A Bayesian framework for comparative quantitative genetics

MAGE: metafounders-assisted genomic estimation of breeding value, a novel additive-dominance single-step model in crossbreeding systems

MOTIVATION

Utilizing both purebred and crossbred data in animal genetics is widely recognized as an optimal strategy for enhancing the predictive accuracy of breeding values. Practically, the different genetic background among several purebred populations and their crossbred offspring populations limits the application of traditional prediction methods. Several studies endeavor to predict the crossbred performance via the partial relationship, which divides the data into distinct sub-populations based on the common genetic background, such as one single purebred population and its corresponding crossbred descendant. However, this strategy makes prediction inaccurate due to ignoring half of the parental information of crossbreed animals. Furthermore, dominance effects, although playing a significant role in crossbreeding systems, cannot be modeled under such a prediction model.

RESULTS

To overcome this weakness, we developed a novel multi-breed single-step model using metafounders to assess ancestral relationships across diverse breeds under a unified framework. We proposed to use multi-breed dominance combined relationship matrices to model additive and dominance effects simultaneously. Our method provides a straightforward way to evaluate the heterosis of crossbreeds and the breeding values of purebred parents efficiently and accurately. We performed simulation and real data analyses to verify the potential of our proposed method. Our proposed model improved prediction accuracy under all scenarios considered compared to commonly used methods.

AVAILABILITY AND IMPLEMENTATION

The software for implementing our method is available at https://github.com/CAU-TeamLiuJF/MAGE.

An exploration into the conversion of dominance to additive genetic variance in contrasting environments

PREMISE

The evolutionary response of a trait to environmental change depends upon the level of additive genetic variance. It has been long argued that sustained selection will tend to deplete additive genetic variance as favored alleles approach fixation. Non-additive genetic variance, due to interactions among alleles within and between loci, does not immediately contribute to an evolutionary response. However, shifts in the allele frequencies within and between interacting loci may convert non-additive variance into additive variance. Here we consider the possibility that an environmental shift may alter allelic interactions in ways that convert dominance into additive genetic variance.

METHODS

We grew a pedigreed population of Brassica rapa in greenhouse and field conditions. The field conditions mimicked agricultural conditions from which the base population was drawn, while the greenhouse featured benign conditions. We used Bayesian models to estimate the additive, dominance, and maternal components of quantitative genetic variance. We also estimated genetic correlations across environments using parental breeding values.

RESULTS

Although the additive genetic variance was elevated in the greenhouse condition, no consistent pattens emerged that would indicate a conversion of dominance variance. The unusually low genetic variance and broad confidence intervals for the variance estimates obtained through this analysis preclude definitive interpretations.

CONCLUSIONS

Further studies are needed to determine whether between-environment changes in additive genetic variance can be traced to conversion of dominance variance.

Can dominance genetic variance be ignored in evolutionary quantitative genetic analyses of wild populations?

Accurately estimating genetic variance components is important for studying evolution in the wild. Empirical work on domesticated and wild outbred populations suggests that dominance genetic variance represents a substantial part of genetic variance, and theoretical work predicts that ignoring dominance can inflate estimates of additive genetic variance. Whether this issue is pervasive in natural systems is unknown, because we lack estimates of dominance variance in wild populations obtained in situ. Here, we estimate dominance and additive genetic variance, maternal variance, and other sources of nongenetic variance in eight traits measured in over 9000 wild nestlings linked through a genetically resolved pedigree. We find that dominance variance, when estimable, does not statistically differ from zero and represents a modest amount (2-36%) of genetic variance. Simulations show that (1) inferences of all variance components for an average trait are unbiased; (2) the power to detect dominance variance is low; (3) ignoring dominance can mildly inflate additive genetic variance and heritability estimates but such inflation becomes substantial when maternal effects are also ignored. These findings hence suggest that dominance is a small source of phenotypic variance in the wild and highlight the importance of proper model construction for accurately estimating evolutionary potential.

