  Since steep declines in a population's size also typically alter its
composition, population bottlenecks are considered highly important for
evolution. However, despite such significance, the mechanisms governing the
impact of a given population bottleneck remain poorly understood. In this
context, we show that long-term post-bottleneck outcomes can depend crucially
on 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 of
post-bottleneck growth. This behaviour is moreover shown to change
non-trivially with different levels of mutation. The underlying mechanism can
be traced to intrinsic fluctuations whose standard deviation decreases in time
with the inverse square root of the growing population size. Crucially, such
decreasing fluctuations couple to the underlying dynamics and result in
distinct regimes of (non-equilibrium) demographic behaviour, delimited by
abrupt transitions at critical population sizes. Seen through this lens, growth
and mutation alter evolutionary outcomes by changing the duration and character
of dynamical phases; a feature that we speculate may be of generic importance
across many systems.
