BBMV: an R package for the estimation of macroevolutionary landscapes

The distribution of traits along phylogenies bears signatures of how ecological and evolutionary processes have interacted to influence phenotypic evolution, which can be deciphered using macroevolutionary models. BBMV implements a model for the evolution of continuous characters on phylogenies that generalizes existing ones, like Brownian motion and the Ornstein‐Uhlenbeck model. In this model quantitative characters evolve under both random diffusion and a deterministic force that can be of any possible shape and strength. The model can be used to infer evolutionary scenarios that remained inaccessible so far, like directional trends, disruptive selection, and even bounded evolution. With this new tool at hand, researchers will be able to test complex hypothesis‐driven scenarios regarding trait evolution, but they will also have the possibility to estimate the shape of the adaptive landscapes in which traits evolved. Ultimately, this will provide a way to infer how ecological processes have influenced phenotypic evolution over long timescales. The BBMV package is implemented in the R statistical language and is freely available on the CRAN repository < https://CRAN.R‐project.org/package=BBMV >. All source code can also be found on < https://github.com/fcboucher/BBMV >, along with a detailed tutorial.     

Adaptive evolution of reproductive and vegetative traits driven by breeding systems

The evolution of inflorescence size, a key trait in reproductive success, was studied in the genus Acer under a perspective of adaptive evolution. Breeding systems, hypothesized to indicate different levels of mating competition, were considered as the selective scenarios defining different optima of inflorescence size. Larger inflorescences, which increase male fitness by generating larger floral displays, were hypothesized to be selected under scenarios with higher competition with unisexuals. An identical approach was used to test if the same selective regimes could be driving the evolution of leaf size, a vegetative trait that was found to be correlated with inflorescence size. A Brownian motion model of inflorescence/leaf-size evolution (which cannot distinguish between changes caused by pure drift processes and changes caused by natural selection in rapidly and randomly changing environments) was compared with several adaptive Ornstein-Uhlenbeck (OU) models, which can quantify the effects of both stochasticity and natural selection. The best-fitting model for inflorescence/leaf-size evolution was an OU model with three optima that increased with the level of mating competition. Both traits evolved under the same selective regimes and in the same direction, confirming a pattern of correlated evolution. These results show that a selective regime hypothetically related to the evolution of a reproductive trait can also explain the evolution of a vegetative trait.     

Diversifying selection drives parallel evolution of gill raker number and body size along the speciation continuum of European whitefish

Adaptive radiation is the evolution of ecological and phenotypical diversity. It arises via ecological opportunity that promotes the exploration of underutilized or novel niches mediating specialization and reproductive isolation. The assumed precondition for rapid local adaptation is diversifying natural selection, but random genetic drift could also be a major driver of this process. We used 27 populations of European whitefish (Coregonus lavaretus) from nine lakes distributed in three neighboring subarctic watercourses in northern Fennoscandia as a model to test the importance of random drift versus diversifying natural selection for parallel evolution of adaptive phenotypic traits. We contrasted variation for two key adaptive phenotypic traits correlated with resource utilization of polymorphic fish; the number of gill rakers and the total length of fish, with the posterior distribution of neutral genetic differentiation from 13 microsatellite loci, to test whether the observed phenotypic divergence could be achieved by random genetic drift alone. Our results show that both traits have been under diversifying selection and that the evolution of these morphs has been driven by isolation through habitat adaptations. We conclude that diversifying selection acting on gill raker number and body size has played a significant role in the ongoing adaptive radiation of European whitefish morphs in this region.     

