Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon

Abstract

Models of adaptive bet-hedging commonly adopt insights from Kelly's famous work on optimal gambling strategies and the financial value of information. In particular, such models seek evolutionary solutions that maximize long term average growth rate of lineages, even in the face of highly stochastic growth trajectories. Here, we argue for extensive departures from the standard approach to better account for evolutionary contingencies. Crucially, we incorporate considerations of volatility minimization, motivated by interim extinction risk in finite populations, within a finite time horizon approach to growth maximization. We find that a game-theoretic competitive-optimality approach best captures these additional constraints, and derive the equilibria solutions under straightforward fitness payoff functions and extinction risks. We show that for both maximal growth and minimal time relative payoffs the log-optimal strategy is a unique pure-strategy symmetric equilibrium, invariant with evolutionary time horizon and robust to low extinction risks.

Phase transitions in optimal betting strategies

“…It would be also interesting to explore more systematically how additional constraints affect the efficient border. The question of adaptative optimization of the bets, where possible non-Markovian or non-ergodic features could arise, is a rich inference problem worth pursuing [10]. Finally, we hope that this framework could open news research directions on evolutionary tradeoffs and Pareto optimality in biology [5,6].…”

“…Kelly's work led to an essential clarification of the concept of information value in biology [7,8], which was very helpful to understand strategies used by biological systems in a fluctuating environment. In particular the bet-hedging strategy turned out to be precisely an optimal strategy of the Kelly type [9,10].…”

Multiple‐batch spawning as a bet‐hedging strategy in highly stochastic environments: An exploratory analysis of Atlantic cod

“…Extensive theoretical work has been developed on the maximization of geometric fitness under stochastic conditions (Cohen, 1966 ; Lewontin & Cohen, 1969 ; Simons, 2002 ; Starrfelt & Kokko, 2012 ; Yoshimura & Clark, 1991 ), but some ambiguities persist (Metz et al, 1992 ; Sæther & Engen, 2015 ). For example, Tal and Tran ( 2020 ) have stressed the need to re‐consider or upgrade the approach of the maximized geometric mean fitness in the search of a bet‐hedging trait. In the present study, we derived the mean geometric fitness using standard nth roots of the multiplicative approach (Seger & Brockmann, 1987 ).…”

Pareto-optimal trade-off for phenotypic switching of populations in a stochastic environment

“…For real application, demographic fluctuations are important because in the end, one is always interested in finite populations in a finite time [17, 24]. These effects cannot be predicted from A alone; one should consider instead the finite time growth rate Λ t and its fluctuations characterized by the variance Var(Λ t ).…”

“…Although there is no simple method to compute that Lyapunov exponent exactly in the general case where the matrices do not commute (except in the case of 2 x 2 matrices as done in [19]), there are a number of useful approximations, which generalize to arbitrary dimensions. For real application, demographic fluctuations are important because in the end, one is always interested in finite populations in a finite time [17,24]. These effects cannot be predicted from Λ alone; one should consider instead the finite time growth rate Λ t and its fluctuations characterized by the variance Var(Λ t ).…”