Optimal Size at Maturity in Size-Structured Populations

Maturity is a critical point in the life cycle, and determining the optimal age or size at maturity is a classical problem in life history theory. Most organisms spend some time in non-reproductive immature stage. To explain the widespread occurrence of delayed maturity, a number of authors made mathematical models with the age-specific fecundity and survival rate, specified functional forms of fecundity and survival rate, and examined the possibility that two hypotheses hold. One hypothesis is that delayed maturation is advantageous when it leads to more fecundity of mature individuals. The other one is that the offspring produced by parents with delayed maturation may have higher survival in their juvenile period. In the present paper, we use the size-structured McKendrick—von Foerster equation as our basic model and obtain five conditions for delayed maturation. Two of these correspond to the above two hypotheses. The other three are new: we show that a discontinuous decrease at maturation in survival or growth rate can favor delayed maturation. We explore several numerical examples showing the operation of these mechanisms.