Estimating a binary character's effect on speciation and extinction

Determining whether speciation and extinction rates depend on the state of a particular character has been of long-standing interest to evolutionary biologists. To assess the effect of a character on diversification rates using likelihood methods requires that we be able to calculate the probability that a group of extant species would have evolved as observed, given a particular model of the character's effect. Here we describe how to calculate this probability for a phylogenetic tree and a two-state (binary) character under a simple model of evolution (the "BiSSE" model, binary-state speciation and extinction). The model involves six parameters, specifying two speciation rates (rate when the lineage is in state 0; rate when in state 1), two extinction rates (when in state 0; when in state 1), and two rates of character state change (from 0 to 1, and from 1 to 0). Using these probability calculations, we can do maximum likelihood inference to estimate the model's parameters and perform hypothesis tests (e.g., is the rate of speciation elevated for one character state over the other?). We demonstrate the application of the method using simulated data with known parameter values.     

Purifying Selection,Drift, and Reversible Mutation with Arbitrarily High Mutation Rates

Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the resulting high diversity levels within a population (hyperdiversity) mean that standard population genetics methods are not trustworthy. We analyze a population genetics model that incorporates purifying selection, reversible mutations, and genetic drift, assuming a stationary population size. We derive analytical results for both population parameters and sample statistics and discuss their implications for studies of natural genetic and epigenetic variation. In particular, we find that (1) many more intermediate-frequency variants are expected than under standard models, even with moderately strong purifying selection, and (2) rates of evolution under purifying selection may be close to, or even exceed, neutral rates. These findings are related to empirical studies of sequence and epigenetic variation.     

Environmental heterogeneity enhances clonal interference

Clonal interference (CI) is a phenomenon that may be important in several asexual microbes. It occurs when population sizes are large and mutation rates to new beneficial alleles are of significant magnitude. Here we explore the role of gene flow and spatial heterogeneity in selection strength in the adaptation of asexuals. We consider a subdivided population of individuals that are adapting, through new beneficial mutations, and that migrate between different patches. The fitness effect of each mutation depends on the patch and all mutations considered are assumed to be unconditionally beneficial. We find that spatial variation in selection pressure affects the rate of adaptive evolution and its qualitative effects depend on the level of gene flow. In particular, we find that both low migration and high levels of heterogeneity lead to enhanced CI. In contrast, for high levels of migration the rate of fixation of adaptive mutations is higher when environmental heterogeneity is present. In addition, we observe that the level of fitness variation is higher and simultaneous fixation of multiple mutations tends to occur in the regime of low migration rates and high heterogeneity.     

Substitution Model of Sequence Evolution for the Human Immunodeficiency Virus Type 1 Subtype B gp120 Gene over the C2-V5 Region

Phylogenetic analyses frequently rely on models of sequence evolution that detail nucleotide substitution rates, nucleotide frequencies, and site-to-site rate heterogeneity. These models can influence hypothesis testing and can affect the accuracy of phylogenetic inferences. Maximum likelihood methods of simultaneously constructing phylogenetic tree topologies and estimating model parameters are computationally intensive, and are not feasible for sample sizes of 25 or greater using personal computers. Techniques that initially construct a tree topology and then use this non-maximized topology to estimate ML substitution rates, however, can quickly arrive at a model of sequence evolution. The accuracy of this two-step estimation technique was tested using simulated data sets with known model parameters. The results showed that for a star-like topology, as is often seen in human immunodeficiency virus type 1 (HIV-1) subtype B sequences, a random starting topology could produce nucleotide substitution rates that were not statistically different than the true rates. Samples were isolated from 100 HIV-1 subtype B infected individuals from the United States and a 620 nt region of the env gene was sequenced for each sample. The sequence data were used to obtain a substitution model of sequence evolution specific for HIV-1 subtype B env by estimating nucleotide substitution rates and the site-to-site heterogeneity in 100 individuals from the United States. The method of estimating the model should provide users of large data sets with a way to quickly compute a model of sequence evolution, while the nucleotide substitution model we identified should prove useful in the phylogenetic analysis of HIV-1 subtype B env sequences. Received: 4 October 2000 / Accepted: 1 March 2001     

Modelling rate distributions using character compatibility: implications for morphological evolution among fossil invertebrates

Rate distributions are important considerations when testing hypotheses about morphological evolution or phylogeny. They also have implications about general processes underlying character evolution. Molecular systematists often assume that rates are Poisson processes with gamma distributions. However, morphological change is the product of multiple probabilistic processes and should theoretically be affected by hierarchical integration of characters. Both factors predict lognormal rate distributions. Here, a simple inverse modelling approach assesses the best single-rate, gamma and lognormal models given observed character compatibility for 115 invertebrate groups. Tests reject the single-rate model for nearly all cases. Moreover, the lognormal outperforms the gamma for character change rates and (especially) state derivation rates. The latter in particular is consistent with integration affecting morphological character evolution.     

