Holling’s ‘Hungry Mantid’ Model for the Invertebrate Functional Response Considered as a Markov Process. Part 0: A Survey of the Main Ideas and Results

Abstract

Holling's 'Hungry mantid' model for the invertebrate functional response considered as •a Markov process. Part 0: A survey of the main ideas and results *) by **)

Holling's ?hungry mantid? model for the invertebrate functional response considered as a Markov process. III. Stable satiation distribution

“…One of the equations proposed by Metz and van Batenburg [13,14,15], as part of their model for predatory behaviour is: The second of these identities can be verified by integration of ( 1.1 a) along the…”

“…3 we shall concentrate on the Cauchy problem ( l. 7). In order to obtain more explicit results, Metz and van Batenburg [13,14,15] formally took the limit w _,, 0, x _,, oo, g = xw remaining constant. It appears that in the limit the mantid's catching behaviour becomes deterministic.…”

“…It appears that in the limit the mantid's catching behaviour becomes deterministic. [13,15] how var(N) can be computed from z(s, t). A straightforward computation using the results of [13,15] shows that and…”

“…In a series of papers [ 13,14,15] Metz and van Ba ten burg presented an analytic reformulation of the theory of predation as propounded by Holling. They started by showing that Holling's assumptions implied that the predator's minimal state space is two-dimensional.…”

“…(In the case of Holling's praying mantid this is due to the fact that its search field decreases with increasing satiation.) This paper, which is self-contained, deals with a number of mathematical questions raised in the papers of Metz and van Batenburg [13,14,15]. These questions are formulated in the first section.…”