An essential aspect of the current theory of adaptive speciation is the maintenance of phenotypic variation and the evolution of stationary stable phenotypic diversity, a phenomenon known as evolutionary branching. Theoretical and empirical evidence suggest that phenotypic variation can be maintained by favoring rare phenotypes, for example, through frequency-dependent selection. However, even when phenotypic variation is provided, the conditions leading to evolutionary branching are not universal. In order to lead to stable diversification, current models of adaptive speciation, such as the Lotka-Volterra competition model, must resort to strong assumptions that range from using unrealistic shape parameters for the competition and carrying capacity functions, modeling separately the generation of discontinuities in niche space, to increasing the dimensionality of phenotypic traits. Here, we introduce a stochastic version of the Lotka-Volterra competition model. We demonstrate that environmental fluctuations suffice to lead consistently to phenotypic diversification and evolutionary branching. Our observations build upon previous findings identifying a role for stochastic fluctuations on the evolution of phenotypic diversity, emphasize the difference between strong versus weak assumptions in the stability of the LVC model, and suggest that the conditions for evolutionary branching are more relaxed than anticipated.
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