The Effect of Bottleneck Size on Evolution in Nested Darwinian Populations

Previous work has shown how a minimal ecological structure consisting of patchily distributed resources and recurrent dispersal between patches can scaffold Darwinian properties onto collections of cells. When the timescale of dispersal is long compared with the time to consume resources, patches evolve such that their size increases, but at the expense of cells whose growth rate decreases within patches. This creates the conditions that initiate evolutionary transitions in individuality. A key assumption of this scaffolding is that a bottleneck is created during dispersal, so patches are founded by single cells. The bottleneck decreases competition within patches and hence creates a strong hereditary link at the level of patches. Here we construct a fully stochastic model of nested Darwinian populations and investigate how larger bottlenecks affect the evolutionary dynamics at both cell and collective levels. It is shown that, up to a point, larger bottlenecks simply slow the dynamics, but at some point, which depends on the parameters of the within-patch model, the direction of evolution toward the equilibrium is reversed. Introducing random bottleneck sizes with some positive probability of smaller sizes can counteract this, even if the probability of smaller bottlenecks is small.