Estimation of additive and non-additive genetic effects for fertility and reproduction traits in North American Holstein cattle using genomic information

Non-additive genetic effects are usually ignored in animal breeding programs due to data structure (e.g., incomplete pedigree), computational limitations and over-parameterization of the models. However, non-additive genetic effects may play an important role in the expression of complex traits in livestock species, such as fertility and reproduction traits. In this study, components of genetic variance for additive and non-additive genetic effects were estimated for a variety of fertility and reproduction traits in Holstein cattle using pedigree and genomic relationship matrices. Four linear models were used: (a) an additive genetic model; (b) a model including both additive and epistatic (additive by additive) genetic effects; (c) a model including both additive and dominance effects; and (d) a full model including additive, epistatic and dominance genetic effects. Nine fertility and reproduction traits were analysed, and models were run separately for heifers (N = 5,825) and cows (N = 6,090). For some traits, a larger proportion of phenotypic variance was explained by non-additive genetic effects compared with additive effects, indicating that epistasis, dominance or a combination thereof is of great importance. Epistatic genetic effects contributed more to the total phenotypic variance than dominance genetic effects. Although these models varied considerably in the partitioning of the components of genetic variance, the models including a non-additive genetic effect did not show a clear advantage over the additive model based on the Akaike information criterion. The partitioning of variance components resulted in a re-ranking of cows based solely on the cows' additive genetic effects between models, indicating that adjusting for non-additive genetic effects could affect selection decisions made in dairy cattle breeding programs. These results suggest that non-additive genetic effects play an important role in some fertility and reproduction traits in Holstein cattle.

Adaptive Alignment of Plasticity With Genetic Variation and Selection

Theoretical research has outlined how selection may shape both genetic variation and the expression of phenotypic plasticity in multivariate trait space. Specifically, research regarding the evolution of patterns of additive genetic variances and covariances (summarized in matrix form as G) and complementary research into how selection may shape adaptive plasticity lead to the general prediction that G, plasticity, and selection surfaces are all expected to align with each other. However, less well discussed is how this prediction might be assessed and how the modeled theoretical processes are expected to manifest in actual populations. Here, we discuss the theoretical foundations of the overarching prediction of alignment, what alignment mathematically means, how researchers might test for alignment and important caveats to this testing. The most important caveat concerns the fact that, for plasticity, the prediction of alignment only applies to cases where plasticity is adaptive, whereas organisms express considerable plasticity that may be neutral or even maladaptive. We detail the ramifications of these alternative expressions of plasticity vis-à-vis predictions of alignment. Finally, we briefly highlight some important interpretations of deviations from the prediction of alignment and what alignment might mean for populations experiencing environmental and selective changes.

Additional considerations to the use of single-step genomic predictions in a dominance setting

Recent publications indicate that single-step models are suitable to estimate breeding values, dominance deviations and total genetic values with acceptable quality. Additive single-step methods implicitly extend known number of allele information from genotyped to non-genotyped animals. This theory is well derived in an additive setting. It was recently shown, at least empirically, that this basic strategy can be extended to dominance with reasonable prediction quality. Our study addressed two additional issues. It illustrated the theoretical basis for extension and validated genomic predictions to dominance based on single-step genomic best linear unbiased prediction theory. This development was then extended to include inbreeding into dominance relationships, which is a currently not yet solved issue. Different parametrizations of dominance relationship matrices were proposed. Five dominance single-step inverse matrices were tested and described as C¹ , C² , C³ , C⁴ and C⁵ . Genotypes were simulated for a real pig population (n = 11,943 animals). In order to avoid any confounding issues with additive effects, pseudo-records including only dominance deviations and residuals were simulated. SNP effects of heterozygous genotypes were summed up to generate true dominance deviations. We added random noise to those values and used them as phenotypes. Accuracy was defined as correlation between true and predicted dominance deviations. We conducted five replicates and estimated accuracies in three sets: between all (S₁ ), non-genotyped (S₂ ) and inbred non-genotyped (S₃ ) animals. Potential bias was assessed by regressing true dominance deviations on predicted values. Matrices accounting for inbreeding (C³ , C⁴ and C⁵ ) best fit. Accuracies were on average 0.77, 0.40 and 0.46 in S₁ , S₂ and S₃ , respectively. In addition, C³ , C⁴ and C⁵ scenarios have shown better accuracies than C¹ and C² , and dominance deviations were less biased. Better matrix compatibility (accuracy and bias) was observed by re-scaling diagonal elements to 1 minus the inbreeding coefficient (C⁵ ).

The genetic architecture of teosinte catalyzed and constrained maize domestication

Crop domestication is a well-established system for understanding evolution. We interrogated the genetic architecture of maize domestication from a quantitative genetics perspective. We analyzed domestication-related traits in a maize landrace and a population of its ancestor, teosinte. We observed strong divergence in the underlying genetic architecture including change in the genetic correlations among traits. Despite striking divergence, selection intensities were low for all traits, indicating that selection under domestication can be weaker than natural selection. Analyses suggest total grain weight per plant was not improved and that genetic correlations placed considerable constraint on selection. We hope our results will motivate crop evolutionists to perform similar work in other crops.

