid genome evolution by transposition

Species hybridization is reviewed focusing on its role as a source of evolutionary novelties. Contrary to the view that hybrids are lineages devoid of evolutionary value, a number of case studies are given that show how hybrids are responsible for reticulate evolution that may lead to the origin of new species. Hybrid evolution is mediated by extensive genome repatterning followed by rapid stabilization and fixation of highly adapted genotypes. Some well-documented cases demonstrate that bursts of transposition follow hybridization and may contribute to the genetic instability observed after hybridization. The mechanism that triggers transposition in hybrids is largely unknown, but coupling of hybrid transposition and demethylation has been observed in mammals and plants. A natural scenario is proposed in which marginal small hybrid populations undergo transposition mediated genome reorganizations accompanied by exogenous and endogenous selection that, in concert with drift, lead to rapid fixation of high fitness hybrid genotypes. These genotypes may represent parental introgressed species or be entirely new species.     

Coalescent histories on phylogenetic networks and detection of hybridization despite incomplete lineage sorting

Analyses of the increasingly available genomic data continue to reveal the extent of hybridization and its role in the evolutionary diversification of various groups of species. We show, through extensive coalescent-based simulations of multilocus data sets on phylogenetic networks, how divergence times before and after hybridization events can result in incomplete lineage sorting with gene tree incongruence signatures identical to those exhibited by hybridization. Evolutionary analysis of such data under the assumption of a species tree model can miss all hybridization events, whereas analysis under the assumption of a species network model would grossly overestimate hybridization events. These issues necessitate a paradigm shift in evolutionary analysis under these scenarios, from a model that assumes a priori a single source of gene tree incongruence to one that integrates multiple sources in a unifying framework. We propose a framework of coalescence within the branches of a phylogenetic network and show how this framework can be used to detect hybridization despite incomplete lineage sorting. We apply the model to simulated data and show that the signature of hybridization can be revealed as long as the interval between the divergence times of the species involved in hybridization is not too small. We reanalyze a data set of 106 loci from 7 in-group Saccharomyces species for which a species tree with no hybridization has been reported in the literature. Our analysis supports the hypothesis that hybridization occurred during the evolution of this group, explaining a large amount of the incongruence in the data. Our findings show that an integrative approach to gene tree incongruence and its reconciliation is needed. Our framework will help in systematically analyzing genomic data for the occurrence of hybridization and elucidating its evolutionary role.     

Testing reticulate evolution of four Vitis species from East Asia using restriction‐site associated DNA sequencing

Reticulate evolution is an important driving force of angiosperm evolution. It has been proposed as an important evolutionary process in Vitis L. subgenus Vitis. Events of natural hybridization and introgression of several taxa native to North America have been hypothesized and discussed. However, there is no convincing evidence of reticulate evolution reported for closely related Vitis taxa from East Asia. We aim to explore natural hybridization and introgression among four closely related Vitis taxa from East Asia (V. amurensis Ruprecht, V. romanetii Romanet du Caillaud, V. shenxiensis C. L. Li, and V. piasezkii Maximowicz) with the restriction‐site associated DNA sequencing technique. A total of 46 accessions, covering the potential morphological and geographic variation of each species, are sequenced. Our results show a complex evolutionary pattern of the four Vitis species. The phylogenetic inference suggests that V. amurensis is monophyletic, however, V. romanetii, V. shenxiensis, and V. piasezkii do not appear to be monophyletic. Significant signals of introgression in some accessions have been detected by population structure analyses. D‐statistics analysis and population structure analyses support the presence of introgression between V. shenxiensis/V. piasezkii and V. romanetii in sympatric populations, but a strong signal of admixture has not been recognized between distantly located populations. Our results provide strong evidence of reticulate evolution among V. romanetii, V. shenxiensis, and V. piasezkii.     

