Orientation of the genetic variance-covariance matrix and the fitness surface for multiple male sexually selected traits

Stabilizing selection has been predicted to change genetic variances and covariances so that the orientation of the genetic variance-covariance matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic variance, more than 99% of the genetic variance was orientated 74.9degrees away from the vector of linear sexual selection, suggesting that open-ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear ( convex) selection. Associating the eigenstructure of G with vectors of linear and nonlinear selection may provide a way of determining what long-term changes in G may be generated by the processes of natural and sexual selection

Phenotypic divergence along lines of genetic variance

Natural populations inhabiting the same environment often independently evolve the same phenotype. Is this replicated evolution a result of genetic constraints imposed by patterns of genetic covariation? We looked for associations between directions of morphological divergence and the orientation of the genetic variance-covariance matrix (G) by using an experimental system of morphological evolution in two allopatric nonsister species of rainbow fish. Replicate populations of both Melanotaenia eachamensis and Melanotaenia duboulayi have independently adapted to lake versus stream hydrodynamic environments. The major axis of divergence (z) among all eight study populations was closely associated with the direction of greatest genetic variance (g(max)), suggesting directional genetic constraint on evolution. However, the direction of hydrodynamic adaptation was strongly associated with vectors of G describing relatively small proportions of the total genetic variance, and was only weakly associated with g(max). In contrast, divergence between replicate populations within each habitat was approximately proportional to the level of genetic variance, a result consistent with theoretical predictions for neutral phenotypic divergence. Divergence between the two species was also primarily along major eigenvectors of G. Our results therefore suggest that hydrodynamic adaptation in rainbow fish was not directionally constrained by the dominant eigenvector of G. Without partitioning divergence as a consequence of the adaptation of interest (here, hydrodynamic adaptation) from divergence due to other processes, empirical studies are likely to overestimate the potential for the major eigenvectors of G to directionally constrain adaptive evolution

Comparing Complex Fitness Surfaces: Among-Population Variation in Mutual Sexual Selection in Drosophila serrata

The problem of synchronization of metacommunities is investigated in this article with reference to a rather general model composed of a chaotic environmental compartment driving a biological compartment. Synchronization in the absence of dispersal (i.e., the so-called Moran effect) is first discussed and shown to occur only when there is no biochaos. In other words, if the biological compartment is reinforcing environmental chaos, dispersal must be strictly above a specified threshold in order to synchronize population dynamics. Moreover, this threshold can be easily determined from the model by computing a special Lyapunov exponent. The application to prey-predator metacommunities points out the influence of frequency and coherence of the environmental noise on synchronization and agrees with all experimental studies performed on the subject

The contribution of selection and genetic constraints to phenotypic divergence

Although divergent natural selection is common in nature, the extent to which genetic constraints bias evolutionary trajectories in its presence remains largely unknown. Here we develop a general framework to integrate estimates of divergent selection and genetic constraints to estimate their contributions to phenotypic divergence among natural populations. We apply these methods to estimates of phenotypic selection and genetic covariance from sexually selected traits that have undergone adaptive divergence among nine natural populations of the fly Drosophila serrata. Despite ongoing sexual selection within populations, differences in its direction among them, and genetic variance for all traits in all populations, divergent sexual selection only weakly resembled the observed pattern of divergence. Accounting for the influence of genetic covariance among the traits significantly improved the alignment between observed and predicted divergence. Our results suggest that the direction in which sexual selection generates divergence may depend on the pattern of genetic constraint in individual populations, ultimately restricting how sexually selected traits may diversify. More generally, we show how evolution is likely to proceed in the direction of major axes of genetic variance, rather than the direction of selection itself, when genetic variance-covariance matrices are ill conditioned and genetic variance is low in the direction of selection

Genetic Constraints and the Evolution of Display Trait Sexual Dimorphism by Natural and Sexual Selection.

The evolution of sexual dimorphism involves an interaction between sex-specific selection and a breakdown of genetic constraints that arise because the two sexes share a genome. We examined genetic constraints and the effect of sex-specific selection on a suite of sexually dimorphic display traits in Drosophila serrata. Sexual dimorphism varied among nine natural populations covering a substantial portion of the species range. Quantitative genetic analyses showed that intersexual genetic correlations were high because of autosomal genetic variance but that the inclusion of X-linked effects reduced genetic correlations substantially, indicating that sex linkage may be an important mechanism by which intersexual genetic constraints are reduced in this species. We then explored the potential for both natural and sexual selection to influence these traits, using a 12-generation laboratory experiment in which we altered the opportunities for each process as flies adapted to a novel environment. Sexual dimorphism evolved, with natural selection reducing sexual dimorphism, whereas sexual selection tended to increase it overall. To this extent, our results are consistent with the hypothesis that sexual selection favors evolutionary divergence of the sexes. However, sex-specific responses to natural and sexual selection contrasted with the classic model because sexual selection affected females rather than males

