In unpredictably varying environments, it is advantageous for individuals to accept a reduction of their short-term reproductive success in exchange for longer-term risk reduction. This phenomenon called bet-hedging, protects individuals from potential damages associated with environment variations. It is universally present in biology for instance in bacteria resistance to antibiotics, in plants delaying germination or in virus evolution. The idea of bet-hedging is perhaps best illustrated using Kelly's model, originally introduced in the context of gambling models such as horse races. The gambler strives to optimize his/her capital growth by placing appropriate bets while the biological population strives to optimize its growth rate. In both cases, optimal strategies correspond to a maximization of the mean fitness/growth rate while minimizing the variance. Here, we revisit Kelly's model, by including a penalization due to risky fluctuations. We find an analog of a phase transition with a coexistence between two optimal strategies, where one has risk and the other one does not; and a general inequality describing a trade-off between the average growth and the risk taken by the gambler .
We will discuss possible applications of these ideas for modeling strategies used by biological systems to cope with uncertain environments.
Reference: L. Dinis et al., Phase transitions in optimal betting strategies, EPL 131, 60005 (2020).