×

zbMATH — the first resource for mathematics

A mechanistic model for partial preferences. (English) Zbl 1037.92048
Summary: Classic prey optimal foraging models assume that individual predators are globally omniscient; that is, they have exact knowledge of prey population densities in the environment. This study examines a spatially explicit individual-based model of a one-predator two-prey system where individual predators are assumed to be omniscient only locally, i.e., to know prey population densities only in the range of their perception. Due to local variations in prey numbers, the probability of acceptance of less profitable prey shifts from the zero–one rule to a gradually decreasing function, for which an explicit formula is derived, giving way to partial preferences. A corresponding predator functional response to more profitable prey is shown to have a sigmoid-like form.

MSC:
92D50 Animal behavior
92D40 Ecology
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bélisle, C.; Cresswell, J., The effects of a limited memory capacity on foraging behavior, Theor. popul. biol., 52, 78-90, (1997) · Zbl 0892.92027
[2] Charnov, E.L., Optimal foraging: attack strategy of a mantid, Am. nat., 110, 141-151, (1976)
[3] Davies, N., Prey selection and the search strategy of the spotted flycatcher (muscicapa striata): A field study of optimal foraging, Animal behav., 25, 1016-1033, (1977)
[4] de Roos, A.M.; McCauley, E.; Wilson, W.G., Mobility versus density-limited predator – prey dynamics on different scales, Proc. R. soc. London ser. B, 246, 117-122, (1991)
[5] Emlen, J.M., The role of time and energy in food preferences, Am. nat., 100, 611-617, (1966)
[6] Erichsen, J.; Krebs, J.; Houston, A., Optimal foraging and cryptic prey, J. animal ecol., 49, 271-276, (1980)
[7] Fryxell, J.M.; Lundberg, P., Diet choice and predator – prey dynamics, Evol. ecol., 8, 407-421, (1994)
[8] Fryxell, J.M.; Lundberg, P., Individual behavior and community dynamics, (1998), Chapman & Hall London
[9] Gleeson, S.K.; Wilson, D.S., Equilibrium diet: optimal foraging and prey coexistence, Oikos, 46, 139-144, (1986)
[10] Goss-Custard, J.D., Optimal foraging and the size selection of worms by redshank, tringa totanus, in the field, Animal behav., 25, 10-29, (1977)
[11] Hirvonen, H.; Ranta, E.; Rita, H.; Peuhkuri, N., Significance of memory properties in prey choice decisions, Ecol. model., 115, 177-189, (1999)
[12] Jones, G., Prey selection by the greater horseshoe bat (rhinolophus ferrumequinum): optimal foraging by echolocation?, J. animal ecol., 59, 587-602, (1990)
[13] Kindvall, O.; Vessby, K.; Berggren, A.; Hartman, G., Individual mobility prevents an allee effect in sparse populations of the bush cricket metrioptera roeseli: an experimental study, Oikos, 81, 449-457, (1998)
[14] Krebs, J.; Erichsen, J.T.; Webber, M.I.; Charnov, E.L., Optimal prey selection in the great tit (parus major), Animal behav., 25, 30-38, (1977)
[15] Křivan, V., Optimal foraging and predator – prey dynamics, Theor. popul. biol., 49, 265-290, (1996) · Zbl 0870.92019
[16] Křivan, V.; Sikder, A., Optimal foraging and predator – prey dynamics, II, Theor. popul. biol., 55, 111-126, (1999) · Zbl 0920.92031
[17] MacArthur, R.H.; Pianka, E., On optimal use of a patchy environment, Am. nat., 100, 603-609, (1966)
[18] Mangel, M.; Roitberg, B., Dynamic information and host acceptance by a tephritid fruit fly, Ecol. entomol., 14, 181-189, (1989)
[19] McCauley, E.; Wilson, W.G.; de Roos, A.M., Dynamics of age-structured and spatially structured predator – prey interactions: individual-based models and population-level formulations, Am. nat., 142, 412-442, (1993)
[20] McNamara, J.M.; Houston, A.I., Partial preferences and foraging, Animal behav., 35, 1084-1099, (1987)
[21] Mitchell, W., Informational constraints on optimally foraging hummingbirds, Oikos, 55, 145-154, (1989)
[22] Mittelbach, G., Foraging efficiency and body size: A study of optimal diet and habitat use by bluegill, Ecology, 62, 1370-1386, (1981)
[23] Murdoch, W.W.; Oaten, A., Predation and population stability, Adv. ecol. res., 9, 1-131, (1975)
[24] Pulliam, H.R., On the theory of optimal diets, Am. nat., 108, 57-74, (1974)
[25] Rechten, C.; Avery, M.; Stevens, A., Optimal prey selection: why do great Tits show partial preferences?, Animal behav., 31, 576-584, (1983)
[26] Rice, W.R., Sensory modality: an example of its effect on optimal foraging behavior, Ecology, 64, 403-406, (1983)
[27] Schmitz, O.J., Commemorating 30 years of optimal foraging theory, Evol. ecol., 11, 631-632, (1997)
[28] Schoener, T.W., Theory of feedings strategies, Annu. rev. ecol. systemat., 11, 369-404, (1971)
[29] Stephens, D.W.; Charnov, E.L., Optimal foraging: some simple stochastic models, Behav. ecol. sociobiol., 10, 251-263, (1982)
[30] Stephens, D.W.; Krebs, J.R., Foraging theory, (1986), Princeton Univ. Press Princeton
[31] Werner, E.E.; Hall, D.J., Optimal foraging and the size selection of prey by the bluegill sunfish (lepomis macrochirus), Ecology, 55, 1042-1052, (1974)
[32] Wilson, W.G., Resolving discrepancies between population models and individual-based simulations, Am. nat., 151, 116-134, (1998)
[33] Wilson, W.G.; de Roos, A.M.; McCauley, E., Spatial instabilities within the diffusive lotka – volterra system: individual-based simulation results, Theor. popul. biol., 43, 91-127, (1993) · Zbl 0768.92026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.