Exploring patterns of interspecific variation in quantitative traits using sequential phylogenetic eigenvector regressions

A number of metrics have been developed for estimating phylogenetic signal in data and to evaluate correlated evolution, inferring broad-scale evolutionary and ecological processes. Here, we proposed an approach called phylogenetic signal-representation (PSR) curve, built upon phylogenetic eigenvector regression (PVR). In PVR, selected eigenvectors extracted from a phylogenetic distance matrix are used to model interspecific variation. In the PSR curve, sequential PVR models are fitted after successively increasing the number of eigenvectors and plotting their R(2) against the accumulated eigenvalues. We used simulations to show that a linear PSR curve is expected under Brownian motion and that its shape changes under alternative evolutionary models. The PSR area, expressing deviations from Brownian motion, is strongly correlated (r= 0.873; P < 0.01) with Blomberg's K-statistics, so nonlinear PSR curves reveal if traits are evolving at a slower or higher rate than expected by Brownian motion. The PSR area is also correlated with phylogenetic half-life under an Ornstein-Uhlenbeck process, suggesting how both methods describe the shape of the relationship between interspecific variation and time since divergence among species. The PSR curve provides an elegant exploratory method to understand deviations from Brownian motion, in terms of acceleration or deceleration of evolutionary rates occurring at large or small phylogenetic distances.     

PATTERNS IN PHYLOGENETIC TREE BALANCE WITH VARIABLE AND EVOLVING SPECIATION RATES

Aspects of phylogenetic tree shape, and in particular tree balance, provide clues to the workings of the macroevolutionary process. I use a simulation approach to explore patterns in tree balance for several models of the evolutionary process under which speciation rates vary through the history of diversifying clades. I demonstrate that when speciation rates depend on an evolving trait of individuals, and are therefore “heritable” along evolutionary lineages, the resulting phylogenies become imbalanced. However, imbalance also results from some (but not all) models of “nonheritable” speciation rate variation. The degree of imbalance increases with the magnitude of speciation rate variation, and then for gradual evolution (but not punctuated equilibria) reaches an asymptote short of the theoretical maximum. Very high levels of rate variation are required to produce imbalance matching that found in real data (estimated phylogenies from the systematic literature). I discuss implications of the simulation results for our understanding of macroevolution.     

Phylogenetic eigenvectors and nonstationarity in the evolution of theropod dinosaur skulls

Despite the long‐standing interest in nonstationarity of both phenotypic evolution and diversification rates, only recently have methods been developed to study this property. Here, we propose a methodological expansion of the phylogenetic signal‐representation (PSR) curve based on phylogenetic eigenvectors to test for nonstationarity. The PSR curve is built by plotting the coefficients of determination R² from phylogenetic eigenvector regression (PVR) models increasing the number of phylogenetic eigenvectors against the accumulated eigenvalues. The PSR curve is linear under a stationary model of trait evolution (i.e. the Brownian motion model). Here we describe the distribution of shifts in the models R² and used a randomization procedure to compare observed and simulated shifts along the PSR curve, which allowed detecting nonstationarity in trait evolution. As an applied example, we show that the main evolutionary pattern of variation in the theropod dinosaur skull was nonstationary, with a significant shift in evolutionary rates in derived oviraptorosaurs, an aberrant group of mostly toothless, crested, birdlike theropods. This result is also supported by a recently proposed Bayesian‐based method (AUTEUR). A significant deviation between Ceratosaurus and Limusaurus terminal branches was also detected. We purport that our new approach is a valuable tool for evolutionary biologists, owing to its simplicity, flexibility and comprehensiveness.     

