Bulletin of Mathematical Biology

, Volume 54, Issue 2–3, pp 445–464 | Cite as

Components of uncertainty in clutch-size optimization

  • Jin Yoshimura
  • William M. Shields
Behavioural Ecology
Received:
Revised:

Abstract

Environmental uncertainty can be both a cause and consequence of chance variation in many of the phenotypic factors associated with the control of clutch size in birds. When such uncertainty inflates or otherwise influences the variance associated with expected reproductive success for any genotype, it will also influence the resulting phenotypic optima. Random variation that affects the evolution of clutch size optima explicitly may occur both within (intra-) and across (inter-) generations. Examples of intra-generational uncertainty could include chance variation in: (1) the quality and quantity of offspring, (2) parental quality, and (3) temporal resources like food. Inter-generational uncertainty would include chance variation in demographic and population characters. With respect to clutch (or litter) size, almost all forms of uncertainty tend to favor an optimum (genetic) strategy with a clutch that is smaller than the clutch associated with the apparent or actual maximal fitness of an individual parent. The overall effect of all the components of uncertainty can be evaluated through the integration of all this phenotypic variation: however each step of the integration is a conditional expectation of each component. Therefore, a single factor analysis may indicate a false optimum, and an integrated analysis of all components is necessary to evaluate the importance of their individual and joint effects on the adaptive evolution of clutch size.

Keywords

Clutch Size Brood Size Environmental Uncertainty Parental Quality Large Clutch 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Literature

