Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium‐term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time‐steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.     

Evolution and maintenance of the environmental component of the phenotypic variance: benefit of plastic traits under changing environments

How environmental variances in quantitative traits are influenced by variable environments is an important problem in evolutionary biology. In this study, the evolution and maintenance of phenotypic variance in a plastic trait under stabilizing selection are investigated. The mapping from genotypic value to phenotypic value of the quantitative trait is approximated by a linear reaction norm, with genotypic effects on its phenotypic mean and sensitivity to environment. The environmental deviation is assumed to be decomposed into environmental quality, which interacts with genotypic value, and residual developmental noise, which is independent of genotype. Environmental quality and the optimal phenotype of stabilizing selection are allowed to randomly fluctuate in both space and time, and individuals migrate equally before development and reproduction among different niches. Analyses show that phenotypic plasticity is adaptive within variable environments if correlations have become established between the optimal phenotype and environmental quality in space and/or time. The evolved plasticity increases with variances in optimal phenotypes and correlations between optimal phenotype and environmental quality; this further induces increases in mean fitness and the environmental variance in the trait. Under certain circumstances, however, the environmental variance may decrease with increase in variation in environmental quality.     

Genetic constraints on wing pattern variation in Lycaeides butterflies: A case study on mapping complex,multifaceted traits in structured populations

Patterns of phenotypic variation within and among species can be shaped and constrained by trait genetic architecture. This is particularly true for complex traits, such as butterfly wing patterns, that consist of multiple elements. Understanding the genetics of complex trait variation across species boundaries is difficult, as it necessitates mapping in structured populations and can involve many loci with small or variable phenotypic effects. Here, we investigate the genetic architecture of complex wing pattern variation in Lycaeides butterflies as a case study of mapping multivariate traits in wild populations that include multiple nominal species or groups. We identify conserved modules of integrated wing pattern elements within populations and species. We show that trait covariances within modules have a genetic basis and thus represent genetic constraints that can channel evolution. Consistent with this, we find evidence that evolutionary changes in wing patterns among populations and species occur in the directions of genetic covariances within these groups. Thus, we show that genetic constraints affect patterns of biological diversity (wing pattern) in Lycaeides, and we provide an analytical template for similar work in other systems.     

Fly wing evolution explained by a neutral model with mutational pleiotropy

To what extent the speed of mutational production of phenotypic variation determines the rate of long-term phenotypic evolution is a central question. Houle et al. recently addressed this question by studying the mutational variances, additive genetic variances, and macroevolution of locations of vein intersections on fly wings, reporting very slow phenotypic evolution relative to the rates of mutational input, high phylogenetic signals, and a strong, linear relationship between the mutational variance of a trait and its rate of evolution. Houle et al. found no existing model of phenotypic evolution to be consistent with all these observations, and proposed the improbable scenario of equal influence of mutational pleiotropy on all traits. Here, we demonstrate that the purported linear relationship between mutational variance and evolutionary divergence is artifactual. We further show that the data are explainable by a simple model in which the wing traits are effectively neutral at least within a range of phenotypic values but their evolutionary rates are differentially reduced because mutations affecting these traits are purged owing to their different pleiotropic effects on other traits that are under stabilizing selection. Thus, the evolutionary patterns of fly wing morphologies are explainable under the existing theoretical framework of phenotypic evolution.     

Genetic analysis of life-history constraint and evolution in a wild ungulate population

Trade-offs among life-history traits are central to evolutionary theory. In quantitative genetic terms, trade-offs may be manifested as negative genetic covariances relative to the direction of selection on phenotypic traits. Although the expression and selection of ecologically important phenotypic variation are fundamentally multivariate phenomena, the in situ quantification of genetic covariances is challenging. Even for life-history traits, where well-developed theory exists with which to relate phenotypic variation to fitness variation, little evidence exists from in situ studies that negative genetic covariances are an important aspect of the genetic architecture of life-history traits. In fact, the majority of reported estimates of genetic covariances among life-history traits are positive. Here we apply theory of the genetics and selection of life histories in organisms with complex life cycles to provide a framework for quantifying the contribution of multivariate genetically based relationships among traits to evolutionary constraint. We use a Bayesian framework to link pedigree-based inference of the genetic basis of variation in life-history traits to evolutionary demography theory regarding how life histories are selected. Our results suggest that genetic covariances may be acting to constrain the evolution of female life-history traits in a wild population of red deer Cervus elaphus: genetic covariances are estimated to reduce the rate of adaptation by about 40%, relative to predicted evolutionary change in the absence of genetic covariances. Furthermore, multivariate phenotypic (rather than genetic) relationships among female life-history traits do not reveal this constraint.     

