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1Mechanistic models may be able to predict how changes in agricultural practice influence farmland bird populations. A key component of these models is the link between food and competitor densities and the rate at which birds consume food, i.e. the functional response.
2This paper tests whether the functional response of a farmland bird, the rook Corvus frugilegus, can be predicted from three parameters: searching speed, food detection distance and handling time. It is often difficult to measure the functional response of farmland birds directly, but it may be possible to measure behavioural parameters more quickly.
3We performed experiments in which rooks fed on a range of artificial food densities in two grass sward heights. Food detection distance was greater in the shorter sward, but sward height did not influence searching speed or handling time. The functional response could be accurately predicted in both sward heights.
4We show that the functional response of a farmland bird can be predicted from 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.
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.
study species and system
The rook was chosen as a study species for two reasons: (i) rooks are relatively large birds, which feed in open farmland habitats and tolerate close proximity to humans (Feare, Dunnet & Patterson 1974), simplifying the observation and the practicality of feeding experiments and (ii) we had a local breeding population of rooks and access to grassland on which sward height could be varied, feeding experiments performed and observed.
The study site was at Winfrith Technology Centre, UK (50°41′N, 2°15′W), on an area of amenity grassland, normally maintained by mechanical mowing at approximately 2-week intervals during the study period. The experimental area was within 500 m of a small rookery (approx. 10–20 pairs) and 1000 m of a larger rookery (approx. 50–100 pairs). Birds from both rookeries usually fed on the grassland surrounding the experimental site, and also fed on the artificial food provided during experiments. Rooks on the study site frequently encountered people as the grassland was surrounded by office buildings and footpaths, and people often walked across the grassland itself. The rooks were also used to feeding on food supplied by people. The natural food of rooks in the study site consisted mainly of soil-dwelling invertebrates such as Tipulidae larvae and earthworms (e.g. Lumbricus sp.). Experiments were performed while the rooks had young in the nest and so birds typically spent the minimum amount of time on the experiment, flying back to the nest once a few food items had been gathered. The birds preferentially fed on the artificial food, ceasing to feed on natural food in the vicinity of experiments when artificial food was provided.
Rooks were fed for 2 weeks before the experiments began, to attract birds into the area, and to accustom them to human presence and the type of food being provided. Experiments were performed between 6 May and 23 May 2005. Experiments were conducted in two 4 × 4 m2 patches (termed cut and uncut), located 8 m from each other, marked at the corners with 50 cm high, 4 × 4 cm2 wooden posts, painted in highly visible orange paint. There was a buffer of at least 4 m of similar habitat around each patch. The patch size was large enough to allow several rooks to feed simultaneously in the area (increasing the chance of detecting interference competition), but small enough to allow any unconsumed food to be quickly located by an observer after an experiment. In the uncut patch, the grass was allowed to grow for 2 weeks before the experiments began (last cut on 19 April), and was allowed to continue growing throughout the experimental period. In the cut patch, the grass was cut as part of the normal cutting regime, and was cut approximately every 2 weeks, depending on weather conditions (cut on 19 April, 4 May and 16 May).
Each experiment was recorded using a video camera (Canon 3CCD XL1, http://www.canon.com) from a window in a building 30 m from the cut patch and 36 m from the uncut patch at a height of 5·2 m. The patches were square to the direction from which they were viewed. The camera zoom was adjusted so that the field of view comprised the whole of a patch. The camera was not moved during the recording of experiments. Experiments were usually carried out in the early afternoon, as there tended to be more rooks in the area at that time, but some were performed in the late morning if rooks were present. During each afternoon or morning, no more than six trials were performed, three in each area. After the final afternoon trial, and on some non-experimental days, some additional food was placed on the experimental patches to encourage the birds to keep feeding in the area.
