Unexpected Patterns of Plastic Energy Allocation in Stochastic Environments

When environmental conditions vary stochastically, individuals accrue fitness benefits by exhibiting phenotypic plasticity. Such benefits may be counterbalanced by costs of plasticity that increase with the exhibited degree of plasticity. Here we introduce and analyze a general dynamic- programming model describing an individuals optimal energy allocation in a stochastic environment. After maturation, individuals decide repeatedly how to allocate incoming energy between reproduction and maintenance. We investigate the optimal fraction of energy invested into reproduction and the resultant degree of plasticity in dependence on the variability and predictability of the environment. Our analyses reveal unexpected patterns of optimal energy allocation. In environments with very low energy availability, all energy is allocated to reproduction, although this implies that individuals will not survive after reproduction. Above a certain threshold of energy availability, the optimal reproductive investment rapidly decreases to a minimum, and even vanishes entirely when the environment is highly variable. With further improvement of energy availability, optimal reproductive investment gradually increases again, until almost all energy is allocated to reproduction. Costs of plasticity affect this allocation pattern only quantitatively. Our results show that optimal reproductive investment does not increase monotonically with growing energy availability and that small changes in energy availability can lead to major variations in optimal energy allocation. Our results help to unify two apparently opposing predictions from life-history theory, that organisms should increase reproductive investment both with improved environmental conditions and when conditions deteriorate ('terminal investment')