Evolutionary Ecology

, Volume 7, Issue 6, pp 576–592

Optimal growth strategies when mortality and production rates are size-dependent


  • N. Perrin
    • Department of Pure and Applied ZoologyUniversity of Reading
    • Department of Behavioural EcologyBern University, Ethologische Station Hasli
  • R. M. Sibly
    • Department of Pure and Applied ZoologyUniversity of Reading
  • N. K. Nichols
    • Department of MathematicsUniversity of Reading

DOI: 10.1007/BF01237822

Cite this article as:
Perrin, N., Sibly, R.M. & Nichols, N.K. Evol Ecol (1993) 7: 576. doi:10.1007/BF01237822


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 reproduction 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 intermediate phase of simultaneous reproduction and growth. Here we show 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 solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.


optimal growth strategyoptimal energy allocationlife-history theoryindeterminate growth

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© Chapman & Hall 1993