  1. Alerstam, T. and G. Högstedt. 1984. How important is clutch size dependent adult mortality?Oikos 43, 254–254.Google Scholar
  2. Alexander, R. M.Optima for Animals. London: Edward Arnold.Google Scholar
  3. Boyce, M. S. and C. M. Perrins. 1987. Optimizing Great Tit clutch size in a fluctuating environment.Ecology 68, 142–153.CrossRefGoogle Scholar
  4. Brady, R. H. 1979. Natural selection and the criteria by which a theory is judged.Syst. Zool. 28, 600–621.CrossRefGoogle Scholar
  5. Brockelman, W. Y. 1975. Competition, the fitness of offspring, and optimal clutch size.Am. Nat. 109, 677–699.CrossRefGoogle Scholar
  6. Bulmer, M. G. 1985. Selection for iteroparity in a variable environment.Am. Nat. 126, 63–71.CrossRefGoogle Scholar
  7. Charnov, E. L. and J. R. Krebs. 1974. On clutch size and fitness.116, 217–219.Google Scholar
  8. Cody, M. L. 1966. A general theory of clutch sizeEvolution 20, 174–184.CrossRefGoogle Scholar
  9. Cohen, D. 1966. Optimizing reproduction in a randomly varying environment.J. theor. Biol. 12, 119–129.CrossRefGoogle Scholar
  10. Cooper, W. S. 1984. Expected time to extinction and the concept of fundamental fitness.J. theor. Biol. 107, 603–629.Google Scholar
  11. Cooper, W. S. and R. H. Kaplan. 1982. Adaptive “coin-flipping”: a decision-theoretic examination of natural selection for random individual variation.J. theor. Biol. 94, 135–151.MathSciNetCrossRefGoogle Scholar
  12. Crossner, K. A. 1977. Natural selection and clutch size in the European Starling.Ecology 58, 885–892.CrossRefGoogle Scholar
  13. Fisher, R. A. 1930.The Genetical Theory of Natural Selection. Oxford, U.K.: Oxford University Press. (Reprint: 1958. New York: Dover).MATHGoogle Scholar
  14. Gustafsson, L. and W. J. Sutherland. 1988. The cost of reproduction in the collared flycatcherFicedula albicollis.Nature 335, 813–815.CrossRefGoogle Scholar
  15. Haldane, J. B. S. and S. D. Jayakar. 1963. Polymorphism due to selection of varying direction.J. Genet. 58, 237–242.CrossRefGoogle Scholar
  16. Högstedt, G. 1980. Evolution of clutch size in birds: adaptive variation in relation to territory quality.Science 210, 1148–1150.Google Scholar
  17. Högstedt, G. 1981. Should there be a positive or a negative correlation between survival of adults in a bird population and their clutch size?Am. Nat. 118, 568–571.CrossRefGoogle Scholar
  18. Klomp, H. 1970. The determination of clutch size in birds. A review.Ardea 58, 1–124.Google Scholar
  19. Krebs, J. R., J. C. Ryan and E. L. Charnov. 1974. Hunting by expectation or optimal foraging? A study of patch use by chickadees.Anim. Behav. 22, 953–964.CrossRefGoogle Scholar
  20. Lack, D. 1947. The significance of clutch size.89, 309–352.Google Scholar
  21. Lack, D. 1954.The Natural Regulation of Animal Numbers. Oxford, U.K.: Oxford University Press.Google Scholar
  22. Lack, D. 1966.Population Studies of Birds. Oxford, U.K.: Clarendon Press.Google Scholar
  23. Levins, R. 1968.Evolution in changing environments. Princeton, NJ: Princeton University Press.Google Scholar
  24. Lewontin, R. C. and D. Cohen. 1969. On population growth in a randomly varying environment.Proc. natn Acad. Sci. U.S.A. 62, 1056–1060.MathSciNetCrossRefGoogle Scholar
  25. Loman, J. 1980. Brood size optimization and adaptation among hooded crows (Corvus corone).122, 494–500.Google Scholar
  26. Mangel, M. and C. W. Clark. 1988.Dynamic Modeling in Behavioral Ecology. Princeton, NJ: Princeton University Press.Google Scholar
  27. Martin, T. E. 1987. Food as a limit on breeding birds: a life-history perspective.Ann. Rev. Ecol. Syst. 18, 453–487.CrossRefGoogle Scholar
  28. Maynard Smith, J. 1978. Optimization theory in evolution.Ann. Rev. Ecol. Syst. 9, 31–56.CrossRefGoogle Scholar
  29. Maynard Smith, J. 1989.Evolutionary Genetics. Oxford, U.K.: Oxford University Press.Google Scholar
  30. Mayo, O. 1983.Natural Selection and Its Constraints. London: Academic Press.Google Scholar
  31. Milkman, R. 1978. Selection differentials and selection coefficients.Genetics 88, 391–403.Google Scholar
  32. Mountford, M. D. 1968. The significance of litter-size.J. Anim. Ecol. 37, 363–367.CrossRefGoogle Scholar
  33. Murphy, E. C. and E. Haukioja. 1986. Clutch size in nidicolous birds. InCurrent Ornithology, Vol. 4, R. F. Johnston (Ed.) pp. 141–180. New York: Plenum.Google Scholar
  34. Murray Jr, B. G. 1979.Population Dynamics. New York: Academic Press.Google Scholar
  35. Murray Jr, B. G. 1985. Evolution of clutch size in tropical species of birds. InNeotropical Ornithology, P. A. Buckley, M. S. Foster, E. S. Morton, R. S. Ridgely and F. G. Buckley (Eds), pp. 505–519. Lawrence, KS: Allen Press.Google Scholar
  36. Murray Jr B. G. and V. Nolan, Jr. 1989. The evolution of clutch size. I. An equation for calculating clutch size.Evolution 43, 1699–1705.CrossRefGoogle Scholar
  37. Murray Jr, B. G., J. W. Fitzpatrick and G. E. Woolfenden. 1989. The evolution of clutch size. II. A test of the Murray-Nolan equation.Evolution 43, 1706–1711.CrossRefGoogle Scholar
  38. Nur, N. 1984. The consequences of brood size for breeding blue tits. II. Nestling weight, offspring survival and optimal brood size.J. Anim. Ecol. 53, 497–517.CrossRefGoogle Scholar
  39. Nur, N. 1988a. The consequences of brood size in breeding blue tits. III. Measuring the cost of reproduction: survival, future fecundity, and differential dispersal.Evolution 42, 351–362.CrossRefGoogle Scholar