Speciation within genomic networks: a case study based on Steatocranus cichlids of the lower Congo rapids

Hybridization in animals is a much more common phenomenon as previously thought and may have profound implications for speciation research. The cichlid genus Steatocranus (Teleostei: Cichlidae), a close relative to members of the East African cichlid radiations, radiated under riverine conditions in the lower Congo rapids and produced a small species flock. Previous phylogenetic analyses suggested that hybridization occurred and contributed to speciation in this genus. A re-analysis of an already published 2000 loci-AFLP data set explicitly testing for patterns of ancient gene flow provided strong evidence for a highly reticulate phylogenetic history of the genus. We provide, to our knowledge, the first example of a complex reticulate network in vertebrates, including multiple closely related species connected through ancient as well as recent gene flow. In this context, the limited validity of strictly bifurcating tree hypotheses as a phylogenetic basis for hypothesis testing in evolutionary biology is discussed.     

Application of ITS sequences of nuclear rDNA in phylogenetic and evolutionary studies of angiosperms

Nuclear rRNA genes (rDNA) in angiosperms are arranged in long tandem repeat ing units, much like those of other higher eukaryotes. Owing to rapid concerted evolution, the repeat units have homogenized or nearly so in most species. The internal transcribed spacer (ITS) of nuclear rDNA is composed of ITS1 and ITS2, which are seperated by 5.8S rDNA. The two spacers, ITS1 (187～298 bp) and ITS2 (187～252 bp), can be readily amplified by PCR and sequenced using universal primers. The sequences contain many vari able sites and potential informative sites among related species, and have been proven to be a useful molecular marker in phylogenetic and evolutionary studies of many angiosperm taxa. It can be used not only in classification and phylogenetic inferences at the levels of family, subfamily, tribe, genus and section, but also in reconstruction of reticulate evolution and de tection of the speciation via hybridization and polyploidization. But this region may not be useful for resolving phylogenetic relationships among families or taxa of higher hierarchy ow- ing to the rapid variation of the ITS sequences.     

Untangling complex histories of genome mergings in high polyploids

Polyploidy, the duplication of entire genomes, plays a major role in plant evolution. In allopolyploids, genome duplication is associated with hybridization between two or more divergent genomes. Successive hybridization and polyploidization events can build up species complexes of allopolyploids with complicated network-like histories, and the evolutionary history of many plant groups cannot be adequately represented by phylogenetic trees because of such reticulate events. The history of complex genome mergings within a high-polyploid species complex in the genus Cerastium (Caryophyllaceae) is here untangled by the use of a network algorithm and noncoding sequences of a low-copy number gene. The resulting network illustrates how hybridization and polyploidization have acted as key evolutionary processes in creating a plant group where high-level allopolyploids clearly outnumber extant parental genomes.     

Ascovirus and its Evolution

Ascoviruses, iridoviruses, asfarviruses and poxviruses are all cytoplasmic DNA viruses. The evolutionary origins of cytoplasmic DNA viruses have never been fully addressed. Morphological, genetic and molecular data were used to test if all four cytoplasmic virus families (Ascoviridae, Iridoviridae, Asfarviridae, and Poxvirirdae) evolved from nuclear replicating baculoviruses and how the four virus groups are related. Molecular phylogenetic analyses using DNA polymerase predicted that cytoplasmic DNA viruses might have evolved from nuclear replicating baculoviruses, and that poxviruses and asfarviruses share a common ancestor with iridoviruses. These three cytoplasmic viruses again shared a common ancestor with ascoviruses. Morphological and genetic data predicted the same evolutionary trend as molecular data predicted. A genome sequence comparison showed that ascoviruses have more baculovirus protein homologues than do iridoviruses, which suggested that ascoviruses have evolved from baculoviruses and iridoviruses evolved from ascoviruses. Poxviruses showed genetic and morphological similarity to other cytoplamic viruses, such as ascoviruses, suggesting it has undergone reticulate evolution via hybridization, recombination and lateral gene transfer with other viruses. Within the ascovirus family, we tested if molecular phylogenetic analyses agree with biological inference; that is, ascovirus had an evolutionary trend of increasing genome size, expanding host range and widening tissue tropism for these viruses. Both molecular and biological data predicted this evolutionary trend. The phylogenetic relationship among the four species of ascovirus was predicted to be that TnAV-2 and HvAV-3 shared a common ancestor with SfAV-1 and the three virus species again shared a common ancestor with DpAV-4.     

