Understanding how organisms adapt to environmental variation is a key challenge of biology. Central to this are bet‐hedging strategies that maximize geometric mean fitness across generations, either by being conservative or diversifying phenotypes. Theoretical models have identified environmental variation across generations with multiplicative fitness effects as driving the evolution of bet‐hedging. However, behavioral ecology has revealed adaptive responses to additive fitness effects of environmental variation within lifetimes, either through insurance or risk‐sensitive strategies. Here, we explore whether the effects of adaptive insurance interact with the evolution of bet‐hedging by varying the position and skew of both arithmetic and geometric mean fitness functions. We find that insurance causes the optimal phenotype to shift from the peak to down the less steeply decreasing side of the fitness function, and that conservative bet‐hedging produces an additional shift on top of this, which decreases as adaptive phenotypic variation from diversifying bet‐hedging increases. When diversifying bet‐hedging is not an option, environmental canalization to reduce phenotypic variation is almost always favored, except where the tails of the fitness function are steeply convex and produce a novel risk‐sensitive increase in phenotypic variance akin to diversifying bet‐hedging. Importantly, using skewed fitness functions, we provide the first model that explicitly addresses how conservative and diversifying bet‐hedging strategies might coexist.

Differential allocation (DA) is the adaptive adjustment of reproductive investment (up or down) according to partner quality. A lack of theoretical treatments has led to some confusion in the interpretation of DA in the empirical literature. We present a formal framework for DA that highlights the nature of reproductive benefits versus costs for females mated to males of different quality. Contrary to popular belief, analytical and stochastic dynamic models both show that additive benefits of male quality on offspring fitness have no effect on optimal levels of female investment and thus cannot produce DA. Instead, if offspring fitness is affected multiplicatively by male quality, or male quality affects the female cost function, DA is expected because of changes in the marginal benefits or costs of extra investment. Additive male quality effects on the female cost function can cause a novel form of weak DA, because reduced costs can slightly favor current over future reproduction. Combinations of these distinct effects in more realistic model scenarios can explain various patterns of positive and negative DA reported for different species and mating systems. Our model therefore sheds new light on the diversity of empirical results by providing a strong conceptual framework for the DA hypothesis.

11Understanding how organisms adapt to environmental variation is a key challenge of biology. Central to 12 this are bet-hedging strategies that maximize geometric mean fitness across generations, either by 13 being conservative or diversifying phenotypes. Theoretical models of bet-hedging and the multiplicative 14 fitness effects of environmental variation across generations have traditionally assumed that 15 environmental conditions are constant within lifetimes. However, behavioral ecology has revealed 16 adaptive responses to additive fitness effects of environmental variation within lifetimes, either through 17 insurance or risk-sensitive strategies. Here we explore whether the effects of adaptive insurance interact 18 with the evolution of bet-hedging by varying the position and skew of fitness functions within and 19 between lifetimes. When insurance causes the optimal phenotype to shift from the peak to down the 20 less steeply decreasing side of the fitness function, then conservative bet-hedging does not generally 21 evolve on top of this, even if diversifying bet-hedging can. Canalization to reduce phenotypic variation 22 within a lifetime is almost always favored, except when the tails of the fitness function are steeply 23 convex and produce a novel risk-sensitive increase in phenotypic variance akin to diversifying bet-24 hedging. Importantly, using skewed fitness functions, we provide the first example of how conservative 25 and diversifying bet-hedging strategies might coexist. 26 Keywords 27Fluctuating selection; environmental stochasticity; variance-sensitivity; geometric mean fitness; cliff-28 edge effect; phenotypic canalization.

In order to understand how organisms cope with ongoing changes in environmental variability, it is necessary to consider multiple adaptations to environmental uncertainty on different time scales. Conservative bet-hedging (CBH) represents a long-term genotype-level strategy maximizing lineage geometric mean fitness in stochastic environments by decreasing individual fitness variance, despite also lowering arithmetic mean fitness. Meanwhile, variance-prone (aka risk-prone) strategies produce greater variance in short-term payoffs, because this increases expected arithmetic mean fitness if the relationship between payoffs and fitness is accelerating. Using evolutionary simulation models, we investigate whether selection for such variance-prone strategies is counteracted by selection for bet-hedging that works to adaptively reduce fitness variance. In our model, variance proneness evolves in fine-grained environments (lower correlations among individuals in energetic state and/or payoffs), and with larger numbers of independent decision events over which resources accumulate prior to selection. Conversely, multiplicative fitness accumulation, caused by coarser environmental grain and fewer decision events selection, favours CBH via greater variance aversion. We discuss examples of variance-sensitive strategies in optimal foraging, migration, life histories and cooperative breeding using this bet-hedging perspective. By linking disparate fields of research studying adaptations to variable environments, we should be better able to understand effects of human-induced rapid environmental change.

Bet‐hedging evolves in fluctuating environments because long‐term genotype success is determined by geometric (rather than arithmetic) mean fitness across generations. Diversifying bet‐hedging produces different specialist offspring, whereas conservative bet‐hedging produces similar generalist offspring. However, many fields, such as behavioral ecology and thermal physiology, typically consider specialist versus generalist strategies only in terms of maximizing arithmetic mean fitness benefits to individuals. Here we model how environmental variability affects optimal amounts of phenotypic variation within and among individuals to maximise genotype fitness, and we disentangle the effects of individual‐level optimization and genotype‐level bet‐hedging by comparing long‐term arithmetic versus geometric mean fitness. For traits with additive fitness effects within lifetimes (e.g. foraging‐related traits), genotypes of similar generalists or diversified specialists perform equally well. However, if fitness effects are multiplicative within lifetimes (e.g. sequential survival probabilities), generalist individuals are always favored. In this case, geometric mean fitness optimization requires even more within‐individual phenotypic variation than does arithmetic mean fitness, causing individuals to be more generalist than required to simply maximize their own expected fitness. In contrast to previous results in the bet‐hedging literature, this generalist conservative bet‐hedging effect is always favored over diversifying bet‐hedging. These results link the evolution of behavioral and ecological specialization with earlier models of bet‐hedging, and we apply our framework to a range of natural phenomena from habitat choice to host specificity in parasites.