Estimating Correlated Rates of Trait Evolution with Uncertainty

Innovation and elaboration on the avian tree of life

Widely documented, megaevolutionary jumps in phenotypic diversity continue to perplex researchers because it remains unclear whether these marked changes can emerge from microevolutionary processes. Here, we tackle this question using new approaches for modeling multivariate traits to evaluate the magnitude and distribution of elaboration and innovation in the evolution of bird beaks. We find that elaboration, evolution along the major axis of phenotypic change, is common at both macro- and megaevolutionary scales, whereas innovation, evolution away from the major axis of phenotypic change, is more prominent at megaevolutionary scales. The major axis of phenotypic change among species beak shapes at megaevolutionary scales is an emergent property of innovation across clades. Our analyses suggest that the reorientation of phenotypes via innovation is a ubiquitous route for divergence that can arise through gradual change alone, opening up further avenues for evolution to explore.

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/.

Modeling the Evolution of Rates of Continuous Trait Evolution

Rates of phenotypic evolution vary markedly across the tree of life, from the accelerated evolution apparent in adaptive radiations to the remarkable evolutionary stasis exhibited by so-called "living fossils". Such rate variation has important consequences for large-scale evolutionary dynamics, generating vast disparities in phenotypic diversity across space, time, and taxa. Despite this, most methods for estimating trait evolution rates assume rates vary deterministically with respect to some variable of interest or change infrequently during a clade's history. These assumptions may cause underfitting of trait evolution models and mislead hypothesis testing. Here, we develop a new trait evolution model that allows rates to vary gradually and stochastically across a clade. Further, we extend this model to accommodate generally decreasing or increasing rates over time, allowing for flexible modeling of "early/late bursts" of trait evolution. We implement a Bayesian method, termed "evolving rates" (evorates for short), to efficiently fit this model to comparative data. Through simulation, we demonstrate that evorates can reliably infer both how and in which lineages trait evolution rates varied during a clade's history. We apply this method to body size evolution in cetaceans, recovering substantial support for an overall slowdown in body size evolution over time with recent bursts among some oceanic dolphins and relative stasis among beaked whales of the genus Mesoplodon. These results unify and expand on previous research, demonstrating the empirical utility of evorates.

Shifts in morphological covariation and evolutionary rates across multiple acquisitions of the trap-jaw mechanism in Strumigenys

A long-standing question in comparative biology is how the evolution of biomechanical systems influences morphological evolution. The need for functional fidelity implies that the evolution of such systems should be associated with tighter morphological covariation, which may promote or dampen rates of morphological evolution. I examine this question across multiple evolutionary origins of the trap-jaw mechanism in the genus Strumigenys. Trap-jaw ants have latch-mediated, spring-actuated systems that amplify the power output of their mandibles. I use Bayesian estimates of covariation and evolutionary rates to test the hypotheses that the evolution of this high-performance system is associated with tighter morphological covariation in the head and mandibles relative to nontrap-jaw forms and that this leads to shifts in rates of morphological evolution. Contrary to these hypotheses, there is no evidence of a large-scale shift to higher covariation in trap-jaw forms, while different traits show both increased and decreased evolutionary rates between forms. These patterns may be indicative of many-to-one mapping and/or mechanical sensitivity in the trap-jaw LaMSA system. Overall, it appears that the evolution of trap-jaw forms in Strumigenys did not require a correlated increase in morphological covariation, partly explaining the proclivity with which the system has evolved.

A simple hierarchical model for heterogeneity in the evolutionary correlation on a phylogenetic tree

Numerous questions in phylogenetic comparative biology revolve around the correlated evolution of two or more phenotypic traits on a phylogeny. In many cases, it may be sufficient to assume a constant value for the evolutionary correlation between characters across all the clades and branches of the tree. Under other circumstances, however, it is desirable or necessary to account for the possibility that the evolutionary correlation differs through time or in different sections of the phylogeny. Here, we present a method designed to fit a hierarchical series of models for heterogeneity in the evolutionary rates and correlation of two quantitative traits on a phylogenetic tree. We apply the method to two datasets: one for different attributes of the buccal morphology in sunfishes (Centrarchidae); and a second for overall body length and relative body depth in rock- and non-rock-dwelling South American iguanian lizards. We also examine the performance of the method for parameter estimation and model selection using a small set of numerical simulations.