  40. Nur, N. 1988b. The cost of reproduction in birds: an examination of the evidence.Ardea 76, 155–168.Google Scholar
  41. O'Connor, R. J. 1978. Brood reduction in birds: selection for fratricide, infanticide and suicide?Anim. Behav. 26, 79–96.MathSciNetCrossRefGoogle Scholar
  42. Perrins, C. M. 1965. Population fluctuations and clutch size in the Great Tij,Parus major L.J. Anim. Ecol. 34, 601–647.CrossRefGoogle Scholar
  43. Perrins, C. M. and P. J. Jones. 1974. The inheritance of clutch size in the Great Tit (Parus major L.).Condor 76, 225–229.Google Scholar
  44. Perrins, C. M. and D. Moss. 1975. Reproductive rates in the great tit.J. Anim. Ecol. 44, 659–706.Google Scholar
  45. Pettifor, R. A., C. M. Perrins and R. H. McCleery. 1988. Individual optimization of clutch size in great tits.Nature 336, 160–162.CrossRefGoogle Scholar
  46. Price, T. and L. Liou. 1989. Selection on clutch size in birds.Am. Nat. 134, 950–959.CrossRefGoogle Scholar
  47. Price, T., M. Kirkpatrick and S. J. Arnold. 1988. Directional selection and the evolution of breeding data in birds.Science 240, 798–799.Google Scholar
  48. Real, L. 1980. Fitness, uncertainty, and the role of diversification in evolution and behavior.Am. Nat. 115, 623–638.MathSciNetCrossRefGoogle Scholar
  49. Real, L. and T. Caraco. 1986. Risk and foraging in stochastic environments.Ann. Rev. Ecol. Syst. 17, 371–390.CrossRefGoogle Scholar
  50. Rockwell, R. F., C. S. Findlay and F. Cooke. 1987. Is there an optimal clutch size in snow geese?Am. Nat. 130, 839–863.CrossRefGoogle Scholar
  51. Royama, T. 1966. Factors governing feeding rate, food requirement and brood size of nestling Great TitsParus major.108, 313–347.Google Scholar
  52. Saiah, H. and N. Perrin. 1990. Autumnal vs spring hatching in the fairy shrimpSiphonophanes grubii (Dybowski) (Crustacea, Anostraca): diversified bet-hedging strategy?Func. Ecol. 4, 769–775.CrossRefGoogle Scholar
  53. Schaffer, W. 1974. Optimal reproductive effort in fluctuating environments.Am. Nat. 108, 783–790.CrossRefGoogle Scholar
  54. Schifferli, L. 1978. Experimental modification of brood size among House SparrowsPasser domesticus.120, 365–369.Google Scholar
  55. Shields, W. M. 1982.Philopatry, Inbreeding, and the Evolution of Sex. Albany, NY: State University of New York Press.Google Scholar
  56. Shields, W. M. and J. R. Crook. 1987. Barn Swallow coloniality: a net cost for group breeding in the Adirondacks?Ecology 68, 1373–1386.CrossRefGoogle Scholar
  57. Slagsvold, T. and J. T. Lifjeld. 1988. Ultimate adjustment of clutch size to parental feeding capacity in a passerine brid.Ecology 69, 1918–1922.CrossRefGoogle Scholar
  58. Smith, J. N. M. 1981. Does high fecundity reduce survival in song sparrows?Evolution 35, 1142–1148.CrossRefGoogle Scholar
  59. Smith, C. C. and S. D. Fretwell. 1974. The optimal balance between size and number of offspring.Am. Nat. 108, 499–506.CrossRefGoogle Scholar
  60. Stearns, S. C. 1976. Life history tactics: a review of the ideas.Quart. Rev. Biol. 51, 3–47.CrossRefGoogle Scholar
  61. Stephens, D. W. 1989. Variance and the value of information.Am. Nat. 134, 128–140.CrossRefGoogle Scholar
  62. Stephens, D. W. and J. R. Krebs. 1986.Foraging Theory. Princeton, NJ: Princeton University Press.Google Scholar
  63. Tuljapurkar, S. D. 1989. An uncertain life: demography in random environments.Theory. Pop. Biol. 35, 227–294.MATHMathSciNetCrossRefGoogle Scholar
  64. Van Noordwijk, A. J., J. H. Van Balen and W. Scharloo. 1981. Heritability of ecologically important traits in the Great Tit. InThe Integrated Study of Bird Populations, H. Klomp and J. W. Woldendorp (Eds), pp. 193–203. Amsterdam: North-Holland.Google Scholar
  65. Williams, G. C. 1966. Natural selection, the cost of reproduction, and a refinement of Lack's principle.Am. Nat. 100, 687–690.CrossRefGoogle Scholar
  66. Winkler, D. W. 1985. Factors determining a clutch size reduction in California Gulls (Larus Californicus): A multi-hypothesis approach.Evolution 39, 667–677.CrossRefGoogle Scholar
  67. Winkler, D. W. and K. Wallin. 1987. Offspring size and number: a life history model linking effort per offspring and total effort.Am. Nat. 129, 708–720.CrossRefGoogle Scholar
  68. Wright, S. 1978.Evolution and the Genetics of Populations. Vol. 4.Variability Within and Among Natural Populations. Chicago, U.S.A.: University of Chicago Press.Google Scholar
  69. Yoshimura, J. 1989. The effects of uncertainty on biological systems: a probabilistic perspective. Ph. D. Thesis, SUNY-ESF, Syraeuse, NY.Google Scholar
  70. Yoshimura, J. and C. W. Clark. 1991. Individual adaptations in stochastic environments.Evol. Ecol. 5, 173–192.CrossRefGoogle Scholar
  71. Yoshimura, J. and W. M. Shields. 1987. Probabilistic optimization of phenotype distributions: a general solution for the effects of uncertainty on natural selection?Evol. Ecol. 1, 125–138.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1991

Authors and Affiliations

  • Jin Yoshimura
    • 1
  • William M. Shields
    • 2
  1. 1.Institute of Applied MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Environmental and Forest BiologyState University of New York College of Environmental Science and ForestrySyracuseU.S.A.

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