## Introduction

In a series of landmark papers Holling (1959a,b, 1966) developed an approach to understanding the process of predation or parasitism which acknowledged that ‘the characteristics of any specific example of a complex process can be determined by the action and interaction of a number of discrete components’. Holling (1966) identified 10 components of the functional response, i.e. the change in the number of prey consumed/hosts parasitized by individual predators or parasites in response to changes of prey/host density (Solomon 1949). Those that are present in all situations he termed ‘basic’ and the others he termed ‘subsidiary’. The three basic components of the response of predators to the density of their prey (*D*) are: (i) the instantaneous rate of discovery (*a*); (ii) the time for which predator and prey are exposed (*T*); and (iii) the handling time per prey captured (*h*) (Holling 1966). These form the basis of Holling’s disc equation (Holling 1959b):

where *N*= number of prey taken by a predator in time *T*. This equation describes a decelerating rate of increase of feeding rate to an asymptotic value as prey density increases (Holling 1959a) and is based on the assumptions that a predator: (i) takes all the prey it encounters (i.e. there is no selectivity), (ii) searches randomly, and that (iii) the predator’s instantaneous rate of discovery, and (iv) the handling time required to kill and consume a prey item are constant and independent of prey density or feeding rate. Holling (1959b) found that the disc equation could explain a functional response generated by a very simple experimental predation system and provide an adequate description of a variety of published host-parasite responses. However, Holling noted that it was ‘dangerous to suppose that it completely *explains* the responses of these parasites’. Subsequently, Hassell, Lawton & Beddington (1976) and Hassell (1978) pointed out that despite the ability of such simple models to describe data, it is unlikely that both the rate of discovery *a* and handling time *h* are constant. Both are functions of several subcomponents, some of which have been shown in studies of invertebrate predators or parasites to vary with prey density or predator feeding rate (Hassell *et al*. 1976; Hassell 1978).

Over the last 30 years functional responses of birds have been widely studied (Goss-Custard 1977a,b; Kenward 1985; Wanink & Zwarts 1985; Kenward & Marcström 1988; Norris & Johnstone 1998; Nielsen 1999; Redpath & Thirgood 1999; Rowcliffe, Sutherland & Watkinson 1999; Fritz, Durant & Guillemain, in press). Type II functional responses that can be described by Holling’s disc equation have been found in several cases. An increasing number of studies have, however, suggested that the assumptions on which the disc equation are based often do not hold and, hence, that this most simple model of predation is inadequate. Wanink & Zwarts (1985) cite several studies in which handling time has been shown to decline with increasing prey density. They also demonstrated that, due to increasing selectivity, neither the rate of discovery nor the handling time of an oystercatcher *Haematopus ostralegus* (L.) feeding upon buried bivalves were constant across all prey densities.

Type II functional responses, like the other two types identified by Holling (1959a), must ultimately reach an upper limit that is set by the subsistence requirements of the predator or parasite (Holling 1959a). However, the form of the disc equation is such that when this ultimate limit does not operate its asymptotic value will be determined by the time required to kill, i.e. the asymptote is the reciprocal of the handing time. Although, in one experiment Holling (1959b) found a close match between measured values of handling time and the estimate derived from the fitted disc equation, this was not the case in another experiment in which the measured handling time was lower than that calculated. Hassell *et al*. (1976) point out that such discrepancies are almost inevitable because the calculated value of handling time includes any periods of non-searching activity. In agreement with this, Wanink & Zwarts (1985) demonstrated that in several studies across a range of taxa the observed mean handling time was considerably less than that necessary to set the plateau of an observed functional response. Thus, another ‘assumption’ of the basic disc equation is often violated.

Holling (1959a) noted that the functional responses of insect parasites searching out their hosts could be expected to be similar in form to those of predators seeking prey. Kleptoparasitism (Rothschild & Clay 1952; Brockmann & Barnard 1979) is a foraging strategy in which kleptoparasites gather food by stealing it from others. In this paper, we present data on the functional response of a kleptoparasitic bird, the Arctic skua *Stercorarius parasiticus* (L.) to the abundance of its hosts, fish-carrying auks (family Alcidae), that they pursue in order to steal their fish.

Arctic skuas kleptoparasitize their victims during the breeding season by intercepting a continuous flow of hosts returning to their nests with fish. Thus, their prey is effectively replenished as it is exploited. It should therefore be possible to make accurate estimates of the constant instantaneous coefficients of the functional response from empirical data (Hassell *et al*. 1976). First, we establish the shape of skuas’ numerical and functional responses, and determine whether the latter can be described by a Type II response. We then seek to establish whether, in this non-experimental study, skuas’ numerical and functional responses are simply spurious, and the result of uncontrolled environmental effects. We then explore whether there is any evidence for confounding predator density effects on one of the key components of the rate at which skuas make successful chases, i.e. the probability that having initiated a chase, they succeed in stealing the fish. Finally, we go on to establish whether the assumptions underlying the disc equation hold true, namely that handling time and rate of discovery are constant, and limiting in the case of the former and, hence, whether Holling’s simple disc equation can adequately explain skuas’ functional response.