During experiments, variable densities of 1 cm3 cubes of tinned ham (Spam, http://www.spam.com) were scattered randomly within one patch. Tinned ham was chosen as the artificial food source because it could easily be cut into fixed-size cubes, had been shown in a previous study to be readily consumed by rooks in the study area (R. A. Stillman, unpublished data), and was preferred over natural food. Preliminary studies found that cubes smaller that 1 cm3 were difficult for an observer to relocate after an experiment and that rooks usually flew away with cubes larger than 1 cm3 rather than consuming them in situ. In each patch, three replicates of seven food cube densities were performed in a random order, 0·25 m−2, 0·5 m−2, 1 m−2, 1·5 m−2, 2 m−2, 2·5 m−2 and 3 m−2. Preliminary studies showed that at densities lower than 0·25 m−2 rooks tended to ignore the area, presumably because the density of food was so low that the birds were unaware of any food being present. These studies also showed that feeding rates approached a maximum at approximately three cubes m−2. The artificial food items were scattered randomly throughout the square. Filming began before the artificial food items were distributed. The experiment began once the first bird entered the square, and continued until the last bird left the patch and the area remained free of birds for 5 min. After this point the patch was considered to be depleted and was searched to determine whether any food cubes remained. To minimize the effect of depletion on the results, only data collected during the first 60 s after the first rook appeared were included in the analysis.
measuring habitat structure
Habitat structure was measured as sward height and the detection angle at which a food cube could be viewed by a human observer. Sward height was measured using an HFRO sward stick (Bircham 1981) on five occasions in each patch during the experimental period, 30 measurements being taken in each patch on each occasion. Detection angle was calculated using an inclinometer as follows. A food cube was positioned on the sward in the same manner as during experiments and its position noted. The observer then moved away from the cube, in a random direction, stopping when 50% of the cube became obscured by the sward. The inclinometer was then used to measure detection angle, i.e. the angle between the ground and a line from the cube to the observer's eye. Thirty angles were measured in each patch, on 2 days in the cut patch and 3 days in the uncut patch.
Videos of the experiments were transferred to a computer and analysed using a purpose-built event recording program, which allowed the timing of different activities to be recorded as well as the screen location of birds and the experimental patches. The screen position of each bird and the time it entered the patch were recorded. Each bird was given a number depending on the number of previous birds that had entered the square, and all its activities while in the square were recorded until it left the square. If it remained on screen and re-entered the square then it retained its original number. However, as the birds were not marked, once they left the screen they were considered to have left the area completely, and if they did return to the square they were allocated a new number. Handling time was measured, for 20 random food captures within each treatment, as the time between a rook first starting to walk, run or fly towards food to when it lifted its bill back to the normal foraging position. Rooks often showed an obvious change in behaviour when they detected a food item. At high rook densities in particular, they rapidly moved towards food items. For a random subset of food captures (20 in each treatment), the screen position of the bird when it appeared to have detected a cube, and the position of the cube (from the rook's final location) was also recorded to derive detection distance. Searching speed was measured by recording the time taken by rooks to walk fixed distances (20 in each treatment). Real distances were calculated using the methods of Moody et al. (1997), using screen and real locations of the corner posts to convert the screen locations of birds to real locations. By estimating a number of known distances within each patch, we found that this method estimated distances of 2–4·5 m to an accuracy of ±4 cm. Aggression between birds was also recorded from when the aggressor first showed a change in behaviour until it returned to searching behaviour again.
describing the functional response
A pilot study had showed that the rook functional response in this system could be described by a hyperbolic function and so we used the Holling disk equation (Holling 1959) to describe the functional response:
( (eqn 1))
where F = feeding rate (food items s−1), a = success rate (Jeschke, Kopp & Tollrian 2002) (m2 s−1), h = food handling time (s per food item) and D = food density (food items m−2). The parameters a and h were estimated using the non-linear regression procedure of SAS (http://www.sas.com) either separately for each treatment or for the combined data set.