Assessment of the relative merits of a few methods to detect evolutionary trends

Some of the most basic questions about the history of life concern evolutionary trends. These include determining whether or not metazoans have become more complex over time, whether or not body size tends to increase over time (the Cope-Depéret rule), or whether or not brain size has increased over time in various taxa, such as mammals and birds. Despite the proliferation of studies on such topics, assessment of the reliability of results in this field is hampered by the variability of techniques used and the lack of statistical validation of these methods. To solve this problem, simulations are performed using a variety of evolutionary models (gradual Brownian motion, speciational Brownian motion, and Ornstein-Uhlenbeck), with or without a drift of variable amplitude, with variable variance of tips, and with bounds placed close or far from the starting values and final means of simulated characters. These are used to assess the relative merits (power, Type I error rate, bias, and mean absolute value of error on slope estimate) of several statistical methods that have recently been used to assess the presence of evolutionary trends in comparative data. Results show widely divergent performance of the methods. The simple, nonphylogenetic regression (SR) and variance partitioning using phylogenetic eigenvector regression (PVR) with a broken stick selection procedure have greatly inflated Type I error rate (0.123-0.180 at a 0.05 threshold), which invalidates their use in this context. However, they have the greatest power. Most variants of Felsenstein's independent contrasts (FIC; five of which are presented) have adequate Type I error rate, although two have a slightly inflated Type I error rate with at least one of the two reference trees (0.064-0.090 error rate at a 0.05 threshold). The power of all contrast-based methods is always much lower than that of SR and PVR, except under Brownian motion with a strong trend and distant bounds. Mean absolute value of error on slope of all FIC methods is slightly higher than that of phylogenetic generalized least squares (PGLS), SR, and PVR. PGLS performs well, with low Type I error rate, low error on regression coefficient, and power comparable with some FIC methods. Four variants of skewness analysis are examined, and a new method to assess significance of results is presented. However, all have consistently low power, except in rare combinations of trees, trend strength, and distance between final means and bounds. Globally, the results clearly show that FIC-based methods and PGLS are globally better than nonphylogenetic methods and variance partitioning with PVR. FIC methods and PGLS are sensitive to the model of evolution (and, hence, to branch length errors). Our results suggest that regressing raw character contrasts against raw geological age contrasts yields a good combination of power and Type I error rate. New software to facilitate batch analysis is presented.     

MODELING STABILIZING SELECTION: EXPANDING THE ORNSTEIN-UHLENBECK MODEL OF ADAPTIVE EVOLUTION

Comparative methods used to study patterns of evolutionary change in a continuous trait on a phylogeny range from Brownian motion processes to models where the trait is assumed to evolve according to an Ornstein-Uhlenbeck (OU) process. Although these models have proved useful in a variety of contexts, they still do not cover all the scenarios biologists want to examine. For models based on the OU process, model complexity is restricted in current implementations by assuming that the rate of stochastic motion and the strength of selection do not vary among selective regimes. Here, we expand the OU model of adaptive evolution to include models that variously relax the assumption of a constant rate and strength of selection. In its most general form, the methods described here can assign each selective regime a separate trait optimum, a rate of stochastic motion parameter, and a parameter for the strength of selection. We use simulations to show that our models can detect meaningful differences in the evolutionary process, especially with larger sample sizes. We also illustrate our method using an empirical example of genome size evolution within a large flowering plant clade.     

Relative embryo length as an adaptation to habitat and life cycle in Apiaceae

? The factors driving the evolution of the relative embryo length in Apiaceae were examined. We tested the hypothesis that seeds with large relative embryo length, because of more rapid germination, are beneficial in dry and open habitats and for short-lived species. We also analyzed to what extent delayed germination as a result of embryo growth can be considered a dormancy mechanism. ? Hypotheses were tested by correlating the relative embryo length with other plant traits, habitat and climatic variables. The adaptive nature of the relative embryo length was determined by comparing the performance of a pure drift, Brownian motion (BM) model of trait evolution with that of a selection-inertia, Ornstein-Uhlenbeck (OU) model. ? A positive correlation of the relative embryo length with germination speed and negative correlations with the amount of habitat shade, longevity and precipitation were found. An OU model, in which the evolution of longer embryos corresponded to a transition to habitats of high light, or to a short life cycle, outperformed significantly a BM model. ? The results indicated that the relative embryo length may have evolved as an adaptation to habitat and life cycle, whereas dormancy was mainly related to temperature at the sampling sites.     

