Abstract
Several optimisation models, like the marginal value theorem (MVT), have been proposed to predict the optimal time foraging animals should remain on patches of resources. These models do not clearly indicate, however, how animals can follow the corresponding predictions. Hence, several proximate patch-leaving decision rules have been proposed. Most if not all of these are based on the animals’ motivation to remain on the patches, but the real behaviours involved in such motivation actually still remain to be identified. Since animals are usually exploiting patches of resources by walking, we developed a model simulating the intra-patch movement decisions of time-limited animals exploiting resources distributed in delimited patches in environments with different resource abundances and distributions. The values of the model parameters were optimised in the different environments by means of a genetic algorithm. Results indicate that simple modifications of the walking pattern of the foraging animals when resources are discovered can lead to patch residence times that appear consistent with the predictions of the MVT. These results provide a more concrete understanding of the optimal patch-leaving decision rules animals should adopt in different environments.
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Bartoń KA, Hovestadt T (2013) Prey density, value, and spatial distribution affect the efficiency of area-restricted search. J Theor Biol 316:61–69
Bartoń KA, Phillips BL, Morales JM, Travis JMJ (2009) The evolution of an ‘intelligent’ dispersal strategy: biased, correlated random walks in patchy landscapes. Oikos 118:309–319
Bartumeus F, da Luz MGE, Viswanathan GM, Catalan J (2005) Animal search strategies: a quantitative random-walk analysis. Ecology 86:3078–3087
Bell WJ (1990) Searching behavior patterns in insects. Ann Rev Entomol 35:447–467
Bell WJ (1991) Searching behaviour. The behavioural ecology of finding resources. Chapman and Hall, London
Benhamou S (1992) Efficiency of area-concentrated searching behaviour in a continuous patchy environment. J Theor Biol 159:67–81
Benhamou S (2007) How many animals really do the lévy walk? Ecology 88:1962–1969
Bovet P, Benhamou S (1988) Spatial analysis of animal’s movement using a correlated random walk model. J Theor Biol 131:419–433
Bruins EBAW, Wajnberg E, Pak GA (1994) Genetic variability in the reactive distance in Trichogramma brassicae after automatic tracking of the walking path. Entomol Exp Appl 72:297–303
Carter MC, Dixon AFG (1982) Habitat quality and the foraging behaviour of coccinelid larvae. J Anim Ecol 51:865–878
Chapman DS, Dytham C, Oxford GS (2007) Landscape and fine-scale movements of a leaf beetle: the importance of boundary behaviour. Oecologia 154:55–64
Charnov EL (1976) Optimal foraging: the marginal value theorem. Theor Popul Biol 9:129–136
Codling EA, Plank MJ, Benhamou S (2008) Random walk models in biology. J R Soc Interface 5:813–834
Colgan PW (1989) Animal motivation. Chapman and Hall, New York
Cronin JT, Hyland K, Abrahamson WG (2001) The pattern, rate and range of within-patch movement of a stem-galling fly. Ecol Entomol 26:16–24
Dall SRX, Cuthill IC (1997) Searching in patches by European starlings, Sturnus vulgaris. Behav Process 39:149–159
de Knegt HJ, Hengeveld GM, van Langevelde F, de Boer WF, Kirkman KP (2007) Patch density determines movement patterns and foraging efficiency of large herbivores. Behav Ecol 18:1065–1072
Driessen G, Bernstein C, van Alphen JJM, Kacelnik A (1995) A count-down mechanism for host search in the parasitoid Venturia canescens. J Anim Ecol 64:117–125
Eliassen S, Jørgensen C, Mangel M, Giske J (2009) Quantifying the adaptive value of learning in foraging behavior. Am Nat 174:478–489
