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Efficient or inaccurate? Analytical and numerical modelling of random search strategies. (English) Zbl 1191.92079

Summary: A large number of observational and theoretical studies have investigated animal movement strategies for finding randomly located food items. Many of these studies have claimed that a particular strategy is advantageous over other strategies or that the spatial distribution of the food items affects the search efficiency. We study a deliberately idealised problem, in which a blind forager searches for re-visitable food items. We show analytically that the forager’s efficiency is completely independent of both its movement strategy and the spatial pattern of the food items and depends only on the density of food in the environment. However, in some cases, apparent optima in search strategies can arise as artefacts of inappropriate and inaccurate numerical simulations. We discuss modifications to the idealised foraging problem that can confer an advantage on certain strategies, including when the forager has some memory or knowledge of the environment; when the food items are non-revisitable; and when the problem is viewed in an evolutionary context.

MSC:

92D50 Animal behavior
92D40 Ecology
65C20 Probabilistic models, generic numerical methods in probability and statistics

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[1] Austin, D., Bowen, W.D., McMillan, J.I., 2004. Intraspecific variation in movement patterns: modelling individual behaviour in a large marine predator. Oikos 105, 15–30. · doi:10.1111/j.0030-1299.1999.12730.x
[2] Bartumeus, F., 2009. Behavioral intermittence, Lévy patterns, and randomness in animal movement. Oikos 118, 488–494.
[3] Bartumeus, F., Catalan, J., Fulco, U.L., Lyra, M.L., Viswanathan, G.M., 2002. Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. Phys. Rev. Lett. 88, 097901. · doi:10.1103/PhysRevLett.88.097901
[4] Bartumeus, F., da Luz, M.G.E., Viswanathan, G.M., Catalan, J., 2005. Animal search strategies: a quantitative random walk analysis. Ecol. 86, 3078–3087. · doi:10.1890/04-1806
[5] Benhamou, S., 2007. How many animals really do the Lévy walk? Ecol. 88, 1962–1969. · doi:10.1890/06-1769.1
[6] Bénichou, O., Coppey, M., Suet, P.-H., Voituriez, R., 2005. Optimal search strategies for hidden targets. Phys. Rev. Lett. 94, 198101. · doi:10.1103/PhysRevLett.94.198101
[7] Bénichou, O., Coppey, M., Moreau, M., Voituriez, R., 2006a. Intermittent search strategies: when losing tine becomes efficient. Europhys. Lett. 75, 349–354. · doi:10.1209/epl/i2006-10100-3
[8] Bénichou, O., Loverdo, C., Moreau, M., Voituriez, R., 2006b. Two-dimensional intermittent search processes: An alternative to Lévy flight strategies. Phys. Rev. E 74, 020102. · doi:10.1103/PhysRevE.74.020102
[9] Bouchard, J.P., Georges, A., 1990. Anomalous diffusion in disordered media. Phys. Rep. 195, 127–293. · doi:10.1016/0370-1573(90)90099-N
[10] Brown, C.T., Liebovitch, L.S., Glendon, R., 2007. Lévy flights in Dobe Ju/’hoansi foraging patterns. Hum. Ecol. 35, 129–138. · doi:10.1007/s10745-006-9083-4
[11] Burrow, J.F., Baxter, P.D., Pitchford, J.W., 2008. Lévy processes, saltatory foraging, and superdiffusion. Math. Mod. Nat. Phenom. 3, 115–130. · Zbl 1337.92171 · doi:10.1051/mmnp:2008060
[12] Clauset, A., Shalizi, C.R., Newman, M.E.J., 2007. Power-law distributions in empirical data. arXiv:0706.1062v1 . · Zbl 1176.62001
[13] Cooper, W.E. Jr., 2005. The foraging mode controversy: both continuous variation and clustering of foraging movements occur. J. Zool. 267, 179–190. · doi:10.1017/S0952836905007375
[14] Currey, J.D., Pitchford, J.W., 2007. Variability of the mechanical properties of bone, and its evolutionary consequences. J. R. Soc. Interface 4, 127–135. · doi:10.1098/rsif.2006.0166
[15] Dall, S.R.X., Giraldeau, L.-A., Olsson, O., McNamara, J.M., Stephens, D.W., 2005. Information and its use by animals in evolutionary ecology. Trend Ecol. Evol. 20, 187–193. · doi:10.1016/j.tree.2005.01.010
[16] Edwards, A.M., Phillips, R.A., Watkins, N.W., Freeman, M.P., Murphy, E.J., Afanasyev, V., Buldyrev, S.V., da Luz, M.G.E., Raposo, E.P., Stanley, H.E., Viswanathan, G.M., 2007. Revisiting Lévy flight search patterns of wandering albatross, bumblebees and deer. Nature 449, 1044–1048. · doi:10.1038/nature06199
[17] Hutchinson, J.M.C., Waser, P.M., 2007. Use, misuse and extensions of ”ideal gas” models of animal encounter. Biol. Rev. 82, 335–359. · doi:10.1111/j.1469-185X.2007.00014.x
[18] James, A., Plank, M.J., Brown, R., 2008. Optimizing the encounter rate in biological interactions: ballistic versus Lévy versus Brownian strategies. Phys. Rev. Lett. 78, 051128.