Spatial processes and evolutionary models: a critical review

Evolution is a fundamentally population level process in which variation, drift and selection produce both temporal and spatial patterns of change. Statistical model fitting is now commonly used to estimate which kind of evolutionary process best explains patterns of change through time using models like Brownian motion, stabilizing selection (Ornstein–Uhlenbeck) and directional selection on traits measured from stratigraphic sequences or on phylogenetic trees. But these models assume that the traits possessed by a species are homogeneous. Spatial processes such as dispersal, gene flow and geographical range changes can produce patterns of trait evolution that do not fit the expectations of standard models, even when evolution at the local‐population level is governed by drift or a typical OU model of selection. The basic properties of population level processes (variation, drift, selection and population size) are reviewed and the relationship between their spatial and temporal dynamics is discussed. Typical evolutionary models used in palaeontology incorporate the temporal component of these dynamics, but not the spatial. Range expansions and contractions introduce rate variability into drift processes, range expansion under a drift model can drive directional change in trait evolution, and spatial selection gradients can create spatial variation in traits that can produce long‐term directional trends and punctuation events depending on the balance between selection strength, gene flow, extirpation probability and model of speciation. Using computational modelling that spatial processes can create evolutionary outcomes that depart from basic population‐level notions from these standard macroevolutionary models.     

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.     

High evolutionary constraints limited adaptive responses to past climate changes in toad skulls

Interactions among traits that build a complex structure may be represented as genetic covariation and correlation. Genetic correlations may act as constraints, deflecting the evolutionary response from the direction of natural selection. We investigated the relative importance of drift, selection, and constraints in driving skull divergence in a group of related toad species. The distributional range of these species encompasses very distinct habitats with important climatic differences and the species are primarily distinguished by differences in their skulls. Some parts of the toad skull, such as the snout, may have functional relevance in reproductive ecology, detecting water cues. Thus, we hypothesized that the species skull divergence was driven by natural selection associated with climatic variation. However, given that all species present high correlations among skull traits, our second prediction was of high constraints deflecting the response to selection. We first extracted the main morphological direction that is expected to be subjected to selection by using within- and between-species covariance matrices. We then used evolutionary regressions to investigate whether divergence along this direction is explained by climatic variation between species. We also used quantitative genetics models to test for a role of random drift versus natural selection in skull divergence and to reconstruct selection gradients along species phylogeny. Climatic variables explained high proportions of between-species variation in the most selected axis. However, most evolutionary responses were not in the direction of selection, but aligned with the direction of allometric size, the dimension of highest phenotypic variance in the ancestral population. We conclude that toad species have responded to selection related to climate in their skulls, yet high evolutionary constraints dominated species divergence and may limit species responses to future climate change.     

Free fitness that always increases in evolution

I here introduce a free fitness function in population biology, which monotonically increases with time and takes its maximum at the evolutionary equilibrium. By suitably defining an "index" for each state, the free fitness is expressed as the average index plus an entropy term. In many cases, the index has a biologically clear meaning, such as the logarithmic population mean fitness. The technique is applicable to any Markov process model (either continuous or discrete) with a positive steady state. I discuss four examples from various branches of population biology: (1) one-locus-two-allele system of population genetics with mutation, selection, and random genetic drift; (2) evolutionary dynamics of quantitative characters; (3) a molecular evolution model; and (4) an ecological succession model. Introducing free fitness clarifies the balance between systematic forces (e.g. natural selection or successional trend toward the climax) and disturbing processes (e.g. random drift).     

