Stochastic Optimal Foraging Theory
We present here the core elements of a stochastic optimal foraging theory (SOFT), essentially, a random search theory for ecologists. SOFT complements classic optimal foraging theory (OFT) in that it assumes fully uninformed searchers in an explicit space
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Abstract We present here the core elements of a stochastic optimal foraging theory (SOFT), essentially, a random search theory for ecologists. SOFT complements classic optimal foraging theory (OFT) in that it assumes fully uninformed searchers in an explicit space. Mathematically, the theory quantifies the time spent by a random walker (the forager) on a spatial region delimited by absorbing boundaries (the targets). The walker starts from a given initial position and has no previous knowledge (nor the possibility to gain knowledge) on target/patch locations. Averages on such process can describe the dynamics of an uninformed forager looking for successive targets in a diverse and dynamical spatial environment. The framework provides a means to advance in the study of search uncertainty and animal information use in natural foraging systems.
F. Bartumeus () Center for Advanced Studies of Blanes, Acc´es Cala Sant Francesc 14, 17300, Blanes, Girona, Spain e-mail: [email protected] E.P. Raposo Laborat´orio de F´ısica Te´orica e Computacional, Departamento de F´ısica, Universidade Federal de Pernambuco, Recife, Brazil e-mail: [email protected] G.M. Viswanathan Departamento de F´ısica Te´orica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, Brazil e-mail: [email protected] M.G.E. da Luz Departamento de F´ısica, Universidade Federal do Paran´a, Curitiba, Brazil e-mail: [email protected] M.A. Lewis et al. (eds.), Dispersal, Individual Movement and Spatial Ecology, Lecture Notes in Mathematics 2071, DOI 10.1007/978-3-642-35497-7 1, © Springer-Verlag Berlin Heidelberg 2013
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1 Introduction Classic optimal foraging theory (OFT) assumes fully informed foragers. Hence, animals can recognize a patch instantaneously, knowing in advance the expected patch quality as well as the average travel time between patches [19]. Stephens and Krebs (1986) called such conceptual framework the complete information assumption [47, 48]. Based on simple cases, theoreticians have addressed the problem of incomplete information [47, 48], acknowledging the presence of environmental uncertainty in foraging processes. The key questions are related to how animals obtain information about the environment while foraging [1, 20, 21, 31, 34]. The use of information to both discriminate the properties of a given patch and to figure out largescale environmental properties have been shown to modify patch-exploitation and patch-leaving strategies [48]. Simple memory rules based on previous environment exploration experiences [32] and potential acquaintance with the travel times between patches [13, 14, 17, 24] also impact on the foraging strategy. Here we introduce a theoretical framework to study aspects of foraging processes rooted on the assumption of complete lack of knowledge and with the virtue of being spatially explicit (here we address the one-dimensional case). In its core formulation, SOFT quantifies the distance traveled (or equivalently time spent) by a random walker that starts mov
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