The process of evolution under domestication has been studied using phylogenetics, population genetics–genomics, quantitative trait locus (QTL) mapping, gene expression assays, and archaeology. Here, we apply an evolutionary quantitative genetic approach to understand the constraints imposed by the genetic architecture of trait variation in teosinte, the wild ancestor of maize, and the consequences of domestication on genetic architecture. Using modern teosinte and maize landrace populations as proxies for the ancestor and domesticate, respectively, we estimated heritabilities, additive and dominance genetic variances, genetic-by-environment variances, genetic correlations, and genetic covariances for 18 domestication-related traits using realized genomic relationships estimated from genome-wide markers. We found a reduction in heritabilities across most traits, and the reduction is stronger in reproductive traits (size and numbers of grains and ears) than vegetative traits. We observed larger depletion in additive genetic variance than dominance genetic variance. Selection intensities during domestication were weak for all traits, with reproductive traits showing the highest values. For 17 of 18 traits, neutral divergence is rejected, suggesting they were targets of selection during domestication. Yield (total grain weight) per plant is the sole trait that selection does not appear to have improved in maize relative to teosinte. From a multivariate evolution perspective, we identified a strong, nonneutral divergence between teosinte and maize landrace genetic variance–covariance matrices (G-matrices). While the structure of G-matrix in teosinte posed considerable genetic constraint on early domestication, the maize landrace G-matrix indicates that the degree of constraint is more unfavorable for further evolution along the same trajectory.

Heritability of telomere variation: it is all about the environment!

Individual differences in telomere length have been linked to survival and senescence. Understanding the heritability of telomere length can provide important insight into individual differences and facilitate our understanding of the evolution of telomeres. However, to gain accurate and meaningful estimates of telomere heritability it is vital that the impact of the environment, and how this may vary, is understood and accounted for. The aim of this review is to raise awareness of this important, but much under-appreciated point. We outline the factors known to impact telomere length and discuss the fact that telomere length is a trait that changes with age. We highlight statistical methods that can separate genetic from environmental effects and control for confounding variables. We then review how well previous studies in vertebrate populations including humans have taken these factors into account. We argue that studies to date either use methodological techniques that confound environmental and genetic effects, or use appropriate methods but lack sufficient power to fully separate these components. We discuss potential solutions. We conclude that we need larger studies, which also span longer time periods, to account for changing environmental effects, if we are to determine meaningful estimates of the genetic component of telomere length.

This article is part of the theme issue ‘Understanding diversity in telomere dynamics'.

Structure and stability of genetic variance-covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three-spined stickleback

The genetic variance-covariance matrix (G) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G-matrices is limited for two reasons. First, phenotypes are high-dimensional, whereas traditional statistical methods are tuned to estimate and analyse low-dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high-dimensional G-matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half-sib breeding design of three-spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low-temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability-as well as the similarity among G-matrices-may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G-matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G, they also illustrate that by enabling the estimation of large G-matrices, the BSFG method can improve predicted evolutionary responses to selection.

Conserved G-matrices of morphological and life-history traits among continental and island blue tit populations

The genetic variance-covariance matrix (G-matrix) summarizes the genetic architecture of multiple traits. It has a central role in the understanding of phenotypic divergence and the quantification of the evolutionary potential of populations. Laboratory experiments have shown that G-matrices can vary rapidly under divergent selective pressures. However, because of the demanding nature of G-matrix estimation and comparison in wild populations, the extent of its spatial variability remains largely unknown. In this study, we investigate spatial variation in G-matrices for morphological and life-history traits using long-term data sets from one continental and three island populations of blue tit (Cyanistes caeruleus) that have experienced contrasting population history and selective environment. We found no evidence for differences in G-matrices among populations. Interestingly, the phenotypic variance-covariance matrices (P) were divergent across populations, suggesting that using P as a substitute for G may be inadequate. These analyses also provide the first evidence in wild populations for additive genetic variation in the incubation period (that is, the period between last egg laid and hatching) in all four populations. Altogether, our results suggest that G-matrices may be stable across populations inhabiting contrasted environments, therefore challenging the results of previous simulation studies and laboratory experiments.

