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Optimal foraging: Some simple stochastic models

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Summary

Some simple stochastic models of optimal foraging are considered. Firstly, mathematical renewal theory is used to make a general model of the combined processes of search, encounter, capture and handling. In the case where patches or prey items are encountered according to a Poisson process the limiting probability distribution of energy gain is found. This distribution is found to be normal and its mean and variance are specified. This result supports the use of Holling's disc equation to specify the rate of energy intake in foraging models. Secondly, a model based on minimization of the probability of death due to an energetic shortfall is presented. The model gives a graphical solution to the problem of optimal choices when mean and variance are related. Thirdly, a worked example using these results is presented. This example suggests that there may be natural relationships between mean and variance which make solutions to the problems of ‘energy maximization’ and ‘minimization of the probability of starvation’ similar. Finally, current trends in stochastic modeling of foraging behavior are critically discussed.

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References

  • Allais M (1953) Le comportement de l'hommme rationnel devant le risque: critique des postulats et axioms de l'ecole americaine. Econometrica 21:503–546

    Google Scholar 

  • Caraco T (1980) On foraging time allocation in a stochastic environment. Ecology 61:119–128

    Google Scholar 

  • Caraco T (1981) Energy budgets, risk and foraging preferences in Dark-eyed juncos, (Junco hymelais). Behav Ecol Sociobiol 8:213–217

    Google Scholar 

  • Caraco T, Martindale S, Whittam TS (1980) An empirical demonstration of risk-sensitive foraging preferences. Anim Behav 28:820–830

    Google Scholar 

  • Charnov EL (1973) Optimal foraging: some theoretical explorations. PhD dissertation, University of Washington

  • Charnov EL (1976a) Optimal foraging: the marginal value theorem. Theor Popul Biol 9:129–136

    Google Scholar 

  • Charnov EL (1976b) Optimal foraging: the attack strategy of a mantid. Am Nat 110:141–151

    Google Scholar 

  • Cox DR (1962) Renewal theory. Methuen, London

    Google Scholar 

  • Gilliam JF, Green RF, Pearson NE (1982) The fallacy of the traffic policeman: a response to Templeton and Lawlor. Am Nat 119:875–878

    Google Scholar 

  • Green RF (1980) Bayesian birds: a simple example of Oaten's stochastic model of optimal foraging. Theor Popul Biol 18:244–256

    Google Scholar 

  • Herrnstein RJ (1964) Aperiodicity as a factor in choice. J Exp Anal Behav 7:179–182

    Google Scholar 

  • Hey JD (1979) Uncertainty in microeconomics. New York University Press, New York

    Google Scholar 

  • Holling CS (1959) Some characteristics of simple types of parasitism. Can Entomol 16:385–398

    Google Scholar 

  • Iwasa Y, Higashi M, Yamamura N (1981) Prey distribution as a factor determining the choice of optimal foraging strategy. Am Nat 117:710–723

    Google Scholar 

  • Keeney RL, Raiffa H (1976) Decisions with multiple objectives: preferences and value trade-offs. Wiley, New York

    Google Scholar 

  • Krebs JR, Erichsen JT, Webber MI, Charnov EL (1977) Optimal prey selection in the great tit (Parus major). Anim Behav 25:30–38

    Google Scholar 

  • Leventhal AM, Morrell RF, Morgan EF, Perkins CM (1959) The relation between mean reward and mean reinforcement. J Exp Psychol 57:284–287

    Google Scholar 

  • MacArthur RH (1972) Geographical ecology. Harper and Row, New York

    Google Scholar 

  • Maynard Smith J (1969) The status of neo-darwinism. In: Waddington CH (ed) Towards a theoretical biology. 2. Sketches. University Press, Edinburgh, pp 82–89

    Google Scholar 

  • Maynard Smith J (1974) Models in ecology. Cambridge University Press, Cambridge

    Google Scholar 

  • McNair JN (1979) A generalized model of optimal diets. Theor Popul Biol 15:159–170

    Google Scholar 

  • McNair JN (in press) Energy reserves and the risk of starvation; some foraging strategies. Am Nat

  • McNamara J (1982) Optimal patch use in a stochastic environment. Theor Popul Biol 21:269–288

    Google Scholar 

  • McNamara J, Houston AI (in press) Short-term behaviour and life-time fitness. In: McFarland DJ (ed) Functional ontogeny. Pitmans, London