Bottleneck Effects on Genetic Variance for Courtship Repertoire

Bottleneck effects on evolutionary potential in mating behavior were addressed through assays of additive genetic variances and resulting phenotypic responses to drift in the courtship repertoires of six two-pair founder-flush lines and two control populations of the housefly. A simulation addressed the complication that an estimate of the genetic variance for a courtship trait (e.g., male performance vigor or the female requirement for copulation) must involve assays against the background behavior of the mating partners. The additive ``environmental' effect of the mating partner's phenotype simply dilutes the net parent-offspring covariance for a trait. However, if there is an interaction with this ``environmental' component, negative parent-offspring covariances can result under conditions of high incompatibility between the population's distributions for male performance and female choice requirements, despite high levels of genetic variance. All six bottlenecked lines exhibited significant differentiation from the controls in at least one measure of the parent-offspring covariance for male performance or female choice (estimated by 50 parent-son and 50 parent-daughter covariances for 10 courtship traits per line) which translated to significant phenotypic drift. However, the average effect across traits or across lines did not yield a significant net increase in genetic variance due to bottlenecks. Concerted phenotypic differentiation due to the founder-flush event provided indirect evidence of directional dominance in a subset of traits. Furthermore, indirect evidence of genotype-environment interactions (potentially producing genotype-genotype effects) was found in the negative parent-offspring covariances predicted by the male-female interaction simulation and by the association of the magnitude of phenotypic drift with the absolute value of the parent-offspring covariance. Hence, nonadditive genetic effects on mating behavior may be important in structuring genetic variance for courtship, although most of the increases in genetic variance would be expected to reflect inbreeding depression with relatively rare situations representing the facilitation of speciation by bottlenecks.     

Testing evolutionary hypotheses about the phylotypic period of zebrafish

Vertebrate embryos pass through a period of morphological similarity, the phylotypic period. Since Haeckel's biogenetic law of recapitulation, proximate and ultimate evolutionary causes of such similarity of embryos were discussed. We test predictions about changes in phenotypic and genetic variances that were derived from three hypotheses about the evolutionary origin of the phylotypic stage, i.e. random, epigenetic effects, and stabilizing selection. The random hypothesis predicts increasing values for phenotypic variances and stable or increasing values for genetic variances; the epigenetic effects hypothesis predicts declining values for phenotypic variances but stable or increasing values of genetic variances, and the stabilizing selection predicts stable phenotypic variances but decreasing genetic variances. We studied zebrafish as a model species, because it can be bred in large numbers as necessary for a quantitative genetics breeding design. A half-sib breeding scheme provided estimates of additive genetic variances from 11 embryonic characters from 12 through to 24 hr after fertilization, i.e. before, during (15-19 hr), and after the phylotypic period. Because additive genetic variances are size dependent, we calculated narrow-sense heritabilities as a size independent gauge of genetic contributions to the phenotype. The results show declining phenotypic variances and stable heritabilities. In conclusion, we reject the random and the stabilizing selection hypotheses and favor ideas about epigenetic effects that constrain the early embryonic development. Additive genetic variance during the phylotypic stage makes it accessible for evolution, thus explaining in a simple and straightforward way why the phylotypic period differs among vertebrates in timing, duration, and morphologies.     

