Evolutionary stability of optimal foraging: partial preferences in the diet and patch models. (English) Zbl 1414.92219
Summary: In this article the patch and diet choice models of the optimal foraging theory are reanalyzed with respect to evolutionary stability of the optimal foraging strategies. In their original setting these fundamental models consider a single consumer only and the resulting fitness functions are both frequency and density independent. Such fitness functions do not allow us to apply the classical game theoretical methods to study an evolutionary stability of optimal foraging strategies for competing animals. In this article frequency and density dependent fitness functions of optimal foraging are derived by separation of time scales in an underlying population dynamical model and corresponding evolutionarily stable strategies are calculated. Contrary to the classical foraging models the results of the present article predict that partial preferences occur in optimal foraging strategies as a consequence of the ecological feedback of consumer preferences on consumer fitness. In the case of the patch occupation model these partial preferences correspond to the ideal free distribution concept while in the case of the diet choice model they correspond to the partial inclusion of the less profitable prey type in predators diet.
MSC:
| 92D50 | Animal behavior |
| 92D15 | Problems related to evolution |
| 91A22 | Evolutionary games |
| 92D25 | Population dynamics (general) |
Keywords:
evolutionarily stable strategy; game theory; ideal free distribution; population growth; predator-prey modelsReferences:
| [1] | Abrams, P. A., Implications of flexible foraging for interspecific interactions: lessons from simple models, Functional Ecology, 24, 7-17 (2010) |
| [2] | Bélisle, C.; Cresswell, J., The effects of a limited memory capacity on foraging behavior, Theoretical Population Biology, 52, 78-90 (1997) · Zbl 0892.92027 |
| [3] | Berec, L.; Křivan, V., A mechanistic model for partial preferences, Theoretical Population Biology, 58, 279-289 (2000) · Zbl 1037.92048 |
| [4] | Berec, M.; Křivan, V.; Berec, L., Are great tits (Parus major) really optimal foragers?, Canadian Journal of Zoology, 81, 780-788 (2003) |
| [5] | Charnov, E. L., Optimal foraging: attack strategy of a mantid, American Naturalist, 110, 141-151 (1976) |
| [6] | Colombo, R.; Křivan, V., Selective strategies in food webs, IMA Journal of Mathematics Applied in Medicine and Biology, 10, 281-291 (1993) · Zbl 0807.92025 |
| [7] | Cressman, R., Evolutionary Dynamics and Extensive Form Games (2003), The MIT Press: The MIT Press Cambridge, MA · Zbl 1067.91001 |
| [8] | Cressman, R.; Křivan, V., Migration dynamics for the ideal free distribution, The American Naturalist, 168, 384-397 (2006) |
| [9] | Cressman, R.; Křivan, V., The ideal free distribution as an evolutionarily stable state in density-dependent population games, Oikos, 119, 1231-1242 (2010) |
| [10] | Cressman, R.; Křivan, V.; Garay, J., Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments, American Naturalist, 164, 473-489 (2004) |
| [11] | DeAngelis, D. L.; Vos, M.; Mooij, W. M.; Abrams, P. A., Feedback effects between the food chain and induced defense strategies, (Rooney, N.; McCann, K. S.; Noakes, D. L.G., From Energetics to Ecosystems: The Dynamics and Structure of Ecological Systems (2007), Springer: Springer Heidelberg), 213-235 |
| [12] | Dercole, F.; Rinaldi, S., Analysis of Evolutionary Processes. The Adaptive Dynamics Approach and its Applications (2008), Princeton University Press: Princeton University Press Princeton · Zbl 1305.92001 |
| [13] | Emlen, J. M., The role of time and energy in food preferences, American Naturalist, 100, 611-617 (1966) |
| [14] | Erichsen, J. T.; Krebs, J. R.; Houston, A. I., Optimal foraging and cryptic prey, Journal of Animal Ecology, 49, 271-276 (1980) |
