Skip to main content
SpringerLink
Log in

Individual variability and spatial heterogeneity in fish population models

  • Papers
  • Published:
Reviews in Fish Biology and Fisheries Aims and scope Submit manuscript

Summary

Fish populations consist of non-identical individuals inhabiting heterogeneous environments and moving about the environment in a manner that maximizes their individual fitness. No study has fully integrated these characteristics of fish populations into a single model. In this paper we propose a new class of model that includes each characteristic in a unified description of populations. To lay the foundation for these models we review models concerning (1) population dynamics in heterogeneous environments, (2) the effects of individual variability on population dynamics, and (3) individual movement and habitat selection rules. The models that we propose allow investigators to explore the population-level consequences of novel changes in the environment, and of different individual fitness maximization strategies. The strengths of our proposed class of model lie in their mechanistic, individual-level description of fish growth, movement and survival. Correctly depicting these mechanisms presents important challenges in developing such models. Despite these challenges, mechanistic models like those we propose should greatly increase our understanding of the interaction between environmental heterogeneity and fish population dynamics and distributions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abrahams M.V. (1989) Foraging guppies and the ideal free distribution: the influence of information on patch choice. Ethology 82, 116–26.

    Google Scholar 

  • Abrahams M.V. and Dill L.M. (1989) A determination of the energetic equivalence of the risk of predation. Ecology 70, 999–1007.

    Google Scholar 

  • Adams S.M. and DeAngelis D.L. (1987) Indirect effects of early bass-shad interactions on predator population structure and food web dynamics. In Kerfoot C. and Sih A., eds. Predation: Direct and Indirect Impacts on Aquatic Communities. Hanover, MA: University Press of New England, pp. 103–17.

    Google Scholar 

  • Aksnes D.L. and Giske J. (1990) Habitat profitability in pelagic environments. Mar. Ecol. Prog. Ser. 64, 209–15.

    Google Scholar 

  • Asknes D.L. and Giske J. (1993) A theoretical model of aquatic visual feeding. Ecol. Modelling 67, 233–50.

    Google Scholar 

  • Andow D.A., Kareiva P.M., Levin S.A. and Okubo A. (1990) Spread of invading organisms. Landscape Ecology 4, 177–88.

    Google Scholar 

  • Barnthouse L.W., Boreman J., Christensen S.W., Goodyear C.P., Van Winkle W. and Vaughan D.S. (1984) Population biology in the courtroom: the Hudson River controversy. BioScience 34, 14–19.

    Google Scholar 

  • Bartsch J. (1988) Numerical simulation of the vertically migrating herring larvae in the North Sea. Meeresforschung 32, 30–45.

    Google Scholar 

  • Bartsch J., Brander K., Heath M., Munk P., Richardson K. and Svendsen E. (1989) Modelling the advection of herring larvae in the North Sea. Nature, Lond 340, 632–6.

    Google Scholar 

  • Begon M., Harper J.L. and Townsend C.R. (1986) Ecology: Individuals, Populations, and Communities. Sunderland, MA.: Sinauer. 876 pp.

    Google Scholar 

  • Bernstein C., Kacelnik A. and Krebs J.R. (1988) Individual decisions and the distribution of predators in a patchy environment. J. Anim. Ecol. 57, 1007–26.

    Google Scholar 

  • Bernstein C., Kacelnik A. and Krebs J.R. (1991) Individual decisions and the distribution of predators in a patchy environment.II. The influence of travel costs and structure of the environment. J. Anim. Ecol. 60, 205–25.

    Google Scholar 

  • Beyer J.E. and Laurence G.C. (1980) A stochastic model of larval fish growth. Ecol. Modelling 8, 109–32.

    Google Scholar 

  • Boreman J., Goodyear C.P. and Christensen S.W. (1981) An empirical methodology for estimating entrainment losses at power plants sited on estuaries. Trans. Am. Fish Soc. 110, 253–60.

    Google Scholar 

  • Breck J.E. (1993) Hurry up and wait: growth of young bluegills in ponds and in simulations with an individual-based model. Trans. Am. Fish. Soc. 122, 467–80.

    Google Scholar 

  • Breck J.E., DeAngelis D.L., Van Winkle W. and Christensen S.W. (1988) Potential importance of spatial and temporal heterogeneity in pH, Al and Ca in allowing survival of a fish population: a model demonstration. Ecol. Modelling 41, 1–16.