  • Oaten A (1977) Optimal foraging in patches: a case for stochasticity. Theor Popul Biol 85:673–690

    Google Scholar 

  • Oster GF, Wilson EO (1978) Caste and ecology and the social insects. Princeton University Press, Princeton, New Jersey

    Google Scholar 

  • Orians GH, Pearson NE (1979) On the theory of central place foraging. In: Horn DJ, Mitchell RD, Stairs GR (eds) Analysis of ecological systems. Ohio State University Press, Columbus, Ohio, pp 155–177

    Google Scholar 

  • Paloheimo JE (1967) On the theory of search. PhD dissertation, University of Toronto

  • Paloheimo JE (1971) On the theory of search. Biometrika 58: 61–75

    Google Scholar 

  • Pearson NE (1974) Optimal foraging theory. Quan Science Paper No 39, Center of Quan Science in forestry, fisheries and wildlife. University of Washington, Seattle, Washington

    Google Scholar 

  • Prys-Jones RP (1977) Aspects of reed-bunting ecology with comparisons with the yellowhammer. D Phil thesis, University of Oxford

  • Pubols BH (1962) Constant versus variable delay of reinforcement. J Comp Physiol Psychol 55:52–56

    Google Scholar 

  • Pulliam HR, (1974) On the theory of optimal diets. Am Nat 108:59–74

    Google Scholar 

  • Pyke GH, Pulliam HR, Charnov EL (1977) Optimal foraging: a selective review of theory and tests. Q Rev Biol 52:137–154

    Google Scholar 

  • Raiffa H (1968) Decision analysis. Addison-Wesley, Reading, Massachussetts

    Google Scholar 

  • Real LA (1980a) Fitness, uncertainty and the law of diminishing returns in evolution and behavior. Am Nat 115:623–638

    Google Scholar 

  • Real LA (1980b) On uncertainty and the law of diminishing returns in evolution and behavior. In: Staddon JER (ed) Limits to action: the allocation of individual behavior. Academic Press, New York, pp 37–64

    Google Scholar 

  • Real LA (1981) Uncertainty and pollinator-plant interactions: the foraging behavior of bees and wasps on artificial flowers. Ecology 62:20–26

    Google Scholar 

  • Schoener TW (1969) Models of optimal size for solitary predators. Am Nat 103:277–313

    Google Scholar 

  • Schoener TW (1971) Theory of feeding strategies. Ann Rev Ecol Syst 2:379–404

    Google Scholar 

  • Smith WL (1955) Regenerative processes. Proc. R Soc Lond [A] 232:6–31

    Google Scholar 

  • Stephens DW (1981) The logic of risk-sensitive foraging preferences. Anim Behav 29:628–629

    Google Scholar 

  • Templeton AR, Lawlor LR (1981) The fallacy of the averages in ecological optimization theory. Am Nat 117:390–383

    Google Scholar 

  • Turelli M, Gillispie JH, Schoener TW (1982) The fallacy of the fallacy of the averages in ecological optimization theory. Am Nat 119:879–884

    Google Scholar 

  • Waddington KD, Allen T, Heinrich B (1981) Floral preference of bumblebees (Bombus adwardsii) in relation to intermittent versus continuous rewards. Anim Behav 29:779–784

    Google Scholar 

  • Werner EE, Hall DJ (1975) Optimal foraging and the size-selection of prey by bluegill sunfish (Lepomis macrochirus). Ecology 55:1042–1052

    Google Scholar 

Download references

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Author notes

  1. D. W. Stephens

    Present address: Smithsonian Institution, Chesapeake Bay Center for Environmental Studies, P.O. Box 28, 21037, Edgewater, Maryland, USA

Authors and Affiliations

  1. Department of Zoology, Edward Grey Institute, South Parks Road, OX1 3PS, Oxford, England

    D. W. Stephens

  2. Department of Biology, University of Utah, 84112, Salt Lake City, Utah, USA

    Eric L. Charnov

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  1. D. W. Stephens
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  2. Eric L. Charnov
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Stephens, D.W., Charnov, E.L. Optimal foraging: Some simple stochastic models. Behav Ecol Sociobiol 10, 251–263 (1982). https://doi.org/10.1007/BF00302814

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