In order to statistically compare the functional responses in cut and uncut treatments, we used a modified version of the Holling disk equation which incorporated the effect of experimental treatment on success rate:
( (eqn 2))
where acut = success rate in cut treatment, auncut= success rate in uncut treatment and T = treatment (1 = uncut, 0 = cut). The parameters auncut, acut and h were estimated using the non-linear regression procedure of SAS for the combined data set. A goodness of fit test was then performed to compare a two-parameter functional response, which assumed that behaviour was the same in both treatments (equation 1 with parameters estimated from the combined data set), with a three-parameter functional response, which assumed that success rate differed between the treatments (equation 2 with parameters estimated from the combined data set). The test determined whether a functional response incorporating differences in success rate explained significantly more variation in feeding rate than a simpler functional response, assuming that behaviour was the same in both treatments.
predicting the functional response
The functional response was predicted by directly measuring each parameter of equation 1, rather than estimating them using non-linear regression. Handling time was measured from the videos as described above. Success rate was calculated from:
( (eqn 3))
where s = walking speed while searching for food (ms−1) and d = mean distance over which food items are discovered (m). Walking speed and detection distance were measured from the videos as described above. The 2 in equation 3 accounts for the fact that detection distance was measured in one direction, but rooks could search twice this distance by looking both to the left and right. In order to statistically compare the predicted functional responses in cut and uncut treatments, each of the parameters in equation 1 were measured either within the cut or uncut treatments, or for the combined data set. A goodness-of-fit test was then performed to compare a two-parameter functional response (equation 1 with parameters measured from the combined data set), with a three parameter functional response (equation 2 with success rate measured for each treatment and handling time measured from the combined data set).
Neither grass height nor detection angle changed significantly during the relatively short duration of the experimental period (linear regression of grass height or detection angle against date; NS in both cases) and so we present summary statistics for the whole experimental period. Not surprisingly, grass height was significantly shorter in the cut patch than in the uncut patch (Table 1). Similarly, detection angle was significantly lower in the cut patch than in the uncut patch (Table 1). This meant that the observer needed to be closer to cubes in the uncut sward before they were detected.
Table 1. Comparison of habitat structure and foraging behaviour in the cut and uncut treatments
Cut mean ± SD (n)
Uncut mean ± SD (n)
Cut vs uncut anova
Grass height (m)
5·28 ± 0·74 (5)
7·02 ± 1·14 (5)
F = 8·17, P = 0·021
Detection angle (°)
13·20 ± 0·19 (2)
23·47 ± 2·77 (3)
F = 24·59, P = 0·016
Searching speed (s) (m s−1)
0·51 ± 0·12 (20)
0·49 ± 0·11 (20)
F = 0·31, P = 0·579
Handling time (h) (s)
1·39 ± 0·77 (20)
1·11 ± 0·35 (20)
F = 2·14, P = 0·152
Detection distance (d) (m)
0·85 ± 0·58 (20)
0·52 ± 0·29 (20)
F = 5·13, P = 0·029
Rooks quickly became accustomed to the experiments, flying to an experimental patch shortly after food had been positioned (sometimes within 30 s), often from long distances (>500 m). They searched for artificial food by walking around a patch, in a very similar way to which they searched for natural food within the study area. Rooks often ran/flew purposefully towards food items once they were detected (especially when other rooks were close by), a behaviour that was clearly different from their slower searching behaviour. The consumption of cubes could be seen clearly on the videos, and we saw no evidence of the consumption of natural prey during the first 60 s of experiments. Individual birds typically consumed 5–10 cubes before flying back to their nest site, and so spent minimum time resting within experimental patches. There were some aggressive interactions between rooks in the experiments, but these tended to be restricted towards the end of an experiment when the amount of food had been depleted substantially. Less aggression occurred during the first 60 s during which our foraging observations were concentrated. All food was consumed in all experiments.
Neither searching speed nor handling time varied significantly between the cut and uncut treatments (Table 1). In contrast, detection distance was significantly greater in the cut patch than in the uncut patch (Table 1).
