Noise-driven Turing patterns in eco-evolutionary models

In large ecosystems, phenotypically significant mutants can arise within a single ecological turnover, creating eco-evolutionary feedback between mutation, selection, and species interactions. Our previous work has shown that mutations and interactions alone can drive phenotypic patterning through a Turing-like instability. However, those results were derived at the mean-field level, neglecting demographic fluctuations that play a crucial role in finite populations. Here we show that demographic noise does more than blur deterministic predictions. It can generate and stabilize phenotypic clusters and expand the domain in which phenotypic patterns exist. We analyze systems with externally supplied mutations and with replication-coupled mutations under fixed ecological kernels and derive criteria for noise-driven Turing patterning by analyzing the power spectrum. These results reveal a general mechanism by which noise generates long-lived structure in evolving ecosystems in regimes where mutation is fast. This stands in contrast to classical phenotypic pattern formation mechanisms, like limiting similarity, which are due to ecological interactions alone. The same principles may underlie the emergence of phenotypic organization in microbial communities and cancer cell populations, where demographic fluctuations and fast mutational processes can govern coexistence and adaptation.