Risky theories - The effects of variance on foraging decisions

American Zoologist

Volumn 36, Issue 4, 1996, Pages 402-434

  Kacelnik, Alex ^a   Bateson, Melissa ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746106102     PISSN: 00031569     EISSN: None     Source Type: Journal    
DOI: 10.1093/icb/36.4.402     Document Type: Article

References (112)

1. Ahearn, W. and P. N. Hineline. 1992. Relative preferences for various bivalued ratio schedules. Anim. Learn. Behav. 20:407-415.
2. Banschbach, V. S. and K. D. Waddington. 1994. Risk-sensitivity in honey-bees - no consensus among individuals and no effect of colony honey stores. Anim. Behav. 47:933-941.
3. Barkan, C. P. L. 1990. A field test of risk-sensitive foraging in black-capped chickadees (Pants atricapillus). Ecology 71:391-400.
4. Barnard, C. J. and C. A. J. Brown. 1985. Risk sensitive foraging in common shrews (Sorex araneus L.). Behav. Ecol. Sociobiol. 16:161-164.
5. Barnard, C. J., C. A. J. Brown, A. Houston, and J. M. McNamara. 1985. Risk-sensitive foraging in common shrews: An interruption model and the effects of mean and variance in reward rate. Behav. Ecol. Sociobiol. 18:139-146.
6. Bateson, M. and A. Kacelnik. 1995a. Preferences for fixed and variable food sources: Variability in amount and delay. J. Exp. Anal. Behav. 63:313-329.
7. Bateson, M. and A. Kacelnik. 19956. Accuracy of memory for amount in the foraging starling (Sturnus vulgaris). Anim. Behav. 50:431-443.
8. Bateson, M. and A. Kacelnik. Starlings' preferences for predictable and unpredictable delays to food: Risk-sensitivity or time discounting? Anim. Behav. (In press).
9. Bateson, M. and A. Kacelnik. 1996. Rate currencies and the foraging starling: The fallacy of the averages revisited. Behav. Ecol. (In press).
10. Bateson, M. and S. C. Whitehead. 1996. The energetic costs of alternative rate currencies in the foraging starling. Ecology 77:1303-1307.
11. Battalio, R. C., J. H. Kagel, and D. N. McDonald. 1985. Animals choices over uncertain outcomes: Some initial experimental results. Amer. Econ. Rev. 75:596-613.
12. Bednekoff, P. A. 1996. Risk-sensitive foraging, fitness, and life histories: Where does reproduction fit into the big picture? Amer. Zool. 36:471-483.
13. Behar, I. 1961. Learned avoidance of non reward. Psych. Rep. 9:43-52.
14. Brunner, D., J. Gibbon, and S. Fairhurst. 1994. Choice between fixed and variable delays with different reward amounts. J. Exp. Psych.: Anim. Behav. Processes 20:331-346.
15. Brunner, D., A. Kacelnik, and J. Gibbon. 1992. Optimal foraging and timing processes in the starling, Sturnus vulgaris: Effect of inter-capture interval. Anim. Behav. 44:597-613.
16. Caraco, T. 1981. Energy budgets, risk and foraging preferences in dark-eyed juncos (Junco hyemalis). Behav. Ecol. Sociobiol. 8:213-217.
17. Caraco, T. 1982. Aspects of risk-aversion in foraging white crowned sparrows. Anim. Behav. 30:719-727.
18. Caraco, T. 1983. White crowned sparrows (Zonotrichia leucophrys) foraging preferences in a risky environment. Behav. Ecol. Sociobiol. 12:63-69.
19. Caraco, T. and S. L. Lima. 1985. Foraging juncos: Interaction of reward mean and variability. Anim. Behav. 33:216-224.
20. Caraco, T., W. U. Blanckenhorn, G. M. Gregory, J. A. Newman, G. M. Recer, and S. M. Zwicker. 1990. Risk-sensitivity: Ambient temperature affects foraging choice. Anim. Behav. 39:338-345.
