Journal of Mathematical Biology

, Volume 33, Issue 5, pp 521–556 | Cite as

Population dynamics and harvesting of semelparous species with phenotypic and genotypic variability in reproductive age

  • Veijo Kaitala
  • Wayne M. Getz
Article

Abstract

We study the evolution of polymorphic life histories in anadromous semelparous salmon and the effects of harvesting. We derive dynamic phenotypic and genetic ESS models for describing the evolutionary dynamics. We show in our deterministic analysis that polymorphisms are not possible in a panmictic random mating population. Instead, genetic or behavioral polymorphisms may be observed in populations with assortative mating systems. Positive assortative mating may be supported and generated by behavioral and phenotypic traits like male mate choice, spawning ground selection by phenotype, or within-river homing-migration-distance by size. In the case of an evolutionarily stable dimorphism, the ESS is characterized by a reproductive ideal free distribution such that at an equilibrium the individuals are indifferent from the fitness point of view between the two life histories of early and late reproduction. Different strategy models - that is, phenotypic and genetic ESS models - yield identical behavioral predictions and, consequently, genetics does not seem to play an important role in the present model. An evolutionary response to increased fishing mortality is obvious and may have resource management implications. High sea fishing mortalities drive the populations toward early spawning. Thus it is possible that unselective harvesting at sea may eliminate, depending on the biological system, behavioral polymorphisms or genetic heterozygozity and drive the population to a monomorphic one. If within-river homing migration distances depend on the size of fish, unselective harvesting at sea, or selective harvesting of spawning runs in rivers, may reduce local population sizes on spawning grounds high up rivers. Finally, harvesting in a population may cause a switch in a dominant life-history strategy in a population so that anticipated sustainable yields cannot be realized in practice.