Evolution of pleiotropy: epistatic interaction pattern supports a mechanistic model underlying variation in genotype-phenotype map

The genotype-phenotype (GP) map consists of developmental and physiological mechanisms mapping genetic onto phenotypic variation. It determines the distribution of heritable phenotypic variance on which selection can act. Comparative studies of morphology as well as of gene regulatory networks show that the GP map itself evolves, yet little is known about the actual evolutionary mechanisms involved. The study of such mechanisms requires exploring the variation in GP maps at the population level, which presently is easier to quantify by statistical genetic methods rather than by regulatory network structures. We focus on the evolution of pleiotropy, a major structural aspect of the GP map. Pleiotropic genes affect multiple traits and underlie genetic covariance between traits, often causing evolutionary constraints. Previous quantitative genetic studies have demonstrated population-level variation in pleiotropy in the form of loci, at which genotypes differ in the genetic covariation between traits. This variation can potentially fuel evolution of the GP map under selection and/or drift. Here, we propose a developmental mechanism underlying population genetic variation in covariance and test its predictions. Specifically, the mechanism predicts that the loci identified as responsible for genetic variation in pleiotropy are involved in trait-specific epistatic interactions. We test this prediction for loci affecting allometric relationships between traits in an advanced intercross between inbred mouse strains. The results consistently support the prediction. We further find a high degree of sign epistasis in these interactions, which we interpret as an indication of adaptive gene complexes within the diverged parental lines.     

Natural selection, evolvability and bias due to environmental covariance in the field in an annual plant

Estimates of the form and magnitude of natural selection based on phenotypic relationships between traits and fitness measures can be biased when environmental factors influence both relative fitness and phenotypic trait values. I quantified genetic variances and covariances, and estimated linear and quadratic selection coefficients, for seven traits of an annual plant grown in the field. For replicates of 50 paternal half-sib families, coefficients of selection were calculated both for individual phenotypic values of the traits and for half-sib family mean values. The potential for evolutionary response was supported by significant heritability and phenotypic directional selection for several traits but contradicted by the absence of significant genetic variation for fitness estimates and evidence of bias in phenotypic selection coefficients due to environmental covariance for at least two of the traits analysed. Only studies of a much wider range of organisms and traits will reveal the frequency and extent of such bias.     

The quantitative genetics of floral trait variation in Lobelia: potential constraints on adaptive evolution

Abstract Although pollinator-mediated natural selection has been measured on many floral traits and in many species, the extent to which selection is constrained from producing optimal floral phenotypes is less frequently studied. In particular, negative correlations between flower size and flower number are hypothesized to be a major constraint on the evolution of floral displays, yet few empirical studies have documented such a trade-off. To determine the potential for genetic constraints on the adaptive evolution of floral displays, I estimated the quantitative genetic basis of floral trait variation in two populations of Lobelia siphilitica . Restricted maximum likelihood (REML) analyses of greenhouse-grown half-sib families were used to estimate genetic variances and covariances for flower number and six measures of flower size. There was significant genetic variation for all seven floral traits in both populations. Flower number was negatively genetically correlated with four measures of flower size in one population and three measures in the other. When the genetic variance-covariance matrices were combined with field estimates of phenotypic selection gradients, the predicted multivariate evolutionary response was less than or opposite in sign to the selection gradient for flower number and five of six measures of flower size, suggesting genetic constraints on the evolution of these traits. More generally, my results indicate that the adaptive evolution of floral displays can be constrained by tradeoffs between flower size and number, as has been assumed by many theoretical models of floral evolution.     

Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.     

Mapping quantitative trait Loci interactions from the maternal and offspring genomes

The expression of most developmental or behavioral traits involves complex interactions between quantitative trait loci (QTL) from the maternal and offspring genomes. The maternal-offspring interactions play a pivotal role in shaping the direction and rate of evolution in terms of their substantial contribution to quantitative genetic (co)variation. To study the genetics and evolution of maternal-offspring interactions, a unifying statistical framework that embraces both the direct and indirect genetic effects of maternal and offspring QTL on any complex trait is developed. This model is derived for a simple backcross design within the maximum-likelihood context, implemented with the EM algorithm. Results from extensive simulations suggest that this model can provide reasonable estimation of additive and dominant effects of the QTL at different generations and their interaction effects derived from the maternal and offspring genomes. Although our model is framed to characterize the actions and interactions of maternal and offspring QTL affecting offspring traits, the idea can be readily extended to decipher the genetic machinery of maternal traits, such as maternal care. Our model provides a powerful means for studying the evolutionary significance of indirect genetic effects in any sexually reproductive organisms.     

