Species competition takes place in a fluctuating environment, so the selective forces on different populations vary through time. In many realistic situations the mean fitness and the amplitude of its temporal variations are abundance-dependent. Here we present a theory of two-species competition with abundance-dependent stochastic fitness variations and solve for the chance of ultimate fixation, the time to absorption and the time to fixation. We then examine the ability of this two-species system to serve as an effective model for high-diversity assemblages and to account for the presence of an intra-specific differential response to environmental variations. The effective model is shown to capture the main features of competition between composite populations.
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