Polymorphism in rapidly changing cyclic environment

Abstract

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic [fine-grained] environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a non-linear fitness that is induced by environmental changes. The non-linear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is examplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment.

Microbial diversity and ecological complexity emerging from environmental variation and horizontal gene transfer in a simple mathematical model

“…The environmental oscillations occur on a fast time scale, whereby the populations are exposed to numerous changes in the environment before approaching any potential equilibrium. We adopted a coarse-graining approach to account for the environmental variations whereby the solution for the composition and total abundance of both populations was obtained as a combination of two components, one delineating the slow-time (coarse grained) behavior and the other capturing the oscillating component [44, 45]. By averaging over the period of environmental variations and retaining the first two leading-order terms of the varying quantities, we obtained the replicator dynamics model with varying total abundance that features fitness contributions derived from two distinct games.…”

“…Horizontal gene transfer plays a crucial role in the preservation of genome diversity [30][31][32][33][34][35][36] but the effects of environmental variations on the microbiome composition remain poorly understood. Evolutionary processes in populations in time-varying environments can drastically differ from those in fixed environments [37][38][39][40][41][42][43][44][45][46][47][48]. The complexity of microbial communities including multiple strains that persist for extended periods of time and widespread HGT among them call for developing theoretical models describing the relationships between strains within complex microbial communities, that are expected to compete with each other, but also constantly exchange genes via HGT.…”

Energy Cost of Dynamical Stabilization: Stored versus Dissipated Energy

“…Dynamical stabilization is an important concept in physics (particle trapping, Floquet engineering) [ 1 , 2 , 3 , 4 ], control theory (vibrational stabilization and robotics) [ 5 , 6 , 7 , 8 ], biology (homeostasis) [ 9 , 10 , 11 , 12 ], animal locomotion [ 13 , 14 ], and population dynamics (polymorphism in time-dependent environments) [ 15 , 16 ]. The meaning of this concept is that certain relevant parameters (concentrations, coordinates) are stabilized against external perturbations by active and frequently self-regulating means.…”

Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation

“…Analysis of nonlinear dynamical equations modelling arXiv:2102.10103v1 [nlin.AO] 17 Feb 2021 various aspects [11][12][13][14][15][16][17][18][19][20][21][22] of evolutionary games is an exciting modern interdisciplinary research area that encompasses problems from biophysics, mathematics, economics, and sociology. In its simplest form, a strategic interaction in a game is supposed to lead to realization of payoff/fitness instantaneously.…”