A general model of functional constraints on phenotypic evolution

A general model of the functional constraints on the rate and direction of phenotypic evolution is developed using a decomposition of the Lande-Arnold model of multivariate phenotypic evolution. The important feature of the model is the F matrix of performance coefficients reflecting the causal relationship between morphophysiological (m-p) and functional performance traits. The structure of F, which reflects the functional architecture of the organism, constrains the shape of the adaptive landscape and thus the rate and direction of m-p trait evolution. The rate of m-p trait evolution is a function of the pattern of coefficients in a row of F. The sums and variances of these rows are related to current concepts of evolvability. The direction of m-p trait evolution through m-p trait space is a function of the functional covariances among m-p traits. The functional covariance between a pair of m-p traits is a measure of how much the traits function together and is computed as the covariance between rows of F. Finally, it is shown that genetic covariances between m-p traits and performance traits are a function of the F matrix, but a G matrix that includes these covariances cannot be used to model functional constraints effectively.     

Mosaic evolution,preadaptation, and the evolution of evolvability in apes

A major goal in postsynthesis evolutionary biology has been to better understand how complex interactions between traits drive movement along and facilitate the formation of distinct evolutionary pathways. I present analyses of a character matrix sampled across the haplorrhine skeleton that revealed several modules of characters displaying distinct patterns in macroevolutionary disparity. Comparison of these patterns to those in neurological development showed that early ape evolution was characterized by an intense regime of evolutionary and developmental flexibility. Shifting and reduced constraint in apes was met with episodic bursts in phenotypic innovation that built a wide array of functional diversity over a foundation of shared developmental and anatomical structure. Shifts in modularity drove dramatic evolutionary changes across the ape body plan in two distinct ways: (1) an episode of relaxed integration early in hominoid evolution coincided with bursts in evolutionary rate across multiple character suites; (2) the formation of two new trait modules along the branch leading to chimps and humans preceded rapid and dramatic evolutionary shifts in the carpus and pelvis. Changes to the structure of evolutionary mosaicism may correspond to enhanced evolvability that has a “preadaptive” effect by catalyzing later episodes of dramatic morphological remodeling.     

PHENOTYPIC PLASTICITY AND EPIGENETIC MARKING: AN ASSESSMENT OF EVIDENCE FOR GENETIC ACCOMMODATION

The relationship between genotype (which is inherited) and phenotype (the target of selection) is mediated by environmental inputs on gene expression, trait development, and phenotypic integration. Phenotypic plasticity or epigenetic modification might influence evolution in two general ways: (1) by stimulating evolutionary responses to environmental change via population persistence or by revealing cryptic genetic variation to selection, and (2) through the process of genetic accommodation, whereby natural selection acts to improve the form, regulation, and phenotypic integration of novel phenotypic variants. We provide an overview of models and mechanisms for how such evolutionary influences may be manifested both for plasticity and epigenetic marking. We point to promising avenues of research, identifying systems that can best be used to address the role of plasticity in evolution, as well as the need to apply our expanding knowledge of genetic and epigenetic mechanisms to our understanding of how genetic accommodation occurs in nature. Our review of a wide variety of studies finds widespread evidence for evolution by genetic accommodation.     

Phenotypic and Evolutionary Consequences of Social Behaviours: Interactions among Individuals Affect Direct Genetic Effects

Traditional quantitative genetics assumes that an individual''s phenotype is determined by both genetic and environmental factors. For many animals, part of the environment is social and provided by parents and other interacting partners. When expression of genes in social partners affects trait expression in a focal individual, indirect genetic effects occur. In this study, we explore the effects of indirect genetic effects on the magnitude and range of phenotypic values in a focal individual in a multi-member model analyzing three possible classes of interactions between individuals. We show that social interactions may not only cause indirect genetic effects but can also modify direct genetic effects. Furthermore, we demonstrate that both direct and indirect genetic effects substantially alter the range of phenotypic values, particularly when a focal trait can influence its own expression via interactions with traits in other individuals. We derive a function predicting the relative importance of direct versus indirect genetic effects. Our model reveals that both direct and indirect genetic effects can depend to a large extent on both group size and interaction strength, altering group mean phenotype and variance. This may lead to scenarios where between group variation is much higher than within group variation despite similar underlying genetic properties, potentially affecting the level of selection. Our analysis highlights key properties of indirect genetic effects with important consequences for trait evolution, the level of selection and potentially speciation.     

