Evolutionary Ecology

, Volume 1, Issue 2, pp 125–138 | Cite as

Probabilistic optimization of phenotype distributions: a general solution for the effects of uncertainty on natural selection?

  • Jin Yoshimura
  • William M. Shields
Papers

Summary

Explorations of optimizing selection often find discrepancies between the theoretically expected and observed phenotypes. Such discrepancies are usually attributed to a variety of potential constraints. We suggest that one common constraint, environmental uncertainty, may reduce the applicability of traditional deterministic or stochastic optimization methods and that many apparent discrepancies might be artifacts of these methods. Since natural selection is essentially a statistical process, we propose that a probabilistic optimization procedure, that includes all of the variability in phenotype distributions and associated fitness potential functions might offer better results. The traditional methods define an optimal gene or genotype as that which produces a phenotype distribution with a mean or other measure of central tendency that equals the value yielding the maximum fitness potential. Our method defines the optimal gene or genotype as that which produces the phenotype distribution that maximizes fitness summed or integrated over its associated fitness potential function. Often the central tendency of the phenotype distribution yielding the probabilistic optimum will differ from the deterministic expectation. This method is an extension of utility theory to any phenotypic character. We illustrate our method using an example based on Price and Waser's (1979) notion of optimal inbreeding via optimal pollen dispersal.

Keywords

probabilistic optimization optimal phenotype distribution adaptation under uncertainty 

