OPTIMAL-GROWTH STRATEGIES WHEN MORTALITY AND PRODUCTION-RATES ARE SIZE-DEPENDENT

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and repro duction is linear. Analyses of the optimal allocation problem to date have generally yielded 'bang-bang' solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no i ntermediate phase of simultaneous reproduction and growth. Here we sho w that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular sol ution to the problem. Our conclusion is that indeterminate growth is o ptimal in more cases than was previously realized. The relevance of ou r results to natural situations is discussed.