Estimating the optimal bottleneck ratio for experimental evolution: The burst-death model

Population bottlenecks are ubiquitous in nature, and are an inherent feature of the experimental protocol for many laboratory selection experiments. These bottlenecks can have profound effects on the rate and trajectory of evolution. In particular, there is a trade-off between sampling the population too frequently and imposing infrequent, but more severe, bottlenecks. In this paper we consider the effects of population bottlenecks, assuming a burst-death model for the life history of the organism under study. This model assumes that generation times are exponentially distributed and that at each generation, individuals in the population have a fixed number of offspring. The model also allows for a constant death rate between bottlenecks. We use this model to estimate the optimal bottleneck ratio, that is, the fraction of the population that should be sampled at each bottleneck in order to maximize the probability that beneficial mutations occur and are not lost. We find that the optimal ratio is roughly constant with respect to many of the model parameters, and that sampling about 20% of the population will maximize the rate of adaptation.