Optimizing the success of random searches

Abstract

We address the general question of what is the best statistical strategy to adapt in order to search efficiently for randomly located objects ('target sites'). It is often assumed in foraging theory that the flight lengths of a forager have a characteristic scale: from this assumption gaussian, Rayleigh and other classical distributions with well-defined variances have arisen. However, such theories cannot explain the long-tailed power-law distributions of flight lengths or flight times that are observed experimentally. Here we study how the search efficiency depends on the probability distribution of flight lengths taken by a forager that can detect target sites only in its limited vicinity. We show that, when the target sites are sparse and can be visited any number of times, an inverse square power-law distribution of flight lengths, corresponding to Lévy flight motion, is an optimal strategy. We test the theory by analysing experimental foraging data on selected insect, mammal and bird species, and find that they are consistent with the predicted inverse square power-law distributions.

Finding Useful Questions: On Bayesian Diagnosticity, Probability, Impact, and Information Gain.

“…Use of normative models as descriptive models, or to facilitate development of descriptive models, is a familiar research strategy (Anderson's 1990(Anderson's , 1991Brunswik's, 1952, molar analysis; Peterson & Beach, 1967;Marr, 1982;Viswanathan, et al, 1999;Oaksford & Chater, 2001;McKenzie, 2003;Baron, 2004). However, Kuhn (1989Kuhn ( , 2000 discusses both the usefulness and limitations of the normative intuitive scientist metaphor as a descriptive model of human cognition.…”

Intermittent random walks for an optimal search strategy: one-dimensional case

“…While earlier work has focused on systematic searches in organized human activities such as rescue operations [1][2][3][4], more recent analyses have been devoted to random strategies [5][6][7][8][9][10][11]. In particular, it has been realized that in the case of the so-called non-destructive search, when the target reappears after some time at the same location, and when the searcher always remains within the system, Lévy flights with randomly reoriented ballistic trajectories provide an optimal search efficiency [5][6][7][8][9].…”

“…That is why efficient search strategies appropriate to specific types of situations are highly desirable. The question of optimal search strategies has motivated a great deal of work within the last years [1][2][3][4][5][6][7][8][9][10][11][12].…”

Lévy stable noise-induced transitions: stochastic resonance, resonant activation and dynamic hysteresis

“…with stationary , independent increments), the assumption about its Gaussianity can be easily violated. The examples range from the description of the dynamics in plasmas [5], diffusion in energy space, self-diffusion in micelle systems, exciton and charge transport in polymers under conformational motion and incoherent atomic radiation trapping -to the spectral analysis of paleoclimatic [6] or economic data [7], motion in optimal search strategies among randomly distributed target sites [8], fluorophore diffusion as studied in photo-bleaching experiments, interstellar scintillations [9], ratcheting devices [10,11] and many others [12].…”