| Summary: | Population bottlenecks involve steep declines in population size as well as changes to composition; they are an important aspect of contemporary evolution, and have been implicated across a wide range of taxa. However, the precise mechanisms by which such bottlenecks translate into altered evolutionary outcomes remain poorly understood. Here, we demonstrate how the fixation probabilities associated with such outcomes can depend nontrivially on the rates of post-bottleneck growth and mutation as a population recovers. Notably, increased population growth can invert naive expectations, driving fixation to attractors that are different to those from within whose basin the bottleneck constrained the population, initially, despite more rapidly suppressing the intrinsic fluctuations that are ostensibly required to switch between basins of attraction. Such behavior moreover only occurs beneath a critical threshold of mutation, which is itself a function of the rate of population growth. We explain our results in terms of statistically distinct regimes of demographic behavior, drawing parallels with the notion of nonequilibrium phase transitions. These regimes are delimited by sharp transitions in time, as a population grows, and ultimately result from a time-dependent antagonism between mutation and the stochastically induced effects of frequency-dependent birth. Recast in this context, the rates of population growth and mutation are seen to control long-term fixation probabilities by altering the duration and character of post-bottleneck dynamical demographic regimes.
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