The evolution of the traplining pollinator role in hummingbirds: specialization is not an evolutionary dead end

Trapliners are pollinators that visit widely dispersed flowers along circuitous foraging routes. The evolution of traplining in hummingbirds is thought to entail morphological specialization through the reciprocal coevolution of longer bills with the long-tubed flowers of widely dispersed plant species. Specialization, such as that exhibited by traplining hummingbirds, is often viewed as both irreversible and an evolutionary dead end. We tested these predictions in a macroevolutionary framework. Specifically, we assessed the relationship between beak morphology and foraging and tested whether transitions to traplining are irreversible and lead to lower rates of diversification as predicted by the hypothesis that specialization is an evolutionary dead end. We find that there have been multiple independent transitions to traplining across the hummingbird phylogeny, but reversals have been rare or incomplete at best. Multiple independent lineages of trapliners have become morphologically specialized, convergently evolving relatively large bills for their body size. Traplining is not an evolutionary dead end however, since trapliners continue to give rise to new traplining species at a rate comparable to non-trapliners.

Analyzing Disparity and Rates of Morphological Evolution with Model-Based Phylogenetic Comparative Methods

Understanding variation in rates of evolution and morphological disparity is a goal of macroevolutionary research. In a phylogenetic comparative methods framework, we present three explicit models for linking the rate of evolution of a trait to the state of another evolving trait. This allows testing hypotheses about causal influences on rates of phenotypic evolution with phylogenetic comparative data. We develop a statistical framework for fitting the models with generalized least-squares regression and use this to discuss issues and limitations in the study of rates of evolution more generally. We show that the power to detect effects on rates of evolution is low in that even strong causal effects are unlikely to explain more than a few percent of observed variance in disparity. We illustrate the models and issues by testing if rates of beak-shape evolution in birds are influenced by brain size, as may be predicted from a Baldwin effect in which presumptively more behaviorally flexible large-brained species generate more novel selection on themselves leading to higher rates of evolution. From an analysis of morphometric data for 645 species, we find evidence that both macro- and microevolution of the beak are faster in birds with larger brains, but with the caveat that there are no consistent effects of relative brain size.[Baldwin effect; beak shape; behavioral drive; bird; brain size; disparity; phylogenetic comparative method; rate of evolution.]

Parallel shape divergence between ecotypes of the limpet Nacella concinna along the Antarctic Peninsula: a new model species for parallel evolution?

Parallel phenotypic divergence is the independent differentiation between phenotypes of the same lineage or species occupying ecologically similar environments in different populations. We tested in the Antarctic limpet Nacella concinna the extent of parallel morphological divergence in littoral and sublittoral ecotypes throughout its distribution range. These ecotypes differ in morphological, behavioural and physiological characteristics. We studied the lateral and dorsal outlines of shells and the genetic variation of the mitochondrial gene Cytochrome Oxidase subunit I from both ecotypes in 17 sample sites along more than 2,000 km. The genetic data indicate that both ecotypes belong to a single evolutionary lineage. The magnitude and direction of phenotypic variation differ between ecotypes across sample sites; completely parallel ecotype-pairs (i.e., they diverge in the same magnitude and in the same direction) were detected in 84.85% of lateral and 65.15% in dorsal view comparisons. Besides, specific traits (relative shell height, position of shell apex, and elliptical/pear-shape outline variation) showed high parallelism. We observed weak morphological covariation between the two shape shell views, indicating that distinct evolutionary forces and environmental pressures could be acting on this limpet shell shape. Our results demonstrate there is a strong parallel morphological divergence pattern in N. concinna along its distribution, making this Antarctic species a suitable model for the study of different evolutionary forces shaping the shell evolution of this limpet.