The best of both worlds: Phylogenetic eigenvector regression and mapping

Eigenfunction analyses have been widely used to model patterns of autocorrelation in time, space and phylogeny. In a phylogenetic context, Diniz-Filho et al. (1998) proposed what they called Phylogenetic Eigenvector Regression (PVR), in which pairwise phylogenetic distances among species are submitted to a Principal Coordinate Analysis, and eigenvectors are then used as explanatory variables in regression, correlation or ANOVAs. More recently, a new approach called Phylogenetic Eigenvector Mapping (PEM) was proposed, with the main advantage of explicitly incorporating a model-based warping in phylogenetic distance in which an Ornstein-Uhlenbeck (O-U) process is fitted to data before eigenvector extraction. Here we compared PVR and PEM in respect to estimated phylogenetic signal, correlated evolution under alternative evolutionary models and phylogenetic imputation, using simulated data. Despite similarity between the two approaches, PEM has a slightly higher prediction ability and is more general than the original PVR. Even so, in a conceptual sense, PEM may provide a technique in the best of both worlds, combining the flexibility of data-driven and empirical eigenfunction analyses and the sounding insights provided by evolutionary models well known in comparative analyses.     

Bayesian model adequacy and choice in phylogenetics

Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global) performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance) of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric bootstrap, accounts for uncertainty in the phylogeny and model parameters.     

Dynamics of chromosome number evolution in the Agrodiaetus phyllis species complex (Insecta: Lepidoptera)

A phylogenetic comparative method was employed to study karyotype evolution in the Agrodiaetus phyllis species complex characterized by high variation in haploid chromosome number (from 10 to 134). We found that different phylogenetic lineages of this group have different rates of chromosome-number changes. Chromosome numbers in the complex possess a phylogenetic signal, and their evolutionary transformation is difficult to explain in terms of punctual and gradual evolution.     

AN EIGENVECTOR METHOD FOR ESTIMATING PHYLOGENETIC INERTIA

We propose a new method to estimate and correct for phylogenetic inertia in comparative data analysis. The method, called phylogenetic eigenvector regression (PVR) starts by performing a principal coordinate analysis on a pairwise phylogenetic distance matrix between species. Traits under analysis are regressed on eigenvectors retained by a broken-stick model in such a way that estimated values express phylogenetic trends in data and residuals express independent evolution of each species. This partitioning is similar to that realized by the spatial autoregressive method, but the method proposed here overcomes the problem of low statistical performance that occurs with autoregressive method when phylogenetic correlation is low or when sample size is too small to detect it. Also, PVR is easier to perform with large samples because it is based on well-known techniques of multivariate and regression analyses. We evaluated the performance of PVR and compared it with the autoregressive method using real datasets and simulations. A detailed worked example using body size evolution of Carnivora mammals indicated that phylogenetic inertia in this trait is elevated and similarly estimated by both methods. In this example, Type I error at α = 0.05 of PVR was equal to 0.048, but an increase in the number of eigenvectors used in the regression increases the error. Also, similarity between PVR and the autoregressive method, defined by correlation between their residuals, decreased by overestimating the number of eigenvalues necessary to express the phylogenetic distance matrix. To evaluate the influence of cladogram topology on the distribution of eigenvalues extracted from the double-centered phylogenetic distance matrix, we analyzed 100 randomly generated cladograms (up to 100 species). Multiple linear regression of log transformed variables indicated that the number of eigenvalues extracted by the broken-stick model can be fully explained by cladogram topology. Therefore, the broken-stick model is an adequate criterion for determining the correct number of eigenvectors to be used by PVR. We also simulated distinct levels of phylogenetic inertia by producing a trend across 10, 25, and 50 species arranged in “comblike” cladograms and then adding random vectors with increased residual variances around this trend. In doing so, we provide an evaluation of the performance of both methods with data generated under different evolutionary models than tested previously. The results showed that both PVR and autoregressive method are efficient in detecting inertia in data when sample size is relatively high (more than 25 species) and when phylogenetic inertia is high. However, PVR is more efficient at smaller sample sizes and when level of phylogenetic inertia is low. These conclusions were also supported by the analysis of 10 real datasets regarding body size evolution in different animal clades. We concluded that PVR can be a useful alternative to an autoregressive method in comparative data analysis.     

