Sireci, M. | bioRxiv Science

bioRxiv2023

Statistical mechanics of phenotypic eco-evolution:from adaptive dynamics to complex diversification

The ecological and evolutionary dynamics of large sets of individuals can be theoretically addressed using ideas and tools from statistical mechanics. This strategy has been addressed in the literature, both in the context of population genetics -whose focus is of genes or "genotypes"-- and in adaptive dynamics, putting the emphasis on traits or "phenotypes". Following this tradition, here we construct a framework allowing us to derive "macroscopic" evolutionary equations from a rather general "microscopic" stochastic dynamics representing the fundamental processes of reproduction, mutation and selection in a large community of individuals, each one characterized by its phenotypic features. Importantly, in our setup, ecological and evolutionary timescales are intertwined, which makes it particularly suitable to describe microbial communities, a timely topic of utmost relevance. Our framework leads to a probabilistic description of the distribution of individuals in phenotypic space --even in the case of arbitrarily large populations-- as encoded in what we call "generalized Crow-Kimura equation" or "generalized replicator-mutator equation". We discuss the limits in which such an equation reduces to the (deterministic) theory of "adaptive dynamics" (i.e. the standard approach to evolutionary dynamics in phenotypic space. Moreover, we emphasize the aspects of the theory that are beyond the reach of standard adaptive dynamics. In particular, by working out, as a guiding example, a simple model of a growing and competing population, we show that the resulting probability distribution can exhibit "dynamical phase transitions" changing from unimodal to bimodal --by means of an evolutionary branching-- or to multimodal, in a cascade of evolutionary branching events. Furthermore, our formalism allows us to rationalize these cascades of transitions using the parsimonious approach of Landaus theory of phase transitions. Finally, we extend the theory to account for finite populations and illustrate the possible consequences of the resulting stochastic or "demographic" effects. Altogether the present framework extends and/or complements existing approaches to evolutionary/adaptive dynamics and paves the way to more systematic studies of e.g. microbial communities as well as to future developments including theoretical analyses of the evolutionary process from the general perspective of non-equilibrium statistical mechanics.

evolutionary biology↗

bioRxiv2022

A macroecological law links abundance correlations with phylogenetic similarity in microbiomes

Multiple ecological forces act together to shape the composition of microbial communities. Phyloecology approaches --which combine phylogenetic relationships with community ecology-- have the potential to disentangle such forces, but are often hard to connect with quantitative predictions from theoretical models. On the other hand, macroecology, which focuses on statistical patterns of abundance and diversity, provides natural connections with theoretical models but often neglects inter-speficic correlations and interactions. Here, we propose a unified framework combining both such approaches to analyze microbial communities. In particular, by using both cross-sectional and longitudinal metagenomic data for species abundances, we reveal the existence of a novel empirical macroecological law establishing that correlations in species-abundance fluctuations across communities decay from positive to null values as a function of phylogenetic similarity in a consistent manner across ecologically distinct microbiomes. We formulate three mechanistic models --relying on alternative ecological forces-- that lead to radically different predictions. We conclude that the empirically observed macroecological pattern can be quantitatively explained as a result of shared fluctuating resources, i.e. environmental filtering and not e.g. as a consequence of species competition. Finally, we also show that the macroecological law is also valid for temporal data of a single community, and that the properties of delayed temporal correlations are reproduced by the model with environmental filtering.

ecology↗