21. Caraco, T., S. Martindale, and T. S. Whittam. 1980. An empirical demonstration of risk sensitive foraging preferences. Anim. Behav. 28:820-830.
22. Caraco, T., A. Kacelnik, N. Mesnick, and M. Smulewitz. 1992. Short-term rate maximization when rewards and delays covary. Anim. Behav. 44:441-447.
23. Cartar, R. V. 1991. A test of risk sensitive foraging in bumble bees. Ecology 72:888-895.
24. Cartar, R. V. and L. M. Dill, 1990. Why are bumble bees risk sensitive foragers? Behav. Ecol. Sociobiol. 26:121-127.
25. Case, D. A., P. Nichols, and E. Fantino. 1995. Pigeon's preference for variable-interval water reinforcement under widely varied water budgets. J. Exp. Anal. Behav. 64:299-311.
26. Charnov, E. L. 1976a. Optimal foraging: Attack strategy of a mantid. Am. Nat. 110:141-151.
27. Charnov, E. L. 1976b. Optimal foraging: The marginal value theorem. Theor. Popul. Biol. 9:129-136.
28. Cicerone, R. A. 1976. Preference for mixed versus constant delay of reinforcement. J. Exp. Anal. Behav. 25:257-261.
29. Clements, K. C. 1990. Risk-aversion in the foraging blue jay, Cyanocitta cristata. Anim. Behav. 40: 182-195.
30. Croy, M. I. and R. N. Hughes. 1991. Effects of food supply, hunger, danger and competition on choice of foraging location by the fifteen-spined stickle-back, Spinachia spinachia L. Anim. Behav. 42: 131-139.
31. Davison, M. C. 1969. Preference for mixed-interval versus fixed-interval schedules. J. Exp. Anal. Behav. 12:247-252.
32. Davison, M. C. 1972. Preference for mixed-interval versus fixed-interval schedules: Number of component intervals. J. Exp. Anal. Behav. 17:169-176.
33. Dickinson, A. 1980. Contemporary Animal Learning Theory. Cambridge University Press, Cambridge.
34. Dunning, J. B. 1993. CRC handbook of avion body masses. Boca Raton, Florida.
35. Epstein, R. 1981. Amount consumed as a function of magazine-cycle duration. Behav. Anal. Lett. 1:63-66.
36. Essock, S. M. and E. P. Rees. 1974. Preference for and effects of variable as opposed to fixed reinforcer duration. J. Exp. Anal. Behav. 21:89-97.
37. Fantino, E. 1967. Preference for mixed versus fixed-ratio schedules. J. Exp. Anal. Behav. 10:35-43.
38. Gibbon, J. 1977. Scalar expectancy theory and Weber's law in animal timing. Psych. Rev. 84:279-325.
39. Gibbon, J., M. D. Baldock, C. Locurto, L. Gold, and H. S. Terrace. 1977. Trial and intertrial durations and autoshaping. J. Exp. Psych.: Anim. Behav. Processes 3:264-284.
40. Gibbon, J., R. M. Church, and W. H. Meek. 1984. Scalar timing in memory. In J. Gibbon and L. Allan (eds.). Timing and Time Perception, pp. 52-77. New York Academy of Sciences, New York.
41. Gibbon, J., R. M. Church, S. Fairhurst, and A. Kacelnik. 1988. Scalar Expectancy Theory and choice between delayed rewards. Psychol. Rev. 95:102-114.
42. Gilliam, J. F., R. F. Green, and N. E. Pearson. 1982. The fallacy of the traffic policeman: A response to Templeton and Lawlor. Amer. Nat. 119:875-878.
43. Green, L. and J. Myerson. 1996. Exponential versus hyperbolic discounting of delayed outcomes: Risk and waiting time. Amer. Zool. 36:496-505.
44. Ha, J. C. 1991. Risk-sensitive foraging: The role of ambient temperature and foraging time. Anim. Behav. 41:528-529.
45. Ha, J. C., P. N. Lehner, and S. D. Farley. 1990. Risk-prone foraging behaviour in captive grey jays Perisoreus canadensis. Anim. Behav. 39:91-96.
