The use of multi-response models to improve inferences about natural selection

Sarah Lesley Dobson , Craig A Walling, Elizabeth A. Mittell, Joel L Pick , Loeske E. B. Kruuk

Natural selection, the relationship between trait and fitness, is a key determinant of evolutionary change and population adaptation. Therefore, accurate estimation of natural selection is important. In 1983, Lande and Arnold proposed a simple regression-based approach which allows the measurement of selection on a range of traits whilst accounting for confounding variables. However, issues remain with its application in wild populations which can bias estimates, including assumptions around causality and whether selection on a trait is hard or soft. We highlight how, when fitness and traits are measured repeatedly across individuals and/or common environments, we can identify these issues by comparing directional selection gradients decomposed across different hierarchical levels. We outline the theory behind this and show how multi-response models provide a readily available statistical tool to implement this approach. We then use an empirical example to illustrate how to implement our method and interpret the results. Our approach builds upon previous works to allow greater inference to be drawn from existing datasets, particularly when no genetic information is available. This should facilitate improved interpretation of estimates of selection in wild populations, and ultimately, our understanding of the selection process.