INTERACTING PHENOTYPES AND THE EVOLUTIONARY PROCESS: I. DIRECT AND INDIRECT GENETIC EFFECTS OF SOCIAL INTERACTIONS

Interacting phenotypes are traits whose expression is affected by interactions with conspecifics. Commonly-studied interacting phenotypes include aggression, courtship, and communication. More extreme examples of interacting phenotypes—traits that exist exclusively as a product of interactions—include social dominance, intraspecific competitive ability, and mating systems. We adopt a quantitative genetic approach to assess genetic influences on interacting phenotypes. We partition genetic and environmental effects so that traits in conspecifics that influence the expression of interacting phenotypes are a component of the environment. When the trait having the effect is heritable, the environmental influence arising from the interaction has a genetic basis and can be incorporated as an indirect genetic effect. However, because it has a genetic basis, this environmental component can evolve. Therefore, to consider the evolution of interacting phenotypes we simultaneously consider changes in the direct genetic contributions to a trait (as a standard quantitative genetic approach would evaluate) as well as changes in the environmental (indirect genetic) contribution to the phenotype. We then explore the ramifications of this model of inheritance on the evolution of interacting phenotypes. The relative rate of evolution in interacting phenotypes can be quite different from that predicted by a standard quantitative genetic analysis. Phenotypic evolution is greatly enhanced or inhibited depending on the nature of the direct and indirect genetic effects. Further, unlike most models of phenotypic evolution, a lack of variation in direct genetic effects does not preclude evolution if there is genetic variance in the indirect genetic contributions. The available empirical evidence regarding the evolution of behavior expressed in interactions, although limited, supports the predictions of our model.     

EXPERIMENTAL EVIDENCE FOR THE EVOLUTION OF INDIRECT GENETIC EFFECTS: CHANGES IN THE INTERACTION EFFECT COEFFICIENT,PSI (Ψ), DUE TO SEXUAL SELECTION

Indirect genetics effects (IGEs)—when the genotype of one individual affects the phenotypic expression of a trait in another—may alter evolutionary trajectories beyond that predicted by standard quantitative genetic theory as a consequence of genotypic evolution of the social environment. For IGEs to occur, the trait of interest must respond to one or more indicator traits in interacting conspecifics. In quantitative genetic models of IGEs, these responses (reaction norms) are termed interaction effect coefficients and are represented by the parameter psi (Ψ). The extent to which Ψ exhibits genetic variation within a population, and may therefore itself evolve, is unknown. Using an experimental evolution approach, we provide evidence for a genetic basis to the phenotypic response caused by IGEs on sexual display traits in Drosophila serrata. We show that evolution of the response is affected by sexual but not natural selection when flies adapt to a novel environment. Our results indicate a further mechanism by which IGEs can alter evolutionary trajectories—the evolution of interaction effects themselves.     

QUANTITATIVE GENETIC MODELS FOR DEVELOPMENT,EPIGENETIC SELECTION,AND PHENOTYPIC EVOLUTION

Herein we describe a general multivariate quantitative genetic model that incorporates two potentially important developmental phenomena, maternal effects and epigenetic effects. Maternal and epigenetic effects are defined as partial regression coefficients and phenotypic variances are derived in terms of age-specific genetic and environmental variances. As a starting point, the traditional quantitative genetic model of additive gene effects and random environmental effects is cast in a developmental time framework. From this framework, we first extend a maternal effects model to include multiple developmental ages for the occurrence of maternal effects. An example of maternal effects occurring at multiple developmental ages is prenatal and postnatal maternal effects in mammals. Subsequently, a model of intrinsic and epigenetic effects in the absence of maternal effects is described. It is shown that genetic correlations can arise through epigenetic effects, and in the absence of other developmental effects, epigenetic effects are in general confounded with age-specific intrinsic genetic effects. Finally, the two effects are incorporated into the basic quantitative genetic model. For this more biologically realistic model combining maternal and epigenetic effects, it is shown that the phenotypic regressions of offspring on mother and offspring on father can be used in some cases to estimate simultaneously maternal effects and epigenetic effects.