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.     

The distribution of fitness effects in an uncertain world

The distribution of fitness effects (DFE) among new mutations plays a critical role in adaptive evolution and the maintenance of genetic variation. Although fitness landscape models predict several key features of the DFE, most theory to date focuses on predictable environmental conditions, while ignoring stochastic environmental fluctuations that feature prominently in the ecology of many organisms. Here, we derive an extension of Fisher's geometric model that incorporates two common effects of environmental variation: (1) nonadaptive genotype‐by‐environment interactions (G × E), in which the phenotype of a given genotype varies across environmental contexts; and (2) random fluctuation of the fitness optimum, which generates fluctuating selection. We show that both factors cause a mismatch between the DFE within single generations and the distribution of geometric mean fitness effects (averaged over multiple generations) that governs long‐term evolutionary change. Such mismatches permit strong evolutionary constraints—despite an abundance of beneficial fitness variation within single environmental contexts—and to conflicting DFE estimates from direct versus indirect inference methods. Finally, our results suggest an intriguing parallel between the genetics and ecology of evolutionary constraints, with environmental fluctuations and pleiotropy placing qualitatively similar limits on the availability of adaptive genetic variation.     

Pleiotropy informed adaptive association test of multiple traits using genome‐wide association study summary data

Genetic variants associated with disease outcomes can be used to develop personalized treatment. To reach this precision medicine goal, hundreds of large‐scale genome‐wide association studies (GWAS) have been conducted in the past decade to search for promising genetic variants associated with various traits. They have successfully identified tens of thousands of disease‐related variants. However, in total these identified variants explain only part of the variation for most complex traits. There remain many genetic variants with small effect sizes to be discovered, which calls for the development of (a) GWAS with more samples and more comprehensively genotyped variants, for example, the NHLBI Trans‐Omics for Precision Medicine (TOPMed) Program is planning to conduct whole genome sequencing on over 100 000 individuals; and (b) novel and more powerful statistical analysis methods. The current dominating GWAS analysis approach is the “single trait” association test, despite the fact that many GWAS are conducted in deeply phenotyped cohorts including many correlated and well‐characterized outcomes, which can help improve the power to detect novel variants if properly analyzed, as suggested by increasing evidence that pleiotropy, where a genetic variant affects multiple traits, is the norm in genome‐phenome associations. We aim to develop pleiotropy informed powerful association test methods across multiple traits for GWAS. Since it is generally very hard to access individual‐level GWAS phenotype and genotype data for those existing GWAS, due to privacy concerns and various logistical considerations, we develop rigorous statistical methods for pleiotropy informed adaptive multitrait association test methods that need only summary association statistics publicly available from most GWAS. We first develop a pleiotropy test, which has powerful performance for truly pleiotropic variants but is sensitive to the pleiotropy assumption. We then develop a pleiotropy informed adaptive test that has robust and powerful performance under various genetic models. We develop accurate and efficient numerical algorithms to compute the analytical P‐value for the proposed adaptive test without the need of resampling or permutation. We illustrate the performance of proposed methods through application to joint association test of GWAS meta‐analysis summary data for several glycemic traits. Our proposed adaptive test identified several novel loci missed by individual trait based GWAS meta‐analysis. All the proposed methods are implemented in a publicly available R package.     

The contribution of epistatic pleiotropy to the genetic architecture of covariation among polygenic traits in mice

