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A framework for the functional analysis of behaviour

Published online by Cambridge University Press:  04 February 2010

Alasdair I. Houston  and
John M. McNamara
Alasdair I. Houston
Affiliation:
Department of Zoology, Edward Grey Institute, University of Oxford, Oxford 0X1 3PS, England
John M. McNamara
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TYI, England
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Abstract

We present a general framework for analyzing the contribution to reproductive success of a behavioural action. An action may make a direct contribution to reproductive success, but even in the absence of a direct contribution it may make an indirect contribution by changing the animal's state. We consider actions over a period of time, and define a reward function that characterizes the relationship between the animal's state at the end of the period and its future reproductive success. Working back from the end of the period using dynamic programming, the optimal action as a function of state and time can be found. The procedure also yields a measure of the cost, in terms of future reproductive success, of a suboptimal action. These costs provide us with a common currency for comparing activities such as eating and drinking, or eating and hiding from predators. The costs also give an indication of the robustness of the conclusions that can be drawn from a model. We review how our framework can be used to analyze optimal foraging decisions in a stochastic environment. We also discuss the modelling of optimal daily routines and provide an illustration based on singing to attract a mate. We use the model to investigate the features that can produce a dawn song burst in birds. State is defined very broadly so that it includes the information an animal has about its environment. Thus, exploration and learning can be included within the framework.

Keywords

adaptationbehavioural ecologycausal explanationdynamic optimizationevolutionforagingfunctional explanationlearningmatchingmaximizationpopulation biologyreproductive successsociobiology
Type
Target Article
Information
Behavioral and Brain Sciences , Volume 11 , Issue 1 , March 1988 , pp. 117 - 130
Copyright
Copyright © Cambridge University Press 1988

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References

Aoki, M. (1967) Optimization of stochastic systems. Academic Press.Google Scholar
Arnold, S. J. (1983) Morphology, performance and fitness. American Zoologist 38:709–19; 23:347–61.Google Scholar
Arnold, S. J. & Wade, M. J. (1984) On the measurement of natural and sexual selection: Applications. Evolution 38:720–34.Google Scholar
Barnard, C. J. & Brown, C. A. J. (1981) Prey size selection and competition in the common shrew (Sorex araneus). Behavioural Ecology and Sociobiobgy 8:239–43.Google Scholar
Barnard, C. J. & Brown, C. A. J. (1985) Competition affects risk-sensitivity in foraging shrews. Behavioural Ecology and Sociobiology 16:379–82.Google Scholar
Barnard, C. J. & Brown, C. A. J. (1985a) Risk sensitivity in foraging common shrews (Sorex araneus L.). Behavioural Ecology and Sociobiology 16:161–64.CrossRefGoogle Scholar
Barnard, C. J., Brown, C. A. J. & Gray-Wallis, F. J. (1983) Time and energy budgeting and competition in common shrews (Sorex araneus). Behavioural Ecology and Sociobiology 13:13–18.CrossRefGoogle Scholar
Barnard, C. J., Brown, C. A. J., Houston, A. I. & McNamara, J. M. (1985) Risk-sensitive foraging in common shrews: An interruption model and the effects of mean and variance in reward rate. Behavioural Ecology and Sociobiology 18:139–46.CrossRefGoogle Scholar
Barnard, C. J. & Hurst, J. (1987) Time constraints and prey selection in common shrews (Sorex araneus). Animal Behaviour 35.CrossRefGoogle Scholar
Barnard, C. J. & Thompson, D. B. A. (1985) Gulls and plovers: The ecology and behaviour of mixed-species feeding groups. Croom Helm.CrossRefGoogle Scholar
Baum, W. M. (1974) Choice in free-ranging wild pigeons. Science 185:78–79.CrossRefGoogle ScholarPubMed
Baum, W. M. (1974a) On two types of deviation from the matching law: Bias and undermatching. Journal of the Experimental Analysis of Behavior 22:231–42.Google Scholar
Baum, W. M. (1983) Studying foraging in the psychological laboratory. In: Animal cognition and behavior, ed. Mellgren, R. L.. North-Holland.Google Scholar
Bellman, R. (1957) Dynamic programming. Princeton University Press.Google ScholarPubMed
Bellman, R. (1961) Adaptive control processes: A guided tour. Princeton University Press.CrossRefGoogle Scholar
Bellman, R. & Dreyfus, S. E. (1962) Applied dynamic programming. Princeton University Press.CrossRefGoogle ScholarPubMed
Belovsky, G. E. (1981) Optimal activity times and habitat choice of moose. Oecologia 48:22–30.CrossRefGoogle ScholarPubMed
Bertsekas, D. P. (1976) Dynamic programming and stochastic control. Academic Press.Google Scholar
Bookstaber, R. & Langsam, J. (1985) On the optimality of coarse behaviour rules. Journal of Theoretical Biology 116:161–93.CrossRefGoogle Scholar
Brown, J. S. & Vincent, T. L. (1987) A theory for the evolutionary game. Theoretical Population Biology 31:140–66.Google Scholar
Bryant, D. M. & Westerterp, K. R. (1983) Time and energy limits to brood size in house martins (Delichon urbica). Journal of Animal Ecology 52:905–25.CrossRefGoogle Scholar
Busino, G. (1975) Sodologia e Storia. Guida.Google Scholar
Calder, W. A. III (in preparation) Territorially, body mass regulation, noeturnal energy conservation, and survivorship of the male broad-tailed hummingbird (Selasphorus platycercus).Google Scholar
Caraco, T. (1980) On foraging time allocation in a stochastic environment. Ecology 61:119–28.CrossRefGoogle Scholar