    Google Scholar 

  • Brown J.L. (1969) The buffer effect and productivity in tit populations. Am. Nat. 103, 347–54.

    Google Scholar 

  • Brugert R.M. and Bjornn T.C. (1991) Habitat use by steelhead and coho salmon and their responses to predators and cover in laboratory streams. Trans. Am. Fish. Soc. 120, 486–93.

    Google Scholar 

  • Cain M.L. (1985) Random search by herbivorous insects: a simulation model. Ecology 66, 876–88.

    Google Scholar 

  • Caraco T., Martindale S. and Whittam T.S. (1980) An empirical demonstration of risk-sensitive foraging preferences. Anim. Behav. 28, 820–30.

    Google Scholar 

  • Caraco T., Blanckenhorn W.U., Gregory G.M., Newman J.A., Recer G.M. and Zwicker S.M. (1990) Risk-sensitivity: ambient temperature effects on foraging. Anim. Behav. 39, 338–45.

    Google Scholar 

  • Cézilly F., Brun B. and Hafner H. (1991) Foraging and fitness. Acta CEcologica 12, 683–96.

    Google Scholar 

  • Charnov E.L. (1976) Optimal foraging, the marginal value theorem. Theoret. Popul. Biol. 9, 129–36.

    Google Scholar 

  • Christensen S.W. and Englert T.L. (1988) Historical development of entrainment models for Hudson River striped bass. Am. Fish. Soc. Monogr. 4, 133–42.

    Google Scholar 

  • Clark C.W. and Levy D.A. (1988) Diel vertical migrations by juvenile sockeye salmon and the antipredation window. Am. Nat. 131, 271–90.

    Google Scholar 

  • Comins H.N. and Blatt D.W.E. (1974) Prey-Predator models in spatially heterogeneous environments. J. theor. Biol. 48, 75–83.

    Google Scholar 

  • Cowan J.H., Rose K.A., Rutherford E.S. and Houde E.D. (1993) Individual-based model of young-of-the-year striped bass population dynamics. II. Factors affecting recruitment in the Potomac River, Maryland. Trans. Am. Fish. Soc. 122, 439–58.

    Google Scholar 

  • Crowley P.H. (1978) Effective size and persistence of ecosystems. Oecologia 35, 185–95.

    Google Scholar 

  • Crowley P.H. (1981) Dispersal and the stability of predator-prey interactions. Am. Nat. 118, 673–701.

    Google Scholar 

  • Crowley P.H., DeVries D.R. and Sih A. (1990) Inadvertent errors and error-constrained optimization: fallible foraging by bluegill sunfish. Behav. Ecol. Sociobiol. 27, 135–44.

    Google Scholar 

  • DeAngelis D.L. and Gross L.J. (1992) Individual-based Models and Approaches in Ecology: Populations, Communities and Ecosystems. New York: Chapman and Hall. 525 pp.

    Google Scholar 

  • DeAngelis D.L. and Rose K.A. (1992) Which individual-based approach is most appropriate for a given problem? In: DeAngelis D.L. and Gross L.J., eds. Individual-based models and approaches in ecology: populations, communities and ecosystems. New York: Chapman & Hall, pp. 67–87.

    Google Scholar 

  • DeAngelis D.L. and Yeh G.T. (1984) An introduction to modeling migratory behavior of fishes. In McCleave J.D., Arnold G.P., Dodson J.J. and Neill W.H., eds Mechanisms of Migration in Fishes. New York: Plenum Publshing Co., pp. 445–69.

    Google Scholar 

  • DeAngelis D.L., Cox D.K. and Coutant C.C. (1979) Cannibalism and size dispersal in young-of-the-year largemouth bass: experiment and model. Ecol. Modelling 8, 133–148.

    Google Scholar 

  • DeAngelis D.L., Godbout L. and Shuter B.J. (1991) Individual-based approach to predicting density-dependent dynamics in smallmouth bass populations. Ecol. Modelling 57, 91–115.

    Google Scholar 

  • DeAngelis D.L., Rose K.A., Crowder L.B., Marschall E.A. and Lika D. (1993) Fish cohort dynamics: applications of complementary modelling approaches. Am. Nat. 142, 604–22.

    Google Scholar 

  • Dempster J.P. and Pollard E. (1986) Spatial heterogeneity, stochasticity and the detection of density dependence in animal populations. Oikos 46, 413–16.

