Population Dynamics in a Changing Environment: Random versus Periodic Switching

Abstract

Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a timevarying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity. The population dynamics is characterized by demographic noise (birth and death events) coupled to a varying environment. We elucidate the similarities and differences of the evolution subject to a stochastically and periodically varying environment. Importantly, the population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations, which results in markedly different asymptotic behaviors between the fixation probability of random and periodic switching. We also determine the detailed conditions under which the fixation probability of the slow strain is maximal.

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

“…(•) Some examples from the nano-and micro-biological world are the events of stochastic resetting due to backtracking interrupting a processive motion of RNA polymerase along DNA upon transcription 33 and an alternating switching between the 3D diffusion-based spreading and 1D recognition-based target search in motion of DNA-binding proteins in DNA coils [91][92][93][94][95] . (•) On the level of simple organisms, stochasticswitching mechanisms between different phenotypes can be mentioned (employed by various bacteria and fungi to optimize adaptation of a phenotypically diverse population of individuals to fluctuating [and, often, irregularly changing] environments [96][97][98][99][100][101] ). (•) strategies for boosting combinatorial-search algorithms [102][103][104] (via adding a controlled amount of randomization (complete backtracks) to minimize the cumulative search time for a set of tasks or make mean search-times more predictable) 104 and dependency-directed backtracking algorithms in hard constraint-satisfaction problems involving artificial intelligence 102 in computer sciences, (•) in visual pattern recognition, picture-viewing-, and visual-search-strategies [105][106][107][108][109] (where large-visualangle jerking-like saccadic motions are interrupted by fixational tremor-like, jiggling microsaccadic "observational" motions [depending, i.a., on the actual task being posed, the contextual information, habituation effects, etc.]…”

Exclusion of the fittest predicts microbial community diversity in fluctuating environments

“…The outcome at this switching rate therefore corresponds to the mean outcome of those two environments. On the other hand, a very fast environmental switching rate ( ν → ∞) corresponds to a scenario where the resource supply is at mean concentration (environmental noise self averages, see, e.g.,Wienand et al (2017, 2018); West and Mobilia (2020); Taitelbaum et al (2020)). How the strength of competition varies at an intermediate switching rate is, however, less intuitive.…”

“…Second, the switching rate is assumed to be symmetric between abundant and scarce resources (and/or toxin supplies, see Appendix 4). One may include more than two environmental conditions or assume asymmetric environmental switching, as in work by Taitelbaum et al (2020), who show that asymmetric switching can non-trivially change the effects of environmental switching. Third, our model focuses on competitive exclusion but other types of interactions can also affect diversity (Rodríguez-Verdugo et al, 2019).…”

“…For simplicity, we assume symmetric random switching (but see Taitelbaum et al (2020) for asymmetric, random and periodic switching). This model combines two sources of noise: birth and death events occur randomly yielding demographic noise, while the environment randomly switches from being harsh to mild and vice versa and drives the population size (Wienand et al, 2017, 2018; West and Mobilia, 2020; Taitelbaum et al, 2020). When the environment becomes harsh (e.g., abundant toxins or scarce resources), the population shrinks and demographic noise can lead to extinction.…”

Environment driven oscillation in an off-lattice May–Leonard model

“…The above mentioned unequal invasion rates could be the result of an environmental factor, which is in general a parallel research avenue in complex systems. Heterogeneous environment can modify dynamical process directly 37 – 43 , which could be a local or a seasonal, or time-dependent change 44 , 45 . But we may control the state of the environment to modify the fractions of competing agents intentionally 46 – 48 .…”