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Disc Equation (disc + equation)
Selected AbstractsDoes Holling's disc equation explain the functional response of a kleptoparasite?JOURNAL OF ANIMAL ECOLOGY, Issue 4 2001R. W. G. Caldow Summary 1Type II functional responses, which can be described by Holling's disc equation, have been found in many studies of predator/prey and host/parasite interactions. However, an increasing number of studies have shown that the assumptions on which the disc equation is based do not necessarily hold. We examine the functional response of kleptoparasitically feeding Arctic skuas (Stercorarius parasiticus L.) to the abundance of fish-carrying auks and, by examination of the assumptions of the disc equation, test whether it can explain the function. 2The rate at which individual skuas make successful chases is a decelerating function of the abundance of auks. However, it would appear that this is not determined by factors that influence their probability of success, but by the rate at which they initiate chases. This too is a decelerating function of the abundance of auks. Arctic skuas have a Type II functional response. 3Although Arctic skuas exhibited a direct numerical response there was no evidence that components of predation connected to the density of predators (direct prey stealing, or increased host avoidance) had any effect on the rate at which individual skuas made chases or were successful in their chases. We conclude that the observed functional response is free from any effects of interference. 4We suggest that abnormally high levels of foraging effort expended by breeding skuas and their poor breeding success in the years of observation argue against the limit to the observed functional response being determined by skuas' energetic requirements. 5Several of the assumptions underlying the disc equation do not hold. The duration of chases (handling time) was not a constant; it decreased with increasing host abundance. Moreover, the chase duration predicted by the disc equation, if handling time limited the functional response, was far in excess of that observed. Furthermore, the observed rate of decline in the searching time per victim with increasing host abundance suggested that skuas' instantaneous rate of discovery was also not constant. Possible reasons for these observations are discussed. The basic disc equation may describe Arctic skuas' functional response, but it cannot explain it. [source] Extension of ideal free resource use to breeding populations and metapopulationsOIKOS, Issue 1 2000C. Patrick Doncaster The concept of an ideal and free use of limiting resources is commonly invoked in behavioural ecology as a null model for predicting the distribution of foraging consumers across heterogeneous habitat. In its original conception, however, its predictions were applied to the longer timescales of habitat selection by breeding birds. Here I present a general model of ideal free resource use, which encompasses classical deterministic models for the dynamics in continuous time of feeding aggregations, breeding populations and metapopulations. I illustrate its key predictions using the consumer functional response given by Holling's disc equation. The predictions are all consistent with classical population dynamics, but at least two of them are not usually recognised as pertaining across all scales. At the fine scale of feeding aggregations, the steady state of an equal intake for all ideal free consumers may be intrinsically unstable, if patches are efficiently exploited by individuals with a non-negligible handling time of resources. At coarser scales, classical models of population and metapopulation dynamics assume exploitation of a homogeneous environment, yet they can yield testable predictions for heterogeneous environments too under the assumption of ideal free resource use. [source] | ||||||||||