    Google Scholar 

  • DeVries D.R., Stein R.A. and Chesson P.L. (1989) Sunfish foraging among patches: the patch-departure decision. Anim. Behav. 37, 455–64.

    Google Scholar 

  • Dill L.M. (1983) Adaptive flexibility in the foraging behavior of fishes. Can J. Fish. Aquat. Sci. 40, 398–408.

    Google Scholar 

  • Dill L.M. (1987) Animal decision making and its ecological consequences: the future of aquatic ecology. Can. J. Zool. 65, 803–11.

    Google Scholar 

  • Dugatkin L.A. and Godin J.-G. (1992) Predator inspection, shoaling and foraging under predation hazard in the Trinidadian guppy, Poecilia reticulata. Env. Biol. Fishes 34, 265–76.

    Google Scholar 

  • Fraser D.F. and Gilliam J.G. (1987) Feeding under predation hazard: responses of the guppy and Hart's rivulus from sites with contrasting predation hazard. Behav. Ecol. Sociobiol. 21, 203–9.

    Google Scholar 

  • Fretwell S.D. (1972) Populations in Seasonal Environments. Princeton, NJ: Princeton Univ. Press. 217 pp.

    Google Scholar 

  • Fretwell S.D. and Lucas H.L. (1970) On territorial behavior and other factors influencing habitat distribution in birds. I. Theoretical development. Acta Biotheor. 19, 16–36.

    Google Scholar 

  • Gilliam J.F. (1982) Habitat Use and Competitive Bottlenecks in Size-structured Populations. East Lancing, MI: Michigan State Univ. 107 pp.

    Google Scholar 

  • Gilliam J.F. and Fraser D.F. (1987) Habitat selection under predation hazard: test of a modern with foraging minnows. Ecology 68, 1856–62.

    Google Scholar 

  • Gilliam J.F. and Fraser D.F. (1988) Resource depletion and habitat segregation by competitors under predation hazard. In Ebenman B. and Persson L., eds. Size-structured Populations. Heidelberg: Springer-Verlag, pp. 173–84.

    Google Scholar 

  • Gilpin M. and Hanski I. (1991) Metapopulation Dynamics: Empirical and Theoretical Investigations. London: Academic Press. 336 pp.

    Google Scholar 

  • Giske J., Skjoldal H.R. and Aksnes D.L. (1993) A conceptual model of distribution of capelin in the Barents Sea. Sarsia 77, 147–56.

    Google Scholar 

  • Godin J.-G. and Keenleyside M. (1984) Foraging on patchily distributed prey by a cichlid fish (Teleostei, Cichlidae): a test of the ideal free distribution theory. Anim. Behav. 32, 120–31.

    Google Scholar 

  • Gotceitas V. and Colgan P. (1990) Behavioural response of juvenile bluegill sunfish to variation in predation risk and food level. Ethology 85, 247–55.

    Google Scholar 

  • Green R.F. (1980) Bayesian birds: a simple example of Oaten's stochastic model of optimal foraging. Theor. Popul. Biol. 18, 244–56.

    Google Scholar 

  • Green R.F. (1984) Stopping rules for optimal foragers. Am. Nat. 123, 30–40.

    Google Scholar 

  • Hamilton D. and May R. (1977) Dispersal in stable habitats. Nature, Lond. 269, 578–81.

    Google Scholar 

  • Hassell M.P. (1980) Some consequences of habitat heterogeneity for population dynamics, Oikos 35, 150–60.

    Google Scholar 

  • Hassell M.P. (1985) Insect natural enemies as regulating factors. J. Anim. Ecol. 54, 323–34.

    Google Scholar 

  • Hassell M.P. (1987) Detecting regulation in patchily distributed animal population. J. Anim. Ecol. 56, 705–13.

    Google Scholar 

  • Hastings A. (1990) Spatial heterogeneity and ecological models. Ecology 71, 426–8.

    Google Scholar 

  • Hill J. and Grossman G.D. (1993) An energetic model of microhabitat use for rainbow trout and rosyside dace. Ecology 74, 685–98.

    Google Scholar 

  • Holtby L.B. and Healey M.C. (1990) Sex-specific life history tactics and risk-taking in coho salmon. Ecology 71, 678–90.