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References

  1. Alexander, R. M. (1982)Optima for Animals, Edward Arnold, London. 112 pp.Google Scholar
  2. Bateson, P. (1978) Sexual imprinting and optimal outbreeding.Nature 273, 659–60.PubMedGoogle Scholar
  3. Bateson, P. (1980) Optimal outbreeding and the development of sexual preferences in Japanese Quail.Z. Tierpsych. 53, 231–44.Google Scholar
  4. Bateson, P. (1983) Optimal outbreeding. InMate choice (P. Bateson, ed.) pp. 257–77. Cambridge University Press, Cambridge, England.Google Scholar
  5. Bell, G. (1982)The masterpiece of nature. The evolution and genetics of sexuality, University of California Press, Los Angeles. 600 pp.Google Scholar
  6. Bernstein, H., Byerly, H. C., Hopf, F. A. and Michod, R. E. (1985) Genetic damage, mutation and the evolution of sex.Science 299, 1277–81.Google Scholar
  7. Boyce, M. S. (1977) Population growth with stochastic fluctuations in the life table.Theor. Pop. Biol. 12, 366–73.Google Scholar
  8. Brady, R. H. (1979) Natural selection and the criteria by which a theory is judged.Syst. Zool. 28, 600–21.Google Scholar
  9. Brown, J. S. and Venable, D. L. (1986) Evolutionary ecology of seed-bank annuals in temporally varying environments.Am. Nat. 127, 31–47.Google Scholar
  10. Bulmer, M. G. (1984) Delayed germination of seeds: Cohen's model revisited.Theor. Pop. Biol. 26, 367–77.Google Scholar
  11. Caraco, T. (1980) On foraging time allocation in a stochastic environment.Ecology 61, 119–28.Google Scholar
  12. Caraco, T. and Chasin, M. (1984) Foraging preferences: response to reward skew.Anim. Behav. 32, 76–85.Google Scholar
  13. Carson, H. L. (1975) The genetics of speciation at the diploid level.Am. Nat. 109, 83–92.Google Scholar
  14. Cody, M. (1974) Optimization in ecology.Science 183, 1156–64.Google Scholar
  15. Cohen, D. (1966) Optimizing reproduction in a randomly varying environment.J. theor. Biol. 12, 119–29.PubMedGoogle Scholar
  16. Cohen, D. (1967) Optimizing reproduction in a randomly varying environment when a correlation may exist between the conditions at the time a choice has to be made and the subsequent outcomes.J. theor. Biol. 16, 1–14.PubMedGoogle Scholar
  17. Crow, J. F. and Kimura, M. (1970)An introduction to population genetics theory, Harper and Row, New York. 591 pp.Google Scholar
  18. DeGroot, M. H. (1970)Optimal statistical decisions, MacGraw Hill, New York. 489 pp.Google Scholar
  19. Eldredge, N. and Gould, S. J. (1972) Punctuated equilibria: an alternative to phyletic gradualism. InModels in paleobiology (T. J. M. Schopf, ed.) pp. 82–115. Freeman, Cooper & Co., San Francisco. 250 pp.Google Scholar
  20. Emlen, J. M. (1966) The role of time and energy in food preference.Am. Nat. 100, 611–17.Google Scholar
  21. Fisher, R. A. (1930)The genetical theory of natural selection, Oxford University Press, Oxford. (Reprint: 1958. Dover, New York) 291 pp.Google Scholar
  22. Gillespie, J. H. (1977) Natural selection for variances in offspring numbers: a new evolutionary principle.Am. Nat. 111, 1010–14.Google Scholar
  23. Gould, S. J. and Eldredge, N. (1977) Punctuated equilibria: the tempo and mode of evolution reconsidered.Paleobiology 3, 115–51.Google Scholar
  24. Gould, S. J. and Lewontin, R. C. (1979) The spandrels of San Marco and the Panglossian paradigm: a critique of the adaptationist programme.Proc. R. Soc. Lond. B 205, 581–98.PubMedGoogle Scholar
  25. Green, R. F. (1980) Bayesian birds: a simple example of Oaten's stochastic model of optimal foraging.Theor. Pop. Biol. 18, 244–56.Google Scholar
  26. Haldane, J. B. S. (1932)The causes of evolution, Harper, New York. 235 pp.Google Scholar
  27. Ho, M.-W. and Saunders, P. T. (1979) Beyond neo-Darwinsim — an epigenetic approach to evolution.J. theor. Biol. 78, 573–91.PubMedGoogle Scholar
  28. Ho, M.-W. and Saunders, P. T. (eds) (1984)Beyond neo-Darwinism: an introduction to the new evolutionary paradigm, Academic Press, London. 376 pp.Google Scholar
  29. Houston, A. I. and McNamara, J. M. (1985) The variability of behaviour and contrained optimization.J. theor. Biol. 112, 265–73.Google Scholar
  30. Iwasa, Y., Higashi, M. and Yamamura, N. (1981) Prey distribution as a factor determining the choice of optimal foraging strategy.Am. Nat. 117, 710–23.Google Scholar
  31. King, D. and Roughgarden, J. (1982) Graded allocation between vegetative and reproductive growth for annual plants in growing seasons of random length.Theor. Pop. Biol. 22, 1–16.Google Scholar
  32. Krebs, J. R., Ryan, J. C. and Charnov, E. L. (1974) Hunting by expectation or optimal foraging? A study of patch use by chickadees.Anim. Behav. 22, 953–64.Google Scholar
  33. Kondrashov, A. S. (1982) Selection against harmful mutations in large sexual and asexual populations.Genet. Res. 40, 325–32.PubMedGoogle Scholar
  34. Levene, H. (1953) Genetic equilibrium when more than one niche is available.Am. Nat. 87, 331–3.Google Scholar
  35. Levins, R. (1968)Evolution in changing environments, Princeton University Press, Princeton, New Jersey. 120 pp.Google Scholar
  36. Levins, R. (1970) Fitness and optimization. InMathematical topics in population genetics (K. Kojima, ed.) pp. 389–400. Springer-Verlag, New York.Google Scholar
  37. Lewontin, R. C. (1974)The genetic basis of evolutionary change, Columbia University Press, New York. 346 pp.Google Scholar
  38. Lewontin, R. C. (1978) Fitness, survival and optimality. InAnalysis of ecological systems (D. H. Horn, R. Mitchell and G. R. Stairs, eds) pp. 3–21. Ohio State University, Columbus.Google Scholar
  39. Lewontin, R. C. (1979) Sociobiology as an adaptationist program.Behav. Sci. 24, 5–14.PubMedGoogle Scholar
  40. Lewontin, R. C. and Cohen, D. (1969) On population growth in a randomly varying environment.Proc. Nat. Acad. Sci. USA 62, 1056–60.PubMedGoogle Scholar
  41. MacArthur, R. H. and Pianka, E. R. (1966) On optimal use of a patchy environment.Am. Nat. 100, 603–9.Google Scholar