[19] Lomholt, M.A., Koren, T., Metzler, R., Klafter, J., 2007. The advantage of Lévy strategies in intermittent search processes. arXiv:0709.2352v1 .
[20] Mackenzie, B.R., Kiørboe, T., 1995. Enconter rates and swimming behaviour of pause–travel and cruise larval fish predators in calm and turbulent laboratory environments. Limnol. Oceanogr. 40, 1278–1289. · doi:10.4319/lo.1995.40.7.1278
[21] Marell, A., Ball, J.P., Hofgaard, A., 2002. Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Lévy flights. Can. J. Zool. 80, 854–865. · doi:10.1139/z02-061
[22] Newman, M.E.J., 2006. Power laws, Pareto distributions and Zipf’s law. Contemp. Phys. 46, 323–351. · doi:10.1080/00107510500052444
[23] Pitchford, J.W., Brindley, J., 2001. Prey patchiness, predator survival and fish recruitment. Bull. Math. Biol. 63, 527–546. · Zbl 1323.92184 · doi:10.1006/bulm.2001.0230
[24] Pitchford, J.W., James, A., Brindley, J., 2005. Quantifying the effects of individual and environmental variability in fish recruitment. Fish. Oceanogr. 14, 156–160. · doi:10.1111/j.1365-2419.2004.00299.x
[25] Plank, M.J., James, A., 2008. Optimal foraging: Lévy pattern or process? J. R. Soc. Interface 5, 1077–1086. · doi:10.1098/rsif.2008.0006
[26] Ramos-Fernández, G., Mateos, J.L., Miramontes, O., Cocho, G., Larralde, H., Ayala-Orozco, B., 2004. Lévy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi). Behav. Ecol. Sociobiol. 55, 223–230. · doi:10.1007/s00265-003-0700-6
[27] Raposo, E.P., Buldyrev, S.V., da Luz, M.G.E., Santos, M.C., Stanley, H.E., Viswanathan, G.M., 2003. Dynamical robustness of Lévy search strategies. Phys. Rev. Lett. 91, 240601. · doi:10.1103/PhysRevLett.91.240601
[28] Real, L.A., 1980. Fitness, uncertainty, and the role of diversification in evolution and behaviour. Am. Nat. 115, 623–638. · doi:10.1086/283588
[29] Reynolds A.M., 2009. Adaptive Lévy walks can outperform composite Brownian walks in non-destructive random searching scenarios. Phys. A: Stat. Mech. Appl. 388, 561–564. · doi:10.1016/j.physa.2008.11.007
[30] Reynolds, A.M., Frye, M.A., 2007. Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PLoS ONE 2, e354. · doi:10.1371/journal.pone.0000354
[31] Reynolds, A.M., Rhodes, C.J., 2009. The Lévy flight paradigm: random search patterns and mechanisms. Ecol. 90, 877–887. · doi:10.1890/08-0153.1
[32] Reynolds, A.M., Smith, A.D., Menzel, R., Greggers, U., Reynolds, D.R., Riley, J.R., 2007. Displaced honey bees perform optimal scale-free search flights. Ecol. 88, 1955–1961. · doi:10.1890/06-1916.1
[33] Ruzicka, J.J., Gallager, S.M., 2006. The saltatory search behaviour of larval cod (Gadus morhua). Deep-sea Res. 53, 2735–2757. · doi:10.1016/j.dsr2.2006.09.003
[34] Santos, M.C., Raposo, E.P., Viswanathan, G.M., da Luz, M.G.E., 2004. Optimal random searches of revisitable targets: crossover from superdiffusive to ballistic random walks. Europhys. Lett. 67, 734–740. · doi:10.1209/epl/i2004-10114-9
[35] Shlesinger, M.F., 2006. Search research. Nature 443, 281–282. · doi:10.1038/443281a
[36] Sims, D.W., Righton, D., Pitchford, J.W., 2007. Minimizing errors in identifying Lévy flight behaviour of organisms. J. Anim. Ecol. 76, 222–229. · doi:10.1111/j.1365-2656.2006.01208.x
[37] Sims, D.W., Southall, E.J., Humphries, N.E., Hays, G.C., Bradshaw, C.J.A., Pitchford, J.W., James, A., Ahmed, M.Z., Brierley, A.S., Hindell, M.A., Morritt, D., Musyl, M.K., Righton, D., Shepard, E.L.C., Wearmouth, V.J., Wilson, R.P., Witt, M.J., Metcalfe, J.D., 2008. Scaling laws of marine predator search behaviour. Nature 451, 1098–1103. · doi:10.1038/nature06518
[38] Travis, J.M.J., Palmer, S.C.F., 2005. Spatial processes can determine the relationship between prey encounter rate and prey density. Biol. Lett. 1, 136–138. · doi:10.1098/rsbl.2004.0293
[39] Viswanathan, G.M., Afanasyev, V., Buldyrev, S.V., Murphy, E.J., Prince, P.A., Stanley, H.E., 1996. Lévy flight search patterns of wandering albatrosses. Nature 381, 413–415. · doi:10.1038/381413a0
[40] Viswanathan, G.M., Buldyrev, S.V., Havlin, S., da Luz, M.G.E., Raposo, E.P., Stanley, H.E., 1999. Optimising the success of random searches. Nature 401, 911–914. · doi:10.1038/44831
[41] Viswanathan, G.M., Afanasyev, V., Buldyrev, S.V., Havlin, S., da Luz, M.G.E., Raposo, E.P., Stanley, H.E., 2000. Lévy flights in random searches. Physica A 282, 1–12. · doi:10.1016/S0378-4371(00)00071-6
[42] Viswanathan, G.M., Afanasyev, V., Buldyrev, S.V., Havlin, S., da Luz, M.G.E., Raposo, E.P., Stanley, H.E., 2001. Lévy flight search patterns of biological organisms. Physica A 295, 85–88. · Zbl 0984.92519 · doi:10.1016/S0378-4371(01)00057-7
[43] Weimerskirch, H., Gault, A., Cherel, Y., 2005. Prey distribution and patchiness: factors in foraging success and efficiency of wandering albatrosses. Ecol. 86, 2611–2622. · doi:10.1890/04-1866
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