Optimal resource allocation in perennial plants: A continuous-time model

Abstract

A continuous-time model, similar to W. M. Schaffer's (1983, Amer. Nat. 121, 418–431) , of growth and reproduction for a perennial herb with discrete growing seasons is considered. Assuming that metabolic rates of reproductive and storage structures are equal, it was possible, through the reduction of the continuous model to a discrete one, to find the optimal allocations to the vegetative, reproductive, and reserve structures. The main feature of the optimal strategy is the existence of an optimal reserve size. The allocation to vegetative structures is, every growing season, the allocation which maximizes the total of reproductive and reserve structures at the end of the season. The relative allocation between reserve and reproductive structures is given, when reproductive success is a linear function of investment, by the fastest growth to the optimal size: no reproduction until the optimal size is reached, and, afterwards, allocation to reproduction of everything beyond what is needed to maintain size R∗. Asymptotic growth to the equilibrium and cycles are possible, when reproductive success is a nonlinear function of investment ( A. Pugliese, 1988, in “Biomathematics and Related Computational Problems” (L. M. Ricciardi, Ed.), Reidel, Dordrecht, to appear ). It has therefore been possible to solve the “general life history problem” ( Schaffer, 1983) when growth is in general a concave function of body size. In the Discussion discrete and continuous-time models are compared; if the real dynamics is described by a continuous model of the type analyzed here, life history predictions made by analyzing the system with a discrete model are upheld.