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A key component of these models is the link between food and competitor densities and the rate at which an individual bird can consume food, i.e. the functional response (Sutherland 1996). These models are based on the short-term functional response, measured while birds are actively feeding, rather than the daily functional response incorporating the proportion of time spent feeding. The functional response must be measured or predicted if models are to realistically predict the effect of depletion or interference competition on animal populations. Several functional responses have been measured for coastal wading birds (Goss-Custard 1977; Piersma et al. 1995; Ens et al. 1996; Goss-Custard et al. 1996; Gill, Sutherland & Norris 2001), which feed in open habitats on a relatively limited range of distinct prey species, simplifying observation of foraging behaviour. Farmland birds usually feed in less open, or more vegetated habitats, making direct observation of their feeding behaviour more problematic. Fewer functional responses have been measured for farmland birds, particularly in natural habitats (Kenward & Sibly 1977; Cresswell 1997). A further difficulty with measuring functional responses in the wild is that animals usually congregate in places in which food is relatively abundant, and so most estimates of feeding rate are derived from food-rich areas. However, it is more important to know how feeding rate changes at low food densities, if the effects of food shortage are to be predicted.
The purpose of this paper is to test whether the functional response of farmland birds might be predicted from a few, quickly measured parameters (i.e. the time to consume a food item, walking speed and the distance over which food is detected). Our premise is that even though it is often difficult to measure the functional response of farmland birds directly, because birds avoid food-scarce places and are frequently concealed from view, it may be possible to obtain long enough behavioural observations, from a limited number of locations, to predict its shape. The shape of the functional response in wading birds (Piersma et al. 1995; Goss-Custard et al. 1996) and the strength of interference competition in wading birds (Stillman et al. 2002b) and a farmland bird (Stillman et al. 2002a) have been predicted in a similar way. Our approach is also consistent with that proposed by Holling (1959) not only to fit functional response equations to data, but also to test basic assumptions of the equations by independently measuring their parameters and predicting functional responses.
We studied a simple system of rooks Corvus frugilegus feeding on artificial food in two grass sward heights, in which the functional response could be measured directly and predicted. However, our experiments were designed to mimic the real system (rooks searching visually for food concealed within a grass sward), and rooks had similar searching behaviour both within and outside experiments. We did not use a natural system because we could not have guaranteed that natural food density would have varied sufficiently. If the observed functional response can be predicted accurately in this simple system, it implies that the approach may also be applicable to more natural systems, simplifying the development of mechanistic models of farmland bird populations.
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In this paper we have shown that the functional response of a farmland bird can be accurately predicted from searching speed, food detection distance and handling time, parameters that can be measured more quickly than the alternative of measuring the functional response directly. This implies that the functional responses of other farmland birds may be predicted using a minimum of information, potentially enabling mechanistic models to be developed to predict how possible changes in agricultural practice, driven by new management subsidies, influence farmland bird populations.
It was not guaranteed that the disk equation (Holling 1959) would adequately describe the observed functional response, or that the few behavioural parameters would have accurately predicted the functional response. An assumption of the disk equation is that the maximum feeding rate at high food densities is limited by handling time. This was true in our simple system, but is often not the case (e.g. Goss-Custard 1977; Hulscher 1982; Wanink & Zwarts 1985; Caldow & Furness 2001). One possible explanation is that birds become more selective as prey density increases and so consume an increasingly narrow range of prey types, causing the number of prey consumed per unit time to decelerate (Hulscher 1982; Wanink & Zwarts 1985). Another is that the limited rate at which the gut can process food limits feeding rate below that which would be determined by handling time alone (Jeschke et al. 2002). Possible reasons why handling time set the asymptote in our study were that the food was of uniform size, removing the possibility of selective foraging, and that birds returned to their nest sites before their guts were full.
