# Transitions in optimal adaptive strategies for populations in fluctuating environments

## TL;DR

This paper investigates how biological populations adapt to fluctuating environments by analyzing optimal strategies like specialization, generalism, and bet-hedging using a mathematical model, revealing new insights especially when environmental fluctuations are temporally correlated.

## Contribution

The study extends existing models by providing analytical results for optimal adaptive strategies in correlated environmental fluctuations, incorporating memory effects and trade-offs.

## Key findings

- Optimal strategies depend on environmental fluctuation statistics.
- Temporal correlations enable memory-based adaptive strategies.
- Results apply to antibiotic resistance and immune response phenomena.

## 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.