  42. Maynard Smith, J. (1978) Optimization theory in evolution.Ann. Rev. Ecol. Syst. 9, 31–56.Google Scholar
  43. Maynard Smith, J. (1982)Evolution and the theory of games, Cambridge University Press, Cambridge, England. 222 pp.Google Scholar
  44. Maynard Smith, J., Burian, R., Kauffman, S., Alberch, P., Campbell, J., Goodwin, B., Lande, R., Raup, D. and Wolpert, L. (1985) Developmental constraints and evolution.Q. Rev. Biol. 60, 256–87.Google Scholar
  45. Mayo, O. (1983)Natural selection and its constraints, Academic Press, London. 145 pp.Google Scholar
  46. Mayr, E. (1983) How to carry out the adaptationist program?Am. Nat. 121, 324–34.Google Scholar
  47. McNair, J. N. (1980) A stochastic foraging model with predator training effects: I. functional response, switching, and run length.Theor. Pop. Biol. 17, 141–66.Google Scholar
  48. McNamara, J. (1982) Optimal patch use in a stochastic environment.Theor. Pop. Biol. 21, 269–88.Google Scholar
  49. Milkman, R. (1978) Selection differentials and selection coefficients.Genetics 88, 391–403.Google Scholar
  50. Monod, J. (1971)Chance and Necessity, Vintage Books, New York. 198 pp.Google Scholar
  51. Oaten, A. (1977) Optimal foraging in patches: a case for stochasticity.Theor. Pop. Biol. 12, 263–85.Google Scholar
  52. Oster, G. and Wilson, E. O. (1978)Caste and ecology in the social insects, Princeton University Press, Princeton, New Jersey. 352 pp.Google Scholar
  53. Price, M. V. and Waser, N. M. (1979) Pollen dispersal and optimal outcrossing inDelphinium nelsonii.Nature 277, 294–6.PubMedGoogle Scholar
  54. Raiffa, H. (1968)Decision analysis. Introductory lectures on choices under uncertainty, Addison-Wesley, Reading, Mass. 309 pp.Google Scholar
  55. Real, L. (1980a) On uncertainty and the law of diminishing returns in evolution and behavior. InLimits to action. The allocation of individual behavior (J. E. R. Staddon, ed.) pp. 37–64. Academic Press, New York.Google Scholar
  56. Real, L. (1980b) Fitness, uncertainty, and the role of diversification in evolution and behavior.Am. Nat. 115, 623–38.Google Scholar
  57. Roughgarden, J. (1979)Theory of population genetics and evolutionary ecology: An introduction, MacMillan Publ. Co., New York. 634 pp.Google Scholar
  58. Rubenstein, D. (1982) Risk, uncertainty and evolutionary strategies. InCurrent problems in sociobiology (King's College Sociobiology Group, eds) pp. 91–111. Cambridge University Press, Cambridge, England.Google Scholar
  59. Shields, W. M. (1979)Philopatry, inbreeding, and the adaptive advantages of sex, Ph. D. Dissertation, Ohio State University, Columbus, Ohio. 423 pp.Google Scholar
  60. Shields, W. M. (1982)Philopatry, inbreeding and the evolution of sex, State University of New York Press, Albany. 245 pp.Google Scholar
  61. Shields, W. M. (1983) Optimal inbreeding and the evolution of philopatry. InThe ecology of animal movement (I. R. Swingland and P. I. Greenwood, eds) pp. 132–59. Oxford University Press, Oxford.Google Scholar
  62. Simon, H. A. (1977)Models of discovery and other topics in the method of science, D. Raidel, Boston, Mass. 456 pp.Google Scholar
  63. Simon, H. A. and Kadane, J. B. (1975) Optimal problem-solving search: All-or-none solutions.Artificial Intelligence 6, 235–47.Google Scholar
  64. Slatkin, M. and Lande, R. (1976) Niche width in a fluctuating environment-density independent model.Am. Nat. 110, 31–55.Google Scholar
  65. Sober, E. (1984)The nature of selection: evolutionary theory in philosophical focus, The MIT Press, Cambridge, Mass. 400 pp.Google Scholar
  66. Stearns, S. C. (1982) The role of development in the evolution of life histories. InEvolution and development (J. T. Bonner, ed.) pp. 237–58. Springer-Verlag, New York.Google Scholar
  67. Stephens, D. W. and Charnov, E. L. (1982) Optimal foraging: some simple stochastic models.Behav. Ecol. Sociobiol. 10, 251–63.Google Scholar
  68. Templeton, A. R. (1981) Mechanisms of speciation — a population genetic approach.Ann. Rev. Ecol. Syst. 12, 23–48.Google Scholar
  69. Tuljapurkar, S. D. and Orzack, S. H. (1980) Population dynamics in variable environments 1. Long-run growth rates and extinction.Theor. Pop. Biol. 18, 314–42.Google Scholar
  70. Waddington, C. H. (1957)The strategy of the genes, George Allen and Unwin, London. 262 pp.Google Scholar
  71. Waddington, C. H. (1962)New patterns in genetics and development, Columbia University Press, New York. 271 pp.Google Scholar
  72. Waddington, K. D. (1983) Pollen flow and optimal outcrossing distance.Am. Nat. 122, 147–51.Google Scholar
  73. Waser, N. M. and Price, M. V. (1983) Optimal and actual outcrossing in plants, and the nature of plant-pollinator interaction. InHandbook of experimental pollination biology (C. E. Jones and R. J. Little, eds) pp. 341–59. Van Nostrand Reinhold, New York.Google Scholar
  74. Williams, G. C. (1966)Adaptation and natural selection, Princeton University Press, Princeton, New Jersey. 307 pp.Google Scholar
  75. Williams, G. C. (1975)Sex and evolution, Princeton University Press, Princeton, New Jersey. 200 pp.Google Scholar
  76. Wright, S. (1931) Evolution in Mendelian populations.Genetics 16, 97–159.Google Scholar
  77. Wright, S. (1977)Evolution and the genetics of populations. Volume 3 Experimental results and evolutionary deductions, The University of Chicago Press, Chicago. 613 pp.Google Scholar
  78. Wright, S. (1978)Evolution and the genetics of populations. Volume 4 Variability within and among natural populations, The University of Chicago Press, Chicago. 580 pp.Google Scholar

Copyright information

© Chapman and Hall Ltd. 1987

Authors and Affiliations

  • Jin Yoshimura
    • 1
  • William M. Shields
    • 1
  1. 1.State University of New York College of Environmental Science and ForestrySyracuseUSA

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