The contribution that pleiotropic effects of individual loci make to covariation among traits is well understood theoretically and is becoming well documented empirically. However, little is known about the role of epistasis in determining patterns of covariation among traits. To address this problem we combine a quantitative trait locus (QTL) analysis with a two-locus model to assess the contribution of epistasis to the genetic architecture of variation and covariation of organ weights and limb bone lengths in a backcross population of mice created from the M16i and CAST/Ei strains. Significant epistasis was exhibited by 14 pairwise combinations of QTL for organ weights and 10 combinations of QTL for limb bone lengths, which contributed, on average, about 5% of the variation in organ weights and 8% in limb bone lengths beyond that of single-locus QTL effects. Epistatic pleiotropy was much more common in the limb bones (seven of 10 epistatic combinations affecting limb bone lengths were pleiotropic) than the organs (three of the 14 epistatic combinations affecting organ weights were pleiotropic). In both cases, epistatic pleiotropy was less common than single-locus pleiotropy. Epistatic pleiotropy accounted for an average of 6% of covariation among organ weights and 21% of covariation among limb bone lengths, which represented an average of one-fifth (for organ weights) and one-third (for limb bone lengths) of the total genetic covariance between traits. Thus, although epistatic pleiotropy made a smaller contribution than single-locus pleiotropy, it clearly made a significant contribution to the genetic architecture of variation/covariation.     

The genetics of phenotypic plasticity. II. Response to selection

We selected on phenotypic plasticity of thorax size in response to temperature in Drosophila melanogaster using a family selection scheme. The results were compared to those of lines selected directly on thorax size. We found that the plasticity of a character does respond to selection and this response is partially independent of the response to selection on the mean of the character. One puzzling result was that a selection limit of zero plasticity was reached in the lines selected for decreased plasticity yet additive genetic variation for plasticity still existed in the lines. We tested the predictions of three models of the genetic basis of phenotypic plasticity: overdominance, pleiotropy, and epistasis. The results mostly support the epistasis model, that the plasticity of a character is determined by separate loci from those determining the mean of the character.     

Modularity in the mammalian dentition: mice and monkeys share a common dental genetic architecture

The concept of modularity provides a useful tool for exploring the relationship between genotype and phenotype. Here, we use quantitative genetics to identify modularity within the mammalian dentition, connecting the genetics of organogenesis to the genetics of population-level variation for a phenotype well represented in the fossil record. We estimated the correlations between dental traits owing to the shared additive effects of genes (pleiotropy) and compared the pleiotropic relationships among homologous traits in two evolutionary distant taxa-mice and baboons. We find that in both mice and baboons, who shared a common ancestor >65 Ma, incisor size variation is genetically independent of molar size variation. Furthermore, baboon premolars show independent genetic variation from incisors, suggesting that a modular genetic architecture separates incisors from these posterior teeth as well. Such genetic independence between modules provides an explanation for the extensive diversity of incisor size variation seen throughout mammalian evolution-variation uncorrelated with equivalent levels of postcanine tooth size variation. The modularity identified here is supported by the odontogenic homeobox code proposed for the patterning of the rodent dentition. The baboon postcanine pattern of incomplete pleiotropy is also consistent with predictions from the morphogenetic field model.     

Spatial scale and divergent patterns of variation in adapted traits in the ocean

The geography of adaptive genetic variation is crucial to species conservation yet poorly understood in marine systems. We analyse the spatial scale of genetic variation in traits that broadly display adaptation throughout the range of a highly dispersive marine species. We conducted common garden experiments on the Atlantic silverside, Menidia menidia, from 39 locations along its 3000 km range thereby mapping genetic variation for growth rate, vertebral number and sex determination. Each trait displayed unique clinal patterns, with significant differences (adaptive or not) occurring over very small distances. Breakpoints in the cline differed among traits, corresponding only partially with presumed eco-geographical boundaries. Because clinal patterns are unique to each selected character, neutral genes or those coding for a single character cannot serve as proxies for the genetic structure as a whole. Conservation plans designed to protect essential genetic subunits of a species will need to account for such complex spatial structures.     

