Analytical results for directional and quadratic selection gradients for log-linear models of fitness functions
1. Established methods for inference about selection gradients involve least-squares regression of fitness on phenotype. While these methods are simple and may generally be quite robust, they do not account well for distributions of fitness. 2. Some progress has previously been made in relating inferences about trait-fitness relationships from generalised linear models to selection gradients in the formal quantitative genetic sense. These approaches involve numerical calculation of average derivatives of relative fitness with respect to phenotype. 3. We present analytical results expressing selection gradients as functions of the coefficients of generalised linear models for fitness in terms of traits. The analytical results allow calculation of univariate and multivariate directional, quadratic, and correlational selection gradients from log-linear and log-quadratic models. 4. The results should be quite generally applicable in selection analysis. They apply to any generalised linear model with a log link function. Furthermore, we show how they apply to some situations including inference of selection from (molecular) paternity data, capture-mark-recapture analysis, and survival analysis. Finally, the results may bridge some gaps between typical approaches in empirical and theoretical studies of natural selection.