Is convergence surprising? An examination of the frequency of convergence in simulated datasets

Although convergence is recognized as a central concept in evolutionary biology, very few tools are available for the quantitative study of this phenomenon. Moreover, although many evolutionary assertions assume that convergence should be rare in the absence of influences on organismal phenotypes such as natural selection or constraint, no studies have tested whether this is the case. I simulate random evolution (Brownian motion model) of quantitative characters along phylogenies with varying numbers of terminal taxa, numbers of traits, variance structure, and tree balance, and quantify the amount of convergence observed in these datasets using four metrics. The amount of convergence observed in a dataset increases with increasing number of taxa and decreasing number of traits, approaching the maximum possible amount of convergence under certain circumstances. Some convergence is expected in almost all datasets. Comparison of empirical datasets to those produced by random evolution provides a test of whether empirical datasets actually show elevated levels of convergence. Out of three test datasets, two show more convergence than expected. Given that high levels of convergence can be produced simply by random evolution, no explanation may be necessary for instances of convergence discovered in an evolutionary investigation.     

Selection in a cycling population: differential response among skeletal traits

Abstract Population density cycles influence phenotypic evolution through both density‐dependent selection during periods of high density and through enhanced genetic drift during periods of low density. We investigated the response of different phenotypic traits to the same density cycles in a population of the yellow‐necked mouse, Apodemus flavicollis, from Bia?owieza National Park in Poland. We examined nonmetric skull traits, skull and mandible size, skull and mandible shape, and transferrin allele frequencies. We found that all of the traits changed significantly over the seven‐year study period. The greatest changes in nonmetric traits and mandible size occurred during periods of increasing density, and the magnitude of changes in skull and mandible shape was correlated with the magnitude of density changes. Frequencies of transferrin alleles changed the most when population density was in decline. Changes among the five phenotypic traits were generally uncorrelated with one another, except for skull and mandible shape. Nonmetric traits were selectively neutral when assessed with Q_ST/F_ST analysis, whereas mandible size, mandible shape, and skull shape showed evidence of fairly strong selection. Selection on skull size was weak or nonexistent. We discuss how different assumptions about the genetic components of variance affect Q_ST estimates when phenotypic variances are substituted for genetic ones. We also found that change in mandible size, mandible shape, skull size, and skull shape were greater than expected under a neutral model given reasonable assumptions about heritability and effective population size.     

Pervasive genetic integration directs the evolution of human skull shape

It has long been unclear whether the different derived cranial traits of modern humans evolved independently in response to separate selection pressures or whether they resulted from the inherent morphological integration throughout the skull. In a novel approach to this issue, we combine evolutionary quantitative genetics and geometric morphometrics to analyze genetic and phenotypic integration in human skull shape. We measured human skulls in the ossuary of Hallstatt (Austria), which offer a unique opportunity because they are associated with genealogical data. Our results indicate pronounced covariation of traits throughout the skull. Separate simulations of selection for localized shape changes corresponding to some of the principal derived characters of modern human skulls produced outcomes that were similar to each other and involved a joint response in all of these traits. The data for both genetic and phenotypic shape variation were not consistent with the hypothesis that the face, cranial base, and cranial vault are completely independent modules but relatively strongly integrated structures. These results indicate pervasive integration in the human skull and suggest a reinterpretation of the selective scenario for human evolution where the origin of any one of the derived characters may have facilitated the evolution of the others.     

A phylogenetic model for investigating correlated evolution of substitution rates and continuous phenotypic characters

The comparative approach is routinely used to test for possible correlations between phenotypic or life-history traits. To correct for phylogenetic inertia, the method of independent contrasts assumes that continuous characters evolve along the phylogeny according to a multivariate Brownian process. Brownian diffusion processes have also been used to describe time variations of the parameters of the substitution process, such as the rate of substitution or the ratio of synonymous to nonsynonymous substitutions. Here, we develop a probabilistic framework for testing the coupling between continuous characters and parameters of the molecular substitution process. Rates of substitution and continuous characters are jointly modeled as a multivariate Brownian diffusion process of unknown covariance matrix. The covariance matrix, the divergence times and the phylogenetic variations of substitution rates and continuous characters are all jointly estimated in a Bayesian Monte Carlo framework, imposing on the covariance matrix a prior conjugate to the Brownian process so as to achieve a greater computational efficiency. The coupling between rates and phenotypes is assessed by measuring the posterior probability of positive or negative covariances, whereas divergence dates and phenotypic variations are marginally reconstructed in the context of the joint analysis. As an illustration, we apply the model to a set of 410 mammalian cytochrome b sequences. We observe a negative correlation between the rate of substitution and mass and longevity, which was previously observed. We also find a positive correlation between ω = dN/dS and mass and longevity, which we interpret as an indirect effect of variations of effective population size, thus in partial agreement with the nearly neutral theory. The method can easily be extended to any parameter of the substitution process and to any continuous phenotypic or environmental character.     

