Dynamic decision-making in uncertain environments I. The principle of dynamic utility
Tóm tắt
Understanding the dynamics or sequences of animal behavior usually involves the application of either dynamic programming or stochastic control methodologies. A difficulty of dynamic programming lies in interpreting numerical output, whereas even relatively simple models of stochastic control are notoriously difficult to solve. Here we develop the theory of dynamic decision-making under probabilistic conditions and risks, assuming individual growth rates of body size are expressed as a simple stochastic process. From our analyses we then derive the optimization of dynamic utility, in which the utility of weight gain, given the current body size, is a logarithmic function: hence the fitness function of an individual varies depending on its current body size. The dynamic utility function also shows that animals are universally sensitive to risk and display risk-averse behaviors. Our result proves the traditional use of expected utility theory and game theory in behavioral studies is valid only as a static model.
Tài liệu tham khảo
Bellman RE (1957) Dynamic programming. Princeton University Press, Princeton
Bellman RE (1961) Adaptive control processes: a guided tour. Princeton University Press, Princeton
Bowers MA, Breland B (1994) Foraging of gray squirrels on an urban-rural gradient: use of the GUD to assess anthropogenic impact. Ecol Appl 6:1135–1142
Caraco T (1980) On foraging time allocation in a stochastic environment. Ecology 61:119–128
Caraco T, Chasin M (1984) Foraging preferences: response to reward skew. Anim Behav 32:76–85
Codding BF, Bliege Bird R, Bird DW (2011) Provisioning offspring and others: risk-energy trade-offs and gender differences in hunter-gatherer foraging strategies. Proc R Soc B 278:2502–2509
Friedman M, Savage LJ (1948) The utility analysis of choices involving risk. J Polit Econ 56:279–304
Gilby RC, Wrangham RW (2007) Risk-prone hunting by chimpanzees (Pantroglodytes schweinfurthii) increases during periods of high diet quality. Behav Ecol Sociobiol 61:1771–1779
Houston AI, McNamara J (1982) A sequential approach to risk-taking. Anim Behav 13:1260–1261
Houston A, Clark C, McNamara J, Mangel M (1988) Dynamic models in behavioural and evolutionary ecology. Nature 332:29–34
Houston AI, Higginson AD, McNamara JM (2011) Optimal foraging for multiple 15 nutrients in an unpredictable environment. Ecol Lett 14:1101–1107
Ito H, Uehara T, Morita S, Tainaka K, Yoshimura J (2013) Foraging behavior in stochastic environments. J Ethol 31:23–28. doi: 10.1007/s10164-012-0344-y
Judson OP (1994) The rise of the individual-based model in ecology. Trends Ecol Evol 9:9–14
Katz PL (1974) A long-term approach to foraging optimization. Am Nat 108:758–782
Mangel M, Clark CW (1986) Towards a unified foraging theory. Ecology 67:1127–1138
Mangel M, Clark CW (1988) Dynamic modeling in behavioral ecology. Princeton University Press, Princeton
Markowitz HM (1952) The utility of wealth. J Political Economy 60:151–158
Maynard Smith J (1989) Evolutionary genetics. Oxford University Press, Oxford
Moses JL, Sih A (1998) Effects of predation risk and food availability on the activity, habitat use, feeding behavior and mating behavior of a pond water strider, Gerris marginatus (Hemiptera). Ethology 104:661–669
Oaten A (1977) Optimal foraging in patches: a case for stochasticity. Theor Popul Biol 12:263–285
Oster GF, Wilson EO (1978) Caste and ecology in the social insects. Princeton University Press, Princeton
Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF (1962) The mathematical theory of optimal processes, Wiley-Interscience, (translated from the Russian)
Real LA (1980a) Fitness, uncertainty, and the role of diversification in evolution and behavior. Am Nat 115:623–638
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
Real LA, Caraco T (1986) Risk and foraging in stochastic environments. Ann Rev Ecol Syst 17:371–390
Sih A (1994) Predation risk and the evolutionary ecology of reproductive behaviour. J Fish Biol 45A:111–130
Stephens DW (1981) The logic of risk-sensitive foraging preferences. Anim Behav 29:628–629
Stephens D, Charnov EL (1982) Optimal foraging: some simple stochastic models. Behav Ecol Sociobiol 10:251–263
Stephens DW, Krebs JR (1986) Foraging theory. Princeton University Press, Princeton
Stephens DW, Brown JS, Ydenberg RC (eds) (2007) Foraging: behavior and ecology. Chicago University Press, Chicago
Strotz RH (1955) Myopia and inconsistency in dynamic utility maximization. Rev Econ Studies 23:165–180
von Neumann J, Morgenstern O (1947) The theory of games and economic behavior, 2nd edn. Princeton University Press, Princeton
Yoshimura J, Clark CW (1991) Individual adaptations in stochastic environments. Evol Ecol 5: 173–192, 430 (Corrigenda)
Yoshimura J, Shields WM (1987) Probabilistic optimization of phenotype distributions: a general solution for the effects of uncertainty on natural selection? Evol Ecol 1:125–138