Genetic variation in pleiotropy: differential epistasis as a source of variation in the allometric relationship between long bone lengths and body weight

Pleiotropy is an aspect of genetic architecture underlying the phenotypic covariance structure. The presence of genetic variation in pleiotropy is necessary for natural selection to shape patterns of covariation between traits. We examined the contribution of differential epistasis to variation in the intertrait relationship and the nature of this variation. Genetic variation in pleiotropy was revealed by mapping quantitative trait loci (QTLs) affecting the allometry of mouse limb and tail length relative to body weight in the mouse-inbred strain LG/J by SM/J intercross. These relationship QTLs (rQTLs) modify relationships between the traits affected by a common pleiotropic locus. We detected 11 rQTLs, mostly affecting allometry of multiple bones. We further identified epistatic interactions responsible for the observed allometric variation. Forty loci that interact epistatically with the detected rQTLs were identified. We demonstrate how these epistatic interactions differentially affect the body size variance and the covariance of traits with body size. We conclude that epistasis, by differentially affecting both the canalization and mean values of the traits of a pleiotropic domain, causes variation in the covariance structure. Variation in pleiotropy maintains evolvability of the genetic architecture, in particular the evolvability of its modular organization.     

Epistatic pleiotropy and the genetic architecture of covariation within early and late-developing skull trait complexes in mice

The role of epistasis as a source of trait variation is well established, but its role as a source of covariation among traits (i.e., as a source of "epistatic pleiotropy") is rarely considered. In this study we examine the relative importance of epistatic pleiotropy in producing covariation within early and late-developing skull trait complexes in a population of mice derived from an intercross of the Large and Small inbred strains. Significant epistasis was found for several pairwise combinations of the 21 quantitative trait loci (QTL) affecting early developing traits and among the 20 QTL affecting late-developing traits. The majority of the epistatic effects were restricted to single traits but epistatic pleiotropy still contributed significantly to covariances. Because of their proportionally larger effects on variances than on covariances, epistatic effects tended to reduce within-group correlations of traits and reduce their overall degree of integration. The expected contributions of single-locus and two-locus epistatic pleiotropic QTL effects to the genetic covariance between traits were analyzed using a two-locus population genetic model. The model demonstrates that, for single-locus or epistatic pleiotropy to contribute to trait covariances in the study population, both traits must show the same pattern of single-locus or epistatic effects. As a result, a large number of the cases where loci show pleiotropic effects do not contribute to the covariance between traits in this population because the loci show a different pattern of effect on the different traits. In general, covariance patterns produced by single-locus and epistatic pleiotropy predicted by the model agreed well with actual values calculated from the QTL analysis. Nearly all single-locus and epistatic pleiotropic effects contributed positive components to covariances between traits, suggesting that genetic integration in the skull is achieved by a complex combination of pleiotropic effects.     

Is modularity necessary for evolvability? Remarks on the relationship between pleiotropy and evolvability

Evolvability is the ability to respond to a selective challenge. This requires the capacity to produce the right kind of variation for selection to act upon. To understand evolvability we therefore need to understand the variational properties of biological organisms. Modularity is a variational property, which has been linked to evolvability. If different characters are able to vary independently, selection will be able to optimize each character separately without interference. But although modularity seems like a good design principle for an evolvable organism, it does not therefore follow that it is the only design that can achieve evolvability. In this essay I analyze the effects of modularity and, more generally, pleiotropy on evolvability. Although, pleiotropy causes interference between the adaptation of different characters, it also increases the variational potential of those characters. The most evolvable genetic architectures may often be those with an intermediate level of integration among characters, and in particular those where pleiotropic effects are variable and able to compensate for each other's constraints.     

Multivariate Mutation-Selection Balance with Constrained Pleiotropic Effects

A multivariate quantitative genetic model is analyzed that is based on the assumption that the genetic variation at a locus j primarily influences an underlying physiological variable yj, while influence on the genotypic values is determined by a kind of "developmental function" which is not changed by mutations at this locus. Assuming additivity among loci the developmental function becomes a linear transformation of the underlying variables y onto the genotypic values x, x = By. In this way the pleiotropic effects become constrained by the structure of the B-matrix. The equilibrium variance under mutation-stabilizing selection balance in infinite and finite populations is derived by using the house of cards approximation. The results are compared to the predictions given by M. Turelli in 1985 for pleiotropic two-character models. It is shown that the B-matrix model gives the same results as Turelli's five-allele model, suggesting that the crucial factor determining the equilibrium variance in multivariate models with pleiotropy is the assumption about constraints on the pleiotropic effects, and not the number of alleles as proposed by Turelli. Finally it is shown that under Gaussian stabilizing selection the structure of the B-matrix has effectively no influence on the mean equilibrium fitness of an infinite population. Hence the B-matrix and consequently to some extent also the structure of the genetic correlation matrix is an almost neutral character. The consequences for the evolution of genetic covariance matrices are discussed.     