Building integral projection models with nonindependent vital rates

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co‐vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs and include cases where the processes co‐vary as a function of time (temporal variation), co‐vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population‐level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life‐history evolution.     

Niche evolution and diversification in a Neotropical radiation of birds (Aves: Furnariidae)

Rapid diversification may be caused by ecological adaptive radiation via niche divergence. In this model, speciation is coupled with niche divergence and lineage diversification is predicted to be correlated with rates of niche evolution. Studies of the role of niche evolution in diversification have generally focused on ecomorphological diversification but climatic‐niche evolution may also be important. We tested these alternatives using a phylogeny of 298 species of ovenbirds (Aves: Furnariidae). We found that within Furnariidae, variation in species richness and diversification rates of subclades were best predicted by rate of climatic‐niche evolution than ecomorphological evolution. Although both are clearly important, univariate regression and multivariate model averaging more consistently supported the climatic‐niche as the best predictor of lineage diversification. Our study adds to the growing body of evidence, suggesting that climatic‐niche divergence may be an important driver of rapid diversification in addition to ecomorphological evolution. However, this pattern may depend on the phylogenetic scale at which rate heterogeneity is examined.     

The impact of rate heterogeneity on inference of phylogenetic models of trait evolution

Rates of trait evolution are known to vary across phylogenies; however, standard evolutionary models assume a homogeneous process of trait change. These simple methods are widely applied in small‐scale phylogenetic studies, whereas models of rate heterogeneity are not, so the prevalence and patterns of potential rate variation in groups up to hundreds of species remain unclear. The extent to which trait evolution is modelled accurately on a given phylogeny is also largely unknown because studies typically lack absolute model fit tests. We investigated these issues by applying both rate‐static and variable‐rates methods on (i) body mass data for 88 avian clades of 10–318 species, and (ii) data simulated under a range of rate‐heterogeneity scenarios. Our results show that rate heterogeneity is present across small‐scaled avian clades, and consequently applying only standard single‐process models prompts inaccurate inferences about the generating evolutionary process. Specifically, these approaches underestimate rate variation, and systematically mislabel temporal trends in trait evolution. Conversely, variable‐rates approaches have superior relative fit (they are the best model) and absolute fit (they describe the data well). We show that rate changes such as single internal branch variations, rate decreases and early bursts are hard to detect, even by variable‐rates models. We also use recently developed absolute adequacy tests to highlight misleading conclusions based on relative fit alone (e.g. a consistent preference for constrained evolution when isolated terminal branch rate increases are present). This work highlights the potential for robust inferences about trait evolution when fitting flexible models in conjunction with tests for absolute model fit.     

Site-to-site variation of synonymous substitution rates

We develop a new model for studying the molecular evolution of protein-coding DNA sequences. In contrast to existing models, we incorporate the potential for site-to-site heterogeneity of both synonymous and nonsynonymous substitution rates. We demonstrate that within-gene heterogeneity of synonymous substitution rates appears to be common. Using the new family of models, we investigate the utility of a variety of new statistical inference procedures, and we pay particular attention to issues surrounding the detection of sites undergoing positive selection. We discuss how failure to model synonymous rate variation in the model can lead to misidentification of sites as positively selected.     

