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Computation of the fitness and functional response of Holling’s “hungry mantid” by the WKB method. (English) Zbl 0713.92029

This paper derives a differential-difference (backward) equation for the “terminal fitness” (expected conditional “reward” as a function of predator satiation) of a predatory insect. The equation is solved for the case where the predator’s gut capacity is large compared to individual prey items (and handling time is negligible). The stationary functional response is also obtained.
Reviewer: C.A.Braumann

MSC:

92D40 Ecology
92D50 Animal behavior
35R10 Partial functional-differential equations
Full Text: DOI

References:

[1] Holling, C. S., The Functional Response of Invertebrate Predator to Prey Density, Mem. of the Ent. Soc. of Can., 48, 1-86 (1966)
[2] Metz, J. A.J.; van Batenburg, F. H.D., Holling’s “Hungry Mantid” Model for the Invertebrate Functional Response Considered as a Markov Process. Part O: A Survey of the Main Ideas and Res, Lect. Notes in Biomath., 54, 29-41 (1985) · Zbl 0616.92009
[3] Metz, J. A.J.; van Batenburg, F. H.D., Holling’s “hungry mantid” Model for the Invertebrate Functional Response Considered as a Markov Process. Part I: The Full Model and Some of its Lim, J. of Math. Bio, 22, 209-239 (1985) · Zbl 0616.92008
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