Abstract
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.
Highlights
How organisms adapt to unpredictable fluctuations in the environment has been an intriguing and important problem for many years in evolutionary biology, and especially recently when predicting adaptive responses to environmental change
In accordance with Bull’s (1987) result, this selection for increased phenotypic variation only appears once the environmental variance σ2θ is larger than the squared width of the fitness function, and the optimal σ2k is equal to σ2θ − ω2
The shift produced when maximizing arithmetic mean fitness represents insurance, but in each case there is a small additional shift when maximizing geometric mean fitness that can be attributed to conservative bet-hedging (CBH), amounting to between 27% for σθ = 0.5 and 1.6% for σθ = 3
Summary
Urban et al 2013). Skew in the function relating a single, continuous phenotypic trait to fitness is commonly seen in nature, occurring whenever costs and benefits differ in how they relate to increasing versus decreasing values of the phenotype, or when the strength of selection acting on the two sides of the phenotypic distribution differs. Common examples are thermal performance curves (Angilletta 2009), optimal clutch or litter sizes (Mountford 1968; Boyce and Perrins 1987; Gamelon et al 2018), and reproductive benefits versus viability costs of sexually selected ornaments (Andersson and Iwasa 1996) In these types of scenarios, uncertainty across instances in any component determining individual fitness will cause the optimal trait value to differ from the trait value at the peak of the fitness function (Yoshimura and Shields 1987; Parker and Smith 1990). An additional shift in the optimal trait value even further away from the cliff edge might be selected for if it lowers fitness variance between generations (despite lowering arithmetic mean fitness in a single generation) Such an effect would essentially constitute a CBH strategy. By using a skewed fitness function to illustrate the effects of insurance versus CBH, we are able to examine these interactions, while modeling DBH alongside CBH in such a way allows us to formally explore Starrfelt and Kokko’s (2012) suggestion regarding an adaptive continuum between these two potentially coexisting forms of bet-hedging
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