Caraco, T. (1981a) Energy budgets, risk and foraging preferences in dark-eyed juncos (Junco hyemalis). Behavioural Ecology and Sociobiology 8:213–17.CrossRefGoogle Scholar
Caraco, T. (1981b) Risk-sensitivity and foraging groups. Ecology 62:527–31.Google Scholar
Caraco, T. (1983) White-crowned sparrows (Zonotrichia leucophrys): Foraging preferences in a risky environment. Behavioural Ecology and Sociobiology 12:63–69.Google Scholar
Caraco, T. & Chasin, M. (1984) Foraging preferences: Response to reward skew. Animal Behaviour 32:76–85.Google Scholar
Caraco, T. & Lima, S. L. (1987) Survivorship, energy budgets and foraging risk. In: Quantitative analysis of behavior. Vol. 6: Foraging, ed. Commons, M. L., Kacelnik, A. & Shettleworth, S. J.. Erlbaum.Google Scholar
Caraco, T., Martindale, S. & Whittam, T. S. (1980) An empirical demonstration of risk sensitive foraging preferences. Animal Behaviour 28:820–30.CrossRefGoogle Scholar
Carpenter, F. L., Paton, D. C. & Hixon, M. A. (1983) Weight gain and adjustment of feeding territory size in migrant hummingbirds. Proceedings of the National Academy of Sciences (U.S.A.) 80:7259–63.CrossRefGoogle ScholarPubMed
Cartan, E. (1945) Les systemes differentiels exterieurs est leur applications geometrique. Exposes de Ceometrie, vol. 14. Hermann.Google Scholar
Case, D. A., Fantino, E. & Wixted, J. (1985) Human observing: Maintained by negative informative stimuli only if correlated with improvement in response efficiency. Journal of the Experimental Analysis of Behavior 43:289–300.CrossRefGoogle ScholarPubMed
Charnov, E. L. (1976) Optimal foraging: Attack strategy of a mantid. American Naturalist 110:141–51.CrossRefGoogle Scholar
Clark, C. W. (1987) The lazy, adaptable lions: A Markovian model of group foraging. Animal Behaviour 35:361–68.Google Scholar
Clark, C. W. & Levy, D. A. (in press) Diel vertical migrations of juvenile sockeye salmon and the antipredation window. American Naturalist.Google Scholar
Clark, C. W. & Mangel, M. (1986) The evolutionary advantages of group foraging. Theoretical Population Biology 30:45–75.CrossRefGoogle Scholar
Collier, G. H. (1982) Determinants of choice. In: Nebraska Symposium on Motivation, ed. Bernstein, D.. University of Nebraska Press.Google Scholar
Collier, G. H. (1983) Life in a closed economy: The ecology of learning and motivation. Advances in analysis of behaviour. Vol. 3: Biological factors in learning, ed. Zeiler, M. D. & Harzem, P.. Wiley.Google Scholar
Collier, G. H., Johnson, D. F., Hill, W. L. & Kaufman, L. W. (1986) The economics of the law of effect. Journal of the Experimental Analysis of Behavior 46:113–36.CrossRefGoogle ScholarPubMed
Craig, R. B., De Angelis, D. L. & Dixon, K. R. (1979) Long- and short-term dynamic optimization models with application to the feeding strategy of the loggerhead shrike. American Naturalist 113:31–51.CrossRefGoogle Scholar
Crowcroft, P. (1955) The life of the shrew. Reinhardt.Google Scholar
Daan, S. (1981) Adaptive daily strategies in behavior. In: Handbook of behavioral neurobiology, vol. 4, ed. Aschoff, J.. Plenum.Google Scholar
Davies, N. B. (1977) Prey selection and the search strategy of the spotted flycatcher (Muscicapa striata): A field study on optimal foraging. Animal Behaviour 25:1016–33.CrossRefGoogle Scholar
Davies, N. B. & Houston, A. I. (1983) Time allocation between territories and flocks and owner-satellite conflict in foraging pred wagtails, Motacilla alba. Journal of Animal Ecology 52:621–34.CrossRefGoogle Scholar
Davison, M. C. (1972) Preference for mixed-interval versus fixed-interval schedules: Number of component intervals. Journal of the Experimental Analysis of Behavior 17:169–76.Google Scholar
Dawkins, M. S. (1983) Battery hens name their price: Consumer demand theory and the measurement of ethological “needs.” Animal Behaviour 31:1195–1205.CrossRefGoogle Scholar
Dawkins, M. S. (in preparation) Behavioural deprivation: A central problem in animal welfare.Google Scholar
Dawkins, R. (1982) The extended phenotype. W. H. Freeman.Google Scholar
DeBenedictis, P. A., Gill, F. B., Hainsworth, F. R., Pyke, G. H. & Wolf, L. L. (1978) Optimal meal size in hummingbirds. American Naturalist 112:301–16.CrossRefGoogle Scholar
De Carlo, L. T. (1985) Matching and maximizing with variable-time schedules. Journal of the Experimental Analysis of Behavior 43:75–81.Google Scholar
De Groot, M. H. (1970) Optimal statistical decisions. McGraw-Hill.Google Scholar
Dennett, D. C. (1971) Intentional systems. Journal of Philosophy 68:87–106.CrossRefGoogle Scholar
Dennett, D. C. (1983) Intentional systems in cognitive ethology: The “Planglossian paradigm” defended. Behavioral and Brain Sciences 6:343–90.Google Scholar
Diamond, J. M., Karasov, W. H., Phan, D. & Carpenter, F. L. (1986) Digestive physiology is a determinant of foraging bout frequency in hummingbirds. Nature 320:62–63.CrossRefGoogle ScholarPubMed
Dill, L. M. (1983) Adaptive flexibility in the foraging behavior of fishes. Canadian Journal of Fisheries and Aquatic Science 40:398–408.CrossRefGoogle Scholar
Dinsmoor, J. A. (1983) Observing and conditioned reinforcement. Behavioral and Brain Sciences 6:693–728.CrossRefGoogle Scholar
Ekman, J. & Rosander, B. (1987) Starvation risk and flock size of the social forager: When is there a flocking cost? Theoretical Population Biology 31:167–77.CrossRefGoogle Scholar
Engen, S., Saether, B.-E. & Stenseth, N. C. (in press) The effect of competition on the ranking of food items. American Naturalist.Google Scholar
Engen, S. & Stenseth, N. C. (in press) Optimal foraging theory: A settheoretical approach. Ecological Modelling.Google Scholar
Engen, S. & Stenseth, N. C. (submitted) Age-specific optimal diets and optimal foraging tactics: A life-historic approach.Google Scholar