Molecular phylogenetic analyses of nuclear and plastid DNA sequences support dysploid and polyploid chromosome number changes and reticulate evolution in the diversification of Melampodium (Millerieae, Asteraceae)

Chromosome evolution (including polyploidy, dysploidy, and structural changes) as well as hybridization and introgression are recognized as important aspects in plant speciation. A suitable group for investigating the evolutionary role of chromosome number changes and reticulation is the medium-sized genus Melampodium (Millerieae, Asteraceae), which contains several chromosome base numbers (x = 9, 10, 11, 12, 14) and a number of polyploid species, including putative allopolyploids. A molecular phylogenetic analysis employing both nuclear (ITS) and plastid (matK) DNA sequences, and including all species of the genus, suggests that chromosome base numbers are predictive of evolutionary lineages within Melampodium. Dysploidy, therefore, has clearly been important during evolution of the group. Reticulate evolution is evident with allopolyploids, which prevail over autopolyploids and several of which are confirmed here for the first time, and also (but less often) on the diploid level. Within sect. Melampodium, the complex pattern of bifurcating phylogenetic structure among diploid taxa overlain by reticulate relationships from allopolyploids has non-trivial implications for intrasectional classification.     

Distinct evolutionary trajectories of MHC class I and class II genes in Old World finches and buntings

Major histocompatibility complex (MHC) genes code for key proteins of the adaptive immune system, which present antigens from intra-cellular (MHC class I) and extra-cellular (MHC class II) pathogens. Because of their unprecedented diversity, MHC genes have long been an object of scientific interest, but due to methodological difficulties in genotyping of duplicated loci, our knowledge on the evolution of the MHC across different vertebrate lineages is still limited. Here, we compared the evolution of MHC class I and class II genes in three sister clades of common passerine birds, finches (Fringillinae and Carduelinae) and buntings (Emberizidae) using a uniform methodological (genotyping and data processing) approach and uniform sample sizes. Our analyses revealed contrasting evolutionary trajectories of the two MHC classes. We found a stronger signature of pervasive positive selection and higher allele diversity (allele numbers) at the MHC class I than class II. In contrast, MHC class II genes showed greater allele divergence (in terms of nucleotide diversity) and a much stronger recombination (gene conversion) signal. Gene copy numbers at both MHC class I and class II evolved via fluctuating selection and drift (Brownian Motion evolution), but the evolutionary rate was higher at class I. Our study constitutes one of few existing examples, where evolution of MHC class I and class II genes was directly compared using a multi-species approach. We recommend that re-focusing MHC research from single-species and single-class approaches towards multi-species analyses of both MHC classes can substantially increase our understanding MHC evolution in a broad phylogenetic context.Subject terms: Molecular evolution, Immunogenetics     

Chromosome number evolves independently of genome size in a clade with nonlocalized centromeres (carex: cyperaceae)

The effects of chromosome rearrangement on genome size are poorly understood. While chromosome duplications and deletions have predictable effects on genome size, chromosome fusion, fission, and translocation do not. In this study, we investigate genome size and chromosome number evolution in 87 species of Carex, one of the most species-rich genera of flowering plants and one that has undergone an exceptionally high rate of chromosome rearrangement. Using phylogenetic generalized least-squares regression, we find that the correlation between chromosome number and genome size in the genus grades from flat or weakly positive at fine phylogenetic scales to weakly negative at deeper phylogenetic scales. The rate of chromosome evolution exhibits a significant increase within a species-rich clade that arose approximately 5 million years ago. Genome size evolution, however, demonstrates a nearly constant rate across the entire tree. We hypothesize that this decoupling of genome size from chromosome number helps explain the high lability of chromosome number in the genus, as it reduces indirect selection on chromosome number.     

Context-Dependent Evolutionary Models for Non-Coding Sequences: An Overview of Several Decades of Research and an Analysis of Laurasiatheria and Primate Evolution

The past decade has seen a growing interest in evolutionary models that relax the assumption of site-independent evolution for non-coding sequences. While phylogenetic inference using such so-called context-dependent models is currently computationally prohibitive, these models have been shown to yield significant increases in model fit compared to site-independent evolutionary models, which remain the most widely used evolutionary models to study substitution patterns and perform phylogenetic inference. Context-dependent models have been shown to be suited to study the spontaneous deamination of cytosine in mammalian sequences. In this paper, I discuss various approaches presented in recent years to model context-dependent evolution. I start with discussing the empirical research and results that have led to the development of these models. To accurately estimate the context-dependent substitution patterns that arise from these models, accurate sampling of substitution histories under such models is required. Further, appropriate model selection techniques to assess model performance has become more important than ever, given the drastic increase in parameters of context-dependent models and the tendency of older model selection techniques to prefer parameter-rich models. I also present new results on two mammalian datasets (Primate and Laurasiatheria data) to shed a light on so-called lineage-dependent context-dependent evolution. I conclude this paper with a discussion on current challenges in the development of context-dependent modeling approaches.     

