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Since steep declines in a population's size also typically alter itscomposition, population bottlenecks are considered highly important forevolution. However, despite such significance, the mechanisms governing theimpact of a given population bottleneck remain poorly understood. In thiscontext, we show that long-term post-bottleneck outcomes can depend cruciallyon the rate at which a diminished population grows whilst recovering. That is,two otherwise identical populations, each having undergone the same bottleneck,can fixate on dramatically different demographics due to different rates ofpost-bottleneck growth. This behaviour is moreover shown to changenon-trivially with different levels of mutation. The underlying mechanism canbe traced to intrinsic fluctuations whose standard deviation decreases in timewith the inverse square root of the growing population size. Crucially, suchdecreasing fluctuations couple to the underlying dynamics and result indistinct regimes of (non-equilibrium) demographic behaviour, delimited byabrupt transitions at critical population sizes. Seen through this lens, growthand mutation alter evolutionary outcomes by changing the duration and characterof dynamical phases; a feature that we speculate may be of generic importanceacross many systems.

Dynamical phases in growing populations: understanding recovery from bottlenecks