The alignment between phenotypic plasticity, the major axis of genetic variation and the response to selection

Phenotypic plasticity is the ability of a genotype to produce more than one phenotype in order to match the environment. Recent theory proposes that the major axis of genetic variation in a phenotypically plastic population can align with the direction of selection. Therefore, theory predicts that plasticity directly aids adaptation by increasing genetic variation in the direction favoured by selection and reflected in plasticity. We evaluated this theory in the freshwater crustacean Daphnia pulex, facing predation risk from two contrasting size-selective predators. We estimated plasticity in several life-history traits, the G matrix of these traits, the selection gradients on reproduction and survival, and the predicted responses to selection. Using these data, we tested whether the genetic lines of least resistance and the predicted response to selection aligned with plasticity. We found predator environment-specific G matrices, but shared genetic architecture across environments resulted in more constraint in the G matrix than in the plasticity of the traits, sometimes preventing alignment of the two. However, as the importance of survival selection increased, the difference between environments in their predicted response to selection increased and resulted in closer alignment between the plasticity and the predicted selection response. Therefore, plasticity may indeed aid adaptation to new environments.

EvolQG - An R package for evolutionary quantitative genetics

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.

EvolQG - An R package for evolutionary quantitative genetics

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.

Estimating sampling error of evolutionary statistics based on genetic covariance matrices using maximum likelihood

We explore the estimation of uncertainty in evolutionary parameters using a recently devised approach for resampling entire additive genetic variance-covariance matrices (G). Large-sample theory shows that maximum-likelihood estimates (including restricted maximum likelihood, REML) asymptotically have a multivariate normal distribution, with covariance matrix derived from the inverse of the information matrix, and mean equal to the estimated G. This suggests that sampling estimates of G from this distribution can be used to assess the variability of estimates of G, and of functions of G. We refer to this as the REML-MVN method. This has been implemented in the mixed-model program WOMBAT. Estimates of sampling variances from REML-MVN were compared to those from the parametric bootstrap and from a Bayesian Markov chain Monte Carlo (MCMC) approach (implemented in the R package MCMCglmm). We apply each approach to evolvability statistics previously estimated for a large, 20-dimensional data set for Drosophila wings. REML-MVN and MCMC sampling variances are close to those estimated with the parametric bootstrap. Both slightly underestimate the error in the best-estimated aspects of the G matrix. REML analysis supports the previous conclusion that the G matrix for this population is full rank. REML-MVN is computationally very efficient, making it an attractive alternative to both data resampling and MCMC approaches to assessing confidence in parameters of evolutionary interest.

Heritability estimates on Hodgkin's lymphoma: a genomic- versus population-based approach

Genome-wide association studies (GWASs) have identified several single-nucleotide polymorphisms (SNPs) influencing the risk of Hodgkin's lymphoma (HL) and demonstrated the association of common genetic variation for this type of cancer. Such evidence for inherited genetic risk is also provided by the family history and the very high concordance between monozygotic twins. However, little is known about the genetic and environmental contributions. A common measure for describing the phenotypic variation due to genetics is the heritability. Using GWAS data on 906 HL cases by considering all typed SNPs simultaneously, we have calculated that the common variance explained by SNPs accounts for >35% of the total variation on the liability scale in HL (95% confidence interval 6-62%). These findings are consistent with similar heritability estimates of ∼ 0.40 (95% confidence interval 0.17-0.58) based on Swedish population data. Our estimates support the underlying polygenic basis for susceptibility to HL, and show that heritability based on the population data is somehow larger than heritability based on the genomic data because of the possibility of some missing heritability in the GWAS data. Besides that there is still major evidence for multiple loci causing HL on chromosomes other than chromosome 6 that need to be detected. Because of limited findings in prior GWASs, it seems worth checking for more loci causing susceptibility to HL.

The evolution and adaptive potential of transcriptional variation in sticklebacks--signatures of selection and widespread heritability

Evidence implicating differential gene expression as a significant driver of evolutionary novelty continues to accumulate, but our understanding of the underlying sources of variation in expression, both environmental and genetic, is wanting. Heritability in particular may be underestimated when inferred from genetic mapping studies, the predominant "genetical genomics" approach to the study of expression variation. Such uncertainty represents a fundamental limitation to testing for adaptive evolution at the transcriptomic level. By studying the inheritance of expression levels in 10,495 genes (10,527 splice variants) in a threespine stickleback pedigree consisting of 563 individuals, half of which were subjected to a thermal treatment, we show that 74-98% of transcripts exhibit significant additive genetic variance. Dominance variance is also prevalent (41-99% of transcripts), and genetic sources of variation seem to play a more significant role in expression variance in the liver than a key environmental variable, temperature. Among-population comparisons suggest that the majority of differential expression in the liver is likely due to neutral divergence; however, we also show that signatures of directional selection may be more prevalent than those of stabilizing selection. This predominantly aligns with the neutral model of evolution for gene expression but also suggests that natural selection may still act on transcriptional variation in the wild. As genetic variation both within- and among-populations ultimately defines adaptive potential, these results indicate that broad adaptive potential may be found within the transcriptome.

