The sympatric speciation is an important phenomenon in the Evolution where a population able to express two different phenotypes gives rise to a new species without a physical separation from the initial population. Our goal is to show as simple assumptions on the initial population phenotypes and the selection process induced by a fluctuating environment allow to define a simple stochastic model that can explain the sympatric speciation via a stochastic bifurcation mechanism. We analyze the dynamical properties of the model and its possible relevance to describe the evolution of the speciation process as the result of enviromental fluctuations, highlighting the control parameters.
Bazzani et al. (2025) studied this question.