Mixed evidence for early bursts of morphological evolution in extant clades

Macroevolutionary theory predicts high rates of evolution should occur early in a clade's history as species exploit ecological opportunity. Evidence from the fossil record has shown a high prevalence of early bursts in morphological evolution, but recent work has provided little evidence for early high rates in the evolution of extant clades. Here, I test the prevalence of early bursts in extant data using phylogenetic comparative methods. Existing models are extended to allow a shift from a background Brownian motion (BM) process to an early burst process within subclades of phylogenies, rather than an early burst being applied to an entire phylogenetic tree. This nested early burst model is compared to other modes of evolution that can occur within subclades, such as evolution with a constraint (Ornstein‐Uhlenbeck model) and nested BM rate shift models. These relaxed models are validated using simulations and then are applied to body size evolution of three major clades of amniotes (mammals, squamates and aves) at different levels of taxonomic organization (order, family). Applying these unconstrained models greatly increases the support for early bursts within nested subclades, and so early bursts are the most common model of evolution when only one shift is analysed. However, the relative fit of early burst models is worse than models that allow for multiple shifts of the BM or OU process. No single‐shift or homogenous model is superior to models of multiple shifts in BM or OU evolution, but the patterns shown by these multirate models are generally congruent with patterns expected from early bursts.     

A comparative method for studying adaptation to a randomly evolving environment

Most phylogenetic comparative methods used for testing adaptive hypotheses make evolutionary assumptions that are not compatible with evolution toward an optimal state. As a consequence they do not correct for maladaptation. The "evolutionary regression" that is returned is more shallow than the optimal relationship between the trait and environment. We show how both evolutionary and optimal regressions, as well as phylogenetic inertia, can be estimated jointly by a comparative method built around an Ornstein-Uhlenbeck model of adaptive evolution. The method considers a single trait adapting to an optimum that is influenced by one or more continuous, randomly changing predictor variables.     

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.     

Gene finding with a hidden Markov model of genome structure and evolution

Motivation: A growing number of genomes are sequenced. The differences in evolutionary pattern between functional regions can thus be observed genome-wide in a whole set of organisms. The diverse evolutionary pattern of different functional regions can be exploited in the process of genomic annotation. The modelling of evolution by the existing comparative gene finders leaves room for improvement. Results: A probabilistic model of both genome structure and evolution is designed. This type of model is called an Evolutionary Hidden Markov Model (EHMM), being composed of an HMM and a set of region-specific evolutionary models based on a phylogenetic tree. All parameters can be estimated by maximum likelihood, including the phylogenetic tree. It can handle any number of aligned genomes, using their phylogenetic tree to model the evolutionary correlations. The time complexity of all algorithms used for handling the model are linear in alignment length and genome number. The model is applied to the problem of gene finding. The benefit of modelling sequence evolution is demonstrated both in a range of simulations and on a set of orthologous human/mouse gene pairs. AVAILABILITY: Free availability over the Internet on www server: http://www.birc.dk/Software/evogene.     

INTEGRATING FOSSILS WITH MOLECULAR PHYLOGENIES IMPROVES INFERENCE OF TRAIT EVOLUTION

Comparative biologists often attempt to draw inferences about tempo and mode in evolution by comparing the fit of evolutionary models to phylogenetic comparative data consisting of a molecular phylogeny with branch lengths and trait measurements from extant taxa. These kinds of approaches ignore historical evidence for evolutionary pattern and process contained in the fossil record. In this article, we show through simulation that incorporation of fossil information dramatically improves our ability to distinguish among models of quantitative trait evolution using comparative data. We further suggest a novel Bayesian approach that allows fossil information to be integrated even when explicit phylogenetic hypotheses are lacking for extinct representatives of extant clades. By applying this approach to a comparative dataset comprising body sizes for caniform carnivorans, we show that incorporation of fossil information not only improves ancestral state estimates relative to those derived from extant taxa alone, but also results in preference of a model of evolution with trend toward large body size over alternative models such as Brownian motion or Ornstein–Uhlenbeck processes. Our approach highlights the importance of considering fossil information when making macroevolutionary inference, and provides a way to integrate the kind of sparse fossil information that is available to most evolutionary biologists.     

Evolution of the genomic rate of recombination in mammals

Rates of recombination vary considerably between species. Despite the significance of this observation for evolutionary biology and genetics, the evolutionary mechanisms that contribute to these interspecific differences are unclear. On fine physical scales, recombination rates appear to evolve rapidly between closely related species, but the mode and tempo of recombination rate evolution on the broader scale is poorly understood. Here, we use phylogenetic comparative methods to begin to characterize the evolutionary processes underlying average genomic recombination rates in mammals. We document a strong phylogenetic effect in recombination rates, indicating that more closely related species tend to have more similar average rates of recombination. We demonstrate that this phylogenetic signal is not an artifact of errors in recombination rate estimation and show that it is robust to uncertainty in the mammalian phylogeny. Neutral evolutionary models present good fits to the data and we find no evidence for heterogeneity in the rate of evolution in recombination across the mammalian tree. These results suggest that observed interspecific variation in average genomic rates of recombination is largely attributable to the steady accumulation of neutral mutations over evolutionary time. Although single recombination hotspots may live and die on short evolutionary time scales, the strong phylogenetic signal in genomic recombination rates indicates that the pace of evolution on this scale may be considerably slower.     

Evaluating evolutionary pressures and phylogenetic signal in earthworms: a case study – the number of typhlosole lamellae in Hormogastridae (Annelida,Oligochaeta)

Rarely have phylogenetic comparative methods been used to study the correlation between phenotypic traits and environmental variables in invertebrates. With the widespread convergence and conservativeness of the morphological characters used in earthworms, these comparative methods could be useful to improve our understanding of their evolution and systematics. One of the most prominent morphological characters in the family Hormogastridae, endemic to Mediterranean areas, is their multilamellar typhlosole, traditionally thought to be an adaptation to soils poor in nutrients. We tested the correlation of body size and soil characteristics with the number of typhlosole lamellae through a phylogenetic generalized least squares (PGLS) analysis. An ultrametric phylogenetic hypothesis was built with a 2580‐bp DNA sequence from 90 populations, used in combination with three morphological and 11 soil variables. The best‐supported model, based on the Akaike information criterion, was obtained by optimizing the parameters lambda (λ), kappa (κ), and delta (δ). The phylogenetic signal was strong for the number of typhlosole lamellae and average body weight, and was lower for soil variables. Increasing body weight appeared to be the main evolutionary pressure behind the increase in the number of typhlosole lamellae, with soil texture and soil richness having a weaker but significant effect. Information on the evolutionary rate of the number of typhlosole lamellae suggested that the early evolution of this character could have strongly shaped its variability, as is found in an adaptive radiation. This work highlights the importance of implementing the phylogenetic comparative method to test evolutionary hypotheses in invertebrate taxa.     

Predicting rates of interspecific interaction from phylogenetic trees

Integrating phylogenetic information can potentially improve our ability to explain species' traits, patterns of community assembly, the network structure of communities, and ecosystem function. In this study, we use mathematical models to explore the ecological and evolutionary factors that modulate the explanatory power of phylogenetic information for communities of species that interact within a single trophic level. We find that phylogenetic relationships among species can influence trait evolution and rates of interaction among species, but only under particular models of species interaction. For example, when interactions within communities are mediated by a mechanism of phenotype matching, phylogenetic trees make specific predictions about trait evolution and rates of interaction. In contrast, if interactions within a community depend on a mechanism of phenotype differences, phylogenetic information has little, if any, predictive power for trait evolution and interaction rate. Together, these results make clear and testable predictions for when and how evolutionary history is expected to influence contemporary rates of species interaction.