    Google Scholar 

  • Houston A.I. (1990) Foraging in the context of life-history: general principles and specific models. In Hughes R.N., ed. Behavioural Mechanisms of Food Selection. Berlin: Springer-Verlag, pp. 23–38.

    Google Scholar 

  • Huffaker C.B. (1958) Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia 27, 343–83.

    Google Scholar 

  • Huston M.A. and DeAngelis D.L. (1987) Size bimodality in monospecific populations: a critical review of potential mechanisms. Am. Nat. 129, 678–707.

    Google Scholar 

  • Huston M.A., DeAngelis D.L. and Post W. (1988) New computer models unify ecological theory. BioScience 38, 682–90.

    Google Scholar 

  • Hyman J.B., McAninch J.B. and DeAngelis D.L. (1991) An individual-based simulation model of herbivory in a heterogeneous landscape. In Turner M.G. and Gardner R.H., eds. Quantitative Methods in Landscape Ecology. Heidelberg: Springer-Verlag, pp. 443–75.

    Google Scholar 

  • Iwasa Y., Higashi M. and Yamamura N. (1981) Prey distribution as a factor determining the choice of optmal foraging strategy. Am. Nat. 117, 710–23.

    Google Scholar 

  • Jager, H.I., DeAngelis, D.L., Sabo, M., Sale, M. and Orth, D. (1993) An individual-based model of smallmouth bass populations in streams. Rivers 4, 000-000 (in press).

    Google Scholar 

  • Kareiva P.M. (1987) Habitat fragmentation and the stability of predator-prey interactions. Nature, Lond. 326, 388–90.

    Google Scholar 

  • Kareiva P.M. (1990) Population dynamics in spatially complex environment: theory and data. Phil. Trans. R. Soc. 330B, 175–90.

    Google Scholar 

  • Kareiva P.M. and Anderson M. (1988) Spatial aspects of species interactions: the wedding of models and experiments. In Hastings A., ed. Community Ecology. Heidelberg: Springer-Verlag, pp. 35–50.

    Google Scholar 

  • Kareiva P.M. and Odell G. (1987) Swarms of predators exhibit “preytaxis” if individuals use area-restricted search. Am. Nat. 130, 233–70.

    Google Scholar 

  • Leggett W.C. (1977) The ecology of fish migrations. A. Rev. Ecol. Syst. 8, 285–308.

    Google Scholar 

  • Levin S.A. (1976) Population dynamic models in heterogeneous environments. A. Rev. Ecol. Syst. 7, 287–310.

    Google Scholar 

  • Levy D.A. (1990a) Reciprocal diel vertical migration behavior in planktivores and zooplankton in British Columbia lakes. Can. J. Fish. Aquat. Sci. 47, 1755–64.

    Google Scholar 

  • Levy D.A. (1990b) Sensory mechanism and selective advantage for diel vertical migration in juvenile sockeye salmon, Oncorhynchus nerka. Can. J. Fish. Aquat. Sci. 47, 1796–1802.

    Google Scholar 

  • Levy D.A. (1991) Acoustic analysis of diel vertical migration behavior of Mysis relicta and kokanee (Oncorhynchus nerka) within Okanagan Lake, British Columbia. Can. J. Fish. Aquat. Sci. 48, 67–72.

    Google Scholar 

  • Łomnicki A. (1978) Individual differences between animals and the natural regulation of their numbers. J. Anim. Ecol. 47, 461–75.

    Google Scholar 

  • Łomnicki A. (1980) Regulation of population density due to individual differences and patchy environment. Oikos 35, 185–93.

    Google Scholar 

  • Łomnicki A. (1988) Population Ecology of Individuals. Princeton, NJ: Princeton Univ. Press. 223 pp.

    Google Scholar 

  • Lomnicki A. and Ombach J. (1984) Resource partitioning within a single species population and population stability: a theoretical model. Theor. Popul. Biol. 24, 21–8.

    Google Scholar 

  • Ludwig D. and Rowe L. (1990) Life-history strategies for energy gain and predator avoidance under time constraints. Am. Nat. 135, 686–707.

    Google Scholar 

  • MacCall A.D. (1990) Dynamic Geography of Marine Fish Populations. Seattle, WA: Univ. Washington Press. 153 pp.

    Google Scholar 

  • McNair J.N. (1982) Optimal giving-up times and the marginal value theorem. Am. Nat. 119, 511–29.

