Comparing measures of breeding inequality and opportunity for selection with sexual selection on a quantitative character in bighorn rams

The opportunity for selection: A slippery concept in ecology and evolution

Natural selection can only occur if individuals differ in fitness. For this reason, the variance in relative fitness has been equated with the 'opportunity for selection' ( I ), which has a long, albeit somewhat controversial, history. In this paper we discuss the use/misuse of I and related metrics in evolutionary ecology. The opportunity is only realised if some fraction of I is caused by trait variation. Thus, I > 0 does not imply that selection is occurring, as sometimes erroneously assumed, because all fitness variation could be independent of phenotype. The selection intensity on any given trait cannot exceed I , but this upper limit will never be reached because (a) stochastic factors always affect fitness, and (b) there might be multiple traits under selection. The expected magnitude of the stochastic component of I is negatively correlated with mean fitness. Uncertainty in realised I is also larger when mean fitness or population/sample size are low. Variation in I across time or space thus can be dominated (or solely driven) by variation in the strength of demographic stochasticity. We illustrate these points using simulations and empirical data from a population study on great tits Parus major. Our analysis shows that the scope for fecundity selection in the great tits is substantially higher when using annual number of recruits as the fitness measure, rather than fledglings or eggs, even after adjusting for the dependence of I on mean fitness. This suggests nonrandom survival of juveniles across families between life stages. Indeed, previous work on this population has shown that offspring recruitment is often nonrandom with respect to clutch size and laying date of parents, for example. We conclude that one cannot make direct inferences about selection based on fitness data alone. However, examining variation in ∆ I F (the opportunity for fecundity selection adjusted for mean fitness) across life stages, years or environments can offer clues as to when/where fecundity selection might be strongest, which can be useful for research planning and experimental design.

How to quantify (the response to) sexual selection on traits

Natural selection operates via fitness components like mating success, fecundity, and longevity, which can be understood as intermediaries in the causal process linking traits to fitness. In particular, sexual selection occurs when traits influence mating or fertilization success, which, in turn, influences fitness. We show how to quantify both these steps in a single path analysis, leading to better estimates of the strength of sexual selection. Our model controls for confounding variables, such as body size or condition, when estimating the relationship between mating and reproductive success. Correspondingly, we define the Bateman gradient and the Jones index using partial rather than simple regressions, which better captures how they are commonly interpreted. The model can be applied both to purely phenotypic data and to quantitative genetic parameters estimated using information on relatedness. The phenotypic approach breaks down selection differentials into a sexually selected and a "remainder" component. The quantitative genetic approach decomposes the estimated evolutionary response to selection analogously. We apply our method to analyze sexual selection in male dusky pipefish, Syngnathus floridae, and in two simulated datasets. We highlight conceptual and statistical limitations of previous path-based approaches, which can lead to substantial misestimation of sexual selection.

Increasing the power of genome wide association studies in natural populations using repeated measures - evaluation and implementation

Genomewide association studies (GWAS) enable detailed dissections of the genetic basis for organisms' ability to adapt to a changing environment. In long‐term studies of natural populations, individuals are often marked at one point in their life and then repeatedly recaptured. It is therefore essential that a method for GWAS includes the process of repeated sampling. In a GWAS, the effects of thousands of single‐nucleotide polymorphisms (SNPs) need to be fitted and any model development is constrained by the computational requirements. A method is therefore required that can fit a highly hierarchical model and at the same time is computationally fast enough to be useful.

Our method fits fixed SNP effects in a linear mixed model that can include both random polygenic effects and permanent environmental effects. In this way, the model can correct for population structure and model repeated measures. The covariance structure of the linear mixed model is first estimated and subsequently used in a generalized least squares setting to fit the SNP effects. The method was evaluated in a simulation study based on observed genotypes from a long‐term study of collared flycatchers in Sweden.

The method we present here was successful in estimating permanent environmental effects from simulated repeated measures data. Additionally, we found that especially for variable phenotypes having large variation between years, the repeated measurements model has a substantial increase in power compared to a model using average phenotypes as a response.

The method is available in the r package RepeatABEL. It increases the power in GWAS having repeated measures, especially for long‐term studies of natural populations, and the R implementation is expected to facilitate modelling of longitudinal data for studies of both animal and human populations.

A rigorous comparison of sexual selection indexes via simulations of diverse mating systems

Sexual selection is a cornerstone of evolutionary theory, but measuring it has proved surprisingly difficult and controversial. Various proxy measures--e.g., the Bateman gradient and the opportunity for sexual selection--are widely used in empirical studies. However, we do not know how reliably these measures predict the strength of sexual selection across natural systems, and most perform poorly in theoretical worst-case scenarios. Here we provide a rigorous comparison of eight commonly used indexes of sexual selection. We simulated 500 biologically plausible mating systems, based on the templates of five well-studied species that cover a diverse range of reproductive life histories. We compared putative indexes to the actual strength of premating sexual selection, measured as the strength of selection on a simulated "mating trait." This method sidesteps a key weakness of empirical studies, which lack an appropriate yardstick against which proxy measures can be assessed. Our model predicts that, far from being useless, the best proxy measures reliably track the strength of sexual selection across biologically realistic scenarios. The maximum intensity of precopulatory sexual selection s'max (the Jones index) outperformed all other indexes and was highly correlated with the strength of sexual selection. In contrast, the Bateman gradient and the opportunity for sexual selection were poor predictors of sexual selection, despite their continuing popularity.