How Demographic Noise Shapes Phenotypic Clusters in Environmental Gradients

Abstract

2Although resources are typically distributed continuously in space, the distribution of species is often organized in discrete clusters. Such clusters have been shown to spontaneously arise in population densities, even in environments with continuously varying conditions, under the phenomenon known as Turing instability. In this work, we consider two models grounded in population dynamics: a one-dimensional model based on the nonlocal Fisher-KPP equation, and a two-dimensional model involving an environmental gradient. We show that phenotypic clusters emerge in these models, and we prove that they do not emerge because of Turing instability, but because of stochasticity. We first consider initial populations that are uniformly distributed in the state space. We show that phenotypic clusters quickly emerge, and that the distances between them depend on population size, that is, on the degree of stochasticity. In addition to the effect of population size, we provide quantitative estimates of the various parameters of the model with an environmental gradient on the equilibrium distance between phenotypic clusters. Next, we start from clearly defined phenotypic clusters and modify the distance between those. We identify three regimes in the connection between population size, the initial distances between clusters, and the distances between clusters at equilibrium. Last, on the two-dimensional model, we relax the hypothesis of complete clonality by varying the effective recombination rate. We explore its effect on phenotypic clustering, and show that phenotypic clustering decays drastically with slight recombination. 1 Non-specialist summaryWe explored the origin of discrete phenotypic clusters in populations living within a continuous space. Unlike previous studies, our research highlights the importance of stochasticity in the emergence of discreteness. We demonstrate this in two types of model: the first considers a single dimension corresponding either to the phenotype or to the resource spectrum, while the second considers a geographic dimension and a phenotypic dimension. We demonstrate how population size and the other model parameters affect the stable minimum distance between coexisting clusters, as well as how the initial distance between the phenotypes influences this distance. Finally, we relax the hypothesis of complete clonality by introducing sexual reproduction and varying an effective recombination rate.