Trait-space patterning is dictated by the tempo and mode of mutation

In large, natural ecosystems, many (≳1) phenotypically relevant mutants can emerge over the characteristic turnover time of the population. When this is the case, there can be 'eco-evolutionary feedback' between the dynamical processes that underlie mutation, selection and ecology. We show that, owing to such feedback, the precise details of the mutational process can have a qualitative impact on the long-term behavior of an eco-evolutionary system, in contrast to the classical population genetic assumption that all mutations can be modeled with an effective, homogeneous rate. We demonstrate this in the context of a version of MacArthur's consumer-resource model in which consumers mutate along a resource preference trait-space. Starting from a stochastic individual-based model, we simulate the system in the case where mutations are exogenously generated at a fixed rate (e.g. via external mutagens) and in the case where mutations are coupled to replication (e.g. via DNA copying errors). We find that, surprisingly, replication-coupled mutations are capable of generating a patterned phase in the limit of fast ecological relaxation - precisely the regime where classical population genetic models are expected to operate. We derive a mean-field description of the stochastic model and show that the patterned phase comes about due to a Turing-like mechanism driven by the non-reciprocal and nonlinear nature of replicative mutations. Furthermore, we show that additional interactions like those due to host defense mechanisms can extend the patterned regime to arbitrarily high dimensional phenotype spaces. We demonstrate that these results are robust to demographic noise and model choices and we discuss systems in which this phenomenology might be relevant.