A likelihood approach for comparing synonymous and nonsynonymous nucleotide substitution rates, with application to the chloroplast genome

A model of DNA sequence evolution applicable to coding regions is presented. This represents the first evolutionary model that accounts for dependencies among nucleotides within a codon. The model uses the codon, as opposed to the nucleotide, as the unit of evolution, and is parameterized in terms of synonymous and nonsynonymous nucleotide substitution rates. One of the model's advantages over those used in methods for estimating synonymous and nonsynonymous substitution rates is that it completely corrects for multiple hits at a codon, rather than taking a parsimony approach and considering only pathways of minimum change between homologous codons. Likelihood-ratio versions of the relative-rate test are constructed and applied to data from the complete chloroplast DNA sequences of Oryza sativa, Nicotiana tabacum, and Marchantia polymorpha. Results of these tests confirm previous findings that substitution rates in the chloroplast genome are subject to both lineage-specific and locus-specific effects. Additionally, the new tests suggest tha the rate heterogeneity is due primarily to differences in nonsynonymous substitution rates. Simulations help confirm previous suggestions that silent sites are saturated, leaving no evidence of heterogeneity in synonymous substitution rates.      

Rate heterogeneity, ancestral character state reconstruction, and the evolution of limb morphology in Lerista (Scincidae, Squamata)

Rates of phenotypic evolution derive from numerous interrelated processes acting at varying spatial and temporal scales and frequently differ substantially among lineages. Although current models employed in reconstructing ancestral character states permit independent rates for distinct types of transition (forward and reverse transitions and transitions between different states), these rates are typically assumed to be identical for all branches in a phylogeny. In this paper, I present a general model of character evolution enabling rate heterogeneity among branches. This model is employed in assessing the extent to which the assumption of uniform transition rates affects reconstructions of ancestral limb morphology in the scincid lizard clade Lerista and, accordingly, the potential for rate variability to mislead inferences of evolutionary patterns. Permitting rate variation among branches significantly improves model fit for both the manus and the pes. A constrained model in which the rate of digit acquisition is assumed to be effectively zero is strongly supported in each case; when compared with a model assuming unconstrained transition rates, this model provides a substantially better fit for the manus and a nearly identical fit for the pes. Ancestral states reconstructed assuming the constrained model imply patterns of limb evolution differing significantly from those implied by reconstructions for uniform-rate models, particularly for the pes; whereas ancestral states for the uniform-rate models consistently entail the reacquisition of pedal digits, those for the model incorporating among-lineage rate heterogeneity imply repeated, unreversed digit loss. These results indicate that the assumption of identical transition rates for all branches in a phylogeny may be inappropriate in modeling the evolution of phenotypic traits and emphasize the need for careful evaluation of phylogenetic tests of Dollo's law.     

Evolutionary rate variation at multiple levels of biological organization in plant mitochondrial DNA

We examined patterns of mitochondrial polymorphism and divergence in the angiosperm genus Silene and found substantial variation in evolutionary rates among species and among lineages within species. Moreover, we found corresponding differences in the amount of polymorphism within species. We argue that, along with our earlier findings of rate variation among genes, these patterns of rate heterogeneity at multiple phylogenetic scales are most likely explained by differences in underlying mutation rates. In contrast, no rate variation was detected in nuclear or chloroplast loci. We conclude that mutation rate heterogeneity is a characteristic of plant mitochondrial sequence evolution at multiple biological scales and may be a crucial determinant of how much polymorphism is maintained within species. These dramatic patterns of variation raise intriguing questions about the mechanisms driving and maintaining mutation rate heterogeneity in plant mitochondrial genomes. Additionally, they should alter our interpretation of many common phylogenetic and population genetic analyses.     

Modeling the evolution of the human mitochondrial genome.

Mitochondrial DNA data have been used extensively to study evolution and early human origins. These applications require estimates of the rate at which nucleotide substitutions occur in the DNA sequence. We consider the problem of estimating substitution rates in the presence of site-to-site rate variation. A coalescent model is presented that allows for different substitution rates for purines and pyrimidines, as well as more detailed models that allow fast and slow rates within each of the purine and pyrimidine classes. A method for estimating such rates is presented. Even for these simple models of site heterogeneity, there are, typically, insufficient data to obtain reliable estimates of site-specific substitution rates. However, estimates of the average rate across all sites appear to be relatively stable even in the presence of site heterogeneity. Simulations of models with site-to-site variation in mutation rate show that hypervariable sites can produce peaks in the pairwise difference curves that have previously been attributed to population dynamics.     