Statistics of eigenvalue dispersion indices: Quantifying the magnitude of phenotypic integration

Analysis of trait covariation plays a pivotal role in the study of phenotypic evolution. The magnitude of covariation is often quantified with statistics based on dispersion of eigenvalues of a covariance or correlation matrix-eigenvalue dispersion indices. This study clarifies the statistical justifications of these statistics and elaborates on their sampling properties. The relative eigenvalue variance of a covariance matrix is known in the statistical literature a test statistic for sphericity, and thus is an appropriate measure of eccentricity of variation. The same of a correlation matrix is equal to the average squared correlation, which has a straightforward interpretation as a measure of integration. Here, expressions for the mean and variance of these statistics are analytically derived under multivariate normality, clarifying the effects of sample size N, number of variables p, and parameters on sampling bias and error. Simulations confirm that approximations involved are reasonably accurate with a moderate sample size (N ≥ 16-64). Importantly, sampling properties of these indices are not adversely affected by a high p:N ratio, promising their utility in high-dimensional phenotypic analyses. They can furthermore be applied to shape variables and phylogenetically structured data with appropriate modifications.

The evolution of siphonophore tentilla for specialized prey capture in the open ocean

Predatory specialization is often associated with the evolution of modifications in the morphology of the prey-capture apparatus. Specialization has been considered an evolutionary “dead end” due to the constraints associated with these morphological changes. However, in predators like siphonophores, armed with modular structures used exclusively for prey capture, this assumption is challenged. Our results show that siphonophores can evolve generalism and new prey-type specializations by modifying the morphological states, modes of evolution, and evolutionary correlations between the parts of their prey-capture apparatus. These findings demonstrate how studying open-ocean nonbilaterian predators can reveal novel patterns and mechanisms in the evolution of specialization. Understanding these evolutionary processes is fundamental to the study of food web structure and complexity.

Predator specialization has often been considered an evolutionary “dead end” due to the constraints associated with the evolution of morphological and functional optimizations throughout the organism. However, in some predators, these changes are localized in separate structures dedicated to prey capture. One of the most extreme cases of this modularity can be observed in siphonophores, a clade of pelagic colonial cnidarians that use tentilla (tentacle side branches armed with nematocysts) exclusively for prey capture. Here we study how siphonophore specialists and generalists evolve, and what morphological changes are associated with these transitions. To answer these questions, we: a) Measured 29 morphological characters of tentacles from 45 siphonophore species, b) mapped these data to a phylogenetic tree, and c) analyzed the evolutionary associations between morphological characters and prey-type data from the literature. Instead of a dead end, we found that siphonophore specialists can evolve into generalists, and that specialists on one prey type have directly evolved into specialists on other prey types. Our results show that siphonophore tentillum morphology has strong evolutionary associations with prey type, and suggest that shifts between prey types are linked to shifts in the morphology, mode of evolution, and evolutionary correlations of tentilla and their nematocysts. The evolutionary history of siphonophore specialization helps build a broader perspective on predatory niche diversification via morphological innovation and evolution. These findings contribute to understanding how specialization and morphological evolution have shaped present-day food webs.

Relaxed Random Walks at Scale

Relaxed random walk (RRW) models of trait evolution introduce branch-specific rate multipliers to modulate the variance of a standard Brownian diffusion process along a phylogeny and more accurately model overdispersed biological data. Increased taxonomic sampling challenges inference under RRWs as the number of unknown parameters grows with the number of taxa. To solve this problem, we present a scalable method to efficiently fit RRWs and infer this branch-specific variation in a Bayesian framework. We develop a Hamiltonian Monte Carlo (HMC) sampler to approximate the high-dimensional, correlated posterior that exploits a closed-form evaluation of the gradient of the trait data log-likelihood with respect to all branch-rate multipliers simultaneously. Our gradient calculation achieves computational complexity that scales only linearly with the number of taxa under study. We compare the efficiency of our HMC sampler to the previously standard univariable Metropolis-Hastings approach while studying the spatial emergence of the West Nile virus in North America in the early 2000s. Our method achieves at least a 6-fold speed increase over the univariable approach. Additionally, we demonstrate the scalability of our method by applying the RRW to study the correlation between five mammalian life history traits in a phylogenetic tree with $3650$ tips.[Bayesian inference; BEAST; Hamiltonian Monte Carlo; life history; phylodynamics, relaxed random walk.].

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.].

