A Geometric Model for Optimal Life History

  • P. D. Taylor
  • G. C. Williams
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 52)


Many authors (Williams, 1966; Gadgil and Bossert, 1970; Taylor et al., 1974; Schaffer, 1979) have considered models of optimal life history strategies. Most generally an organism at any particular age or size has a quantity of available resources which he can spend on maintenance, growth and/or reproduction, and his problem is to allocate these resources optimally. His objective is to maximize some measure of fitness or lifetime reproductive value. This optimization problem can be quite complex because decisions made at one stage may affect resources available at subsequent stages. Thus the mathematical analysis can be difficult and simple general patterns are hard to perceive. Our purpose is to consider a simple model which is quite general, and for which optimal allocation of resources can be determined by graphical analysis of suitable functions.


Life History Parental Care Optimal Allocation Suitable Function Continuous Time Model 
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  1. Gadgil, M., and W. Bossert (1970): Life history consequences of natural selection, Am. Nat. 102:52-64.Google Scholar
  2. Schaffer, W.M. (1979): Equivalence of maximizing reproductive value and fitness in the case of reproductive strategies, Proc. NatZ. Acad. Sci. USA 76: 3567 - 3569.MATHCrossRefGoogle Scholar
  3. Taylor, H.M., R.S. Gourley, C.E. Lawrence, and R.S. Kaplan (1974): Natural selection of life history attributes: an analytical approach, Theor. PopuZ. Biol. 5: 104 - 122.MathSciNetCrossRefGoogle Scholar
  4. Williams, G.C. (1966): Natural selection, the costs of reproduction, and a refinement of Lack's principle, Am. Nat. 100: 687 - 690.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • P. D. Taylor
  • G. C. Williams

There are no affiliations available

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