Sex in space-time: How discrete interactions favor sexual reproduction

Abstract

The prevalence of sexual reproduction in nature remains an evolutionary paradox, given its substantial costs compared to asexual alternatives. While genetic explanations such as the Red Queen hypothesis emphasize coevolution with parasites, the role of spatiotemporal discreteness and population structure has been under-explored. Spatial structure matters because real populations are finite, interact locally, and are subject to demographic noise, factors that can fundamentally alter evolutionary outcomes. Here, we show that the discrete, nonlinear character of interactions between hosts and pathogens, when combined with spatial diffusion in low-dimensional habitats, naturally favors sexual reproduction. Using stochastic reaction-diffusion models and renormalization group analysis, we demonstrate that asexual populations face certain extinction in dimensions 𝑑 ≤ 2 due to discreteness-induced extinction (DIE), whereas sexual populations can persist and form stabilizing clusters. The mechanism hinges on the recurrence of random walks in low dimensions, which ensures pathogen-host encounters for asexuals but promotes protective clustering for sexuals. Our results suggest that the advantage of sex may emerge from purely physical and demographic constraints, independent of genetic mechanisms, thereby offering a new perspective on this classic evolutionary puzzle.