Craniofacial form and function in Metriorhynchidae (Crocodylomorpha: Thalattosuchia): modelling phenotypic evolution with maximum-likelihood methods

Metriorhynchid crocodylomorphs were the only group of archosaurs to fully adapt to a pelagic lifestyle. During the Jurassic and Early Cretaceous, this group diversified into a variety of ecological and morphological types, from large super-predators with a broad short snout and serrated teeth to specialized piscivores/teuthophages with an elongate tubular snout and uncarinated teeth. Here, we use an integrated repertoire of geometric morphometric (form), biomechanical finite-element analysis (FEA; function) and phylogenetic data to examine the nature of craniofacial evolution in this clade. FEA stress values significantly correlate with morphometric values representing skull length and breadth, indicating that form and function are associated. Maximum-likelihood methods, which assess which of several models of evolution best explain the distribution of form and function data on a phylogenetic tree, show that the two major metriorhynchid subclades underwent different evolutionary modes. In geosaurines, both form and function are best explained as evolving under 'random' Brownian motion, whereas in metriorhynchines, the form metrics are best explained as evolving under stasis and the function metric as undergoing a directional change (towards most efficient low-stress piscivory). This suggests that the two subclades were under different selection pressures, and that metriorhynchines with similar skull shape were driven to become functionally divergent.     

Selectionism and neutralism in molecular evolution

Charles Darwin proposed that evolution occurs primarily by natural selection, but this view has been controversial from the beginning. Two of the major opposing views have been mutationism and neutralism. Early molecular studies suggested that most amino acid substitutions in proteins are neutral or nearly neutral and the functional change of proteins occurs by a few key amino acid substitutions. This suggestion generated an intense controversy over selectionism and neutralism. This controversy is partially caused by Kimura's definition of neutrality, which was too strict (|2Ns|< or =1). If we define neutral mutations as the mutations that do not change the function of gene products appreciably, many controversies disappear because slightly deleterious and slightly advantageous mutations are engulfed by neutral mutations. The ratio of the rate of nonsynonymous nucleotide substitution to that of synonymous substitution is a useful quantity to study positive Darwinian selection operating at highly variable genetic loci, but it does not necessarily detect adaptively important codons. Previously, multigene families were thought to evolve following the model of concerted evolution, but new evidence indicates that most of them evolve by a birth-and-death process of duplicate genes. It is now clear that most phenotypic characters or genetic systems such as the adaptive immune system in vertebrates are controlled by the interaction of a number of multigene families, which are often evolutionarily related and are subject to birth-and-death evolution. Therefore, it is important to study the mechanisms of gene family interaction for understanding phenotypic evolution. Because gene duplication occurs more or less at random, phenotypic evolution contains some fortuitous elements, though the environmental factors also play an important role. The randomness of phenotypic evolution is qualitatively different from allele frequency changes by random genetic drift. However, there is some similarity between phenotypic and molecular evolution with respect to functional or environmental constraints and evolutionary rate. It appears that mutation (including gene duplication and other DNA changes) is the driving force of evolution at both the genic and the phenotypic levels.     

