Selection and evolution of causally covarying traits

When traits cause variation in fitness, the distribution of phenotype, weighted by fitness, necessarily changes. The degree to which traits cause fitness variation is therefore of central importance to evolutionary biology. Multivariate selection gradients are the main quantity used to describe components of trait-fitness covariation, but they quantify the direct effects of traits on (relative) fitness, which are not necessarily the total effects of traits on fitness. Despite considerable use in evolutionary ecology, path analytic characterizations of the total effects of traits on fitness have not been formally incorporated into quantitative genetic theory. By formally defining "extended" selection gradients, which are the total effects of traits on fitness, as opposed to the existing definition of selection gradients, a more intuitive scheme for characterizing selection is obtained. Extended selection gradients are distinct quantities, differing from the standard definition of selection gradients not only in the statistical means by which they may be assessed and the assumptions required for their estimation from observational data, but also in their fundamental biological meaning. Like direct selection gradients, extended selection gradients can be combined with genetic inference of multivariate phenotypic variation to provide quantitative prediction of microevolutionary trajectories.

Analogues of the fundamental and secondary theorems of selection, assuming a log-normal distribution of expected fitness

It is increasingly common for studies of evolution in natural populations to infer the quantitative genetic basis of fitness (e.g., the additive genetic variance for relative fitness), and of relationships between traits and fitness (e.g., the additive genetic covariance of traits with relative fitness). There is a certain amount of tension between the theory that justifies estimating these quantities, and methodological considerations relevant to their empirical estimation. In particular, the additive genetic variances and covariances involving relative fitness are justified by the fundamental and secondary theorems of selection, which pertain to relative fitness on the scale that it is expressed. However, naturally-occurring fitness distributions lend themselves to analysis with generalized linear mixed models (GLMMs), which conduct analysis on a different scale, typically on the scale of the logarithm of expected values, from which fitness is expressed. This note presents relations between evolutionary change in traits, and the rate of adaptation in fitness, and log quantitative genetic parameters of fitness, potentially reducing the discord between theoretical and methodological considerations to the operationalization of the secondary and fundamental theorems of selection.

Evolutionary stasis of a heritable morphological trait in a wild fish population despite apparent directional selection

Comparing observed versus theoretically expected evolutionary responses is important for our understanding of the evolutionary process, and for assessing how species may cope with anthropogenic change. Here, we document directional selection for larger female size in Atlantic salmon, using pedigree-derived estimates of lifetime reproductive success as a fitness measure. We show the trait is heritable and, thus, capable of responding to selection. The Breeder's Equation, which predicts microevolution as the product of phenotypic selection and heritability, predicted evolution of larger size. This was at odds, however, with the observed lack of either phenotypic or genetic temporal trends in body size, a so-called "paradox of stasis." To investigate this paradox, we estimated the additive genetic covariance between trait and fitness, which provides a prediction of evolutionary change according to Robertson's secondary theorem of selection (STS) that is unbiased by missing variables. The STS prediction was consistent with the observed stasis. Decomposition of phenotypic selection gradients into genetic and environmental components revealed a potential upward bias, implying unmeasured factors that covary with trait and fitness. These results showcase the power of pedigreed, wild population studies-which have largely been limited to birds and mammals-to study evolutionary processes on contemporary timescales.

Environmental Change, If Unaccounted, Prevents Detection of Cryptic Evolution in a Wild Population

AbstractDetecting contemporary evolution requires demonstrating that genetic change has occurred. Mixed effects models allow estimation of quantitative genetic parameters and are widely used to study evolution in wild populations. However, predictions of evolution based on these parameters frequently fail to match observations. Here, we applied three commonly used quantitative genetic approaches to predict the evolution of size at maturity in a wild population of Trinidadian guppies. Crucially, we tested our predictions against evolutionary change observed in common-garden experiments performed on samples from the same population. We show that standard quantitative genetic models underestimated or failed to detect the cryptic evolution of this trait as demonstrated by the common-garden experiments. The models failed because (1) size at maturity and fitness both decreased with increases in population density, (2) offspring experienced higher population densities than their parents, and (3) selection on size was strongest at high densities. When we accounted for environmental change, predictions better matched observations in the common-garden experiments, although substantial uncertainty remained. Our results demonstrate that predictions of evolution are unreliable if environmental change is not appropriately captured in models.