    Google Scholar 

  • McNamara J.M. (1990a) The starvation-predation trade-off and some behavioural and ecological consequences. In Hughes R.N., ed. Behavioural Mechanisms of Food Selection. Berlin: Springer-Verlag, pp. 39–59.

    Google Scholar 

  • McNamara J.M. (1990b) The policy which maximizes long term survival of an animal faced with the risks of starvation and predation. Adv. Appl. Prob. 22, 295–308.

    Google Scholar 

  • McNamara J.M. and Houston A.I. (1986) The common currency for behavioral decisions. Am. Nat. 127, 358–78.

    Google Scholar 

  • McNamara J.M. and Houston A.I. (1987) Starvation and predation as factors limiting population size. Ecology 68, 1515–19.

    Google Scholar 

  • McNamara J.M. and Houston A.I. (1989) State-dependent contests for food. J. Theor. Biol. 137, 457–79.

    Google Scholar 

  • Madenjian C.P. (1991) Limits to growth of young-of-the-year walleye (Stizostedion vitreum vitreum): an individual-based model perspective. Can. J. Fish. Aquat. Sci. 48, 1492–9.

    Google Scholar 

  • Madenjian C.P. and Carpenter S.R. (1991) Individual-based model for growth of young-of-the-year walleye: a piece of recruitment puzzle. Ecol. Appl. 1, 268–79.

    Google Scholar 

  • Madenjian C.P., Johnson B.M. and Carpenter S.R. (1991) Stocking strategies for fingerling walleyes: an individual-based model approach. Ecol. Appl. 1, 280–88.

    Google Scholar 

  • Magurran A.E. (1990) The adaptive significance of schooling as an anti-predator defence in fish. Annls. zool. fennici 27, 51–66.

    Google Scholar 

  • Magurran A.E. and Pitcher T.J. (1987) Provenance, shoal size and the sociobiology of predatorevasion behavior in minnow shoals. Proc. R. Soc. 229B, 439–65.

    Google Scholar 

  • Mangel M. and Clark C.W. (1986) Towards a unified foraging theory. Ecology 67, 1127–38.

    Google Scholar 

  • Mangel M. and Clark C.W. (1988) Dynamic Modeling in Behavioral Ecology. Princeton, NJ: Princeton Univ. Press. 308 pp.

    Google Scholar 

  • Marschall E.A., Chesson P.L. and Stein R.A. (1989) Foraging in a patchy environment: preyencounter rate and residence time distributions. Anim. Behav. 37, 444–54.

    Google Scholar 

  • May R.M. (1981a) Models for single species populations. In May R.M., ed. Theoretical Ecology: Principles and Applications. Oxford: Blackwell Scientific, pp. 5–29.

    Google Scholar 

  • May R.M. (1981b) Models for two interacting populations. In May R.M., ed. Theoretical Ecology: Principles and Applications. Oxford: Blackwell Scientific, pp. 78–104.

    Google Scholar 

  • May R.M. (1989) Detecting density dependence in imaginary worlds. Nature, Lond. 338, 16–17.

    Google Scholar 

  • Maynard Smith J. (1982) Evolution and the Theory of Games. Princeton, NJ: Princeton Univ. Press. 224 pp.

    Google Scholar 

  • Meinhardt H. (1982) Models of biological pattern formation. New York City, NY, USA: Academic Press. 230 pp.

    Google Scholar 

  • Milinski M. (1979) An evolutionarily stable feeding strategy in sticklebacks. Z. Tierpsychol. 51, 36–40.

    Google Scholar 

  • Milinski M. (1984) Competitive resource sharing: an experimental test of a learning rule for ESSs. Anim. Behav. 32, 233–42.

    Google Scholar 

  • Mimura M. and Murray J.D. (1978) On a diffusive prey-predator model which exibits patchiness. J. theor. Biol. 75, 249–62.

    Google Scholar 

  • Mountford M.D. (1988) Population regulation, density dependence, and heterogeneity. J. Anim. Ecol. 57, 845–58.

    Google Scholar 

  • Murray J.D. (1989) Mathematical Biology. Berlin: Springer-Verlag. 767 pp.

    Google Scholar 

  • Murray J.D., Stanley E.A. and Brown D.L. (1986) On the spatial spread of rabies among foxes. Proc. R. Soc. 229B, 111–50.