The fact that we accurately measured food detection distance was also not guaranteed. However, rooks showed a clear change in behaviour when moving towards food. We would not have been able to measure detection distance as accurately if their behaviour was less clear or if we had incorrectly assessed when a rook detected food. The extent to which our methods can be applied to other species depends on the ease with which food detection distance can be measured. Several other species often show clear changes in behaviour when detecting prey, for example, egrets and herons often lunge towards their prey, and seed-feeding finches, buntings and sparrows often hop purposefully towards food (R. A. Stillman, personal observations). Additionally, Caldow & Furness (2001) estimated the food detection distance of Artic Skuas, Stercorarius parasiticus, kleptoparasitizing fish from auks returning from their feeding grounds. Measuring distances travelled will not always be as straightforward as in the present study, but a range of techniques are available, including correlating distance travelled with time, counting paces or measuring distance travelled across a video image (Poole, Stillman & Norris, in press). It may be necessary to measure food detection distance by experimentally feeding animals low densities of food, as animals may only make very small or no movements when food is very abundant. Although difficulties exist, the current study demonstrated that if food detection distance can be measured, it can be used, with searching speed and handling time, to predict the functional response, at least in a relatively simple system.
In other systems, the functional response may also depend on factors such as the amount of interference competition, or a trade-off between foraging and vigilance. Interference competition will reduce feeding rates at high competitor densities, and will be more likely to occur in systems in which handling time is long, food is highly aggregated or prey are mobile and can escape to refuges (e.g. Yates, Stillman & Goss-Custard 2000; Stillman et al. 2002b). The strength of interference competition can be accurately predicted from simple behavioural parameters (e.g. the duration of disputes over prey or the distance over which attacks are launched) (e.g. Stillman et al. 2002b), and so it will be necessary to use functional responses incorporating competitor density when interference competition is significant. Vigilance may compromise foraging (e.g. Lima & Bednekoff 1999) and so increased vigilance may reduce feeding rate. Additionally, vigilance may coincide with handling prey (e.g. both vigilance and handling may occur with the head up), making it more difficult to accurately measure handling time, unless the distinction between handling and vigilance is clear. Functional responses incorporating vigilance time will be required in systems in which vigilance is known to be important.
Previous studies have shown that ground-foraging birds prefer to feed in shorter vegetation swards (Devereux et al. 2004), and that models based on foraging height preference can accurately predict which birds will be found in different habitat structures (Martin & Possingham 2005). We showed that rooks could search a larger area per unit time in shorter vegetation, because the food was less concealed in this vegetation. An alternative possibility is that longer vegetation or other obstructions reduces the speed at which animals can move through the habitat (e.g. Butler, Bradbury & Whittingham 2005), but this was not the case in our study as the searching speed of rooks was uninfluenced by vegetation height. The fitted gradient of the functional response at cube densities up to 1 m−2 was steeper in the shorter vegetation, and the predicted functional response explained significantly more variation in feeding rate when assuming that success rate was higher in the shorter sward. In contrast, incorporating between-treatment variation in success rate did not improve the amount of variation explained by the fitted functional response (i.e. the fitted functional response did not differ significantly between treatments). A possible reason why the fitted functional response differed between swards heights at low cube densities, but not over its entire range, is that the influence of sward height diminished at cube densities over 1 m−2. Therefore, the influence of sward height was less evident over the entire range of cube densities, than it was at low densities. Irrespective of the influence of sward height on the functional response, direct measurement of behavioural parameters was still able to accurately predict the observed functional response.
Our study was restricted to grassland, but several declining farmland birds (e.g. finches, sparrows and buntings) feed on seeds in arable land. These species are smaller than rooks and often feed in habitats in which they are usually concealed from view (e.g. stubble fields), making direct observation of the functional response more difficult than in larger species. Fortunately, seed-feeding birds can be attracted to artificially supplied food, and can be housed in the laboratory, hence allowing functional responses to be measured directly either in the field (Kenward & Sibly 1977; Dolman 1995; Cresswell 1997) or laboratory (Whittingham & Markland 2002; Butler & Gillings 2004). Each of these studies has measured the functional response or a component of the functional response in a farmland bird or closely related species. As far as we are aware no other study has predicted the functional response in farmland birds directly from observed behavioural parameters. This approach is distinct from estimating parameters of the functional response using regression techniques, because it potentially requires fewer observations, from birds feeding in a smaller range of food densities, and can also be used to predict the functional response at food densities below those at which birds usually feed. We believe that the approach adopted in this paper could also be applied to seed-feeding farmland birds.