| [15] | Eshel, I., Evolutionary and continuous stability, Journal of Theoretical Biology, 103, 99-111 (1983) |
| [16] | Eshel, I.; Motro, U.; Sansone, E., Continuous stability and evolutionary convergence, Journal of Theoretical Biology, 185, 333-343 (1997) |
| [17] | Fretwell, D. S.; Lucas, H. L., On territorial behavior and other factors influencing habitat distribution in birds, Acta Biotheoretica, 19, 16-32 (1969) |
| [18] | Fryxell, J. M.; Lundberg, P., Diet choice and predator-prey dynamics, Evolutionary Ecology, 8, 407-421 (1994) |
| [19] | Fryxell, J. M.; Lundberg, P., Individual Behavior and Community Dynamics (1997), Chapman & Hall: Chapman & Hall London, UK |
| [20] | Hirvonen, H.; Ranta, E.; Rita, H.; Peuhkuri, N., Significance of memory properties in prey choice decisions, Ecological Modelling, 115, 177-189 (1999) |
| [21] | Hofbauer, J.; Sigmund, K., Evolutionary Games and Population Dynamics (1998), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0914.90287 |
| [22] | Huxel, G. R.; McCann, K., Food web stability: the influence of trophic flows across habitats, The American Naturalist, 152, 460-469 (1998) |
| [23] | Krebs, J. R.; Erichsen, J. T.; Webber, M. I.; Charnov, E. L., Optimal prey selection in the great tit (Parus major), Animal Behaviour, 25, 30-38 (1977) |
| [24] | Křivan, V., Optimal foraging and predator-prey dynamics, Theoretical Population Biology, 49, 265-290 (1996) · Zbl 0870.92019 |
| [25] | Křivan, V., Dynamic ideal free distribution: effects of optimal patch choice on predator-prey dynamics, American Naturalist, 149, 164-178 (1997) |
| [26] | Křivan, V.; Cressman, R., On evolutionary stability in prey-predator models with fast behavioral dynamics, Evolutionary Ecology Research, 11, 227-251 (2009) |
| [27] | Křivan, V.; Cressman, R.; Schneider, C., The ideal free distribution: a review and synthesis of the game theoretic perspective, Theoretical Population Biology, 73, 403-425 (2008) · Zbl 1210.92053 |
| [28] | Křivan, V.; Schmitz, O. J., Adaptive foraging and flexible food web topology, Evolutionary Ecology Research, 5, 623-652 (2003) |
| [29] | Křivan, V.; Sirot, E., Habitat selection by two competing species in a two-habitat environment, American Naturalist, 160, 214-234 (2002) |
| [30] | Ma, B.; Abrams, P.; Brassil, C., Dynamic versus instantaneous models of diet choice, American Naturalist, 162, 668-684 (2003) |
| [31] | MacArthur, R. H.; Pianka, E. R., On optimal use of a patchy environment, American Naturalist, 100, 603-609 (1966) |
| [32] | Mangel, M.; Roitberg, B., Dynamic information and host acceptance by a tephritid fruit fly, Ecological Entomology, 14, 181-189 (1989) |
| [33] | Maynard Smith, J.; Price, G. R., The logic of animal conflict, Nature, 246, 15-18 (1973) · Zbl 1369.92134 |
| [34] | McNamara, J. M.; Houston, A. I., Partial preferences and foraging, Animal Behaviour, 35, 1084-1099 (1987) |
| [35] | McPeek, M. A.; Holt, R. D., The evolution of dispersal in spatially and temporally varying environments, The American Naturalist, 140, 1010-1027 (1992) |
| [36] | Morris, D. W., Shadows of predation: habitat-selecting consumers eclipse competition between coexisting prey, Evolutionary Ecology, 17, 393-422 (2003) |
| [37] | Padrón, V.; Trevisan, M. C., Environmentally induced dispersal under heterogeneous logistic growth, Mathematical Bioscience, 199, 160-174 (2006) · Zbl 1086.92054 |
| [38] | Rechten, C.; Avery, M.; Stevens, A., Optimal prey selection: why do great tits show partial preferences?, Animal Behaviour, 31, 576-584 (1983) |
| [39] | Stephens, D. W.; Krebs, J. R., Foraging Theory (1986), Princeton University Press: Princeton University Press Princeton, NJ, USA |
| [40] | Vincent, T. L.; Brown, J. S., Evolutionary Game Theory, Natural Selection and Darwinian Dynamics (2005), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 1140.91015 |
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