    Google Scholar 

  • Namba T. (1980) Density-dependent dispersal and spatial distribution of a population. J. theor. Biol. 86, 351–63.

    Google Scholar 

  • Neill W.H. (1979) Patch use under predation hazard: behavior in a simple stochastic environment. Oikos 61, 29–44.

    Google Scholar 

  • Okubo A., Maini P.K., Williamson M.H. and Murray J.D. (1989) On the spatial spread of the grey squirrel in Britain. Proc. R. Soc. 238B, 113–25.

    Google Scholar 

  • Parker G.A. and Sutherland W.J. (1986) Ideal free distributions when individuals differ in competitive ability: phenotype limited ideal free models. Anim. Behav. 34, 1222–42.

    Google Scholar 

  • Patten B.C. (1964) The rational decision process in salmon migration. J. Cons. Int. Explor. Mer 28, 410–17.

    Google Scholar 

  • Pitcher T.J., Lang S.H. and Turner J.A. (1988) A risk-balancing trade off between foraging rewards and predation hazard in a shoaling fish. Behav. Ecol. Sociobiol. 22, 225–8.

    Google Scholar 

  • Possingham H.P. and Roughgarden J. (1990) Spatial population dynamics of a marine organism with a complex life cycle. Ecology 71, 973–965.

    Google Scholar 

  • Power M.E. (1984) Habitat quality and the distribution of algae-grazing catfish in a Panamanian stream. J. Anim. Ecol. 53, 357–74.

    Google Scholar 

  • Pulliam H.R. (1988) Sources, sinks and population regulation. Am. Nat. 132, 652–61.

    Google Scholar 

  • Pulliam H.R. (1989) Individual behavior and the procurement of essential resources. In Roughgarden J., May R.M. and Levin S.A. eds. Perspectives in Ecological Theory. Princeton, NJ: Princeton Univ. Press, pp. 25–38.

    Google Scholar 

  • Pulliam H.R. and Danielson B.J. (1991) Sources, sinks and habitat selection: a landscape perspective on population dynamics. Am. Nat. 137, S50-S66.

    Google Scholar 

  • Pyke G.H. (1984) Optimal foraging theory: a critical review. A. Rev. Ecol. Syst. 15, 523–75.

    Google Scholar 

  • Rose K.A. and Cowan J.H. (1993) Individual-based model of young-of-the-year striped bass population dynamics. I. Model description and baseline simulations. Trans. Am. Fish. Soc. 122, 415–39.

    Google Scholar 

  • Rosland R. (1993) Applying Stochastic Dynamic Programming to Simulate the Diel Vertical Distribution of a Pelagic Planktivorous Fish. Bergen, Norway: Department of Fisheries and Marine Biology, University of Bergen. 98 pp.

    Google Scholar 

  • Sabat A.M. (1990) Reproductive Effort and Success in a Brood Guarding Male Fish, the Rock Bass (Ambloplites rupestris): an Experimental and Theoretical Approach. Albany, NY: State Univ. of New York at Albany. 140 pp.

    Google Scholar 

  • Saila S.B. and Flowers J.M. (1968) Movements and behaviour of berried female lobsters displaced from offshore area to Narragansett Bay, Rhode Island. J. Cons. Int. Explor. Mer 31, 342–51.

    Google Scholar 

  • Saila S.B. and Flowers J.M. (1969) Toward a generalized model of fish migration. Trans. Am. Fish. Soc. 98, 582–8.

    Google Scholar 

  • Saila S.B. and Shappy R.A. (1963) Random movement and orientation in salmon migrations. J. Cons. Int. Explor. Mer. 28, 153–66.

    Google Scholar 

  • Schlosser I.J. (1988) Predation risk and habitat selection by two size classes of a stream cyprinid: experimental test of a hypothesis. Oikos 53, 36–40.

    Google Scholar 

  • Schoener T.W. (1986) Mechanistic approaches to community ecology: a new reductionism? Am. Zool. 26, 81–106.

    Google Scholar 

  • Shirvell C.S. (1990) Role of instream rootwads as juvenile coho salmon (Oncorhynchus kisutch) and steelhead trout (O. mykiss) cover habitat under varying streamflows. Can. J. Fish. Aquat. Sci. 47, 852–61.

    Google Scholar 

  • Skellam J.G. (1951) Random dispersal in theoretical populations. Biometrica 38, 196–218.

