Beyond the (geometric) mean: stochastic models undermine deterministic predictions of bet hedger evolution

Abstract

Bet hedging is a ubiquitous strategy for risk reduction in the face of unpredictable environmental change where a lineage lowers its variance in fitness across environments at the expense of also lowering its arithmetic mean fitness. Previously, deterministic research has quantified this trade-off using geometric mean fitness (GMF), and has found that bet hedging is expected to evolve if and only if it has a higher GMF than the wild-type. We introduce a novel stochastic framework that leverages both individual-based simulations and Markov chain numerics to capture the effects of stochasticity in the phenotypic distribution of diversified bet hedger offspring, in environmental regime, and in reproductive output. We find that modeling stochasticity can alter the sign of selection for the bet hedger compared to the deterministic predictions. We show that stochasticity in phenotype and in environment drive the sign of selection to differ from the deterministic prediction in opposing ways: phenotypic stochasticity causes bet hedging to be less beneficial than predicted, while environmental stochasticity causes bet hedging to be more beneficial than predicted. We conclude that existing, deterministic methods may not be sufficient to predict when bet hedging traits are adaptive.

Balancing the risks of mating: biogeographic evidence of cleistogamy as a bet hedging strategy

“…Given the low relative fitness of the chasmogamous flower morphs, empirical studies of dimorphic cleistogamy have been unable to show that the strategy increases geometric mean fitness relative to complete cleistogamy (Oakley et al [2007]). Interestingly, recent theoretical work has found that bet hedging strategies can be more adaptive than geometric mean fitness predicts (Weissman et al [2024], Zhou and Xue [2022]). In Weissman et al [2024], we demonstrated that bet hedging can be beneficial at sufficiently large population sizes, even when the geometric mean fitness of the bet hedger is less than that of a resident wild-type.…”

“…Interestingly, recent theoretical work has found that bet hedging strategies can be more adaptive than geometric mean fitness predicts (Weissman et al [2024], Zhou and Xue [2022]). In Weissman et al [2024], we demonstrated that bet hedging can be beneficial at sufficiently large population sizes, even when the geometric mean fitness of the bet hedger is less than that of a resident wild-type. This suggests that dimorphic cleistogamy may be adaptive, even if it causes a decrease in geometric mean fitness relative to complete cleistogamy.…”