Evolutionary constraints in high-dimensional trait sets

Genetic variation for individual traits is typically abundant, but for some multivariate combinations it is very low, suggesting that evolutionary limits might be generated by the geometric distribution of genetic variance. To test this prediction, we artificially selected along all eight genetic eigenvectors of a set of eight quantitative traits in Drosophila serrata. After six generations of 50% truncation selection, at least one replicate population of all treatments responded to selection, allowing us to reject a null genetic subspace as a cause of evolutionary constraint in this system. However, while all three replicate populations of the first five selection treatments displayed a significant response, the remaining three, characterized by low genetic variance in their selection indexes in the base population, displayed inconsistent responses to selection. The observation that only four of the nine replicate populations evolved in response to the direct selection applied to them in these low genetic variance treatments, led us to conclude that a nearly null subspace did limit evolution. Dimensions associated with low genetic variance are often found in multivariate analyses of standing genetic variance in morphological traits, suggesting that the nearly null genetic subspace may be a common mechanism of evolutionary constraint in nature.

On estimation and identifiability issues of sex-linked inheritance with a case study of pigmentation in Swiss barn owl (Tyto alba)

Genetic evaluation using animal models or pedigree-based models generally assume only autosomal inheritance. Bayesian animal models provide a flexible framework for genetic evaluation, and we show how the model readily can accommodate situations where the trait of interest is influenced by both autosomal and sex-linked inheritance. This allows for simultaneous calculation of autosomal and sex-chromosomal additive genetic effects. Inferences were performed using integrated nested Laplace approximations (INLA), a nonsampling-based Bayesian inference methodology. We provide a detailed description of how to calculate the inverse of the X- or Z-chromosomal additive genetic relationship matrix, needed for inference. The case study of eumelanic spot diameter in a Swiss barn owl (Tyto alba) population shows that this trait is substantially influenced by variation in genes on the Z-chromosome ( and ). Further, a simulation study for this study system shows that the animal model accounting for both autosomal and sex-chromosome-linked inheritance is identifiable, that is, the two effects can be distinguished, and provides accurate inference on the variance components.

Can invasions occur without change? A comparison of G-matrices and selection in the peach-potato aphid, Myzus persicae

Most evolutionary research on biological invasions has focused on changes seen between the native and invaded range for a particular species. However, it is likely that species that live in human-modified habitats in their native range might have evolved specific adaptations to those environments, which increase the likelihood of establishment and spread in similar human-altered environments. From a quantitative genetic perspective, this hypothesis suggests that both native and introduced populations should reside at or near the same adaptive peak. Therefore, we should observe no overall changes in the G (genetic variance-covariance) matrices between native and introduced ranges, and stabilizing selection on fitness-related traits in all populations. We tested these predictions comparing three populations of the worldwide pest Myzus persicae from the Middle East (native range) and the UK and Chile (separately introduced ranges). In general, our results provide mixed support for this idea, but further comparisons of other species are needed. In particular, we found that there has been some limited evolution in the studied traits, with the Middle East population differing from the UK and Chilean populations. This was reflected in the structure of the G-matrices, in which Chile differed from both UK and Middle East populations. Furthermore, the amount of genetic variation was massively reduced in Chile in comparison with UK and Middle East populations. Finally, we found no detectable selection on any trait in the three populations, but clones from the introduced ranges started to reproduce later, were smaller, had smaller offspring, and had lower reproductive fitness than clones from the native range.

Animal models and integrated nested Laplace approximations

Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian animal models. We analyze animal models for both synthetic case studies and house sparrow (Passer domesticus) population case studies with Gaussian, binomial, and Poisson likelihoods using INLA. Inference results are compared with results using Markov Chain Monte Carlo methods. For model choice we use difference in deviance information criteria (DIC). We suggest and show how to evaluate differences in DIC by comparing them with sampling results from simulation studies. We also introduce an R package, AnimalINLA, for easy and fast inference for Bayesian Animal models using INLA.

