A lottery model of density-dependent selection in evolutionary genetics

Fitness is typically represented in heavily simplified terms in evolutionary genetics, often using constant selection coefficients, to make it easier to infer or predict how type frequencies change over time. This excludes fundamental ecological factors such as dynamic population size or density-dependence from the most genetically-realistic treatments of evolution, a problem that inspired MacArthur’s influential but problematic r/K theory. Following the spirit of r/K-selection as a general-purpose theory of density-dependent selection, we develop a new model of density-dependent selection by generalizing the fixed-density classic lottery model of territorial acquisition to accommodate arbitrary population densities. We show that, with density dependence, co-existence is possible in the lottery model in a stable environment. Inspired by natural Drosophila populations, we consider co-existence under strong, seasonally-fluctuating selection coupled to large cycles in population density, and show that co-existence (stable polymorphism) is promoted via a combination of the classic storage effect and density-regulated population growth. We also show that the only significant bias introduced by selection at the different environmental extremes of Grime’s triangle is the relative importance of competitive ability at different densities, confirming an important role for phenotypic constraints in shaping “primary strategies”. 2 . 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/10.1101/102087 doi: bioRxiv preprint first posted online Jan. 21, 2017;