A Bayesian Approach for Inferring the Impact of a Discrete Character on Rates of Continuous-Character Evolution in the Presence of Background-Rate Variation

Understanding how and why rates of character evolution vary across the Tree of Life is central to many evolutionary questions; for example, does the trophic apparatus (a set of continuous characters) evolve at a higher rate in fish lineages that dwell in reef versus nonreef habitats (a discrete character)? Existing approaches for inferring the relationship between a discrete character and rates of continuous-character evolution rely on comparing a null model (in which rates of continuous-character evolution are constant across lineages) to an alternative model (in which rates of continuous-character evolution depend on the state of the discrete character under consideration). However, these approaches are susceptible to a "straw-man" effect: the influence of the discrete character is inflated because the null model is extremely unrealistic. Here, we describe MuSSCRat, a Bayesian approach for inferring the impact of a discrete trait on rates of continuous-character evolution in the presence of alternative sources of rate variation ("background-rate variation"). We demonstrate by simulation that our method is able to reliably infer the degree of state-dependent rate variation, and show that ignoring background-rate variation leads to biased inferences regarding the degree of state-dependent rate variation in grunts (the fish group Haemulidae). [Bayesian phylogenetic comparative methods; continuous-character evolution; data augmentation; discrete-character evolution.].

Comparative Analyses of Phenotypic Sequences Using Phylogenetic Trees

Phenotypic sequences are a type of multivariate trait organized structurally, such as teeth distributed along the dental arch, or temporally, such as the stages of an ontogenetic series. Unlike other multivariate traits, the elements of a phenotypic sequence are distributed along an ordered set, which allows for distinct evolutionary patterns between neighboring and distant positions. In fact, sequence traits share many characteristics with molecular sequences, although important distinctions pose challenges to current comparative methods. We implement an approach to estimate rates of trait evolution that explicitly incorporates the sequence organization of traits. We apply models to study the temporal pattern evolution of cricket calling songs. We test whether neighboring positions along a phenotypic sequence have correlated rates of evolution or whether rate variation is independent of sequence position. Our results show that cricket song evolution is strongly autocorrelated and that models perform well when used with sequence phenotypes even under small sample sizes. Our approach is flexible and can be applied to any multivariate trait with discrete units organized in a sequence-like structure.

Detecting Mosaic Patterns in Macroevolutionary Disparity

Evolutionary biologists have long sought to understand the full complexity in pattern and process that shapes organismal diversity. Although phylogenetic comparative methods are often used to reconstruct complex evolutionary dynamics, they are typically limited to a single phenotypic trait. Extensions that accommodate multiple traits lack the ability to partition multidimensional data sets into a set of mosaic suites of evolutionarily linked characters. I introduce a comparative framework that identifies heterogeneity in evolutionary patterns across large data sets of continuous traits. Using a model of continuous trait evolution based on the differential accumulation of disparity across lineages in a phylogeny, the approach algorithmically partitions traits into a set of character suites that best explains the data, where each suite displays a distinct pattern in phylogenetic morphological disparity. When applied to empirical data, the approach revealed a mosaic pattern predicted by developmental biology. The evolutionary distinctiveness of individual suites can be investigated in more detail either by fitting conventional comparative models or by directly studying the phylogenetic patterns in disparity recovered during the analysis. This framework can supplement existing comparative approaches by inferring the complex, integrated patterns that shape evolution across the body plan from disparate developmental, morphometric, and environmental sources of phenotypic data.

A Bayesian extension of phylogenetic generalized least squares: Incorporating uncertainty in the comparative study of trait relationships and evolutionary rates

Phylogenetic comparative methods use tree topology, branch lengths, and models of phenotypic change to take into account nonindependence in statistical analysis. However, these methods normally assume that trees and models are known without error. Approaches relying on evolutionary regimes also assume specific distributions of character states across a tree, which often result from ancestral state reconstructions that are subject to uncertainty. Several methods have been proposed to deal with some of these sources of uncertainty, but approaches accounting for all of them are less common. Here, we show how Bayesian statistics facilitates this task while relaxing the homogeneous rate assumption of the well-known phylogenetic generalized least squares (PGLS) framework. This Bayesian formulation allows uncertainty about phylogeny, evolutionary regimes, or other statistical parameters to be taken into account for studies as simple as testing for coevolution in two traits or as complex as testing whether bursts of phenotypic change are associated with evolutionary shifts in intertrait correlations. A mixture of validation approaches indicates that the approach has good inferential properties and predictive performance. We provide suggestions for implementation and show its usefulness by exploring the coevolution of ankle posture and forefoot proportions in Carnivora.