Quantitative genetic divergence and standing genetic (co)variance in thermal reaction norms along latitude

Although the potential to adapt to warmer climate is constrained by genetic trade-offs, our understanding of how selection and mutation shape genetic (co)variances in thermal reaction norms is poor. Using 71 isofemale lines of the fly Sepsis punctum, originating from northern, central, and southern European climates, we tested for divergence in juvenile development rate across latitude at five experimental temperatures. To investigate effects of evolutionary history in different climates on standing genetic variation in reaction norms, we further compared genetic (co)variances between regions. Flies were reared on either high or low food resources to explore the role of energy acquisition in determining genetic trade-offs between different temperatures. Although the latter had only weak effects on the strength and sign of genetic correlations, genetic architecture differed significantly between climatic regions, implying that evolution of reaction norms proceeds via different trajectories at high latitude versus low latitude in this system. Accordingly, regional genetic architecture was correlated to region-specific differentiation. Moreover, hot development temperatures were associated with low genetic variance and stronger genetic correlations compared to cooler temperatures. We discuss the evolutionary potential of thermal reaction norms in light of their underlying genetic architectures, evolutionary histories, and the materialization of trade-offs in natural environments.

Limited plasticity in the phenotypic variance-covariance matrix for male advertisement calls in the black field cricket, Teleogryllus commodus

Phenotypic integration and plasticity are central to our understanding of how complex phenotypic traits evolve. Evolutionary change in complex quantitative traits can be predicted using the multivariate breeders' equation, but such predictions are only accurate if the matrices involved are stable over evolutionary time. Recent study, however, suggests that these matrices are temporally plastic, spatially variable and themselves evolvable. The data available on phenotypic variance-covariance matrix (P) stability are sparse, and largely focused on morphological traits. Here, we compared P for the structure of the complex sexual advertisement call of six divergent allopatric populations of the Australian black field cricket, Teleogryllus commodus. We measured a subset of calls from wild-caught crickets from each of the populations and then a second subset after rearing crickets under common-garden conditions for three generations. In a second experiment, crickets from each population were reared in the laboratory on high- and low-nutrient diets and their calls recorded. In both experiments, we estimated P for call traits and used multiple methods to compare them statistically (Flury hierarchy, geometric subspace comparisons and random skewers). Despite considerable variation in means and variances of individual call traits, the structure of P was largely conserved among populations, across generations and between our rearing diets. Our finding that P remains largely stable, among populations and between environmental conditions, suggests that selection has preserved the structure of call traits in order that they can function as an integrated unit.

Comparing G: multivariate analysis of genetic variation in multiple populations

The additive genetic variance-covariance matrix (G) summarizes the multivariate genetic relationships among a set of traits. The geometry of G describes the distribution of multivariate genetic variance, and generates genetic constraints that bias the direction of evolution. Determining if and how the multivariate genetic variance evolves has been limited by a number of analytical challenges in comparing G-matrices. Current methods for the comparison of G typically share several drawbacks: metrics that lack a direct relationship to evolutionary theory, the inability to be applied in conjunction with complex experimental designs, difficulties with determining statistical confidence in inferred differences and an inherently pair-wise focus. Here, we present a cohesive and general analytical framework for the comparative analysis of G that addresses these issues, and that incorporates and extends current methods with a strong geometrical basis. We describe the application of random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the decomposition of the multivariate breeders equation, all within a Bayesian framework. We illustrate these methods using data from an artificial selection experiment on eight traits in Drosophila serrata, where a multi-generational pedigree was available to estimate G in each of six populations. One method, the tensor, elegantly captures all of the variation in genetic variance among populations, and allows the identification of the trait combinations that differ most in genetic variance. The tensor approach is likely to be the most generally applicable method to the comparison of G-matrices from any sampling or experimental design.

Quantifying multivariate plasticity: genetic variation in resource acquisition drives plasticity in resource allocation to components of life history

Acquisition and allocation of resources are central to life-history theory. However, empirical work typically focuses only on allocation despite the fact that relationships between fitness components may be governed by differences in the ability of individuals to acquire resources across environments. Here, we outline a statistical framework to partition the genetic basis of multivariate plasticity into independent axes of genetic variation, and quantify for the first time, the extent to which specific traits drive multitrait genotype-environment interactions. Our framework generalises to analyses of plasticity, growth and ageing. We apply this approach to a unique, large-scale, multivariate study of acquisition, allocation and plasticity in the life history of the cricket, Gryllus firmus. We demonstrate that resource acquisition and allocation are genetically correlated, and that plasticity in trade-offs between allocation to components of fitness is 90% dependent on genetic variance for total resource acquisition. These results suggest that genotype-environment effects for resource acquisition can maintain variation in life-history components that are typically observed in the wild.