46. Hamm, S. L. and S. J. Shettleworth. 1987. Risk aversion in pigeons. J. Exp. Psych.: Anim. Behav. Processes 13:376-383.
47. Harder, L. and L. A. Real. 1987. Why are bumble bees risk-averse? Ecology 68:1104-1108.
48. Hastjarjo, T., A. Silerberg, and S. R. Hursh. 1990. Risky choice as a function of amount and variance in food supply. J. Exp. Anal. Behav. 53:155-161.
49. Herrnstein, R. J. 1964. Aperiodicity as a factor in choice. J. Exp. Anal. Behav. 7:179-182.
50. Hodges, C. M. and Wolf, L. L. 1981. Optimal foraging in bumblebees: Why is nectar left behind in flowers? Behav. Ecol. Sociobiol. 9:41-44.
51. Houston, A. and J. McNamara. 1985. The choice of two prey types that minimises the probability of starvation. Behav. Ecol. Sociobiol. 17:135-141.
52. Houston, A. I. 1991. Risk-sensitive foraging theory and operant psychology. J. Exp. Anal, of Behav. 56:585-589.
53. Houston, A. I. and J. M. McNamara. 1982. A sequential approach to risk-taking. Anim. Behav. 30:1260-1261.
54. Houston, A. I. and J. M. McNamara. 1990. Risk-sensitive foraging and temperature. Trends Ecol. Evol. 5:131-132.
55. Kacelnik, A. and I. C. Cuthill. 1987. Starlings and optimal foraging theory: Modelling in a fractal world. In A. C. Kamil, J. R. Krebs, and H. R. Pulliam (eds.), Foraging theory. Plenum Press, New York.
56. Kacelnik, A., D. Brunner, and J. Gibbon. 1990. Timing mechanisms in optimal foraging: Some applications of scalar expectancy theory. In R. N. Hughes (ed.), NATO ASI Series, Series G: Ecological Sciences. Vol. G 20, pp. 63-81. Springer-Verlag, Berlin.
57. Kagel, J. H., L. Green, and T. Caraco. 1986a. When foragers discount the future: Constraint or adaptation? Anim. Behav. 34:271-283.
58. Kagel, J. H., D. N. MacDonald, R. C. Battalio, S. White, and L. Green. 19866. Risk-aversion in rats (Rattus norvegicus) under varying levels of resource availability. J. Comp. Psychol. 100:95-100.
59. Kahneman, D. and A. Tversky. 1984. Choices, values and frames. Am. Psych. 39:341-350.
60. Krebs, J. R., D. W. Stephens, and W. J. Sutherland. 1983. Perspectives in optimal foraging. In A. H. Brush and G. A. Clark (eds.), Perspectives in ornithology, pp. 165-216. Cambridge University Press, New York.
61. Lattal, K. A. 1991. Scheduling positive reinforcers. In I. H. Iversen and K. A. Lattal (eds.) Experimental analysis of behavior, part 1, pp. 87-134. Elsevier, Amsterdam.
62. Lawes, M. J. and M. R. Perrin. 1995. Risk-sensitive foraging behaviour of the round-eared elephant shrew (Macroscelides proboscideus). Behav. Ecol. Sociobiol. 37:31-37.
63. Leventhal, A. M., R. F. Morell, E. J. Morgan, and C. C. Perkins. 1959. The relation between mean reward and mean reinforcement. J. Exp. Psychol. 59:284-287.
64. Logan, F. A. 1965. Decision making by rats: Uncertain outcome choices. J. Comp. Physiol. Psychol. 59:246-251.
65. Mazur, J. E. 1984. Tests of an equivalence rule for fixed and variable reinforcer delays. J. Exp. Psychol.: Anim. Behav. Proc. 10:426-436.
66. Mazur, J. E. 1985. Probability and delay of reinforcement as factors in discrete-trial choice. J. Exp. Anal. Behav. 43:341-351.