FACTORS DETERMINING THE ACCURACY OF CLADOGRAM ESTIMATION: EVALUATION USING COMPUTER SIMULATION

We developed a simulation model of phylogenesis with which we generated a large number of phylogenies and associated data matrices. We examined the characteristics of these and evaluated the success of three taxonomic methods (Wagner parsimony, character compatibility, and UPGMA clustering) as estimators of phylogeny, paying particular attention to the consequences of changes in certain evolutionary assumptions: relative rate of evolution in three different evolutionary contexts (phyletic, parent lineage, and daughter lineage); relative rate of evolution in different directions (novel forward, convergent forward, or reverse); variation of evolutionary rates; and topology of the phylogenetic tree. Except for variation of evolutionary rates, all the evolutionary parameters that we controlled had significant effects on accuracy of phylogenetic reconstructions. Unexpectedly, the topology of the phylogeny was the most important single factor affecting accuracy; some phylogenies are more readily estimated than others for simply historical reasons. We conclude that none of the three estimation methods is very accurate, that the differences in accuracy among them are rather small, and that historical effects (the branching pattern of a phylogeny) may outweigh biological effects in determining the accuracy with which a phylogeny can be reconstructed.     

Keeping it simple: flowering plants tend to retain, and revert to, simple leaves

? A wide range of factors (developmental, physiological, ecological) with unpredictable interactions control variation in leaf form. Here, we examined the distribution of leaf morphologies (simple and complex forms) across angiosperms in a phylogenetic context to detect patterns in the directions of changes in leaf shape. ? Seven datasets (diverse angiosperms and six nested clades, Sapindales, Apiales, Papaveraceae, Fabaceae, Lepidium, Solanum) were analysed using maximum likelihood and parsimony methods to estimate asymmetries in rates of change among character states. ? Simple leaves are most frequent among angiosperm lineages today, were inferred to be ancestral in angiosperms and tended to be retained in evolution (stasis). Complex leaves slowly originated ('gains') and quickly reverted to simple leaves ('losses') multiple times, with a significantly greater rate of losses than gains. Lobed leaves may be a labile intermediate step between different forms. The nested clades showed mixed trends; Solanum, like the angiosperms in general, had higher rates of losses than gains, but the other clades had higher rates of gains than losses. ? The angiosperm-wide pattern could be taken as a null model to test leaf evolution patterns in particular clades, in which patterns of variation suggest clade-specific processes that have yet to be investigated fully.     

The primary divisions of life: a phylogenomic approach employing composition-heterogeneous methods

The three-domains tree, which depicts eukaryotes and archaebacteria as monophyletic sister groups, is the dominant model for early eukaryotic evolution. By contrast, the ‘eocyte hypothesis’, where eukaryotes are proposed to have originated from within the archaebacteria as sister to the Crenarchaeota (also called the eocytes), has been largely neglected in the literature. We have investigated support for these two competing hypotheses from molecular sequence data using methods that attempt to accommodate the across-site compositional heterogeneity and across-tree compositional and rate matrix heterogeneity that are manifest features of these data. When ribosomal RNA genes were analysed using standard methods that do not adequately model these kinds of heterogeneity, the three-domains tree was supported. However, this support was eroded or lost when composition-heterogeneous models were used, with concomitant increase in support for the eocyte tree for eukaryotic origins. Analysis of combined amino acid sequences from 41 protein-coding genes supported the eocyte tree, whether or not composition-heterogeneous models were used. The possible effects of substitutional saturation of our data were examined using simulation; these results suggested that saturation is delayed by among-site rate variation in the sequences, and that phylogenetic signal for ancient relationships is plausibly present in these data.     

Genetic variation for phenotypically invariant traits detected in teosinte: implications for the evolution of novel forms.

How new discrete states of morphological traits evolve is poorly understood. One possibility is that single-gene changes underlie the evolution of new discrete character states and that evolution is dependent on the occurrence of new single-gene mutations. Another possibility is that multiple-gene changes are required to elevate an individual or population above a threshold required to produce the new character state. A prediction of the latter model is that genetic variation for the traits should exist in natural populations in the absence of phenotypic variation. To test this idea, we studied traits that are phenotypically invariant within teosinte and for which teosinte is discretely different from its near relative, maize. By employing a QTL mapping strategy to analyze the progeny of a testcross between an F(1) of two teosintes and a maize inbred line, we identified cryptic genetic variation in teosinte for traits that are invariant in teosinte. We argue that such cryptic genetic variation can contribute to the evolution of novelty when reconfigured to exceed the threshold necessary for phenotypic expression or by acting to modify or stabilize the effects of major mutations.     