Evolution of the climatic niche in scaly tree ferns (Cyatheaceae,Polypodiopsida)

Although climatic niche conservatism has been assumed by a large number of studies focused on climatic niche evolution, there are examples of climatic niche diversification and adaptation to changing climates. In this article, we reconstruct a climatic niche of scaly tree ferns (Cyatheaceae) using a rigorous analytical procedure which combines climatic niche modelling with reconstruction of continuous characters given a phylogenetic hypothesis. To estimate the limits to climatic niches of species, we used climate envelope modelling and ordination. Ancestral climatic niches of species were reconstructed by maximum likelihood and least‐squares analyses. We observed a trend towards niche conservatism with occasional events of niche transformations in scaly tree ferns. We discuss the implications of our study with respect to the potential and limitations for applications of niche modelling to evolutionary studies. We suggest that future studies of evolution of climatic niches could be considerably improved by employing approaches enabling reconstruction of continuous response to climatic gradients. Further progress may also be achieved by exploring models of character evolution other than the Brownian motion model. © 2010 The Linnean Society of London, Botanical Journal of the Linnean Society, 2011, 165 , 1–19.     

Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales

We tested the ability of six quantitative genetic models to explain the evolution of phenotypic means using an extensive database compiled by Gingerich. Our approach differs from past efforts in that we use explicit models of evolutionary process, with parameters estimated from contemporary populations, to analyze a large sample of divergence data on many different timescales. We show that one quantitative genetic model yields a good fit to data on phenotypic divergence across timescales ranging from a few generations to 10 million generations. The key feature of this model is a fitness optimum that moves within fixed limits. Conversely, a model of neutral evolution, models with a stationary optimum that undergoes Brownian or white noise motion, a model with a moving optimum, and a peak shift model all fail to account for the data on most or all timescales. We discuss our results within the framework of Simpson's concept of adaptive landscapes and zones. Our analysis suggests that the underlying process causing phenotypic stasis is adaptation to an optimum that moves within an adaptive zone with stable boundaries. We discuss the implication of our results for comparative studies and phylogeny inference based on phenotypic characters.     

How many processes are responsible for phenotypic evolution?

SUMMARY In addressing phenotypic evolution, this article reconsiders natural selection, random drift, developmental constraints, and internal selection in the new extended context of evolutionary developmental biology. The change of perspective from the "evolution of phenotypes" toward an "evolution of ontogenies" (evo-devo perspective) affects the reciprocal relationships among these different processes. Random drift and natural selection are sibling processes: two forms of post-productional sorting among alternative developmental trajectories, the former random, the latter nonrandom. Developmental constraint is a compound concept; it contains even some forms of natural ("external" and "internal") selection. A narrower definition ("reproductive constraints") is proposed. Internal selection is not a selection caused by an internal agent. It is a form of environment-independent selection depending on the level of the organism's internal developmental or functional coordination. Selection and constraints are the main deterministic processes in phenotypic evolution but they are not opposing forces. Indeed, they are continuously interacting processes of evolutionary change, but with different roles that should not be confused.     

The complex effects of mass extinctions on morphological disparity

Studies of biodiversity through deep time have been a staple for biologists and paleontologists for over 60 years. Investigations of species richness (diversity) revealed that at least five mass extinctions punctuated the last half billion years, each seeing the rapid demise of a large proportion of contemporary taxa. In contrast to diversity, the response of morphological diversity (disparity) to mass extinctions is unclear. Generally, diversity and disparity are decoupled, such that diversity may decline as morphological disparity increases, and vice versa. Here, we develop simulations to model disparity changes across mass extinctions using continuous traits and birth-death trees. We find no simple null for disparity change following a mass extinction but do observe general patterns. The range of trait values decreases following either random or trait-selective mass extinctions, whereas variance and the density of morphospace occupation only decline following trait-selective events. General trends may differentiate random and trait-selective mass extinctions, but methods struggle to identify trait selectivity. Long-term effects of mass extinction trait selectivity change support for phylogenetic comparative methods away from the simulated Brownian motion toward Ornstein-Uhlenbeck and Early Burst models. We find that morphological change over mass extinction is best studied by quantifying multiple aspects of morphospace occupation.