67. Mazur, J. E. 1986. Fixed and variable ratios and delays: Further tests of an equivalence rule. J. Exp. Psychol.: Anim. Behav. Proc. 12:116-124.
68. Mazur, J. E. 1987. An adjusting procedure for studying delayed reinforcement. In M. L. Commons, J. E. Mazur, J. A. Nevin and H. Rachlin (eds.), Quantitative Analyses of Behaviour: The effect of delay and of intervening events on reinforcement value, pp. 55-73. Erlbaum, Hilsdale, New Jersey.
69. Mazur, J. E. 1989. Theories of probabilistic reinforcement. J. Exp. Anal. Behav. 51:87-99.
70. McNamara, J. 1983. Optimal control of the diffusion coefficient of a simple diffusion process. Math. Oper. Res. 8:373-380.
71. McNamara, J. M. 1984. Control of a diffusion by switching between two drift-diffusion coefficient pairs. SIAM J. Cont. 22:87-94.
72. McNamara, J. M. 1996. Risk-prone behaviour under rules which have evolved in a changing environment. Amer. Zool. 36:484-495.
73. McNamara, J. M. and A. I. Houston. 1987. A general framework for understanding the effects of variability and interruptions on foraging behaviour. Acta Biotheoretica 36:3-22.
74. McNamara, J. M. and A. I. Houston. 1990. Starvation and predation in a patchy environment. In B. Shorrocks and I. R. Swingland (eds.), Living in a patchy environment, pp. 23-43. Oxford University Press, Oxford.
75. McNamara, J. M. and A. I. Houston. 1992. Risk-sensitive foraging: A review of the theory. Bull. Math. Biol. 54:355-378.
76. McNamara, J. M., S. Merad, and A. I. Houston, 1991. A model of risk-sensitive foraging for a reproducing animal. Anim. Behav. 41:787-792.
77. Menlove, R. L., H. M. Inden, and E. G. Madden. 1979. Preference for fixed over variable access to food. Anim. Learn. Behav. 7:499-503.
78. Mitchell, W. A. and T. J. Valone. 1990. The optimization research program: Studying adaptations and their function. Quart. Rev. Biol. 65:43-52.
79. Montague, P. R., P. Dayan, C. Person, and T. J. Sejnowski. 1995. Bee foraging in uncertain environments using predictive hebbian learning. Nature 377:725-728.
80. Moore, F. R. and P. A. Simm. 1986. Risk-sensitive foraging by a migratory bird (Dendroica coronata). Experientia 42:1054-1056.
81. Morris, C. J. 1986. The effects of occasional short (FR1) reinforcement ratios on choice behaviour. Psych. Rec. 36:63-68.
82. Myerson, J. and L. Green. 1995. Discounting of delayed rewards: Models of individual choice. J. Exp. Anal. Behav. 64:263-276.
83. Perez, S. M. and Waddington, K. D. 1996. Carpenter bee (Xylocopa micans) risk-indifference and a review of nectarivore risk-sensitivity studies. Amer. Zool. 36:435-446.
84. Possingham, H. P., A. I. Houston, and J. M. McNamara. 1990. Risk-averse foraging in bees: A comment on the model of Harder and Real. Ecology 71:1622-1624.
85. Pubols, B. H. 1962. Constant versus variable delay to reinforcement. J. Comp. Physiol. Psychol. 55:52-56.
86. Real, L. A. 1981. Uncertainty and pollinator-plant interactions: The foraging behavior of bees and wasps on artificial flowers. Ecology 62:20-26.
87. Real, L. A., J. Ott, and E. Silverfine. 1982. On the trade-off between mean and variance in foraging: An experimental analysis with bumblebees. Ecology 63:1617-1623.
88. Reboreda, J. C. and A. Kacelnik. 1991. Risk sensitivity in starlings: Variability in food amount and food delay. Behav. Ecol. 2:301-308.
89. Rider, D. P. 1983a. Preference for mixed versus constant delays of reinforcement: Effect of probability of the short, mixed delay. J. Exp. Anal. Behav. 39:257-266.