Comparative analyses for adaptive radiations

Biologists generally agree that most morphological variation between closely related species is adaptive. The most common method of comparative analysis to test for co-evolved character variation is based on a Brownian-motion model of character evolution. If we are to test for the evolution of character-covariation, and we believe that characters have evolved adaptively to fill niches during an adaptive radiation, then it is appropriate to employ appropriate models for character evolution. We show here that under several models of adaptive character evolution and coevolution during an adaptive radiation, which result in closely related species being more similar to each other than to more distantly related species, cross-species analyses are statistically more appropriate than contrast analyses. If the evolution of some traits fits the Brownian-motion model, while others evolve to fill niches during an adaptive radiation, it might be necessary to identify the number of relevant niche dimensions and the modes of character evolution before deciding on appropriate statistical procedures. Alternatively, maximum-likelihood procedures might be used to determine appropriate transformations of phylogenetic branch lengths that accord with particular models of character evolution.     

TESTING FOR UNEQUAL AMOUNTS OF EVOLUTION IN A CONTINUOUS CHARACTER ON DIFFERENT BRANCHES OF A PHYLOGENETIC TREE USING LINEAR AND SQUARED-CHANGE PARSIMONY: AN EXAMPLE USING LESSER ANTILLEAN ANOLIS LIZARDS

Although a large body of work investigating tests of correlated evolution of two continuous characters exists, hypotheses such as character displacement are really tests of whether substantial evolutionary change has occurred on a particular branch or branches of the phylogenetic tree. In this study, we present a methodology for testing such a hypothesis using ancestral character state reconstruction and simulation. Furthermore, we suggest how to investigate the robustness of the hypothesis test by varying the reconstruction methods or simulation parameters. As a case study, we tested a hypothesis of character displacement in body size of Caribbean Anolis lizards. We compared squared-change, weighted squared-change, and linear parsimony reconstruction methods, gradual Brownian motion and speciational models of evolution, and several resolution methods for linear parsimony. We used ancestor reconstruction methods to infer the amount of body size evolution, and tested whether evolutionary change in body size was greater on branches of the phylogenetic tree in which a transition from occupying a single-species island to a two-species island occurred. Simulations were used to generate null distributions of reconstructed body size change. The hypothesis of character displacement was tested using Wilcoxon Rank-Sums. When tested against simulated null distributions, all of the reconstruction methods resulted in more significant P-values than when standard statistical tables were used. These results confirm that P-values for tests using ancestor reconstruction methods should be assessed via simulation rather than from standard statistical tables. Linear parsimony can produce an infinite number of most parsimonious reconstructions in continuous characters. We present an example of assessing the robustness of our statistical test by exploring the sample space of possible resolutions. We compare ACCTRAN and DELTRAN resolutions of ambiguous character reconstructions in linear parsimony to the most and least conservative resolutions for our particular hypothesis.     

Maximum-likelihood models for combined analyses of multiple sequence data

Models of nucleotide substitution were constructed for combined analyses of heterogeneous sequence data (such as those of multiple genes) from the same set of species. The models account for different aspects of the heterogeneity in the evolutionary process of different genes, such as differences in nucleotide frequencies, in substitution rate bias (for example, the transition/transversion rate bias), and in the extent of rate variation across sites. Model parameters were estimated by maximum likelihood and the likelihood ratio test was used to test hypotheses concerning sequence evolution, such as rate constancy among lineages (the assumption of a molecular clock) and proportionality of branch lengths for different genes. The example data from a segment of the mitochondrial genome of six hominoid species (human, common and pygmy chimpanzees, gorilla, orangutan, and siamang) were analyzed. Nucleotides at the three codon positions in the protein-coding regions and from the tRNA-coding regions were considered heterogeneous data sets. Statistical tests showed that the amount of evolution in the sequence data reflected in the estimated branch lengths can be explained by the codon-position effect and lineage effect of substitution rates. The assumption of a molecular clock could not be rejected when the data were analyzed separately or when the rate variation among sites was ignored. However, significant differences in substitution rate among lineages were found when the data sets were combined and when the rate variation among sites was accounted for in the models. Under the assumption that the orangutan and African apes diverged 13 million years ago, the combined analysis of the sequence data estimated the times for the human-chimpanzee separation and for the separation of the gorilla as 4.3 and 6.8 million years ago, respectively.