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To Grow or Not to Grow: Optimal Resource Allocation for Daphnia

We constructed a discrete-time model for growth and reproduction of the cladoceran Daphnia and solved it numerically for resource allocation patterns to maximize the intrinsic rate of increase r under various environmental conditions. Conditions modeled include different functional forms for the size dependencies of predation risk and net production. Growth after maturity can maximize r when net production and survival rate increase with body size. The optimal period for growth after maturity increases with the reproductive life span, but the life span need not be long to favor growth. The shape of the net production curve influences the extent to which body size is increased by delaying maturity or by growing after maturity. When net production increases with body size but survival rate does not, growth after maturity is not optimal. However, simultaneous allocation to growth and reproduction can occur in the instar (time step) preceding maturity.