A simple procedure for the comparison of covariance matrices

Background

Comparing the covariation patterns of populations or species is a basic step in the evolutionary analysis of quantitative traits. Here I propose a new, simple method to make this comparison in two population samples that is based on comparing the variance explained in each sample by the eigenvectors of its own covariance matrix with that explained by the covariance matrix eigenvectors of the other sample. The rationale of this procedure is that the matrix eigenvectors of two similar samples would explain similar amounts of variance in the two samples. I use computer simulation and morphological covariance matrices from the two morphs in a marine snail hybrid zone to show how the proposed procedure can be used to measure the contribution of the matrices orientation and shape to the overall differentiation.

Results

I show how this procedure can detect even modest differences between matrices calculated with moderately sized samples, and how it can be used as the basis for more detailed analyses of the nature of these differences.

Conclusions

The new procedure constitutes a useful resource for the comparison of covariance matrices. It could fill the gap between procedures resulting in a single, overall measure of differentiation, and analytical methods based on multiple model comparison not providing such a measure.

The majority of genetic variation in orangutan personality and subjective well-being is nonadditive

The heritability of human personality is well-established. Recent research indicates that nonadditive genetic effects, such as dominance and epistasis, play a large role in personality variation. One possible explanation for the latter finding is that there has been recent selection on human personality. To test this possibility, we estimated additive and nonadditive genetic variance in personality and subjective well-being of zoo-housed orangutans. More than half of the genetic variance in these traits could be attributed to nonadditive genetic effects, modeled as dominance. Subjective well-being had genetic overlap with personality, though less so than has been found in humans or chimpanzees. Since a large portion of nonadditive genetic variance in personality is not unique to humans, the nonadditivity of human personality is not sufficient evidence for recent selection of personality in humans. Nonadditive genetic variance may be a general feature of the genetic structure of personality in primates and other animals.

A new method to uncover signatures of divergent and stabilizing selection in quantitative traits

While it is well understood that the pace of evolution depends on the interplay between natural selection, random genetic drift, mutation, and gene flow, it is not always easy to disentangle the relative roles of these factors with data from natural populations. One popular approach to infer whether the observed degree of population differentiation has been influenced by local adaptation is the comparison of neutral marker gene differentiation (as reflected in FST) and quantitative trait divergence (as reflected in QST). However, this method may lead to compromised statistical power, because FST and QST are summary statistics which neglect information on specific pairs of populations, and because current multivariate tests of neutrality involve an averaging procedure over the traits. Further, most FST-QST comparisons actually replace QST by its expectation over the evolutionary process and are thus theoretically flawed. To overcome these caveats, we derived the statistical distribution of population means generated by random genetic drift and used the probability density of this distribution to test whether the observed pattern could be generated by drift alone. We show that our method can differentiate between genetic drift and selection as a cause of population differentiation even in cases with FST=QST and demonstrate with simulated data that it disentangles drift from selection more accurately than conventional FST-QST tests especially when data sets are small.

Utilizing Gaussian Markov random field properties of Bayesian animal models

In this article, we demonstrate how Gaussian Markov random field properties give large computational benefits and new opportunities for the Bayesian animal model. We make inference by computing the posteriors for important quantitative genetic variables. For the single-trait animal model, a nonsampling-based approximation is presented. For the multitrait model, we set up a robust and fast Markov chain Monte Carlo algorithm. The proposed methodology was used to analyze quantitative genetic properties of morphological traits of a wild house sparrow population. Results for single- and multitrait models were compared.

Measuring selection in contemporary human populations

Are humans currently evolving? This question can be answered using data on lifetime reproductive success, multiple traits and genetic variation and covariation in those traits. Such data are available in existing long-term, multigeneration studies - both clinical and epidemiological - but they have not yet been widely used to address contemporary human evolution. Here we review methods to predict evolutionary change and attempts to measure selection and inheritance in humans. We also assemble examples of long-term studies in which additional measurements of evolution could be made. The evidence strongly suggests that we are evolving and that our nature is dynamic, not static.