Erwin, M. R. (1985) Foraging decisions, patch use, and seasonality in egrets (Aves: Ciconiiformes). Ecology 66:837–44.CrossRefGoogle Scholar
Fantino, E. & Abarca, N. (1985) Choice, optimal foraging, and the delay-reduction hypothesis. Behavioral and Brain Sciences 8:315–30.CrossRefGoogle Scholar
Fantino, E. & Case, D. A. (1983) Human observing: Maintained by stimuli correlated with reinforcement but not extinction. Journal of the Experimental Analysis of Behavior 40:193–210.Google Scholar
Fantino, E., Case, D. A. & Altus, D. (1983) Observing reward-informative and -uninformative stimuli by normal children of different ages. Journal of Experimental Child Psychology 36:437–52.CrossRefGoogle Scholar
Fisher, R. A. (1930) The genetic theory of natural selection. Clarendon Press.Google Scholar
Freed, L. A. (1981) Loss of mass in breeding wrens: Stress or adaptation? Ecology 62:1179–86.CrossRefGoogle Scholar
Freeman, S. & MacFarland, D. J. (1982) The Darwinian objective function and adaptive behaviour. In: Functional ontogeny, ed. Morse, D. H. (1985) Reproductive success and foraging of the crab spider Misumena vatia. Oecologia 65:194–200.Google Scholar
Gillespie, R. G. & Caraco, T. (1987) Risk-sensitive foraging strategies of two spider populations. Ecology 68:887–99.Google Scholar
Gilliam, J. F. (1982) Habitat use and competitive bottlenecks in sizestructured fish populations. Unpub. Ph.D. thesis, Michigan State University.Google Scholar
Gilliam, J. F. & Fraser, D. F. (1987) Habitat selection when foraging under predatio hazard: A model and a test with stream-dwelling minnows. Ecology 68:1856–62.CrossRefGoogle Scholar
Goodman, D. (1982) Optimal life histories, optimal notation and the value of reproductive value. American Naturalist 119:803–23.CrossRefGoogle Scholar
Gould, S. J. & Lewontin, R. C. (1979) The spandrels of San Marco and the Panglossian paradigm: A critique of the adaptationist programme. Proceedings of the Royal Society of London, Series B 205:581–98.Google Scholar
Grafen, A. (1984) Natural selection, kin selection and group selection. In: Behavioural ecology: An evolutionary approach. 2nd edition, ed. Krebs, J. R. & Davies, N. B.. Blackwell.Google Scholar
Grafen, A. (in press) On the uses of data on lifetime reproductive success. In: Reproductive success, ed. Clutton-Brock, T. H.. University of Chicago Press.Google Scholar
Green, R. F. (1984) Stopping rules for optimal foragers. American Naturalist 123:30–40.CrossRefGoogle Scholar
Green, R. F. (1987) Stochastic models of optimal foraging. In: Foraging behavior, ed. Kamil, A. C., Krebs, J. R. & Pulliam, H. R.. Plenum.Google Scholar
Greene, P. R. (1985) Running on flat turns: Experiments, theory, and applications. Journal of Biomechanical Engineering 107:96–103.Google Scholar
Hamm, S. L. & Shettleworth, S. J. (in press) Risk aversion in pigeons. Journal of Experimental Psychology: Animal Behavior Processes.Google Scholar
Hanski, I. (1985) What does a shrew do in an energy crisis? In: Behavioural ecology: Ecological consequences of adaptive behaviour, ed. Sibley, R. M. & Smith, R. H.. Blackwell.Google Scholar
Heiner, R. A. (1983) The origin of predictable behavior. American Economic Review 73:560–95.Google Scholar
Heiner, R. A. (1985) Origin of predictable behavior: Further modeling and applications. American Economic Review 75:391–96.Google Scholar
Heiner, R. A. (1985a) Uncertainty, signal detection experiments, and modeling behavior. In: Economics as a process, ed. Langlois, R.. Cambridge University Press.Google Scholar
Heiner, R. A. (in press) The necessity of imperfect decisions. Journal of Economic Behavior and Organization.Google Scholar
Heiner, R. A. (in press a) Origin of predictable dynamic behavior. Journal of Economic Behavior and Organization.Google Scholar
Heiner, R. A. (forthcoming) Imperfect decisions, evolutionary stability and predictable behavior: The origin of rules over flexible optimizing. In: Quantitative analyses of behavior. Vol. 9, ed. Commons, M. L. & Herrnstein, R. J.. Behavioral Economics.Google Scholar
Heller, R. & Milinski, M. (1979) Optimal foraging of sticklebacks on swarming prey. Animal Behaviour 27:1127–41.CrossRefGoogle Scholar
Herrnstein, R. J. (1961) Relative and absolute strength of response as a function of reinforcement. Journal of the Experimental Analysis of Behavior 4:267–72.Google Scholar
Herrnstein, R. J. (1964) Aperiodicity as a factor in choice. Journal of the Experimental Analysis of Behavior 7:179–82.Google Scholar
Herrnstein, R. J. (1970) On the law of effect. Journal of the Experimental Analysis of Behavior 13:243–66.CrossRefGoogle ScholarPubMed
Herrnstein, R. J. & Heyman, G. M. (1979) Is matching compatible with reinforcement maximization on concurrent variable interval, variable ratio? Journal of the Experimental Analysis of Behavior 31:209–23.Google Scholar
Herrnstein, R. J. & Vaughan, W. Jr. (1980) Melioration and behavioral allocation. In: Limits to action, ed. Staddon, J. E. R.. Academic Press.Google Scholar
Heyman, G. M. & Herrnstein, R. J. (1986) More on concurrent interval-ratio schedules. Journal of the Experimental Analysis of Behavior 46:331–51.Google Scholar
Heyman, G. M. & Luce, R. D. (1979) Operant matching is not a logical consequence of maximizing reinforcement rate. Animal Learning and Behavior 7:133–40.CrossRefGoogle Scholar
Hodges, C. M. (1985) Bumble bee foraging: The threshold departure rule. Ecology 66:179–87.CrossRefGoogle Scholar
Hopfield, J. J. & Tank, D. W. (1985) “Neural” computation of decisions in optimization problems. Biological Cybernetics 52:141–52.CrossRefGoogle ScholarPubMed
Houston, A. I. (1980) Godzilla v. the creature from the black lagoon. In: The analysis of motivational processes, ed. Toates, F. M. & Halliday, T. R.. Academic Press.Google Scholar
Houston, A. I. (1983) Optimality theory and matching. Behaviour Analysis Letters 3:1–15.Google Scholar
Houston, A. I. (1986) The matching law applies to wagtails foraging in the wild. Journal of the Experimental Analysis of Behavior 45:15–18.Google Scholar
Houston, A. I. (1987) The control of foraging decisions. In: Quantitative analyses of behavior. Vol. 6: Foraging, ed. Commons, M. L., Kacelnik, A., & Shettleworth, S. J.. Erlbaum.Google Scholar
Houston, A. I., Kacelnik, A. & McNamara, J. M. (1982) Some learning rules for acquiring information. In: Functional ontogeny, ed. McFarland, D. J.. Pitman.Google Scholar
Houston, A. I. & McNamara, J. M. (1981) How to maximize reward rate on two variable-interval paradigms. Journal of the Experimental Analysis of Behavior 35:367–96.Google Scholar
Houston, A. I. & McNamara, J. M. (1982) A sequential approach to risk-taking. Animal Behaviour 30:1260–61.Google Scholar
Houston, A. I. & McNamara, J. M. (1984) Imperfectly optimal animals: A correction. Behavioural Ecology and Sociobiology 15:61–64.Google Scholar
Houston, A. I. & McNamara, J. M. (1985) The choice of two prey types that minimises the probability of starvation. Behavioural Ecology and Sociobiology 17:135–41.Google Scholar
Houston, A. I. & McNamara, J. M. (1986) Evaluating the selection pressure on foraging decisions. In: Relevance of models and theories in ethology, ed. Campan, R. & Zayan, R.. Toulouse: Privat Press.Google Scholar
Houston, A. I. & McNamara, J. M. (1987) Singing to attract a mate – a stochastic dynamic game. Journal of Theoretical Biology 129:57–68.Google Scholar
Houston, A. I. & McNamara, J. M. (in press a) The value of food: Effects of open and closed economies. Animal Behaviour.Google Scholar
Houston, A. I. & McNamara, J. M. (in press b) Fighting for food: A dynamic version of the Hawk-Dove game. Evolutionary Ecology.Google Scholar
Houston, A. I., McNamara, J. M. & Sumida, B. H. (1987) Relative allocation can depend on schedule parameters when behavioral parameters are constant. Journal of the Experimental Analysis of Behavior 47:127–32.CrossRefGoogle ScholarPubMed
Houston, A. I. & Staddon, J. E. R. (1981) Optimality principles and behaviour: It's all for the best. Behavioral and Brain Sciences 4:395–96.Google Scholar
Houston, A. I. & Sumida, B. H. (1987) Learning rules, matching and frequency dependence. Journal of Theoretical Biology 126:289–308.Google Scholar
Houston, A. I., Sumida, B. H. & McNamara, J. M. (1987) Maximization of reinforcement rate on concurrent chains. Journal of the Experimental Analysis of Behavior 48:133–43.Google Scholar
Howland, H. C. (1974) Optimal strategies for predator avoidance: The relative importance of speed and maneuverability. Journal of Theoretical Biology 47:333–50.Google Scholar
Hursh, S. R. (1978) The economics of daily consumption controlling food and water-reinforced responding. Journal of the Experimental Analysis of Behavior 29:475–91.CrossRefGoogle ScholarPubMed
Hursh, S. R. (1980) Economic concepts for the analysis of behavior. Journal of the Experimental Analysis of Behavior 34:219–38.Google Scholar
Hursh, S. R. (1984) Behavioral economics. Journal of the Experimental Analysis of Behavior 42:435–52.CrossRefGoogle ScholarPubMed
Iwasa, Y., Higashi, M. & Yamamuia, N. (1981) Prey distribution as a factor determining the choice of optimal foraging strategy. American Naturalist 117:710–23.Google Scholar
Iwasa, Y., Suzuki, Y. & Matsuda, H. (1984) Theory of oviposition strategy of parasitoids. I. Effect of mortality and limiting egg number. Theoretical Population Biology 26:205–27.Google Scholar
Kagel, J. H., Green, L. & Caraco, T. (1986) When foragers discount the future: Constraint or adaptation? Animal Behaviour 34:217–83.Google Scholar
Kagel, J. H., MacDonald, D. N., Battalio, R. C., White, S. & Green, L. (1986) Risk aversion in rats (Rattus norvegicus) under varying levels of resource availability. Journal of Comparative Psychology 100:95–100.CrossRefGoogle Scholar
Kamil, A. C. (1983) Optimal foraging theory and the psychology of learning. American Zoologist 23:291–302.Google Scholar
Kamil, A. C., Peters, J. & Lindstrom, F. J. (1982) An ecological perspective on the study of the allocation of behavior. In: Quantitative analyses of behavior: Matching and maximizing accounts, ed. Commons, M. L., Herrnstein, R. J. & Rachlin, H.. Ballinger.Google Scholar
Kamil, A. C., Yoerg, S. I. & Clements, K. C. (in press) Rules to leave by: Patch departure in foraging blue jays. Animal Behaviour.Google Scholar
Karasov, W. H., Phan, D., Diamond, J. M. & Carpenter, F. L. (1986) Food passage and intestinal nutrient absorption in hummingbirds. Auk 103:453–64.Google Scholar
Kareem, A. M. & Barnard, C. J. (1982) The importance of kinship and familiarity in social interactions between mice. Animal Behaviour 30:594–601.Google Scholar
Karlin, S. & Taylor, H. M. (1975) A first course in stochastic processes. Academic Press.Google Scholar
Katz, P. L. (1974) A long-term approach to foraging optimization. American Naturalist 108:758–82.CrossRefGoogle Scholar
Killeen, P. (1968) On the measurement of reinforcement frequency in the study of preference. Journal of the Experimental Analysis of Behavior 11:263–69.Google Scholar
King, J. R. (1972) Adaptive periodic fat storage by birds. In: Proceedings of the sixteenth international ornithological congress, ed. Voous, K. H.. E. J. Brill.Google Scholar
King, J. R. & Murphy, M. E. (1985) Periods of nutritional stress in the annual cycles of endotherms: Fact or fiction? American Zoologist 25:955–64.CrossRefGoogle Scholar
Krebs, J. R. & Davies, N. B., eds. (1984) Behavioural ecology: An evolutionary approach, 2nd edition. Blackwell.Google Scholar
Krebs, J. R., Kacelnik, A. & Taylor, P. (1978) Test of optimal sampling by foraging tits. Nature 275:27–31.Google Scholar
Krebs, J. R., Stephens, D. W. & Sutherland, W. J. (1983) Perspectives in optimal foraging. In: Perspectives in ornithology, ed. Brush, A. H. & Clark, G. A. Jr. Cambridge University Press.Google Scholar
Kugler, P. N. & Turvey, M. T. (1987) Information, natural law, and the selfassembly of rhythmic movement. Erlbaum.Google Scholar
Lande, R. & Arnold, S. J. (1983) The measurement of selection on correlated characters. Evolution 37:1210–26.Google Scholar
Larson, R. E. & Casti, J. L. (1982) Principles of dynamic programming. Part II: Advanced theory and applications. Marcel Dekker.Google Scholar
Lea, S. E. G. (1979) Foraging and reinforcement schedules in the pigeon: Optimal and non-optimal aspects of choice. Animal Behaviour 27:875–86.Google Scholar
Lea, S. E. G. (1981) Correlation and continuity in foraging behaviour. In: Advances in analysis of behaviour, vol. 2, ed. Harzem, P. & Zeiler, M. H.. Wiley.Google Scholar
Lendrem, D. W. (1983) Predation risk and vigilance in the blue tit (Parus caeruleus). Behavioural Ecology and Sociobiology 14:9–13.Google Scholar
Levine, R. (1966) The strategy of model building in population biology. American Scientist 54:421–31.Google Scholar
Lewontin, R. C. (1979) Fitness, survival and optimality. In: Analysis of ecological systems, ed. Hom, R. D., Stairs, E. R. & Mitchell, R. D.. OhioState University Press.Google Scholar
Leyhausen, P. (1979) Cat behavior. Garland.Google Scholar
Li, C. C. (1976) First course in population genetics. Boxwood Press.Google Scholar
Lima, S. L. (1983) Downy woodpecker foraging behavior: Foraging by expectation and energy intake rate. Oecologia 58:232–37.Google Scholar
Lima, S. L. (1985) Maximizing feeding efficiency and minimizing time exposed to predators: A trade-off in the black-capped chickadee. Oecologia 66:60–7.Google Scholar
Lima, S. L. (1986) Predation risk and unpredictable feeding conditions: Determinants of body mass in birds. Ecology 67:377–85.CrossRefGoogle Scholar
Logan, F. A. (1965) Decision making by rats: Uncertain outcome choices. Journal of Comparative and Physiological Psychology 59:246–51.Google Scholar
Logue, A. W. & Chavarro, A. (1987) Effect on choice of absolute and relative values of reinforcer delay, amount, and frequency. Journal of Experimental Psychology: Animal Behavior Processes 13:280–91.Google Scholar
Logue, A. W. & Pena-Correal, T. E. (1984) Responding during reinforcement delay in a self-control paradigm. Journal of the Experimental Analysis of Behavior 41:267–77.Google Scholar
Logue, A. W. & Pena-Correal, T. E. (1985) The effect of food deprivation on self-control. Behavioural Processes 10:355–68.Google Scholar
Logue, A. W., Rodriguez, M. L., Pena-Correal, T. E. & Mauro, B. C. (1984) Choice in a self-control paradigm: Quantification of experience-based differences. Journal of the Experimental Analysis of Behavior 41:53–67.Google Scholar
Lorenz, K. Z. & Leyhausen, P. (1973) Motivation of human and animal behavior. Van Nostrand.Google Scholar
Lucas, J. (1983) The role of foraging time constraints and variable prey encounter in optimal diet choice. American Naturalist 122:191–209.Google Scholar
Lucas, J. (1985) Time constraints and diet choice: Different predictions from different models. American Naturalist 126:680–705.Google Scholar
Lucas, J. R. & Grafen, A. (1985) Partial prey consumption by ambush predators. Journal of Theoretical Biology 113:455–73.Google Scholar
Macevicz, S. & Oster, G. (1976) Modeling social insect populations. II: Optimal reproductive strategies in annual eusocial insect colonies. Behavioural Ecology and Sociobiology 1:265–82.Google Scholar
Mangel, M. (1985) Decision and control in uncertain resource systems. Academic Press.Google Scholar
Mangel, M. (1987) Oviposition site selection and clutch size in insects. Journal of Mathematical Biology 25:1–22.CrossRefGoogle Scholar
Mangel, M. (submitted) A dynamic theory of diet selection,Google Scholar
Mangel, M.(unpublished) Dynamic foraging strategies of web-building spiders. Manuscript.Google Scholar
Mangel, M. & Clark, C. W. (1983) Uncertainty, search, and information in fisheries. Journal of the International Council for the Exploration of the Seas 41:93–103.Google Scholar
Mangel, M. & Clark, C. W. (1986) Towards a unified foraging theory. Ecology 67:1127–38.Google Scholar
Marwine, A. & Collier, G. (1979) The rat at the waterhole. Journal of Comparative and Physiological Psychology 93:391–402.Google Scholar
Masman, D. (1986) The annual cycle of the kestrel. Unpub. Ph.D. thesis, University of Groningen.Google Scholar
Maynard Smith, J. (1978) Optimization theory in evolution. Annual Review of Ecology and Systematics 9:31–56.Google Scholar
Maynard Smith, J. (1982) Evolution and the theory of games. Cambridge University Press.Google Scholar
Maynard Smith, J. (1984) Game theory and the evolution of behaviour. Behavioral and Brain Sciences 7:95–125.Google Scholar
Mazur, J. E. (1981) Optimization theory fails to predict performance of pigeons in a two-response situation. Science 241:823–25.Google Scholar
Mazur, J. E. & Coe, D. (1987) Tests of transitivity in choices between fixed and variable reinforcer delays. Journal of the Experimental Analysis of Behavior 47:287–97.Google Scholar
McCleery, R. H. (1977) On satiation curves. Animal Behaviour 25:1005–15.Google Scholar
McCleery, R. H. (1978) Optimal behaviour sequences and decision making. In: Behavioral ecology (1st ed.), ed. Krebs, J. R. & Davies, N. B.. Blackwell.Google Scholar
McFarland, D. J. (1977) Decision making in animals. Nature 269:15–21.Google Scholar
McFarland, D. J. & Wright, P. J. (1969) Water conservation by inhibition of food intake. Physiology and Behavior 4:95–99.Google Scholar
McNamara, J. M. (1982) Optimal patch use in a stochastic environment. Theoretical Population Biology 21:269–88.Google Scholar
McNamara, J. M. (1984) Control of a diffusion by switching between two drift-diffusion coefficient pairs. Society of Industrial and Applied Mathematics Journal of Control and Optimization 22:87–94.Google Scholar
McNamara, J. M. & Houston, A. I. (1980) The application of a statistical decision theory to animal behaviour. Journal of Theoretical Biology 85:673–90.Google Scholar
McNamara, J. M. & Houston, A. I. (1982) Short-term behaviour and life-time fitness. In: Functional ontogeny, ed. McFarland, D. J.. Pitman.Google Scholar
McNamara, J. M. & Houston, A. I. (1983) Optimal responding on variable interval schedules. Behaviour Analysis Letters 3:157–70.Google Scholar
McNamara, J. M. & Houston, A. I. (1985) Optimal foraging and learning. Journal of Theoretical Biology 117:231–49.Google Scholar
McNamara, J. M. & Houston, A. I. (1986) The common currency for behavioral decisions. American Naturalist 127:358–78.Google Scholar
McNamara, J. M. & Houston, A. I. (1987) Foraging in patches: There's more to life than the marginal value theorem. In: Quantitative analyses of behavior. Vol. 6: Foraging, ed. Commons, M. L., Kacelnik, A. & Shettleworth, S. J.. Erlbaum.Google Scholar
McNamara, J. M. & Houston, A. I. (1987a) A general framework for understanding the effects of variability and interruptions on foraging behaviour. Acta Biotheorectica 36:3–22.CrossRefGoogle ScholarPubMed
McNamara, J. M. & Houston, A. I. (1987b) Partial preferences and foraging. Animal Behaviour 35:1084–99.Google Scholar
McNamara, J. M. & Houston, A. I. (1987c) Starvation and predation as factors limiting population size. Ecology 68:1515–19.Google Scholar
McNamara, J. M., Houston, A. I., Lima, S. L. & Mangel, (unpublished) Optimal daily routines of foraging for a small bird in winter.Google Scholar
McNamara, J. M., Mace, R. H. & Houston, A. I. (1987) Optimal daily routines of singing and foraging in a bird singing to attract a mate. Behavioural Ecology and Sociobiology 20:399–405.Google Scholar
Metcalfe, N. B. & Furness, R. W. (1984) Changing priorities: The effect of pre-migratory fattening on the trade-off between foraging and vigilance. Behavioural Ecology and Sociobiology 15:203–6.Google Scholar
Metcalfe, N. B., Huntingford, F. A. & Thorpe, J. E. (1987) The influence of predation risk on the feeding motivation and foraging strategy of juvenile Atlantic salmon. Animal Behaviour 35:901–11.Google Scholar
Milinski, M. (1987) Tit for tat in sticklebacks and the evolution of cooperation. Nature 325:433–35.Google Scholar
Milinski, M. & Heller, R. (1978) Influence of a predator on the optimal foraging behaviour of sticklebacks (Gasterosteus aculeatus). Nature 275:642–44.Google Scholar
Misner, C., Thome, K. & Wheeler, J. A. (1973) Gravitation. W. H. Freeman.Google Scholar
Mitchell, B., McCowan, D. & Nicholson, I. A. (1976) Annual cycles of body weight and condition in Scottish red deer (Cervus elaphus). Journal of Zoology (London) 180:107–27.Google Scholar
Morse, D. H. (1979) Prey capture by the crab spider Misumena calycina (Araneae: Thomisidae). Oecologia 39:309–19.Google Scholar
Mrosovsky, N. & Powley, T. L. (1977) Set points for body weight and fat. Behavioral Biology 20:205–23.Google Scholar
Mrosovsky, N. & Sherry, D. F. (1980) Animal anorexias. Science 207:837–42.Google Scholar
Nagy, K. A. (1987) Field metabolic rate and food requirement scaling in mammals and birds. Ecological Monographs 57:111–28.Google Scholar
Navarick, D. J. & Fantino, E. (1972) Transitivity as a property of choice. Journal of the Experimental Analysis of Behavior 18:389–401.Google Scholar
Neuringer, A. J. (1969) Animals respond for food in the presence of free food. Science 166:399–401.Google Scholar
Oaten, A. (1977) Optimal foraging in patches: A case for stochasticity. Theoretical Population Biology 12:263–85.Google Scholar
Osborne, S. R. (1977) The free food (contra freeloading) phenomenon: A review and analysis. Animal Learning and Behavior 5:221–35.Google Scholar
Oster, G. F. & Wilson, E. O. (1978) Caste and ecology in the social insects. Princeton University Press.Google Scholar
Parker, G. A. (1984) Evolutionarily stable strategies. In; Behavioural ecology (2nd ed.), ed. Krebs, J. R. & Davies, N. B.. Blackwell.Google Scholar
Peeke, H. V. S. & Veno, A. (1973) Stimulus specificity of habituated aggression in the stickleback. Behavioural Biology 8:427–32.Google Scholar
Pierce, G. J. & Ollason, J. G. (1987) Eight reasons why optimal foraging theory is a complete waste of time. Oikos 49:111–18.Google Scholar
Powers, W. T. (1973) Behavior: The control of perception. Aldine/Walter de Gruyter.Google Scholar
Pulliam, H. R. (1974) On the theory of optimal diets. American Naturalist 108:59–74.Google Scholar
Pulliam, H. R. & Caraco, T. (1984) Living in groups: Is there an optimal group size? In: Behavioural ecology: An evolutionary approach (2nd ed), ed. Krebs, J. R. & Davies, N. B.. Blackwell.Google Scholar
Pulliam, H. R. & Millikan, C. C. (1982) Social organization in the nonreproductive season. In: Avian biology, vol. 6, ed. Farner, D. S. & King, J. R.. Academic Press.Google Scholar
Pyke, G. H. (1984) Optimal foraging theory: A critical review. Annual Review of Ecology and Systematics 15:523–75.Google Scholar
Rachlin, H., Battalio, R. C., Kagel, J. H. & Green, L. (1981) Maximization theory in behavioral psychology. Behavioral and Brain Sciences 4:371–88.Google Scholar
Rachlin, H., Green, L., Kagel, J. H. & Battalio, R. C. (1976) Economic demand theory and psychological Studies of choice. In: The psychology of learning and motivation, vol. 10, ed. Bower, G. H.. Academic Press.Google Scholar