90. Rider, D. P. 19836. Choice for aperiodic versus periodic ratio schedules: A comparison of concurrent and concurrent-chains procedures. J. Exp. Anal. Behav. 40:225-237.
91. Rodriguez, M. L. and A. W. Logue. 1988. Adjusting delay to reinforcement: Comparing choice in pigeons and humans. J. Exp. Psych.: Anim. Behav. Processes 14:105-117.
92. Samuelson, P. A. 1937. A note on the measurement of utility. Rev. Econ. Stud. 4:155-161.
93. Smallwood, P. D. 1996. An introduction to risk-sensitivity: Using Jensen's inequality to clarify evolutionary arguments of adaptation and constraint. Amer. Zool. 36:392-401.
94. Snyderman, M. 1987. Prey selection and self-control. In M. L. Commons, J. E. Mazur, J. A. Nevin and H. Rachlin (eds.), Quantitative Analyses of Behaviour, pp. 283-308. Lawrence Erlbaum Associates, Hillsdale, New Jersey.
95. Staddon, J. E. R. and N. K. Innis. 1966. Preference for fixed vs. variable amounts of reward. Psychon. Sci. 4:193-194.
96. Stephens, D. W. 1981. The logic of risk-sensitive foraging preferences. Anim. Behav. 29:628-629.
97. Stephens, D. W. and J. R. Krebs. 1986. Foraging theory. Princeton University Press, Princeton.
98. Stephens, D. W. and R. C. Ydenberg. 1982. Risk aversion in the great tit. In D. W. Stephens Stochasticity in foraging theory: Risk and information, Unpublished DPhil Thesis, Oxford University.
99. Templeton, A. R. and L. R. Lawlor. 1981. The fallacy of the averages in ecological optimisation theory. Am. Nat. 117:390-393.
100. Tinbergen, N. 1963. On aims and methods of ethology. Z. Tierpsychol. 20:410-433.
101. Turelli, M., J. H. Gillespie, and T. W. Shoener. 1982. The fallacy of the fallacy of the averages in ecological optimization theory. Amer. Nat. 119:879-884.
102. Tuttle, E. M., L. Wulfson, and T. Caraco. 1990. Risk-aversion, relative abundance of resources and for-aging preferences. Behav. Ecol. Sociobiol. 26: 165-171.
103. Waddington, K. D. 1995. Bumblebees do not respond to variance in nectar concentration. Ethology 101: 33-38.
104. Waddington, K. D., T. Allen, and B. Heinrich. 1981. Floral preferences of bumblebees (Bombus edwardsii) in relation to intermittent versus continuous rewards. Anim. Behav. 29:779-784.
105. Wagenaar, W. A. 1988. Paradoxes of gambling behaviour. Erlbaum, Hove.
106. Wunderle, J. M. and Z. Cotto-Navarro. 1988. Constant vs. variable risk-aversion in foraging bananaquits. Ecology 69:1434-1438.
107. Wunderle, J. M. and T. G. O'Brien. 1985. Risk-aversion in hand reared bananaquits. Behav. Ecol. Sociobiol. 17:371-380.
108. Wunderle, J. M., M. Santa-Castro, and N. Fletcher. 1987. Risk-averse foraging by bananaquits on negative energy budgets. Behav. Ecol. Sociobiol. 21:249-255.
109. Yoccoz, N. G., S. Engen, and N. C. Stenseth. 1993. Optimal foraging: The importance of environmental stochasticity and accuracy in parameter estimation. Am. Nat. 141:139-157.
110. Young, J. S. 1981. Discrete-trial choice in pigeons: Effects of reinforcer magnitude. J. Exp. Anal. Behav. 35:23-29.
111. Young, R. J., H. Clayton, and C. J. Barnard. 1990. Risk sensitive foraging in bitterlings, Rhodeus sericus: Effects of food requirement and breeding site quality. Anim. Behav. 40:288-297.
112. Zabludoff, S. D., J. Wecker, and T. Caraco. 1988. For-aging choice in laboratory rats: Constant vs. variable delay. Behav. Processes 16:95-110.