Bayesian inference of genetic parameters based on conditional decompositions of multivariate normal distributions

It is widely recognized that the mixed linear model is an important tool for parameter estimation in the analysis of complex pedigrees, which includes both pedigree and genomic information, and where mutually dependent genetic factors are often assumed to follow multivariate normal distributions of high dimension. We have developed a Bayesian statistical method based on the decomposition of the multivariate normal prior distribution into products of conditional univariate distributions. This procedure permits computationally demanding genetic evaluations of complex pedigrees, within the user-friendly computer package WinBUGS. To demonstrate and evaluate the flexibility of the method, we analyzed two example pedigrees: a large noninbred pedigree of Scots pine (Pinus sylvestris L.) that includes additive and dominance polygenic relationships and a simulated pedigree where genomic relationships have been calculated on the basis of a dense marker map. The analysis showed that our method was fast and provided accurate estimates and that it should therefore be a helpful tool for estimating genetic parameters of complex pedigrees quickly and reliably.

Indirect genetic effects in a sex-limited trait: the case of breeding time in red-billed gulls

Female reproductive performance can be strongly affected by male care, so that breeding time, a trait expressed only by females, can be seen as one trait determined by both male and female genotypes. Animal model analyses of a 46-year study of red-billed gulls (Larus novaehollandiae scopulinus) revealed that laying date was not heritable in females (h(2) = 0.001 +/- 0.030), but significantly so in males (h(2) = 0.134 +/- 0.029). Heritability of breeding time in males probably reflects genetic variability in some other trait such as courtship feeding ability. In line with predictions of evolutionary models incorporating indirect genetic effects, the strong and consistent directional selection for advanced breeding time has not resulted in detectable selection response in males. Our results demonstrate that a female trait is largely determined by genetic characteristics of its mate, and hence, any evolutionary change in red-billed gull breeding time depends critically on genetic variation in males.

Correlated inbreeding among relatives: occurrence, magnitude, and implications

Understanding the magnitude and causes of genetic and phenotypic resemblance among relatives is key to understanding evolutionary processes. Contrary to basic expectation, individual coefficients of inbreeding (f) were recently hypothesized to be intrinsically correlated across parents and offspring in structured populations, potentially creating an additional source of phenotypic resemblance in traits that show inbreeding depression. To test this hypothesis, we used individual-based simulations to quantify the parent-offspring correlations in f arising under random mating in populations of different size, immigration rate, and mating system. Parent-offspring correlations in f were typically positive (median r approximately 0.2-0.4) in relatively small and isolated populations. Relatively inbred parents therefore produced relatively inbred offspring on average, although the magnitude of this effect varied considerably among replicate populations. Correlations were higher given more generations of random mating, greater variance in reproductive success, polygynous rather than monogamous mating, and for midparent-offspring rather than parent-offspring relationships. Furthermore, f was also positively correlated across half-siblings, and closer relatives had more similar inbreeding coefficients across entire generations. Such intrinsic resemblance in f among relatives could provide an additional genetic benefit of mate choice and bias quantitative genetic analyses that do not account for correlated inbreeding depression.

The rate of ageing in a long-lived bird is not heritable

A senescent decline in performance occurs in late age in many organisms, and is thought to be partly due to additive genetic effects. Here annual fitness, estimated as the age-specific sum of survival and reproduction, was used to test for genetic variance in ageing in a population of common gulls, Larus canus. Data on 3986 individuals collected over a 34-year period indicate a dramatic senescent decline in late life. We also find that annual fitness is heritable and that individuals vary in their rates of ageing. However, counter to theoretical expectations, we find no support for a heritable component to the variance in rates of senescence. Increases in the among-individual (permanent environment) and residual variance components initiate an increase in the total phenotypic variance for annual fitness with age. This finding suggests that older birds are more sensitive to environmental effects, and that old age causes an overall pattern of declining h(2) of annual fitness. Our findings suggest that individual-specific factors do have a role in determining the rate of senescence in this population, but that additive genetic variance for the rate of senescence is either absent or small.

Introduction. Evolutionary dynamics of wild populations: the use of long-term pedigree data

Studies of populations in the wild can provide unique insights into the forces driving evolutionary dynamics. This themed issue of Proc. R. Soc. B focuses on new developments in long-term analyses of animal populations where pedigree information has been collected. These address fundamental questions in evolutionary biology concerning the genetic basis of phenotypic diversity, patterns of natural and sexual selection, the occurrence of inbreeding and inbreeding depression, and speciation. Contributions include the analysis of evolutionary responses to climate change, exploration of the genetic basis of senescence, the exploitation of advances in molecular genetic technology, and reviews of developments in quantitative genetic methodology. We discuss here common themes, specific problems and pointers for future research.

Efficient Markov chain Monte Carlo implementation of Bayesian analysis of additive and dominance genetic variances in noninbred pedigrees

Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler.