Analytical results for directional and quadratic selection gradients for log-linear models of fitness functions

11 1. Established methods for inference about selection gradients involve least-squares regression 12 of fitness on phenotype. While these methods are simple and may generally be quite robust, 13 they do not account well for distributions of fitness. 14 2. Some progress has previously been made in relating inferences about trait-fitness rela15 tionships from generalised linear models to selection gradients in the formal quantitative 16 genetic sense. These approaches involve numerical calculation of average derivatives of 17 relative fitness with respect to phenotype. 18 3. We present analytical results expressing selection gradients as functions of the coefficients 19 of generalised linear models for fitness in terms of traits. The analytical results allow 20 calculation of univariate and multivariate directional, quadratic, and correlational selection 21 gradients from log-linear and log-quadratic models. 22 4. The results should be quite generally applicable in selection analysis. They apply to any 23 generalised linear model with a log link function. Furthermore, we show how they apply to 24 some situations including inference of selection from (molecular) paternity data, capture25 mark-recapture analysis, and survival analysis. Finally, the results may bridge some gaps 26 between typical approaches in empirical and theoretical studies of natural selection. 27 . CC-BY 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/040618 doi: bioRxiv preprint first posted online Feb. 22, 2016;