Beyond Brownian Motion and the Ornstein-Uhlenbeck Process: Stochastic Diffusion Models for the Evolution of Quantitative Characters

Gaussian processes, such as Brownian motion and the Ornstein-Uhlenbeck process, have been popular models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. However, they have drawbacks that limit their utility. Here we describe new, non-Gaussian stochastic differential equation (diffusion) models of quantitative trait evolution. We present general methods for deriving new diffusion models and develop new software for fitting non-Gaussian evolutionary models to trait data. The theory of stochastic processes provides a mathematical framework for understanding the properties of current and future phylogenetic comparative methods. Attention to the mathematical details of models of trait evolution and diversification may help avoid some pitfalls when using stochastic processes to model macroevolution.

Phylogenetic Comparative Methods and the Evolution of Multivariate Phenotypes

Evolutionary biology is multivariate, and advances in phylogenetic comparative methods for multivariate phenotypes have surged to accommodate this fact. Evolutionary trends in multivariate phenotypes are derived from distances and directions between species in a multivariate phenotype space. For these patterns to be interpretable, phenotypes should be characterized by traits in commensurate units and scale. Visualizing such trends, as is achieved with phylomorphospaces, should continue to play a prominent role in macroevolutionary analyses. Evaluating phylogenetic generalized least squares (PGLS) models (e.g., phylogenetic analysis of variance and regression) is valuable, but using parametric procedures is limited to only a few phenotypic variables. In contrast, nonparametric, permutation-based PGLS methods provide a flexible alternative and are thus preferred for high-dimensional multivariate phenotypes. Permutation-based methods for evaluating covariation within multivariate phenotypes are also well established and can test evolutionary trends in phenotypic integration. However, comparing evolutionary rates and modes in multivariate phenotypes remains an important area of future development.

Physiological evolution during adaptive radiation: A test of the island effect in Anolis lizards

Phenotypic evolution is often exceptionally rapid on islands, resulting in numerous, ecologically diverse species. Although adaptive radiation proceeds along various phenotypic axes, the island effect of faster evolution has been mostly tested with regard to morphology. Here, we leveraged the physiological diversity and species richness of Anolis lizards to examine the evolutionary dynamics of three key traits: heat tolerance, body temperature, and cold tolerance. Contrary to expectation, we discovered slower heat tolerance evolution on islands. Additionally, island species evolve toward higher optimal body temperatures than mainland species. Higher optima and slower evolution in upper physiological limits are consistent with the Bogert effect, or evolutionary inertia due to thermoregulation. Correspondingly, body temperature is higher and more stable on islands than on the American mainland, despite similarity in thermal environments. Greater thermoregulation on islands may occur due to ecological release from competitors and predators compared to mainland environments. By reducing the costs of thermoregulation, ecological opportunity on islands may actually stymie, rather than hasten, physiological evolution. Our results emphasize that physiological diversity is an important axis of ecological differentiation in the adaptive radiation of anoles, and that behavior can impart distinct macroevolutionary footprints on physiological diversity on islands and continents.

Terrestriality constrains salamander limb diversification: Implications for the evolution of pentadactyly

Patterns of phenotypic evolution can abruptly shift as species move between adaptive zones. Extant salamanders display three distinct life cycle strategies that range from aquatic to terrestrial (biphasic), to fully aquatic (paedomorphic) and to fully terrestrial (direct development). Life cycle variation is associated with changes in body form such as loss of digits, limb reduction or body elongation. However, the relationships among these traits and life cycle strategy remain unresolved. Here, we use a Bayesian modelling approach to test whether life cycle transitions by salamanders have influenced rates, optima and integration of primary locomotory structures (limbs and trunk). We show that paedomorphic salamanders have elevated rates of limb evolution with optima shifted towards smaller size and fewer digits compared to all other salamanders. Rate of hindlimb digit evolution is shown to decrease in a gradient as life cycles become more terrestrial. Paedomorphs have a higher correlation between hindlimb digit loss and increases in vertebral number, as well as reduced correlations between limb lengths. Our results support the idea that terrestrial plantigrade locomotion constrains limb evolution and, when lifted, leads to higher rates of trait diversification and shifts in optima and integration. The basic tetrapod body form of most salamanders and the independent losses of terrestrial life stages provide an important framework for understanding the evolutionary and developmental mechanisms behind major shifts in ecological zones as seen among early tetrapods during their transition from water to land.