    Google Scholar 

  • Stephens D.W. and Krebs J.R. (1986) Foraging Theory. Princeton, NJ: Princeton Univ. Press. 247 pp.

    Google Scholar 

  • Stewart-Oaten A. (1982) Minimax strategies for a predator-prey game. Theor. Popul. Biol. 22, 410–24.

    Google Scholar 

  • Taylor L.R. and Taylor R.A.J. (1977) Aggregation, migration and population mechanics. Nature, Lond. 265, 415–21.

    Google Scholar 

  • Taylor R.A.J. (1981a) The behavioral basis of redistribution. I. The Δ-model concept. J. Anim. Ecol. 50, 573–86.

    Google Scholar 

  • Taylor R.A.J. (1981b) The behavioral basis of redistribution. II. simulations of the Δ-model. J. Anim. Ecol. 50, 587–604.

    Google Scholar 

  • Trebitz A.S. (1991) Timing of spawning in largemouth bass: implications of an individual based model. Ecol. Modelling 59, 203–27.

    Google Scholar 

  • Turchin P. (1989) Population consequences of aggregative movement. J. Anim. Ecol. 58, 75–100.

    Google Scholar 

  • Turchin P. and Kareiva P.M. (1989) Aggregation in Aphis varians: an effective strategy for producing predation risk. Ecology 70, 1008–16.

    Google Scholar 

  • Turner A.M. and Mittlebach G.G. (1990) Predator avoidance and community structure: interactions among piscivores, planktivores, and plankton. Ecology 71, 2241–54.

    Google Scholar 

  • Tyler J.A. (1991) Habitat Selection and Foraging Behavior in Stream Fish: Ideal Free Models and Experiments with Blacknose Dace, Rhinicthys atratulus. Albany, NY: State Univ. of New York at Albany. 122 pp.

    Google Scholar 

  • Walters C.J., Hannah C.G. and Thompson K. (1992) A microcomputer program for simulating effects of physical transport process on fish larvae. Fish. Oceanogr. 1, 11–19.

    Google Scholar 

  • Werner E.E. and Hall D.J. (1976) Niche shifts in sunfishes: experimental evidence and significance. Science 191, 404–6.

    Google Scholar 

  • Werner E.E. and Hall D.J. (1979) Foraging efficiency and habitat switching in competing sunfishes. Ecology 60, 256–64.

    Google Scholar 

  • Werner E.E. and Gilliam J.F. (1984) The ontogenetic niche and species interactions in size-structured populations. Annu. Rev. Ecol. Syst. 15, 393–425.

    Google Scholar 

  • Werner E.E., Gilliam J.F., Hall D.J. and Mittlebach G.G. (1983a) An experimental test of the effects of predation risk on habitat use in fish. Ecology 64, 1540–8.

    Google Scholar 

  • Werner E.E., Gilliam J.F., Hall D.J. and Mittlebach G.G. (1983b) An experimental test of the effects of predation risk on habitat use in fish. Ecology 64, 1540–1548.

    Google Scholar 

  • Werner E.E., Mittlebach G.G., Hall D.J. and Gilliam J.F. (1983a) Experimental tests of optimal habitat use in fish: the role of relative habitat profitability. Ecology 64, 1525–39.

    Google Scholar 

  • Werner E.E., Mittlebach G.G., Hall D.J. and Gilliam J.F. (1983b) Experimental tests of optimal habitat use in fish: the role of relative habitat profitability. Ecology 64, 1525–39.

    Google Scholar 

  • Wiens J.A. (1976) Population responses to patchy environments. A. Rev. Ecol. Syst. 7, 81–120.

    Google Scholar 

  • Yano E. (1978) A simulation model of searching behaviour of a parasite. Res. Popul. Ecol. 20, 105–22.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Environmental Sciences Division, Oak Ridge National Laboratory, P.O. Box 2008, MS-6038, 37831, Oak Ridge, TN, USA

    Jeffrey A. Tyler & Kenneth A. Rose

Authors
  1. Jeffrey A. Tyler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kenneth A. Rose
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tyler, J.A., Rose, K.A. Individual variability and spatial heterogeneity in fish population models. Rev Fish Biol Fisheries 4, 91–123 (1994). https://doi.org/10.1007/BF00043262

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00043262

Keywords

Search

Navigation