Summary
The general life history problem concerns the optimal allocation of resources to growth, survival and reproduction. We analysed this problem for a perennial model organism that decides once each year to switch from growth to reproduction. As a fitness measure we used the Malthusian parameterr, which we calculated from the Euler-Lotka equation. Trade-offs were incorporated by assuming that fecundity is size dependent, so that increased fecundity could only be gained by devoting more time to growth and less time to reproduction. To calculate numerically the optimalr for different growth dynamics and mortality regimes, we used a simplified version of the simulated annealing method. The major differences among optimal life histories resulted from different accumulation patterns of intrinsic mortalities resulting from reproductive costs. If these mortalities were accumulated throughout life, i.e. if they were senescent, a bangbang strategy was optimal, in which there was a single switch from growth to reproduction: after the age at maturity all resources were allocated to reproduction. If reproductive costs did not carry over from year to year, i.e. if they were not senescent, the optimal resource allocation resulted in a graded switch strategy and growth became indeterminate. Our numerical approach brings two major advantages for solving optimization problems in life history theory. First, its implementation is very simple, even for complex models that are analytically intractable. Such intractability emerged in our model when we introduced reproductive costs representing an intrinsic mortality. Second, it is not a backward algorithm. This means that lifespan does not have to be fixed at the begining of the computation. Instead, lifespan itself is a trait that can evolve. We suggest that heuristic algorithms are good tools for solving complex optimality problems in life history theory, in particular questions concerning the evolution of lifespan and senescence.
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References
Abrams, P.A. (1991) The fitness costs of senescence: the evolutionary importance of events in early adult life.Evol. Ecol. 5 343–60.
Abrams, P.A. (1993) Does increased mortality favor the evolution of more rapid senescence?Evolution 47 877–87.
Berrigan, D. and Koella, J.C. (1994) The evolution of reaction norms: simple models for age and size at maturity.J. Evol. Biol. 7 549–66.
Caswell, H. (1989) Life-history strategies. InEcological concepts (J.M. Chevett, ed.), pp. 285–307. Blackwell Scientific, Oxford.
Charlesworth, B. (1980)Evolution in Age-structured Populations. Cambridge University Press, Cambridge.
Charlesworth, B. (1990) Evolution: life and times of the guppy.Nature 346 313–14.
Dueck, G. (1993) New optimization heuristics. The great deluge algorithm and the record-to-record-travel.J. Comput. Phys. 104 86–92.
Dueck, G. and Scheuer, T. (1990) Threshold accepting: a general purpose optimization appearing superior to simulated annealing.J. Comput. Phys. 90 161–75.
Hamilton, W.D. (1966) The moulding of senescence by natural selection.J. Theor. Biol. 12 12–45.
Houston, A.I., Clark, C.W., McNamara, J.M. and Mangel, M. (1988) Dynamic models in behavioural and evolutionary ecology.Nature 332 29–34.
Jones, J.S. (1990) Living fast and dying young.Nature 348 288–9.
Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. (1983) Optimization by simulated annealing.Science 220 671–80.
Kozlowski, J. (1993) Measuring fitness in life-history studies.Trends Ecol. Evol. 8 84–5.
Kozlowski, J. and Uchmanski, J. (1987) Optimal individual growth and reproduction in perennial species with indeterminate growth.Evol. Ecol. 1 214–30.
Lawler, E.L., Leustra, J.K., Rinnooy Kan, A.H.G. and Shmoys, D.B. (1985)The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization. Wiley Interscience, New York.
McNamara, J.M. (1991) Optimal life histories: A generalisation of the Perron-Frobenius Theorem.Theor. Pop. Biol. 40 230–45.
McNamara, J.M. (1993) Evolutionary paths in strategy space: An improvement algorithm for life history strategies.J. Theor. Biol. 161 23–37.
Mangel, M. and Clark, C.W. (1988)Dynamic Modeling in Behavioral Ecology. Princeton University Press, Princeton.
Medawar, P.B. (1952)An Unsolved Problem of Biology. H.K. Lewis, London.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. and Teller, E. (1953) Equation of state calculations for fast computing machines.J. Chem. Phys. 21 1087.
Perrin, N. and Sibly, R.M. (1993) Dynamic models of energy allocation and investment.Ann. Rev. Ecol. Syst. 24 379–410.
Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1988)Numerical Recipes in C. The Art of Scientific Computing. Cambridge University Press, Cambridge.
Roff, D.A. (1984) The evolution of life history parameters in teleosts.Can. J. Fish. Aquat. Sci. 41 989–1000.
Roff, D.A. (1992)The Evolution of Life Histories. Chapman & Hall, New York.
Schaffer, W.M. (1983) The application of optimal control theory to the general life history problem.Am. Nat. 121 418–31.
Schaffer, W.M., Inouye, R.S. and Whittam, T.S. (1982) Energy allocation by an annual plant when the effects of seasonality on growth and reproduction are decoupled.Am. Nat. 120 787–815.
Siler, W. (1979) A competing-risk model for animal mortality.Ecology 60 750–7.
Stearns, S.C. (1992)The Evolution of Life Histories. Oxford University Press, Oxford.
Stearns, S.C. and Koella, J.C. (1986) The evolution of phenotypic plasticity in life-history traits: predictions of reaction norms for age and size at maturity.Evolution 40 893–913.
van Noordwijk, A.J. and de Jong, G. (1986) Acquisition and allocation of resources: their influence on variation in life history tactics.Am. Nat. 128 137–42.
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Blarer, A., Doebeli, M. Heuristic optimization of the general life history problem: A novel approach. Evol Ecol 10, 81–96 (1996). https://doi.org/10.1007/BF01239349
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DOI: https://doi.org/10.1007/BF01239349