Focardi S, Marcellini P, Montanaro P (1996) Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. J Anim Ecol 65:606–620
Fraser CP, Ruxton GD, Broom M (2006) Public information and patch estimation for group foragers: a re-evaluation of patch-quitting strategies in a patchy environment. Oikos 112:311–321
Galis F, van Alphen JJM (1981) Patch time allocation and search intensity of Asobara tabida Nees (Braconidae), a larval parasitoid of Drosophila. Neth J Zool 31:596–611
Gardner SM, van Lenteren JC (1986) Characterisation of the arrestment responses of Trichogramma evanescens. Oecologia 68:265–270
Gossard TW, Jones RE (1977) The effects of age and weather on egg-laying in Pieris rapae L. J Appl Ecol 14:65–71
Green RF (1984) Stopping rules for optimal foragers. Am Nat 123:30–43
Green RF (2006) A simpler, more general method of finding the optimal foraging strategy for Bayesian bird. Oikos 112:274–284
Hancock PE, Milner-Gulland EJ (2006) Optimal movement strategies for social foragers in unpredictable environments. Ecology 87:2094–2102
Hoffmeister TS, Wajnberg E (2008) Finding optimal behaviors with genetic algorithms. In: Wajnberg E, Bernstein C, van Alphen J (eds) Behavioural ecology of insect parasitoids—from theoretical approaches to field applications. Blackwell Publishing, Oxford, pp 384–401
Holyoak M, Casagrandi R, Nathan R, Revilla E, Spiegel O (2008) Trends and missing parts in the study of movement ecology. P Natl Acad Sci USA 105:19060–19065
Houston AI (1987) The control of foraging decisions. In: Commons ML, Kacelnik A, Shettleworth SJ (eds) Quantitative analyses of behavior. Foraging, vol 4. Erlbaum, Hillsdale pp 41–61
Iwasa Y, Higashi M, Yamamura N (1981) Prey distribution as a factor determining the choice of optimal foraging strategy. Am Nat 117:710–723
Lefebvre D, Pierre J, Outreman Y, Pierre J-S (2007) Patch departure rules in Bumblebees: evidence of a decremental motivational mechanism. Behav Ecol Sociobiol 61:1707–1715
Liu Y-Q, Bernstein C, Thiel A (2009) Travel duration, energetic expenditure, and patch exploitation in the parasitic wasp Venturia canescens. Behav Ecol Sociobiol 63:1459–1469
McIntyre NE, Wiens JA (1999) Interactions between landscape structure and animal behaviour: the roles of heterogeneously distributed resources and food deprivation on movement patterns. Landscape Ecol 14:437–447
McNamara JM, Houston AI (1985) Optimal foraging and learning. J Theor Biol 117:231–249
McNamara JM, Houston AI (1987) Memory and the efficient use of information. J Theor Biol 125:385–395
McNamara JM, Houston AI (2009) Integrating function and mechanism. Trends Ecol Evol 24:670–675
Nathan R, Getz WM, Revilla E, Holyoak M, Kadmon R, Saltz D, Smouse PE (2008) A movement ecology paradigm for unifying organismal movement research. P Natl Acad Sci USA 105:19052–19059
Nelson JM, Roitberg BD (1995) Flexible patch time allocation by the leafminer parasitoid, Opius dimidiatus. Ecol Entomol 20:245–252
Nonacs P (2001) State dependent behavior and the marginal value theorem. Behav Ecol 12:71–83
Nonaka E, Holme P (2007) Agent-based model approach to optimal foraging in heterogeneous landscapes: effects of patch clumpiness. Ecography 30:777–788
Outreman Y, Le Ralec A, Wajnberg E, Pierre J-S (2005) Effects of within- and among-patch experiences on the patch-leaving decision rules in an insect parasitoid. Behav Ecol Sociobiol 58:208–217
Pierre J-S, Masson J-P, Wajnberg E (2012) Patch leaving rules: a stochastic version of a well-known deterministic motivational model. J Theor Biol 313:1–11
R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, http://www.R-project.org/. ISBN 3-900051-07-0
Reynolds AM (2012) Fitness-maximizing foragers can use information about patch quality to decide how to search for and within patches: optimal Lévy walk searching patterns from optimal foraging theory. J Roy Soc Inter 9:1568–1575