Rachlin, H., Kagel, J. H. & Green, L. (1980) Substitutability in time allocation. Psychological Review 87:355–74.Google Scholar
Real, L. A. (1980) Fitness, uncertainty, and the role of diversification in evolution and behavior. American Naturalist 115:623–38.Google Scholar
Real, L. A. & Caraco, T. (1986) Risk and foraging in stochastic environments: Theory and evidence. Annual Review of Ecology and Systematics 17:371–90.Google Scholar
Rechten, C., Avery, M. & Stephens, A. (1983) Optimal prey selection: Why do great tits show partial preferences? Animal Behaviour 31:576–84.CrossRefGoogle Scholar
Reeke, G. N. & Edelman, G. M. (1986) Recognition automata based on selective neural networks. In: Structure and dynamics of nucleic acids, proteins, and membranes, ed. Clementi, E. & Chin, S.. Plenum.Google Scholar
Reyer, U. & Westerterp, K. (1985) Parental energy expenditure: A proximate cause of helper recruitment in the pied kingfisher (Ceryle rudis). Behavioural Ecology and Sociobiology 17:363–69.CrossRefGoogle Scholar
Rijnsdorp, A., Daan, S. & Dijkstra, C. (1981) Hunting in the kestrel, Falco tinnunculus, and the adaptive significance of daily habits. Oecologia 50:391–406.Google Scholar
Rodriguez, M. L. & Logue, A. W. (1986) Independence of the amount and delay ratios in the generalized matching law. Animal Learning and Behavior 14:29–37.Google Scholar
Roitberg, B. & Mangel, M. (submitted) Dynamic information and host selection by a tephritid fruit fly.Google Scholar
Romanes, J. J. (1892) Darwin and after Darwin, vol. 1. Open Court.Google Scholar
Ross, S. (1983) Introduction to stochastic dynamic programming. Academic Press.Google Scholar
Rowland, W. J. & Sevenster, P. (1985) Sign stimuli in the threespine stickleback: A re-examination and extension of some classic experiments. Behaviour 93:241–57.Google Scholar
Rumelhart, D. E. & McClelland, J. L. (1986) Parallel distributed processing: Explorations in the microstructure of cognition. MIT Press.Google Scholar
Sargent, R. C. (1985) Territoriality and reproductive trade-offs in the threespine stickleback. Behaviour 93:217–26.Google Scholar
Savageau, M. (1976) Biochemical systems analysis. Addison-Wesley.Google Scholar
Schaffer, W. M. (1974) Selection for optimal life histories: The effects of age structure. Ecology 55:291–303.Google Scholar
Schaffer, W. M. (1983) The application of optimal control theory to the general life history problem. American Saturalist 121:418–31.Google Scholar
Schaller, G. B. (1968) Hunting behaviour of the cheetah in the Serengeti National Park, Tanzania. East African Wildlife Journal 6:95–100.Google Scholar
Schmalhausen, J. J. (1946) Faktorii evoluzii; teoria stabiliziriushevo otbora. Akademia Nauk SSK.Google Scholar
Schoener, T. W. (1971) Theory of feeding strategies. Annual Review of Ecology and Systematics 2:369–404.Google Scholar
Schoener, T. W. (1986) Mechanistic approaches to community ecology: A new reductionism? American Zoologist 26:81–106.Google Scholar
Scudo, F. M. (1987) Ethology, ecology, and philosophy. Rivista di Biologia – Biology Forum 80(2):252–56.Google Scholar
Shaw, R. E. & Alley, T. (1984) How to draw learning curves: Their use and justification. In: Issues in the ecological study of learning, ed. Johnston, T. & Pietrewicz, A.. Erlbaum.Google Scholar
Sherry, D. F. (1985) Food storage by birds and mammals. Advances in the Study of Behaviour 15:153–88.Google Scholar
Sherry, D. F., Mrosovsky, N. & Hogan, J. A. (1980) Weight loss and anorexia during incubation in birds. Journal of Comparative and Physiological Psychology 94:89–98.Google Scholar
Shimp, C. P. (1969) Optimal behavior in free-operant experiments. Psychological Review 76:97–112.Google Scholar
Sibly, R. M. & Calow, P. (1983) An integrated approach to life cycle evolution using selective landscapes. Journal of Theoretical Biology 102:527–47.Google Scholar
Sibly, R. M., Calow, P. & Nichols, N. (1985) Are patterns of growth adaptive? Journal of Theoretical Biology 112:553–74.Google Scholar
Sibly, R. M. & McCleery, R. (1985) Optimal decision rules for herring gulls. Animal Behaviour 33:445–65.Google Scholar
Sibly, R. M. & McFarland, D. J. (1974) A state-space approach to motivation. In: Motivational control systems analysis, ed. McFartand, D. J.. Academic Press.Google Scholar
Sibly, R. M. & McFarland, D. J. (1976) On the fitness of behaviour sequences. American Naturalist 110:601–17.Google Scholar
Sih, A. (1980) Optimal behavior: Can foragers balance two conflicting demands? Science 210:1041–43.Google Scholar
Sih, A. (1982) Foraging strategies and the avoidance of predation by an aquatic insect, Notonecta hoffmanni. Ecology 63:786–96.Google Scholar
Skinner, B. F. (1984) Methods and theories in the experimental analysis of behavior. Behavioral and Brain Sciences 7:511–41.Google Scholar
Snyderman, M. (1983) Optimal prey selection: The effects of food deprivation. Behavioral Analysis Letters 3:359–69.Google Scholar
Staddon, J. E. R. (1979) Operant behavior as adaptation to constraint. Journal of Experimental Psychology: General 108:48–67.Google Scholar
Staddon, J. E. R., Hinson, J. M. & Kram, R. (1981) Optimal choice. Journal of Experimental Analysis of Behavior 35:397–412.Google Scholar
Staddon, J. E. R. & Reid, A. K. (1987) Adaptation to reward. In: Foraging behavior, ed. Kamil, A. C., Krebs, J. R. & Pulliam, H. R.. Plenum.Google Scholar
Stanley, B. V. & Wootton, R. J. (1986) Effects of ration and male density on the territoriality and nest-building of male threespined sticklebacks. Animal Behaviour 34:527–35.Google Scholar
Stearns, S. C. (1976) Life-history tactics: A review of the ideas. Quarterly Review of Biology 51:3–47.Google Scholar