Effects of spontaneous mutation accumulation on sex ratio traits in a parasitoid wasp

Sex allocation theory has proved extremely successful at predicting when individuals should adjust the sex of their offspring in response to environmental conditions. However, we know rather little about the underlying genetics of sex ratio or how genetic architecture might constrain adaptive sex-ratio behavior. We examined how mutation influenced genetic variation in the sex ratios produced by the parasitoid wasp Nasonia vitripennis. In a mutation accumulation experiment, we determined the mutability of sex ratio, and compared this with the amount of genetic variation observed in natural populations. We found that the mutability (h(2)(m)) ranges from 0.001 to 0.002, similar to estimates for life-history traits in other organisms. These estimates suggest one mutation every 5-60 generations, which shift the sex ratio by approximately 0.01 (proportion males). In this and other studies, the genetic variation in N. vitripennis sex ratio ranged from 0.02 to 0.17 (broad-sense heritability, H(2)). If sex ratio is maintained by mutation-selection balance, a higher genetic variance would be expected given our mutational parameters. Instead, the observed genetic variance perhaps suggests additional selection against sex-ratio mutations with deleterious effects on other fitness traits as well as sex ratio (i.e., pleiotropy), as has been argued to be the case more generally.     

Comparative analyses for adaptive radiations

Biologists generally agree that most morphological variation between closely related species is adaptive. The most common method of comparative analysis to test for co-evolved character variation is based on a Brownian-motion model of character evolution. If we are to test for the evolution of character-covariation, and we believe that characters have evolved adaptively to fill niches during an adaptive radiation, then it is appropriate to employ appropriate models for character evolution. We show here that under several models of adaptive character evolution and coevolution during an adaptive radiation, which result in closely related species being more similar to each other than to more distantly related species, cross-species analyses are statistically more appropriate than contrast analyses. If the evolution of some traits fits the Brownian-motion model, while others evolve to fill niches during an adaptive radiation, it might be necessary to identify the number of relevant niche dimensions and the modes of character evolution before deciding on appropriate statistical procedures. Alternatively, maximum-likelihood procedures might be used to determine appropriate transformations of phylogenetic branch lengths that accord with particular models of character evolution.     

Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

A model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or long-established cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.     

Expression of genetic and environmental variation during ageing

Summary A selection experiment with Drosophila melanogaster was carried out to test some theories of ageing by calculating genetic parameters for a reproductive fitness trait at different ages. Successful selection for increased lifespan showed that longevity is a trait under genetic control. Positive genetic correlations between early and late fitness were found. These results do not support the pleiotropy theory of ageing which predicts a negative genetic correlation. Both environmental and additive genetic variation clearly increased with age. Increased environmental variation probably reflects the individuals' difficulties in coping with environmental stress. The increase in additive genetic variation supports the mutation accumulation theory of ageing, as well as other theories that postulate increased additive genetic variation with age.     