Primate numts and reticulate evolution of capped and golden leaf monkeys (Primates: Colobinae)

A recent phylogenetic study of langurs and leaf monkeys of South Asia suggested a reticulate evolution of capped and golden leaf monkeys through ancient hybridization between Semnopithecus and Trachypithecus. To test this hybridization scenario, I analysed nuclear copies of the mitochondrial cytochrome b gene (numts) from capped, golden and Phayre’s leaf monkeys. These numts were aligned with mitochondrial cytochrome b sequences of various species belonging to the genera Semnopithecus and Trachypithecus. In the phylogenetic tree derived from this alignment, the numts fell into three distinct clades (A, B and C) suggesting three independent integration events. Clade A was basal to Semnopithecus, and clades B and C were basal to Trachypithecus. Among the numts in clades A and C were sequences derived from species not represented in their respective sister mitochondrial groups. This unusual placement of certain numts is taken as additional support for the hybridization scenario. Based on the molecular dating of these integration events, hybridization is estimated to have occurred around 7.1 to 3.4 million years ago. Capped and golden leaf monkeys might have to be assigned to a new genus to reconcile their unique evolutionary history. Additionally, northeast India appears to be a ‘hot spot’ for lineages that might have evolved through reticulate evolution.     

TRANSLATING BETWEEN MICROEVOLUTIONARY PROCESS AND MACROEVOLUTIONARY PATTERNS: THE CORRELATION STRUCTURE OF INTERSPECIFIC DATA

As species evolve along a phylogenetic tree, we expect closely related species to retain some phenotypic similarities due to their shared evolutionary histories. The amount of expected similarity depends both on the hierarchical phylogenetic structure, and on the specific magnitude and types of evolutionary changes that accumulate during each generation. In this study, we show how models of microevolutionary change can be translated into the resulting macroevolutionary patterns. We illustrate how the structure of phenotypic covariances expected in interspecific measurements can be derived, and how this structure depends on the microevolutionary forces guiding phenotypic change at each generation. We then explore the covariance structure expected from several simple microevolutionary models of phenotypic evolution, including various combinations of random genetic drift, directional selection, stabilizing selection, and environmental change, as well as models of punctuated or burst-like evolution. We find that stabilizing selection leads to patterns of exponential decrease of between species covariance with phylogenetic distance. This is different from the usual linear patterns of decrease assumed in most comparative and systematic methods. Nevertheless, linear patterns of decrease can result from many processes in addition to random genetic drift, such as directional and fluctuating selection as well as modes of punctuated change. Our framework can be used to develop methods for (1) phylogenetic reconstruction; (2) inference of the evolutionary process from comparative data; and (3) conducting or evaluating statistical analyses of comparative data while taking phylogenetic history into account.     

Reconstruction of biogeographic and evolutionary networks using reticulograms

A reticulogram is a general network capable of representing a reticulate evolutionary structure. It is particularly useful for portraying relationships among organisms that may be related in a nonunique way to their common ancestor - relationships that cannot be represented by a dendrogram or a phylogenetic tree. We propose a new method for constructing reticulograms that represent a given distance matrix. Reticulate evolution applies first to phylogenetic problems; it has been found in nature, for example, in the within-species microevolution of eukaryotes and in lateral gene transfer in bacteria. In this paper, we propose a new method for reconstructing reticulation networks and we develop applications of the reticulate evolution model to ecological biogeographic, population microevolutionary, and hybridization problems. The first example considers a spatially constrained reticulogram representing the postglacial dispersal of freshwater fishes in the Québec peninsula; the reticulogram provides a better model of postglacial dispersal than does a tree model. The second example depicts the morphological similarities among local populations of muskrats in a river valley in Belgium; adding supplementary branches to a tree depicting the river network leads to a better representation of the morphological distances among local populations of muskrats than does a tree structure. A third example involves hybrids between plants of the genus Aphelandra.