Key words

Population dynamics modeling Evolutionarily stable strategies Polymorphic life histories Age-at-maturity Harvesting 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Armstrong, R. A., McGehee, R.: Competitive exclusion, American Naturalist 115, 151–170 (1980)Google Scholar
  2. van Baalen, M., Sabelis, M. W.: Coevolution of patch selection strategies of predator and prey and the consequences for ecological stability, American Naturalist 142, 446–470 (1993)Google Scholar
  3. Bergh, M. O., Getz, W. M.: Stability of discrete age-structured and aggregated delay-difference population models. Journal of Mathematical Biology 26, 551–581 (1988)Google Scholar
  4. Bergh, M. O., Getz, W. M.: Stability and harvesting of competing populations with genetic variation in life history strategies, Theoretical Population Biology 36, 77–124 (1989)Google Scholar
  5. Brown, J., Vincent, T.: A theory for the evolutionary game, Theoretical Population Biology 31, 140–166 (1987)Google Scholar
  6. Charlesworth, B.: Evolution in age-structured populations. Cambridge University Press, Cambridge (1980)Google Scholar
  7. Edelstein-Keshet, L.: Mathematical Models in Biology, Random House, New York: 1989Google Scholar
  8. Ellner, S.: ESS germination rates in randomly varying environments. l. Logistic type models. Theoretical Population Biology 28, 50–79 (1985a)Google Scholar
  9. Ellner, S.: ESS germination rates in randomly varying environments. 11. Reciprocal yield-law type models. Theoretical Population Biology 28, 80–116 (1985b)Google Scholar
  10. Ferriere, R. H., and Gatto, M.: Chaotic populations dynamics can result from natural selection. Proc. R. Soc. Lond. B, 51, 33–38 (1993).Google Scholar
  11. Fisher, A. C., Hanemann, W. M., Keeler, A. G.: Integrating fishery and water resource management: A biological model of a California salmon fishery, Journal of Environmental Economics and Management 20, 234–261 (1991)Google Scholar
  12. Foote, C. J.: Male mate choice dependent on male size in salmon. Behaviour 106, 63–80 (1988)Google Scholar
  13. Foote, C. J., Larkin, P. A.: The role of male choice in assortative mating of sockey salmon and kokanee, the anadromous and nonanadromous forms of Oncorhychus nerka. Behaviour 106, 43–62 (1988)Google Scholar
  14. Fraidenburg, M. E., Lincoln, R. H.: Wilk Chinook salmon management: an international conservation challenge, North American Journal of Fisheries Management 5, 311–329 (1985)Google Scholar
  15. Fredin, R. A.: Trends in North Pacific salmon fisheries, pp. 59–119 in J. W. McNeil and D. C. Himsworth (eds.), Salmonid ecosystems of the North Pacific, Oregon State University Press, Corvallis.Google Scholar
  16. Getz, W. M., Haight, R. G.: Population Harvesting. Demongraphic Models of Fish, Forest, and Animal Resources, Princeton University Press, Princeton, New Jersey: 1989Google Scholar
  17. Getz, W. M., Kaitala, V.: Ecogenetic models, competition, and heteropatry, Theoretical Population Biology 36, 34–58 (1989)Google Scholar
  18. Getz, W. M., Kaitala, V.: Ecogenetic analysis and evolutionary stable strategies in harvested populations, pp. 187–203 in T. K. Stokes, J. M. McGlade and R. Law (eds.), The Exploitation of Evolving Resources, Lecture Notes in Biomathematics, vol. 99, Springer-Verlag, Berlin (1993)Google Scholar
  19. Hastings, A.: Can spatial variation alone lead to selection for dispersal. Theoretical Population Biology 24, 244–251 (1983)Google Scholar
  20. Hines, W. G. S.: Evolutionary stable strategies: a review of basic theory. Theoretical Population Biology 31, 195–272 (1987)Google Scholar
  21. Jonsson, B., Hindar, K.: Reproductive strategy of dwarf and normal Arctic Charr (Salvelinus alpinus) from Vangsvatnet Lake, Western Norway, Canadian Journal of Fisheries Aquatic Sciences 39, 1404–1413 (1982)Google Scholar
  22. Kaitala, V.: Evolutionary stable migration in salmon - a simulation study of homing and straying, Annales Zoologici Fennici 27 (Special Issue “Behaviour of Fish - Ecological Consequences”), 131–138 (1990)Google Scholar
  23. Kaitala, V., Kaitala, A., Getz, W. M.: Evolutionary stable dispersal of waterstrider in a temporally and spatially heterogeneous environment, Evolutionary Ecology, 3, 283–298 (1989)Google Scholar
  24. Kaitala, A., Kaitala, V., Lundberg, P.: A theory of partial migration, American Naturalist 142, 59–81 (1993)Google Scholar
  25. L'Abee-Lund, J. H.: Variation within and between rivers in adult size and sea age at maturity of anadromous brown trout, Salmo trutta, Canadian Journal of Fisheries Aquatic Science 48, 1015–1021 (1991)Google Scholar
  26. Law, R., Grey, D. R.: Evolution of yields from populations with age-specific cropping. Evolutionary Ecology 3, 343–359 (1989)Google Scholar
  27. Levin, S. A., Cohen, D., Hastings, A.: Dispersal strategies in patchy environments. Theoretical Population Biology 26, 165–191 (1984)Google Scholar
  28. Luenberger, D. G., Introduction to dynamic systems. Theory, models and applications. John Wiley & Sons, New York: 1979Google Scholar
  29. May, R. M., Oster, G. F.: Bifurcations and dynamic complexity in simple ecological models. American Naturalist 110, 573–590 (1976)Google Scholar
  30. Maynard Smith, J.: Evolution and the theory of games. American Scientist 64, 41–45 (1976)Google Scholar
  31. Maynard Smith, J.: Evolution and the theory of games. Cambridge University Press, New York: 1982Google Scholar
  32. Ricker, W. E.: Stock and recruitment, Journal of Fisheries Research Board of Canada 11, 559–623 (1954)Google Scholar
  33. Roff, D. A.: The evolution of life histories. Theory and analysis. Chapman and Hall, New York, 1992Google Scholar
  34. Roughgarden, J.: Theory of population genetics and evolutionary ecology: An introduction. Macmillan, New York: 1979Google Scholar
  35. Ryan, M. J., Pease, C. M., Morris, M. R.: A genetic polymorphism in the swordtail Xiphophorus nigrensis: Testing the prediction of equal fitnesses. American Naturalist 139, 21–31 (1992)Google Scholar
  36. Steams, S. C.: The evolution of life-histories. Oxford University Press, New York, 1992Google Scholar
  37. Taylor, P. D.: Evolutionary stability in one-parameter models under weak selection. Theor. Pop. Biol. 36, 125–143 (1989)Google Scholar
  38. Taylor, P. D., Getz, W. M.: An inclusive fitness model for the evolutionary advantage of sibmating. Evolutionary Ecology 8 61–69 (1994)Google Scholar
  39. Thomas, B.: Genetical ESS-models. I. Concepts and basic model, Theoretical Population Biology 28, 18–32 (1985a)Google Scholar
  40. Thomas, B.: Genetical ESS-models. II. Multi-strategy models and multiple alleles, Theoretical Population Biology 28, 33–49 (1985b)Google Scholar
  41. Waples, R. S., Teel, D. J.: Conservation genetics of Pacific salmon. I. Temporal changes in allele frequency, Conservation Biology 4, 144–156 (1990)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Veijo Kaitala
    • 1
  • Wayne M. Getz
    • 2
  1. 1.Systems Analysis LaboratoryHelsinki University of TechnologyEspooFinland
  2. 2.Department of Environmental Sciences, Policy, and ManagementUniversity of CaliforniaBerkeleyUSA

Personalised recommendations