  Game theory ideas provide a useful framework for studying evolutionary
dynamics in a well-mixed environment. This approach, however, typically
enforces a strictly fixed overall population size, deemphasizing natural growth
processes. We study a competitive Lotka-Volterra model, with number
fluctuations, that accounts for natural population growth and encompasses
interaction scenarios typical of evolutionary games. We show that, in an
appropriate limit, the model describes standard evolutionary games with both
genetic drift and overall population size fluctuations. However, there are also
regimes where a varying population size can strongly influence the evolutionary
dynamics. We focus on the strong mutualism scenario and demonstrate that
standard evolutionary game theory fails to describe our simulation results. We
then analytically and numerically determine fixation probabilities as well as
mean fixation times using matched asymptotic expansions, taking into account
the population size degree of freedom. These results elucidate the interplay
between population dynamics and evolutionary dynamics in well-mixed systems.