Roitberg BD (1985) Search dynamics in fruit-parasitic insects. J Insect Physiol 31:865–872
Ruxton GD, Beauchamp G (2008) The application of genetic algorithms in behavioural ecology, illustrated with a model of anti-predator vigilance. J Theor Biol 250:435–448
Stephens DW, Krebs JR (1986) Foraging theory. Princeton University Press, Princeton
Stillman RA, Sutherland WJ (1990) The optimal search patterns in a patchy environment. J Theor Biol 145:177–182
Strand MR, Vinson SB (1982) Behavioral response of the parasitoid Cardiochiles nigriceps to a kairomone. Entomol Exp Appl 31:308–315
Sumida BH, Houston AI, McNamara JM, Hamilton WD (1990) Genetic algorithms and evolution. J Theor Biol 147:59–84
Tentelier C, Desouhant E, Fauvergue X (2006) Habitat assessment by parasitoids: mechanisms for patch use behavior. Behav Ecol 17:515–521
Thiel A, Hoffmeister TS (2004) Knowing your habitat: linking patch-encounter rate and patch exploitation in parasitoids. Behav Ecol 15:419–425
Turchin PB (1986) Modeling the effect of host patch size on Mexican bean beetle emigration. Ecology 67:124–132
Turchin P (1998) Quantitative analysis of movement: measuring and modeling population redistribution in plants and animals. Sinauer Associates, Sunderland
van Alphen JJM, Bernstein C, Driessen G (2003) Information acquisition and time allocation in insect parasitoids. Trends Ecol Evol 18:81–87
Waage JK (1978) Arrestment responses of the parasitoid, Nemeritis canescens, to a contact chemical produced by its host, Plodia interpunctella. Physiol Entomol 3:135–146
Waage JK (1979) Foraging for patchily-distributed hosts by the parasitoid, Nemeritis canescens. J Anim Ecol 48:353–371
Wajnberg E (2006) Time allocation strategies in insect parasitoids: from ultimate predictions to proximate behavioural mechanisms. Behav Ecol Sociobiol 60:589–611
Wajnberg E (2012) Multi-objective behavioural mechanisms are adopted by foraging animals to achieve several optimality goals simultaneously. J Anim Ecol 81:503–511
Wajnberg E, Colazza S (1998) Genetic variability in the area searched by a parasitic wasp. Analysis from automatic video tracking of the walking path. J Insect Physiol 44:437–444
Wajnberg E, Curty C, Colazza S (2004) Genetic variation in the mechanisms of direct mutual interference in a parasitic wasp: consequences in terms of patch-time allocation. J Anim Ecol 73:1179–1189
Wajnberg E, Coquillard P, Vet LEM, Hoffmeister T (2012) Optimal resource allocation to survival and reproduction in parasitic wasps foraging in fragmented habitats. PLoS ONE 7:e38227
Whitley D (1989) The GENITOR algorithm and selective pressure: why rank-based allocation of reproductive trials is best. In: Schaffer D (ed) Proceedings of the 3rd International Conference on Genetic Algorithms. Morgan Kaufmann, Waltham, pp 116–121
Zollner PA, Lima SL (1999) Search strategies for landscape-level interpatch movements. Ecology 80:1019–1030
Acknowledgements
S. Benhamou, V. Calcagno, P. Crowley, E. Desouhant and J.S. Pierre are thanked for their comments on an early version of the manuscript. The code of the simulation model was developed thanks to the GAlib, a C++ library that provided tools for implementing genetic algorithms (http://lancet.mit.edu/ga/), and was run on the cluster of the INRA MIGALE bioinformatics platform (http://migale.jouy.inra.fr).
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Wajnberg, E., Hoffmeister, T.S. & Coquillard, P. Optimal within-patch movement strategies for optimising patch residence time: an agent-based modelling approach. Behav Ecol Sociobiol 67, 2053–2063 (2013). https://doi.org/10.1007/s00265-013-1615-5
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DOI: https://doi.org/10.1007/s00265-013-1615-5