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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 ageneralist phenotype that compromise between conditions, or population-wisediversification (bet-hedging). Which strategy provides the largest selectiveadvantage in the long run depends on the range of accessible phenotypes and thestatistics of the environmental fluctuations. Here, we analyze this problem ina simple mathematical model of population growth. First, we review and extend agraphical method to identify the nature of the optimal strategy when theenvironmental fluctuations are uncorrelated. Temporal correlations inenvironmental fluctuations open up new strategies that rely on memory but aremathematically challenging to study: we present here new analytical results toaddress this challenge. We illustrate our general approach by analyzing optimaladaptive strategies in the presence of trade-offs that constrain the range ofaccessible phenotypes. Our results extend several previous studies and haveapplications to a variety of biological phenomena, from antibiotic resistancein bacteria to immune responses in vertebrates.

Transitions in optimal adaptive strategies for populations in fluctuating environments