The Nature and Extent of Mutational Pleiotropy in Gene Expression of Male Drosophila serrata

The nature and extent of mutational pleiotropy remain largely unknown, despite the central role that pleiotropy plays in many areas of biology, including human disease, agricultural production, and evolution. Here, we investigate the variation in 11,604 gene expression traits among 41 mutation accumulation (MA) lines of Drosophila serrata. We first confirmed that these expression phenotypes were heritable, detecting genetic variation in 96% of them in an outbred, natural population of D. serrata. Among the MA lines, 3385 (29%) of expression traits were variable, with a mean mutational heritability of 0.0005. In most traits, variation was generated by mutations of relatively small phenotypic effect; putative mutations with effects of greater than one phenotypic standard deviation were observed for only 8% of traits. With most (71%) traits unaffected by any mutation, our data provide no support for universal pleiotropy. We further characterized mutational pleiotropy in the 3385 variable traits, using sets of 5, randomly assigned, traits. Covariance among traits chosen at random with respect to their biological function is expected only if pleiotropy is extensive. Taking an analytical approach in which the variance unique to each trait in the random 5-trait sets was partitioned from variance shared among traits, we detected significant (at 5% false discovery rate) mutational covariance in 21% of sets. This frequency of statistically supported covariance implied that at least some mutations must pleiotropically affect a substantial number of traits (>70; 0.6% of all measured traits).     

Impact of epistasis and pleiotropy on evolutionary adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.     

FISHER'S GEOMETRIC MODEL WITH A MOVING OPTIMUM

Fisher's geometric model has been widely used to study the effects of pleiotropy and organismic complexity on phenotypic adaptation. Here, we study a version of Fisher's model in which a population adapts to a gradually moving optimum. Key parameters are the rate of environmental change, the dimensionality of phenotype space, and the patterns of mutational and selectional correlations. We focus on the distribution of adaptive substitutions, that is, the multivariate distribution of the phenotypic effects of fixed beneficial mutations. Our main results are based on an “adaptive‐walk approximation,” which is checked against individual‐based simulations. We find that (1) the distribution of adaptive substitutions is strongly affected by the ecological dynamics and largely depends on a single composite parameter γ, which scales the rate of environmental change by the “adaptive potential” of the population; (2) the distribution of adaptive substitution reflects the shape of the fitness landscape if the environment changes slowly, whereas it mirrors the distribution of new mutations if the environment changes fast; (3) in contrast to classical models of adaptation assuming a constant optimum, with a moving optimum, more complex organisms evolve via larger adaptive steps.     

Pleiotropy, apparent stabilizing selection and uncovering fitness optima

Evolutionary theory has emphasized that the evolution of single traits cannot be understood in isolation when pleiotropy is present. Widespread pleiotropy causes the appearance of stabilizing selection on metric traits owing to joint effects with fitness, and results in the genetic variation being concentrated in relatively few combinations of the measured traits. In this review, we show how trait combinations with high levels of genetic variation can be used to uncover fitness optima that are defined by apparent stabilizing selection. Defining fitness optima in this way could provide one avenue by which researchers can overcome the problem posed by measuring the myriad of traits that must influence fitness, or by measuring total fitness itself.     

The extent and genetic basis of phenotypic divergence in life history traits in Mimulus guttatus

Differential natural selection acting on populations in contrasting environments often results in adaptive divergence in multivariate phenotypes. Multivariate trait divergence across populations could be caused by selection on pleiotropic alleles or through many independent loci with trait‐specific effects. Here, we assess patterns of association between a suite of traits contributing to life history divergence in the common monkey flower, Mimulus guttatus, and examine the genetic architecture underlying these correlations. A common garden survey of 74 populations representing annual and perennial strategies from across the native range revealed strong correlations between vegetative and reproductive traits. To determine whether these multitrait patterns arise from pleiotropic or independent loci, we mapped QTLs using an approach combining high‐throughput sequencing with bulk segregant analysis on a cross between populations with divergent life histories. We find extensive pleiotropy for QTLs related to flowering time and stolon production, a key feature of the perennial strategy. Candidate genes related to axillary meristem development colocalize with the QTLs in a manner consistent with either pleiotropic or independent QTL effects. Further, these results are analogous to previous work showing pleiotropy‐mediated genetic correlations within a single population of M. guttatus experiencing heterogeneous selection. Our findings of strong multivariate trait associations and pleiotropic QTLs suggest that patterns of genetic variation may determine the trajectory of adaptive divergence.