describing the functional response
Feeding rate increased at a decelerating rate with increased food density in both treatments (Fig. 1). For starting cube densities of 0–1 cubes m−2, feeding rate was positively related to food density in both treatments (linear regression; cut treatment feeding rate = 0·021 (SE = 0·035, P = 0·565) + 0·348 (SE = 0·099, P = 0·010) × cube density, n = 9; uncut treatment feeding rate = 0·027 (SE = 0·024, P = 0·298) + 0·159 (SE = 0·054, P = 0·021) × cube density, n = 9), but increased more rapidly in the cut treatment (linear regression without intercept (as intercepts not significantly different from zero in previous analysis); feeding rate = 0·400 (SE = 0·041, P = 0·000); cube density −0·188 (SE = 0·052, P = 0·002); cube density × treatment, n = 18, where treatment = 0 for cut and 1 for uncut treatments). Within this cube density range, a two-parameter regression incorporating cube density and the interaction between cube density and treatment provided improved fit over a one-parameter model incorporating cube density alone (F-ratio goodness of fit test; F = 13·22, df = 1, 16, P = 0·002). For starting cube densities of 1·5 m−2 or more, feeding rate was unrelated to food density in both treatments (linear regression; cut treatment feeding rate = 0·288 + 0·101 (SE = 0·064, P = 0·145) × cube density, n = 12; uncut treatment feeding rate = 0·324 + 0·047 (SE = 0·078, P = 0·561) × Cube density, n = 12 and mean feeding rate over this range did not differ between treatments (analysis of variance; F = 0·68, n cut/uncut = 12, P = 0·419). The difference between treatments was therefore only apparent at low food densities.
The functional response was plotted as feeding rate in the first 60 s vs the mean number of cubes present in the first 60 s. Equation 1 described the functional response more accurately in the cut (R2 = 79·4%) than in the uncut treatment (R2 = 66·7%) (Table 2; Fig. 1), and the fitted handling times were not significantly different from the observed handling times. This is evidence that the maximum intake rate at high food densities is limited by handling time, an assumption of equation 1. To test whether interference competition was influencing feeding rate we regressed residual feeding rate after fitting equation 1 against the mean number of rooks on a patch during the first 60 s. Rook density (m−2) was unrelated to residual (observed – fitted) feeding rate in both treatments (linear regression; cut treatment residual = 0·006 + 0·041 (SE = 0·183, P = 0·826) × bird density, n = 21; uncut treatment residual = −0·028 + 0·107 (SE = 0·270, P = 0·696) × bird density, n = 21, and so we conclude that interference was not significantly influencing feeding rate at the start of experiments. Even though both the observed success rate (Table 1) and the functional response gradient at low cube densities (see above) differed between treatments, the fitted functional response did not explain significantly more variation in feeding rate when assuming that success rate differed between treatments (F-ratio goodness of fit test comparing the fits to all data of equation 1 (two parameters; no between-treatment variation) and equation 2 (three parameters; between-treatment variation) (see Table 2 for parameters); F = 3·37, df = 1, 39, P = 0·074).
Table 2. Parameters (± standard error (n)) used to describe and predict the functional response of rooks consuming artificial food in cut and uncut patches. The columns show the data subset for which parameters were fitted or measured. The descriptive parameters were obtained by fitting equation 1 or 2 to the relationship between feeding rate and food density. Equation 2 could only be fit to the combined data. All fitted parameters were significantly different from zero (P < 0·05). The predictive parameters were obtained from observations of rook behaviour. Observed success rate was calculated from equation 3 and so is not presented with a standard error or sample size. Searching speed and handling time did not differ significantly between treatments and so observed values were measured for both treatments combined
The functional response was predicted from mean searching speed and handling time across treatments (as these variables did not differ between treatments) and food detection distance measured in the cut and uncut treatments (as this variable did differ between treatments) (Table 2; Fig. 1). The functional response was more accurately predicted in the uncut treatment (R2 = 73·1%) than in the cut treatment (R2 = 65·7%), but the proportion of variation explained was close to that for the fitted models, and the predicted functional response never deviated from the fitted by more than 0·05 cubes s−1. In contrast to the fitted functional response, the predicted functional response did explain significantly more variation in feeding rate when assuming that success rate differed between treatments (F-ratio goodness of fit test comparing the predictions of equation 1, with all parameters measured from the combined data set, and equation 2, with success rate measured separately for each treatment (see Table 2 for parameters); F = 4·12, df = 1, 39, P = 0·049).
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.
We are very grateful to Colin House and Chris Barrett for allowing us to conduct experiments at Winfrith Technology Centre, and the grounds staff for maintaining the grass height in our experiments. We are also very grateful to Richard Caldow, Sarah Durell, John Goss-Custard, Will Cresswell, Charles Fox and an anonymous referee for providing very valuable comments on the manuscript.