Using average autonomy to test whether behavioral syndromes constrain evolution

Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing [Formula: see text] matrices

Theory predicts that the additive genetic covariance ([Formula: see text]) matrix determines a population's short-term (in)ability to respond to directional selection-evolvability in the Hansen-Houle sense-which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining the averages of these measures across all possible selection gradients, but explicit formulae for most of these average measures have not been known. Previous authors relied either on approximations by the delta method, whose accuracy is generally unknown, or Monte Carlo evaluations (including the random skewers analysis), which necessarily involve random fluctuations. This study presents new, exact expressions for the average conditional evolvability, average autonomy, average respondability, average flexibility, average response difference, and average response correlation, utilizing their mathematical structures as ratios of quadratic forms. The new expressions are infinite series involving top-order zonal and invariant polynomials of matrix arguments, and can be numerically evaluated as their partial sums with, for some measures, known error bounds. Whenever these partial sums numerically converge within reasonable computational time and memory, they will replace the previous approximate methods. In addition, new expressions are derived for the average measures under a general normal distribution for the selection gradient, extending the applicability of these measures into a substantially broader class of selection regimes.

Statistics of eigenvalue dispersion indices: Quantifying the magnitude of phenotypic integration

Analysis of trait covariation plays a pivotal role in the study of phenotypic evolution. The magnitude of covariation is often quantified with statistics based on dispersion of eigenvalues of a covariance or correlation matrix-eigenvalue dispersion indices. This study clarifies the statistical justifications of these statistics and elaborates on their sampling properties. The relative eigenvalue variance of a covariance matrix is known in the statistical literature a test statistic for sphericity, and thus is an appropriate measure of eccentricity of variation. The same of a correlation matrix is equal to the average squared correlation, which has a straightforward interpretation as a measure of integration. Here, expressions for the mean and variance of these statistics are analytically derived under multivariate normality, clarifying the effects of sample size N, number of variables p, and parameters on sampling bias and error. Simulations confirm that approximations involved are reasonably accurate with a moderate sample size (N ≥ 16-64). Importantly, sampling properties of these indices are not adversely affected by a high p:N ratio, promising their utility in high-dimensional phenotypic analyses. They can furthermore be applied to shape variables and phylogenetically structured data with appropriate modifications.

Protein deprivation facilitates the independent evolution of behavior and morphology

Ecological conditions such as nutrition can change genetic covariances between traits and accelerate or slow down trait evolution. As adaptive trait correlations can become maladaptive following rapid environmental change, poor or stressful environments are expected to weaken genetic covariances, thereby increasing the opportunity for independent evolution of traits. Here, we demonstrate the differences in genetic covariance among multiple behavioral and morphological traits (exploration, aggression, and body weight) between southern field crickets (Gryllus bimaculatus) raised in favorable (free-choice) versus stressful (protein-deprived) nutritional environments. We also quantify the extent to which differences in genetic covariance structures contribute to the potential for the independent evolution of these traits. We demonstrate that protein-deprived environments tend to increase the potential for traits to evolve independently, which is caused by genetic covariances that are significantly weaker for crickets raised on protein-deprived versus free-choice diets. The weakening effects of stressful environments on genetic covariances tended to be stronger in males than in females. The weakening of the genetic covariance between traits under stressful nutritional environments was expected to facilitate the opportunity for adaptive evolution across generations. Therefore, the multivariate gene-by-environment interactions revealed here may facilitate behavioral and morphological adaptations to rapid environmental change.

Alternative reproductive tactics shape within-species variation in behavioral syndromes

Multiple behaviors can correlate with each other at the individual level (behavioral syndrome), and behavioral syndromes can vary in their direction between populations within a species. Within-species variation in behavioral syndromes is predicted to be associated with alternative reproductive tactics (ARTs), which evolve under different selection regimes. Here, we tested this using a water strider species, Gerris gracilicornis, in which males employ 2 ARTs that are fixed for life: signaling males (producing courtship ripples) versus nonsignaling males (producing no courtship ripples). We measured multiple behaviors in males with both of these ARTs and compared behavioral syndromes between them. Our results showed that signaling males were more active and attempted to mate more frequently than nonsignaling males. This shaped an overall behavioral syndrome between activities in mating and nonmating contexts when we pooled both ARTs. In addition, the behavioral syndromes between cautiousness and mating activity differed significantly between ARTs. In signaling males, the syndrome was significantly negative: signaling males more eager to mate tended to leave their refuges more rapidly. However, mating activity and cautiousness were not correlated in nonsignaling males. This might be because active males, in the context of predation risk and mating, were favored during the evolution and maintenance of the unique intimidating courtship tactic of G. gracilicornis males. Thus, our findings suggest that ARTs facilitate behavioral divergence and also contribute to the evolution of tactic-specific behavioral syndromes. We also show that research on ARTs and behavioral syndromes can be harmonized to study behavioral variation.