Stearns, S. C. (1977) The evolution of life-history traits: A critique of the theory and a review of the data. Annual Review of Ecology and Systematics 8:145–71.Google Scholar
Stearns, S. C. (1980) A new view of life-history evolution. Oikos 35:266–81.Google Scholar
Stearns, S. C. & Koella, J. C. (1986) The evolution of phenotypie plasticity in life-history traits: Predictions of reaction norms for age and size at maturity. Evolution 40:893–913.Google Scholar
Stenseth, N. C. (1986) Darwinian evolution in ecosystems: A survey of some ideas and difficulties together with some possible solutions. In: Complexity, language, and life: Mathematical approaches, ed. Casti, J. L. & Karlqvist, A.. Biomathematics, Springer Verlag.Google Scholar
Stenseth, N. C. & Maynard Smith, J. (1984) Coevolution in ecosystems; Red Queen evolution or stasis? Evolution 38:870–80.Google Scholar
Stephens, D. W. (1981) The logic of risk-sensitive foraging preferences. Animal Behaviour 29:628–29.Google Scholar
Stephens, D. W. & Chamov, E. L. (1982) Optimal foraging: Some simple stochastic models. Behavioural Ecology and Sodobiology 10:251–63.CrossRefGoogle Scholar
Stephens, D. W. & Krebs, J. R. (1986) Foraging theory. Princeton University Press.Google Scholar
Taylor, H. M., Gourley, R. S., Lawrence, C. E. & Kaplan, R. S. (1974) Natural selection of life history attributes: An analytical approach. Theoretical Population Biology 5:104–22.CrossRefGoogle ScholarPubMed
Thompson, D. B. A. (1983) Prey assessment by plovers (Charadriidae): Net rate of energy intake and vulnerability to kleptoparasites. Animal Behaviour 31:1226–36.Google Scholar
Timberlake, W., Gawley, D. J. & Lucas, G. A. (1987) Time horizons in rats foraging for food in temporally separated patches. Journal of Experimental Psychology: Animal Behavior Processes 13:302–9.Google Scholar
Timberlake, W. & Lucas, G. A. (in press) Behavior systems and learning: From misbehavior to general principles. In: Contemporary learning theories, ed. Klein, S. B. & Mowrer, R. R.. Erlbaum.Google Scholar
Tinbergen, J. M. (1981) Foraging decisions in starlings (Sturnus vulgaris L.). Ardea 69:1–67.Google Scholar
Tinbergen, N. (1951) The study of instinct. Clarendon Press.Google Scholar
Toates, F. M. (1979a) Water and energy in the interaction of thirst and hunger. In: Chemical influences on behaviour, ed. Brown, K. & Cooper, S. J.. Academic Press.Google Scholar
Toates, F. M. (1979b) Homeostasis and drinking. Behavioral and Brain Sciences 2:95–139.Google Scholar
Ukegbu, A. A. & Huntingford, F. A. (1987) Brood value and life expectations as determinants of parental investment in the threespined stickleback. Ethology.Google Scholar
Valenstein, E. S. (1967) Selection of nutritive and non-nutritive solutions under different conditions of need. Journal of Comparative and Physiological Psychology 63:429–33.Google Scholar
Vaughan, W. Jr. & Miller, H. L. Jr. (1984) Optimization versus responsestrength accounts of behavior. Journal of Experimental Analysis of Behavior 42:337–48.Google Scholar
Vogel, P. (1976) Energy consumption of European and African shrews. Acta Theriologica 21:195–206.Google Scholar
Wallace, R. F., Osborne, S., Norborg, J. & Fantino, E. (1973) Stimulus change contemporaneous with food presentation maintains responding in the presence of free food. Science 182:1038–39.Google Scholar
Ward, P. (1977) Fat and protein reserves of starlings. Annual Report of the Institute of Terrestrial Ecology, Cambridge, England, pp. 54–56.Google Scholar
Weins, J. A. (1977) On competition and variable environments. American Scientist 65:590–97.Google Scholar
Werner, E. E. & Gilliam, J. F. (1984) The ontogenetic niche and species interactions in size-structured populations. Annual Review of Ecology and Systematics 15:393–425.Google Scholar
Werner, E. E., Gilliam, J. F., Hall, D. J. & Mittelbach, G. G. (1983) An experimental test of the effects of predation risk on habitat use in fish. Ecology 64:1540–48.Google Scholar
Westerterp, K. R. & Drent, R. (1985) Energetic costs and energy-saving mechanisms in parental care of free-living passerine birds as determined by the D218O method. Acta XVIII Congressus Internationalis Ornithologici Moscow, pp. 392–98.Google Scholar
Westerterp, K. R., Gortmaker, W. & Wijngaarden, H. (1982) An energetic optimum in brood-raising in the starling (Sturnus vulgaris L.): An experimental study. Ardea 70:153–62.Google Scholar
Williams, B. K. & Nichols, J. D. (1984) Optimal timing in biological processes. American Naturalist 123:1–19.Google Scholar
Williams, G. C. (1985) A defense of reductionism in evolutionary biology. In: Oxford surveys in evolutionary biology, vol. 2, ed. Dawkins, R. & Ridley, M.. Oxford University Press.Google Scholar
Williams, J. B. & Nagy, K. A. (1985) Water flux and energetics of nestling savannah sparrows in the field. Physiological Zoology 58:515–25.Google Scholar
Winn, B. E. & Vestal, B. M. (1986) Kin recognition and choice of males by wild female house mice (Mus musculus). Journal of Comparative Psychology 100:72–75.Google Scholar
Winterhalder, B. (1986) Diet choice, risk, and food sharing in a stochastic environment. Journal of Anthropological Archaeology 5:369–92.Google Scholar
Wolf, L. L. & Hainsworth, F. R. (1977) Temporal patterning of feeding by hummingbirds. Animal Behaviour 25:976–89.Google Scholar
Yanai, J. & McCleam, G. E. (1972) Assortative mating in mice and the incest taboo. Nature 238:281–82.Google Scholar
Ydenberg, R. C. & Clark, C. W. (unpublished) Aerobic vs. anaerobic diving strategies of Western grebes (Aechmophorus occidentalis). Manuscript.Google Scholar
Ydenberg, R. C. & Dill, L. M. (1986) The economics of fleeing from predators. Advances in the Study of Behavior 16:229–49.Google Scholar