Dynamical demographic phases explain how population growth and mutation control the evolutionary impact of bottlenecks

Crosato, Emanuele; Philippson, Jeffrey N.; Thutupalli, Shashi; Morris, Richard G.

doi:10.1103/physrevresearch.5.013093

Cited by 2 publications

(1 citation statement)

References 42 publications

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“…As a matter of fact, the consequences of demographic fluctuations have been extensively studied in the context of population genetics [13,66], evolutionary game theory [130][131][132][133][134] and AD [80,88,98,135]. In addition to introducing fluctuations around deterministic behavior, demographic fluctuations have been shown to give rise to unexpected phenomenology such as, e.g., evolutionary tunneling, population bottlenecks, and inversion of the direction of selection, to name but a few examples [132,136,137].…”

Section: Stochastic Finite Size Fluctuationsmentioning

confidence: 99%

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

Sireci¹,

Muñoz²

2023

Preprint

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The ecological and evolutionary dynamics of large sets of individuals can be naturally addressed from a theoretical perspective using ideas and tools from statistical mechanics. This parallelism has been extensively discussed and exploited in the literature, both in the context of population genetics and in phenotypic evolutionary or adaptive dynamics. Following this tradition, here we construct a framework allowing us to derive ‘macroscopic’ evolutionary equations from a rather general ‘microscopic’ stochastic dynamics representing the processes of reproduction, mutation and selection in a large community of individuals, each one characterized by its phenotypic features. In this set up, ecological and evolutionary timescales are intertwined, which makes it particularly suitable to describe microbial communities, a timely topic of utmost relevance. Our framework leads, even in the limit of infinitely large populations, to a probabilistic description of the distribution of individuals in phenotypic space, 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 theory of ‘adaptive dynamics’ (i.e. the standard approach to evolutionary dynamics in phenotypic space, which usually focuses on the mean or at most the variance of such distributions). Moreover, we emphasize the aspects of the theory that are beyond the reach of standard adaptive dynamics. In particular, working out, as an example, a simple model of a growing and competing population, we show that the resulting probability distribution can possibly 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 events as a cascade of ‘dynamical phase transitions’, using the parsimonious approach of Landau’s 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 perspective of non-equilibrium statistical mechanics.

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Section: Stochastic Finite Size Fluctuationsmentioning

confidence: 99%

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

Sireci¹,

Muñoz²

2023

Preprint

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

Sireci,

Muñoz

2024

Phys. Rev. Research

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The ecological and evolutionary dynamics of large populations can be addressed theoretically using concepts and methodologies from statistical mechanics. This approach has been extensively discussed in the literature, both within the realm of population genetics, which focuses on genes or “genotypes,” and in adaptive dynamics, which emphasizes traits or “phenotypes.” Following this tradition, here we construct a theoretical framework allowing us to derive “macroscopic” evolutionary equations from a 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. The framework leads to a probabilistic description—even in the case of arbitrarily large populations—of the distribution of individuals in phenotypic space as encoded in what we call the “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 developing a simple model of a growing and competing population as an illustrative example, we demonstrate that the resulting probability distribution can undergo “dynamical phase transitions.” These transitions may involve shifts from a unimodal distribution to a bimodal distribution, generated by an evolutionary branching event, or to a multimodal distribution through a cascade of evolutionary branching events. Furthermore, our formalism allows us to rationalize these cascades using the parsimonious approach of Landau's 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 and adaptive dynamics and paves the way to more systematic studies of microbial communities as well as to future developments including theoretical analyses of the evolutionary process from the general perspective of nonequilibrium statistical mechanics. Published by the American Physical Society 2024

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Dynamical demographic phases explain how population growth and mutation control the evolutionary impact of bottlenecks

Cited by 2 publications

References 42 publications

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

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

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

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