Journal of Mathematical Biology

, Volume 33, Issue 5, pp 521–556

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

  • Veijo Kaitala
  • Wayne M. Getz

DOI: 10.1007/BF00163041

Cite this article as:
Kaitala, V. & Getz, W.M. J. Math. Biol. (1995) 33: 521. doi:10.1007/BF00163041


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 

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

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