Transitions in optimal adaptive strategies for populations in fluctuating environments

Abstract

Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist phenotype that compromise between conditions, or population-wise diversification (bet-hedging). Which strategy provides the largest selective advantage in the long run depends on the range of accessible phenotypes and the statistics of the environmental fluctuations. Here, we analyze this problem in a simple mathematical model of population growth. First, we review and extend a graphical method to identify the nature of the optimal strategy when the environmental fluctuations are uncorrelated. Temporal correlations in environmental fluctuations open up new strategies that rely on memory but are mathematically challenging to study: we present here new analytical results to address this challenge. We illustrate our general approach by analyzing optimal adaptive strategies in the presence of trade-offs that constrain the range of accessible phenotypes. Our results extend several previous studies and have applications to a variety of biological phenomena, from antibiotic resistance in bacteria to immune responses in vertebrates.

Environment-to-phenotype mapping and adaptation strategies in varying environments

“…Since a phenotype can be close to only one of the archetypes, there is a trade-off between the fitness values in different environments. In this case, the shape of the phenotype distribution can be understood by analyzing the geometry of the "fitness set" [8,40].…”

“…(A10). By locating the point within the extended fitness set that maximizes the long-term growth rate, Λ = µ p µ log f µ , one can find the optimal phenotypic response and the phenotype distribution [8].…”

“…Such phenotypic responses to the environment are modified through the process of evolution, which gives rise to different forms of adaptation. Several adaptation strategies, as described below, have been studied both experimentally and theoretically [1][2][3][4][5][6][7][8]. In this paper, we adopt the phenomenological approach to study biological adaptation by modeling general forms of phenotypic responses to environmental conditions.…”

Exploration-exploitation tradeoffs dictate the optimal distributions of phenotypes for populations subject to fitness fluctuations

“…the persistence of a sub-population of resistant but slow-growing bacteria within a popula-tion subject to high doses of antibiotics [15,16]. Starting with [17], several mathematical models have shown that switching between different phenotypes at the individual cell level can be advantageous in rapidly changing conditions, depending essentially on (i) the statistics of environmental fluctuations and (ii) the specific coupling between the environment and the allowed phenotypes [18][19][20][21][22][23][24][25][26][27][28]. Such models capture the physical and mathematical complexity of these systems starting from minimal assumptions about the environment and/or the space of feasible phenotypes.…”

Adapt or perish: Evolutionary rescue in a gradually deteriorating environment

“…Studying the evolutionary rescue of a population in 14 a gradually deteriorating environment requires accounting for simultaneous continuous time variations of fitness, 15 population size and population composition, which makes it complex. Varying patterns of selection have recently 16 been the focus of significant interest, mainly in the case of switches between different environment states, highlighting 17 their strong effect on evolution [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Despite its practical relevance, the case of a continuously varying fitness has 18 been comparatively less studied, with a focus on stabilizing selection [36,37] or on the fate of a single beneficial 19 mutation [1][2][3].…”