  We study the probability of fixation in a stochastic two-species competition
model. By identifying a naturally occurring fast timescale, we derive an
approximation to the associated backward Kolmogorov equation that allows us to
obtain an explicit closed form solution for the probability of fixation of
either species. We use our result to study fitness tradeoff strategies and show
that, despite some tradeoffs having nearly negligible effects on the
corresponding deterministic dynamics, they can have large implications for the
outcome of the stochastic system.
