Evolutionary Phase Transitions in Random Environments

Abstract

We present analytical results for long-term growth rates of structured populations in randomly fluctuating environments, which we apply to predict how cellular response networks evolve. We show that networks which respond rapidly to a stimulus will evolve phenotypic memory exclusively under random (i.e. non-periodic) environments. We identify the evolutionary phase diagram for simple response networks, which we show can exhibit both continuous and discontinuous transitions. Our approach enables exact analysis of diverse evolutionary systems, from viral epidemics to emergence of drug resistance.

Transitions in optimal adaptive strategies for populations in fluctuating environments

“…As noticed in previous studies, temporal correlations in the environmental conditions influences the choice of optimal adaptation strategies [14,18,26]. The intermediate timescale regime, where the environmental correlation time is of the same order as the generation time, has been notoriously difficult to handle analytically.…”

“…Possible extensions of our results include the influence of non-random environmental changes, such as periodic environments [14,18,21,27], constraints on relative switching rates [16,17,27], active sensing mechanisms [3] and heritable plasticity [13,19], or finite population size effects [28]. Some of these factors are known to lead to transitions between adaptive strategies, e.g.…”

“…Some of these factors are known to lead to transitions between adaptive strategies, e.g. the variability of environmental durations [18], or cause the transitions to become discontinuous, e.g. when switching rates are constrained to be independent of phenotype [16,17,27].…”

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.…”

Delays in Fitness Adjustment Can Lead to Coexistence of Hierarchically Interacting Species

“…Thus, microbial diversity in soil is thought to be supported by the highly porous and fragmented structure of this habitat [11], and the fluctuating environmental conditions that individual bacteria experience there [10].Here, we ask how the influence of spatial structure, characterized by intrinsic variation between local environments, and the delayed adjustment to changes of these environments, can affect the long-term behaviour of species in a simple model system. Indeed, it is wellknown that such delays in physiological responses (here, adjustment of fitness or growth rate) occur in microbes, following externally imposed changes in the environment [12][13][14][15], such as nutrient composition, or antibiotic stress [16][17][18][19][20][21][22]. Here, we focus on changes that occur because species move between different habitats.…”