Divergent selection and the evolution of signal traits and mating preferences

Mating preferences are common in natural populations, and their divergence among populations is considered an important source of reproductive isolation during speciation. Although mechanisms for the divergence of mating preferences have received substantial theoretical treatment, complementary experimental tests are lacking. We conducted a laboratory evolution experiment, using the fruit fly Drosophila serrata, to explore the role of divergent selection between environments in the evolution of female mating preferences. Replicate populations of D. serrata were derived from a common ancestor and propagated in one of three resource environments: two novel environments and the ancestral laboratory environment. Adaptation to both novel environments involved changes in cuticular hydrocarbons, traits that predict mating success in these populations. Furthermore, female mating preferences for these cuticular hydrocarbons also diverged among populations. A component of this divergence occurred among treatment environments, accounting for at least 17.4% of the among- population divergence in linear mating preferences and 17.2% of the among-population divergence in nonlinear mating preferences. The divergence of mating preferences in correlation with environment is consistent with the classic by- product model of speciation in which premating isolation evolves as a side effect of divergent selection adapting populations to their different environments

The phenome-wide distribution of genetic variance

A general observation emerging from estimates of additive genetic variance in sets of functionally or developmentally related traits is that much of the genetic variance is restricted to few trait combinations as a consequence of genetic covariance among traits. While this biased distribution of genetic variance among functionally related traits is now well documented, how it translates to the broader phenome and therefore any trait combination under selection in a given environment is unknown. We show that 8,750 gene expression traits measured in adult male Drosophila serrata exhibit widespread genetic covariance among random sets of five traits, implying that pleiotropy is common. Ultimately, to understand the phenome-wide distribution of genetic variance, very large additive genetic variance-covariance matrices (G) are required to be estimated. We draw upon recent advances in matrix theory for completing high-dimensional matrices to estimate the 8,750-trait G and show that large numbers of gene expression traits genetically covary as a consequence of a single genetic factor. Using gene ontology term enrichment analysis, we show that the major axis of genetic variance among expression traits successfully identified genetic covariance among genes involved in multiple modes of transcriptional regulation. Our approach provides a practical empirical framework for the genetic analysis of high-dimensional phenome-wide trait sets and for the investigation of the extent of high-dimensional genetic constraint

An expressed sequence tag (EST) library for Drosophila serrata, a model system for sexual selection and climatic adaptation studies

The native Australian fly Drosophila serrata belongs to the highly speciose montium subgroup of the melanogaster species group. It has recently emerged as an excellent model system with which to address a number of important questions, including the evolution of traits under sexual selection and traits involved in climatic adaptation along latitudinal gradients. Understanding the molecular genetic basis of such traits has been limited by a lack of genomic resources for this species. Here, we present the first expressed sequence tag (EST) collection for D. serrata that will enable the identification of genes underlying sexually-selected phenotypes and physiological responses to environmental change and may help resolve controversial phylogenetic relationships within the montium subgroup

Maintenance of quantitative genetic variance in complex, multitrait phenotypes:the contribution of rare, large effect variants in 2 Drosophila species

The interaction of evolutionary processes to determine quantitative genetic variation has implications for contemporary and future phenotypic evolution, as well as for our ability to detect causal genetic variants. While theoretical studies have provided robust predictions to discriminate among competing models, empirical assessment of these has been limited. In particular, theory highlights the importance of pleiotropy in resolving observations of selection and mutation, but empirical investigations have typically been limited to few traits. Here, we applied high-dimensional Bayesian Sparse Factor Genetic modeling to gene expression datasets in 2 species, Drosophila melanogaster and Drosophila serrata, to explore the distributions of genetic variance across high-dimensional phenotypic space. Surprisingly, most of the heritable trait covariation was due to few lines (genotypes) with extreme [>3 interquartile ranges (IQR) from the median] values. Intriguingly, while genotypes extreme for a multivariate factor also tended to have a higher proportion of individual traits that were extreme, we also observed genotypes that were extreme for multivariate factors but not for any individual trait. We observed other consistent differences between heritable multivariate factors with outlier lines vs those factors without extreme values, including differences in gene functions. We use these observations to identify further data required to advance our understanding of the evolutionary dynamics and nature of standing genetic variation for quantitative traits

On the number of limit cycles of the Lienard equation

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.Comment: 10 pages, 5 figures. Submitted to Physical Review