A multispecies coalescent model for quantitative traits

Fast Bayesian Inference of Phylogenies from Multiple Continuous Characters

Time-scaled phylogenetic trees are an ultimate goal of evolutionary biology and a necessary ingredient in comparative studies. The accumulation of genomic data has resolved the tree of life to a great extent, yet timing evolutionary events remain challenging if not impossible without external information such as fossil ages and morphological characters. Methods for incorporating morphology in tree estimation have lagged behind their molecular counterparts, especially in the case of continuous characters. Despite recent advances, such tools are still direly needed as we approach the limits of what molecules can teach us. Here, we implement a suite of state-of-the-art methods for leveraging continuous morphology in phylogenetics, and by conducting extensive simulation studies we thoroughly validate and explore our methods' properties. While retaining model generality and scalability, we make it possible to estimate absolute and relative divergence times from multiple continuous characters while accounting for uncertainty. We compile and analyze one of the most data-type diverse data sets to date, comprised of contemporaneous and ancient molecular sequences, and discrete and continuous morphological characters from living and extinct Carnivora taxa. We conclude by synthesizing lessons about our method's behavior, and suggest future research venues.

Homoplastic versus xenoplastic evolution: exploring the emergence of key intrinsic and extrinsic traits in the montane genus Soldanella (Primulaceae)

Specific ecological conditions in the high mountain environment exert a selective pressure that often leads to convergent trait evolution. Reticulations induced by incomplete lineage sorting and introgression can lead to discordant trait patterns among gene and species trees (hemiplasy/xenoplasy), providing a false illusion that the traits under study are homoplastic. Using phylogenetic species networks, we explored the effect of gene exchange on trait evolution in Soldanella, a genus profoundly influenced by historical introgression. At least three features evolved independently multiple times: the single-flowered dwarf phenotype, dysploid cytotype, and ecological generalism. The present analyses also indicated that the recurring occurrence of stoloniferous growth might have been prompted by an introgression event between an ancestral lineage and a still extant species, although its emergence via convergent evolution cannot be completely ruled out. Phylogenetic regression suggested that the independent evolution of larger genomes in snowbells is most likely a result of the interplay between hybridization events of dysploid and euploid taxa and hostile environments at the range margins of the genus. The emergence of key intrinsic and extrinsic traits in snowbells has been significantly impacted not only by convergent evolution but also by historical and recent introgression events.

Implications of gene tree heterogeneity on downstream phylogenetic analyses: A case study employing the Fair Proportion index

Many questions in evolutionary biology require the specification of a phylogeny for downstream phylogenetic analyses. However, with the increasingly widespread availability of genomic data, phylogenetic studies are often confronted with conflicting signal in the form of genomic heterogeneity and incongruence between gene trees and the species tree. This raises the question of determining what data and phylogeny should be used in downstream analyses, and to what extent the choice of phylogeny (e.g., gene trees versus species trees) impacts the analyses and their outcomes. In this paper, we study this question in the realm of phylogenetic diversity indices, which provide ways to prioritize species for conservation based on their relative evolutionary isolation on a phylogeny, and are thus one example of downstream phylogenetic analyses. We use the Fair Proportion (FP) index, also known as the evolutionary distinctiveness score, and explore the variability in species rankings based on gene trees as compared to the species tree for several empirical data sets. Our results indicate that prioritization rankings among species vary greatly depending on the underlying phylogeny, suggesting that the choice of phylogeny is a major influence in assessing phylogenetic diversity in a conservation setting. While we use phylogenetic diversity conservation as an example, we suspect that other types of downstream phylogenetic analyses such as ancestral state reconstruction are similarly affected by genomic heterogeneity and incongruence. Our aim is thus to raise awareness of this issue and inspire new research on which evolutionary information (species trees, gene trees, or a combination of both) should form the basis for analyses in these settings.

Unifying approaches from statistical genetics and phylogenetics for mapping phenotypes in structured populations

In both statistical genetics and phylogenetics, a major goal is to identify correlations between genetic loci or other aspects of the phenotype or environment and a focal trait. In these two fields, there are sophisticated but disparate statistical traditions aimed at these tasks. The disconnect between their respective approaches is becoming untenable as questions in medicine, conservation biology, and evolutionary biology increasingly rely on integrating data from within and among species, and once-clear conceptual divisions are becoming increasingly blurred. To help bridge this divide, we derive a general model describing the covariance between the genetic contributions to the quantitative phenotypes of different individuals. Taking this approach shows that standard models in both statistical genetics (e.g., Genome-Wide Association Studies; GWAS) and phylogenetic comparative biology (e.g., phylogenetic regression) can be interpreted as special cases of this more general quantitative-genetic model. The fact that these models share the same core architecture means that we can build a unified understanding of the strengths and limitations of different methods for controlling for genetic structure when testing for associations. We develop intuition for why and when spurious correlations may occur using analytical theory and conduct population-genetic and phylogenetic simulations of quantitative traits. The structural similarity of problems in statistical genetics and phylogenetics enables us to take methodological advances from one field and apply them in the other. We demonstrate this by showing how a standard GWAS technique-including both the genetic relatedness matrix (GRM) as well as its leading eigenvectors, corresponding to the principal components of the genotype matrix, in a regression model-can mitigate spurious correlations in phylogenetic analyses. As a case study of this, we re-examine an analysis testing for co-evolution of expression levels between genes across a fungal phylogeny, and show that including covariance matrix eigenvectors as covariates decreases the false positive rate while simultaneously increasing the true positive rate. More generally, this work provides a foundation for more integrative approaches for understanding the genetic architecture of phenotypes and how evolutionary processes shape it.

PhyloJunction: a computational framework for simulating, developing, and teaching evolutionary models

We introduce PhyloJunction, a computational framework designed to facilitate the prototyping, testing, and characterization of evolutionary models. PhyloJunction is distributed as an open-source Python library that can be used to implement a variety of models, through its flexible graphical modeling architecture and dedicated model specification language. Model design and use are exposed to users via command-line and graphical interfaces, which integrate the steps of simulating, summarizing, and visualizing data. This paper describes the features of PhyloJunction - which include, but are not limited to, a general implementation of a popular family of phylogenetic diversification models - and, moving forward, how it may be expanded to not only include new models, but to also become a platform for conducting and teaching statistical learning.

Evaluating the Performance of Widely Used Phylogenetic Models for Gene Expression Evolution

Phylogenetic comparative methods are increasingly used to test hypotheses about the evolutionary processes that drive divergence in gene expression among species. However, it is unknown whether the distributional assumptions of phylogenetic models designed for quantitative phenotypic traits are realistic for expression data and importantly, the reliability of conclusions of phylogenetic comparative studies of gene expression may depend on whether the data is well described by the chosen model. To evaluate this, we first fit several phylogenetic models of trait evolution to 8 previously published comparative expression datasets, comprising a total of 54,774 genes with 145,927 unique gene-tissue combinations. Using a previously developed approach, we then assessed how well the best model of the set described the data in an absolute (not just relative) sense. First, we find that Ornstein-Uhlenbeck models, in which expression values are constrained around an optimum, were the preferred models for 66% of gene-tissue combinations. Second, we find that for 61% of gene-tissue combinations, the best-fit model of the set was found to perform well; the rest were found to be performing poorly by at least one of the test statistics we examined. Third, we find that when simple models do not perform well, this appears to be typically a consequence of failing to fully account for heterogeneity in the rate of the evolution. We advocate that assessment of model performance should become a routine component of phylogenetic comparative expression studies; doing so can improve the reliability of inferences and inspire the development of novel models.

The genomic landscape, causes, and consequences of extensive phylogenomic discordance in Old World mice and rats

A species tree is a central concept in evolutionary biology whereby a single branching phylogeny reflects relationships among species. However, the phylogenies of different genomic regions often differ from the species tree. Although tree discordance is often widespread in phylogenomic studies, we still lack a clear understanding of how variation in phylogenetic patterns is shaped by genome biology or the extent to which discordance may compromise comparative studies. We characterized patterns of phylogenomic discordance across the murine rodents (Old World mice and rats) - a large and ecologically diverse group that gave rise to the mouse and rat model systems. Combining new linked-read genome assemblies for seven murine species with eleven published rodent genomes, we first used ultra-conserved elements (UCEs) to infer a robust species tree. We then used whole genomes to examine finer-scale patterns of discordance and found that phylogenies built from proximate chromosomal regions had similar phylogenies. However, there was no relationship between tree similarity and local recombination rates in house mice, suggesting that genetic linkage influences phylogenetic patterns over deeper timescales. This signal may be independent of contemporary recombination landscapes. We also detected a strong influence of linked selection whereby purifying selection at UCEs led to less discordance, while genes experiencing positive selection showed more discordant and variable phylogenetic signals. Finally, we show that assuming a single species tree can result in high error rates when testing for positive selection under different models. Collectively, our results highlight the complex relationship between phylogenetic inference and genome biology and underscore how failure to account for this complexity can mislead comparative genomic studies.

Evaluating the Performance of Widely Used Phylogenetic Models for Gene Expression Evolution

Phylogenetic comparative methods are increasingly used to test hypotheses about the evolutionary processes that drive divergence in gene expression among species. However, it is unknown whether the distributional assumptions of phylogenetic models designed for quantitative phenotypic traits are realistic for expression data and importantly, the reliability of conclusions of phylogenetic comparative studies of gene expression may depend on whether the data is well-described by the chosen model. To evaluate this, we first fit several phylogenetic models of trait evolution to 8 previously published comparative expression datasets, comprising a total of 54,774 genes with 145,927 unique gene-tissue combinations. Using a previously developed approach, we then assessed how well the best model of the set described the data in an absolute (not just relative) sense. First, we find that Ornstein-Uhlenbeck models, in which expression values are constrained around an optimum, were the preferred model for 66% of gene-tissue combinations. Second, we find that for 61% of gene-tissue combinations, the best fit model of the set was found to perform well; the rest were found to be performing poorly by at least one of the test statistics we examined. Third, we find that when simple models do not perform well, this appears to be typically a consequence of failing to fully account for heterogeneity in the rate of the evolution. We advocate that assessment of model performance should become a routine component of phylogenetic comparative expression studies; doing so can improve the reliability of inferences and inspire the development of novel models.

Phylogenomic comparative methods: Accurate evolutionary inferences in the presence of gene tree discordance

Phylogenetic comparative methods have long been a mainstay of evolutionary biology, allowing for the study of trait evolution across species while accounting for their common ancestry. These analyses typically assume a single, bifurcating phylogenetic tree describing the shared history among species. However, modern phylogenomic analyses have shown that genomes are often composed of mosaic histories that can disagree both with the species tree and with each other-so-called discordant gene trees. These gene trees describe shared histories that are not captured by the species tree, and therefore that are unaccounted for in classic comparative approaches. The application of standard comparative methods to species histories containing discordance leads to incorrect inferences about the timing, direction, and rate of evolution. Here, we develop two approaches for incorporating gene tree histories into comparative methods: one that constructs an updated phylogenetic variance-covariance matrix from gene trees, and another that applies Felsenstein's pruning algorithm over a set of gene trees to calculate trait histories and likelihoods. Using simulation, we demonstrate that our approaches generate much more accurate estimates of tree-wide rates of trait evolution than standard methods. We apply our methods to two clades of the wild tomato genus Solanum with varying rates of discordance, demonstrating the contribution of gene tree discordance to variation in a set of floral traits. Our approaches have the potential to be applied to a broad range of classic inference problems in phylogenetics, including ancestral state reconstruction and the inference of lineage-specific rate shifts.

CAGEE: Computational Analysis of Gene Expression Evolution

Despite the increasing abundance of whole transcriptome data, few methods are available to analyze global gene expression across phylogenies. Here, we present a new software package (Computational Analysis of Gene Expression Evolution [CAGEE]) for inferring patterns of increases and decreases in gene expression across a phylogenetic tree, as well as the rate at which these changes occur. In contrast to previous methods that treat each gene independently, CAGEE can calculate genome-wide rates of gene expression, along with ancestral states for each gene. The statistical approach developed here makes it possible to infer lineage-specific shifts in rates of evolution across the genome, in addition to possible differences in rates among multiple tissues sampled from the same species. We demonstrate the accuracy and robustness of our method on simulated data and apply it to a data set of ovule gene expression collected from multiple self-compatible and self-incompatible species in the genus Solanum to test hypotheses about the evolutionary forces acting during mating system shifts. These comparisons allow us to highlight the power of CAGEE, demonstrating its utility for use in any empirical system and for the analysis of most morphological traits. Our software is available at https://github.com/hahnlab/CAGEE/.

The effects of introgression across thousands of quantitative traits revealed by gene expression in wild tomatoes

It is now understood that introgression can serve as powerful evolutionary force, providing genetic variation that can shape the course of trait evolution. Introgression also induces a shared evolutionary history that is not captured by the species phylogeny, potentially complicating evolutionary analyses that use a species tree. Such analyses are often carried out on gene expression data across species, where the measurement of thousands of trait values allows for powerful inferences while controlling for shared phylogeny. Here, we present a Brownian motion model for quantitative trait evolution under the multispecies network coalescent framework, demonstrating that introgression can generate apparently convergent patterns of evolution when averaged across thousands of quantitative traits. We test our theoretical predictions using whole-transcriptome expression data from ovules in the wild tomato genus Solanum. Examining two sub-clades that both have evidence for post-speciation introgression, but that differ substantially in its magnitude, we find patterns of evolution that are consistent with histories of introgression in both the sign and magnitude of ovule gene expression. Additionally, in the sub-clade with a higher rate of introgression, we observe a correlation between local gene tree topology and expression similarity, implicating a role for introgressed cis-regulatory variation in generating these broad-scale patterns. Our results reveal a general role for introgression in shaping patterns of variation across many thousands of quantitative traits, and provide a framework for testing for these effects using simple model-informed predictions.

It is now known from studying large genetic datasets that species often hybridize and cross with each other over many generations – a phenomenon known as introgression. Introgression introduces new genetic variation into a population, and this variation can cause traits to be shared among the introgressing species. When researchers study the evolution of trait variation among species, this source of trait sharing is rarely accounted for. Here, we present a statistical model of the effects of introgression on trait variation. This model predicts that, when averaged across many thousands of traits, introgressing species are consistently more similar than expected from standard approaches. Researchers studying gene expression often consider the expression of many thousands of genes, making this a case where the expected effects of introgression are likely to manifest. We tested our model prediction using ovule gene expression data from the wild tomato genus Solanum, in two groups of species with evidence of historical introgression. We found that patterns of expression similarity in both groups are consistent with their histories of introgression and the predictions from our model. Our results highlight the importance of accounting for introgression as a source of trait variation among species.

Phylogenomic assessment of the role of hybridization and introgression in trait evolution

Trait evolution among a set of species-a central theme in evolutionary biology-has long been understood and analyzed with respect to a species tree. However, the field of phylogenomics, which has been propelled by advances in sequencing technologies, has ushered in the era of species/gene tree incongruence and, consequently, a more nuanced understanding of trait evolution. For a trait whose states are incongruent with the branching patterns in the species tree, the same state could have arisen independently in different species (homoplasy) or followed the branching patterns of gene trees, incongruent with the species tree (hemiplasy). Another evolutionary process whose extent and significance are better revealed by phylogenomic studies is gene flow between different species. In this work, we present a phylogenomic method for assessing the role of hybridization and introgression in the evolution of polymorphic or monomorphic binary traits. We apply the method to simulated evolutionary scenarios to demonstrate the interplay between the parameters of the evolutionary history and the role of introgression in a binary trait's evolution (which we call xenoplasy). Very importantly, we demonstrate, including on a biological data set, that inferring a species tree and using it for trait evolution analysis in the presence of gene flow could lead to misleading hypotheses about trait evolution.

Novel Integrative Modeling of Molecules and Morphology across Evolutionary Timescales

Evolutionary models account for either population- or species-level processes but usually not both. We introduce a new model, the FBD-MSC, which makes it possible for the first time to integrate both the genealogical and fossilization phenomena, by means of the multispecies coalescent (MSC) and the fossilized birth–death (FBD) processes. Using this model, we reconstruct the phylogeny representing all extant and many fossil Caninae, recovering both the relative and absolute time of speciation events. We quantify known inaccuracy issues with divergence time estimates using the popular strategy of concatenating molecular alignments and show that the FBD-MSC solves them. Our new integrative method and empirical results advance the paradigm and practice of probabilistic total evidence analyses in evolutionary biology.[Caninae; fossilized birth–death; molecular clock; multispecies coalescent; phylogenetics; species trees.]

Of Traits and Trees: Probabilistic Distances under Continuous Trait Models for Dissecting the Interplay among Phylogeny, Model, and Data

Stochastic models of character trait evolution have become a cornerstone of evolutionary biology in an array of contexts. While probabilistic models have been used extensively for statistical inference, they have largely been ignored for the purpose of measuring distances between phylogeny-aware models. Recent contributions to the problem of phylogenetic distance computation have highlighted the importance of explicitly considering evolutionary model parameters and their impacts on molecular sequence data when quantifying dissimilarity between trees. By comparing two phylogenies in terms of their induced probability distributions that are functions of many model parameters, these distances can be more informative than traditional approaches that rely strictly on differences in topology or branch lengths alone. Currently, however, these approaches are designed for comparing models of nucleotide substitution and gene tree distributions, and thus, are unable to address other classes of traits and associated models that may be of interest to evolutionary biologists. Here, we expand the principles of probabilistic phylogenetic distances to compute tree distances under models of continuous trait evolution along a phylogeny. By explicitly considering both the degree of relatedness among species and the evolutionary processes that collectively give rise to character traits, these distances provide a foundation for comparing models and their predictions, and for quantifying the impacts of assuming one phylogenetic background over another while studying the evolution of a particular trait. We demonstrate the properties of these approaches using theory, simulations, and several empirical data sets that highlight potential uses of probabilistic distances in many scenarios. We also introduce an open-source R package named PRDATR for easy application by the scientific community for computing phylogenetic distances under models of character trait evolution.[Brownian motion; comparative methods; phylogeny; quantitative traits.].

Introgression is widespread in the radiation of carnivorous Nepenthes pitcher plants

Introgression and hybridization are important processes in plant evolution, but they are difficult to study from a phylogenetic perspective, because they conflict with the bifurcating evolutionary history typically depicted in phylogenetic models. The role of hybridization in plant evolution is best documented in the form of allo-polyploidizations. In contrast, homoploid hybridization and introgression are less explored, although they may be crucial in adaptive radiations. Here we employ genome-wide data (ddRAD-seq, transcriptomes) to investigate the evolutionary history of Nepenthes, a radiation of c. 160 species of iconic carnivorous plants mainly from tropical Asia. Our data indicates that the main radiation is only c. 5 million years old, and confirms previous bifurcating phylogenies. However, due to a greatly expanded number of loci, we were able test for the first time the long-standing hypotheses of introgression and historical hybridization. The genus presents one very clear case of organellar capture between two distantly related but sympatric groups. Furthermore, all Nepenthes species show introgression signals in their nuclear genomes, as uncovered by a general survey of ABBA-BABA-like statistics. The ancestor of the rapid main radiation shows ancestry from two deeply diverged lineages, as indicated by phylogenetic network analyses. All major clades of the main radiation show further introgression both within and between each other, as suggested by admixture graphs. Our study supports the hypothesis that rapid adaptive radiations are hotspots of introgression in the tree of life, and highlights the need to consider non-treelike processes in evolutionary studies of Nepenthes in particular.

Phylogenomic conflict coincides with rapid morphological innovation

Evolutionary biologists have long been fascinated with the episodes of rapid phenotypic innovation that underlie the emergence of major lineages. Although our understanding of the environmental and ecological contexts of such episodes has steadily increased, it has remained unclear how population processes contribute to emergent macroevolutionary patterns. One insight gleaned from phylogenomics is that gene-tree conflict, frequently caused by population-level processes, is often rampant during the origin of major lineages. With the understanding that phylogenomic conflict is often driven by complex population processes, we hypothesized that there may be a direct correspondence between instances of high conflict and elevated rates of phenotypic innovation if both patterns result from the same processes. We evaluated this hypothesis in six clades spanning vertebrates and plants. We found that the most conflict-rich regions of these six clades also tended to experience the highest rates of phenotypic innovation, suggesting that population processes shaping both phenotypic and genomic evolution may leave signatures at deep timescales. Closer examination of the biological significance of phylogenomic conflict may yield improved connections between micro- and macroevolution and increase our understanding of the processes that shape the origin of major lineages across the Tree of Life.

Investigating Morphological Complexes Using Informational Dissonance and Bayes Factors: A Case Study in Corbiculate Bees

It is widely recognized that different regions of a genome often have different evolutionary histories and that ignoring this variation when estimating phylogenies can be misleading. However, the extent to which this is also true for morphological data is still largely unknown. Discordance among morphological traits might plausibly arise due to either variable convergent selection pressures or else phenomena such as hemiplasy. Here, we investigate patterns of discordance among 282 morphological characters, which we scored for 50 bee species particularly targeting corbiculate bees, a group that includes the well-known eusocial honeybees and bumblebees. As a starting point for selecting the most meaningful partitions in the data, we grouped characters as morphological modules, highly integrated trait complexes that as a result of developmental constraints or coordinated selection we expect to share an evolutionary history and trajectory. In order to assess conflict and coherence across and within these morphological modules, we used recently developed approaches for computing Bayesian phylogenetic information allied with model comparisons using Bayes factors. We found that despite considerable conflict among morphological complexes, accounting for among-character and among-partition rate variation with individual gamma distributions, rate multipliers, and linked branch lengths can lead to coherent phylogenetic inference using morphological data. We suggest that evaluating information content and dissonance among partitions is a useful step in estimating phylogenies from morphological data, just as it is with molecular data. Furthermore, we argue that adopting emerging approaches for investigating dissonance in genomic datasets may provide new insights into the integration and evolution of anatomical complexes. [Apidae; entropy; morphological modules; phenotypic integration; phylogenetic information.].

On the Effect of Asymmetrical Trait Inheritance on Models of Trait Evolution

Current phylogenetic comparative methods modeling quantitative trait evolution generally assume that, during speciation, phenotypes are inherited identically between the two daughter species. This, however, neglects the fact that species consist of a set of individuals, each bearing its own trait value. Indeed, because descendent populations after speciation are samples of a parent population, we can expect their mean phenotypes to randomly differ from one another potentially generating a "jump" of mean phenotypes due to asymmetrical trait inheritance at cladogenesis. Here, we aim to clarify the effect of asymmetrical trait inheritance at speciation on macroevolutionary analyses, focusing on model testing and parameter estimation using some of the most common models of quantitative trait evolution. We developed an individual-based simulation framework in which the evolution of phenotypes is determined by trait changes at the individual level accumulating across generations, and cladogenesis occurs then by separation of subsets of the individuals into new lineages. Through simulations, we assess the magnitude of phenotypic jumps at cladogenesis under different modes of trait inheritance at speciation. We show that even small jumps can strongly alter both the results of model selection and parameter estimations, potentially affecting the biological interpretation of the estimated mode of evolution of a trait. Our results call for caution when interpreting analyses of trait evolution, while highlighting the importance of testing a wide range of alternative models. In the light of our findings, we propose that future methodological advances in comparative methods should more explicitly model the intraspecific variability around species mean phenotypes and how it is inherited at speciation.

Determining the probability of hemiplasy in the presence of incomplete lineage sorting and introgression

The incongruence of character states with phylogenetic relationships is often interpreted as evidence of convergent evolution. However, trait evolution along discordant gene trees can also generate these incongruences - a phenomenon known as hemiplasy. Classic comparative methods do not account for discordance, resulting in incorrect inferences about the number, timing, and direction of trait transitions. Biological sources of discordance include incomplete lineage sorting (ILS) and introgression, but only ILS has received theoretical consideration in the context of hemiplasy. Here, we present a model that shows introgression makes hemiplasy more likely, such that methods that account for ILS alone will be conservative. We also present a method and software (HeIST) for making statistical inferences about the probability of hemiplasy and homoplasy in large datasets that contain both ILS and introgression. We apply our methods to two empirical datasets, finding that hemiplasy is likely to contribute to the observed trait incongruences in both.

Gene expression of functionally-related genes coevolves across fungal species: detecting coevolution of gene expression using phylogenetic comparative methods

BACKGROUND

Researchers often measure changes in gene expression across conditions to better understand the shared functional roles and regulatory mechanisms of different genes. Analogous to this is comparing gene expression across species, which can improve our understanding of the evolutionary processes shaping the evolution of both individual genes and functional pathways. One area of interest is determining genes showing signals of coevolution, which can also indicate potential functional similarity, analogous to co-expression analysis often performed across conditions for a single species. However, as with any trait, comparing gene expression across species can be confounded by the non-independence of species due to shared ancestry, making standard hypothesis testing inappropriate.

RESULTS

We compared RNA-Seq data across 18 fungal species using a multivariate Brownian Motion phylogenetic comparative method (PCM), which allowed us to quantify coevolution between protein pairs while directly accounting for the shared ancestry of the species. Our work indicates proteins which physically-interact show stronger signals of coevolution than randomly-generated pairs. Interactions with stronger empirical and computational evidence also showing stronger signals of coevolution. We examined the effects of number of protein interactions and gene expression levels on coevolution, finding both factors are overall poor predictors of the strength of coevolution between a protein pair. Simulations further demonstrate the potential issues of analyzing gene expression coevolution without accounting for shared ancestry in a standard hypothesis testing framework. Furthermore, our simulations indicate the use of a randomly-generated null distribution as a means of determining statistical significance for detecting coevolving genes with phylogenetically-uncorrected correlations, as has previously been done, is less accurate than PCMs, although is a significant improvement over standard hypothesis testing. These methods are further improved by using a phylogenetically-corrected correlation metric.

CONCLUSIONS

Our work highlights potential benefits of using PCMs to detect gene expression coevolution from high-throughput omics scale data. This framework can be built upon to investigate other evolutionary hypotheses, such as changes in transcription regulatory mechanisms across species.

Independent evolution of ancestral and novel defenses in a genus of toxic plants (Erysimum, Brassicaceae)

Phytochemical diversity is thought to result from coevolutionary cycles as specialization in herbivores imposes diversifying selection on plant chemical defenses. Plants in the speciose genus Erysimum (Brassicaceae) produce both ancestral glucosinolates and evolutionarily novel cardenolides as defenses. Here we test macroevolutionary hypotheses on co-expression, co-regulation, and diversification of these potentially redundant defenses across this genus. We sequenced and assembled the genome of E. cheiranthoides and foliar transcriptomes of 47 additional Erysimum species to construct a phylogeny from 9868 orthologous genes, revealing several geographic clades but also high levels of gene discordance. Concentrations, inducibility, and diversity of the two defenses varied independently among species, with no evidence for trade-offs. Closely related, geographically co-occurring species shared similar cardenolide traits, but not glucosinolate traits, likely as a result of specific selective pressures acting on each defense. Ancestral and novel chemical defenses in Erysimum thus appear to provide complementary rather than redundant functions.

Integrating natural history collections and comparative genomics to study the genetic architecture of convergent evolution

Evolutionary convergence has been long considered primary evidence of adaptation driven by natural selection and provides opportunities to explore evolutionary repeatability and predictability. In recent years, there has been increased interest in exploring the genetic mechanisms underlying convergent evolution, in part, owing to the advent of genomic techniques. However, the current 'genomics gold rush' in studies of convergence has overshadowed the reality that most trait classifications are quite broadly defined, resulting in incomplete or potentially biased interpretations of results. Genomic studies of convergence would be greatly improved by integrating deep 'vertical', natural history knowledge with 'horizontal' knowledge focusing on the breadth of taxonomic diversity. Natural history collections have and continue to be best positioned for increasing our comprehensive understanding of phenotypic diversity, with modern practices of digitization and databasing of morphological traits providing exciting improvements in our ability to evaluate the degree of morphological convergence. Combining more detailed phenotypic data with the well-established field of genomics will enable scientists to make progress on an important goal in biology: to understand the degree to which genetic or molecular convergence is associated with phenotypic convergence. Although the fields of comparative biology or comparative genomics alone can separately reveal important insights into convergent evolution, here we suggest that the synergistic and complementary roles of natural history collection-derived phenomic data and comparative genomics methods can be particularly powerful in together elucidating the genomic basis of convergent evolution among higher taxa. This article is part of the theme issue 'Convergent evolution in the genomics era: new insights and directions'.

Population genomics perspectives on convergent adaptation

Convergent adaptation is the independent evolution of similar traits conferring a fitness advantage in two or more lineages. Cases of convergent adaptation inform our ideas about the ecological and molecular basis of adaptation. In judging the degree to which putative cases of convergent adaptation provide an independent replication of the process of adaptation, it is necessary to establish the degree to which the evolutionary change is unexpected under null models and to show that selection has repeatedly, independently driven these changes. Here, we discuss the issues that arise from these questions particularly for closely related populations, where gene flow and standing variation add additional layers of complexity. We outline a conceptual framework to guide intuition as to the extent to which evolutionary change represents the independent gain of information owing to selection and show that this is a measure of how surprised we should be by convergence. Additionally, we summarize the ways population and quantitative genetics and genomics may help us address questions related to convergent adaptation, as well as open new questions and avenues of research. This article is part of the theme issue 'Convergent evolution in the genomics era: new insights and directions'.

The perils of intralocus recombination for inferences of molecular convergence

Accurate inferences of convergence require that the appropriate tree topology be used. If there is a mismatch between the tree a trait has evolved along and the tree used for analysis, then false inferences of convergence ('hemiplasy') can occur. To avoid problems of hemiplasy when there are high levels of gene tree discordance with the species tree, researchers have begun to construct tree topologies from individual loci. However, due to intralocus recombination, even locus-specific trees may contain multiple topologies within them. This implies that the use of individual tree topologies discordant with the species tree can still lead to incorrect inferences about molecular convergence. Here, we examine the frequency with which single exons and single protein-coding genes contain multiple underlying tree topologies, in primates and Drosophila, and quantify the effects of hemiplasy when using trees inferred from individual loci. In both clades, we find that there are most often multiple diagnosable topologies within single exons and whole genes, with 91% of Drosophila protein-coding genes containing multiple topologies. Because of this underlying topological heterogeneity, even using trees inferred from individual protein-coding genes results in 25% and 38% of substitutions falsely labelled as convergent in primates and Drosophila, respectively. While constructing local trees can reduce the problem of hemiplasy, our results suggest that it will be difficult to completely avoid false inferences of convergence. We conclude by suggesting several ways forward in the analysis of convergent evolution, for both molecular and morphological characters. This article is part of the theme issue 'Convergent evolution in the genomics era: new insights and directions'.

The Effects of Demography and Genetics on the Neutral Distribution of Quantitative Traits

Neutral models for quantitative trait evolution are useful for identifying phenotypes under selection. These models often assume normally distributed phenotypes. This assumption may be violated when a trait is affected by relatively few variants or when the effects of those variants arise from skewed or heavy tailed distributions. Molecular phenotypes such as gene expression levels may have these properties. To accommodate deviations from normality, models making fewer assumptions about the underlying genetics and patterns of variation are needed. Here, we develop a general neutral model for quantitative trait variation using a coalescent approach. This model allows interpretation of trait distributions in terms of familiar population genetic parameters because it is based on the coalescent. We show how the normal distribution resulting from the infinitesimal limit, where the number of loci grows large as the effect size per mutation becomes small, depends only on expected pairwise coalescent times. We then demonstrate how deviations from normality depend on demography through the distribution of coalescence times as well as through genetic parameters. In particular, population growth events exacerbate deviations while bottlenecks reduce them. We demonstrate the practical applications of this model by showing how to sample from the neutral distribution of [Formula: see text], the ratio of the variance between subpopulations to that in the overall population. We further show it is likely impossible to distinguish sparsity from skewed or heavy tailed mutational effects using only sampled trait values. The model analyzed here greatly expands the parameter space for neutral trait models.

Embracing heterogeneity: coalescing the Tree of Life and the future of phylogenomics

Building the Tree of Life (ToL) is a major challenge of modern biology, requiring advances in cyberinfrastructure, data collection, theory, and more. Here, we argue that phylogenomics stands to benefit by embracing the many heterogeneous genomic signals emerging from the first decade of large-scale phylogenetic analysis spawned by high-throughput sequencing (HTS). Such signals include those most commonly encountered in phylogenomic datasets, such as incomplete lineage sorting, but also those reticulate processes emerging with greater frequency, such as recombination and introgression. Here we focus specifically on how phylogenetic methods can accommodate the heterogeneity incurred by such population genetic processes; we do not discuss phylogenetic methods that ignore such processes, such as concatenation or supermatrix approaches or supertrees. We suggest that methods of data acquisition and the types of markers used in phylogenomics will remain restricted until a posteriori methods of marker choice are made possible with routine whole-genome sequencing of taxa of interest. We discuss limitations and potential extensions of a model supporting innovation in phylogenomics today, the multispecies coalescent model (MSC). Macroevolutionary models that use phylogenies, such as character mapping, often ignore the heterogeneity on which building phylogenies increasingly rely and suggest that assimilating such heterogeneity is an important goal moving forward. Finally, we argue that an integrative cyberinfrastructure linking all steps of the process of building the ToL, from specimen acquisition in the field to publication and tracking of phylogenomic data, as well as a culture that values contributors at each step, are essential for progress.

Bayesian placement of fossils on phylogenies using quantitative morphometric data

Jointly developing a comprehensive tree of life from living and fossil taxa has long been a fundamental goal in evolutionary biology. One major challenge has stemmed from difficulties in merging evidence from extant and extinct organisms. While these efforts have resulted in varying stages of synthesis, they have been hindered by their dependence on qualitative descriptions of morphology. Though rarely applied to phylogenetic inference, traditional and geometric morphometric data can improve these issues by generating more rigorous ways to quantify variation in morphological structures. They may also facilitate the rapid and objective aggregation of large morphological datasets. I describe a new Bayesian method that leverages quantitative trait data to reconstruct the positions of fossil taxa on fixed reference trees composed of extant taxa. Unlike most formulations of phylogenetic Brownian motion models, this method expresses branch lengths in units of morphological disparity, suggesting a new framework through which to construct Bayesian node calibration priors for molecular dating and explore comparative patterns in morphological disparity. I am hopeful that the approach described here will help to facilitate a deeper integration of neo- and paleontological data to move morphological phylogenetics further into the genomic era.