1. Functional response models that predict the relationship between feeding rate and food density often include only two behavioural parameters, handling time and searching rate. However, vigilance can occupy a large proportion of foraging time and, consequently, may affect the functional response. Previous functional response models of granivorous birds showed no effect of vigilance on predicted feeding rates; these models assumed that all of handling time is compatible with vigilance and, therefore, overestimated the potential time for cost free vigilance to occur.
2. Here we have derived a new functional response model that incorporates the proportion of time spent vigilant (v) and the proportion of handling time that is compatible with vigilance (p). This model allows for the relationship between vigilance and handling to vary from completely compatible to mutually exclusive, and degrees in between.
3. To determine whether vigilance can affect the functional response of a granivorous bird, grey partridge Perdix perdix L, we measured the functional response and associated behavioural parameters, and used the behavioural estimates to parameterize the model. Any deviation from the feeding rates predicted using a model without vigilance indicates that vigilance is affecting the predicted functional response.
4. We found that vigilance only affected the predicted functional response at very low food densities (<3 seeds m−2). Simulations show how the potential for vigilance to affect feeding rate (i.e. the values of p given v) increases as v increases. We parameterized the model using data from chaffinches Fringilla coelebs, which were shown to spend >50% of their foraging time vigilant, and found that even with a high value of p vigilance reduced feeding rates at higher seed densities.
5. This study shows that vigilance can affect the feeding rate of a granivorous bird when either the proportion of time spent vigilant is high or the proportion of compatible handling time is low. This may affect larger scale ecological processes, i.e. spatial distribution of foragers and patterns of resource depletion, as individuals try to mitigate the effects of vigilance by maximizing their feeding rate whilst minimizing their predation risk.
Functional response models used to describe the relationship between feeding rate and food density (Sutherland 1996) often simplify foraging behaviour into only two components, searching rate and handling time. These models, most notably the Holling’s disc equation (Holling 1959), assume that searching rate limits feeding rate at low food densities, when food is harder to find, but handling time becomes more limiting as food density increases. However, anti-predator behaviours, including vigilance, are a major component of foraging (Treves 2000) and have been shown in some species to occupy a high proportion of foraging time (Inger et al. 2006; Fernandez-Juricic & Beauchamp 2008; Smart, Stillman & Norris 2008; Baker, Stillman & Bullock 2009). Under some conditions, vigilance could become the major factor limiting feeding rate and, consequently, affecting the functional response. To-date, attempts to incorporate the proportion of time spent vigilant into functional response models of granivorous birds have provided no significant improvements in the models predictive power (Smart, Stillman & Norris 2008; Baker, Stillman & Bullock 2009), however, these models have not accounted for some key implications stemming from the interaction between handling and vigilance.
Handling time, defined as the total time taken to capture and consume one food item (Stephens & Krebs 1986), also includes components that are not compatible with vigilance, i.e. approaching and picking up the prey item, and this distinction might be crucial to understanding the affect of vigilance on the functional response. Cowlishaw et al. (2004) showed that the ratio of compatible handling time to searching time can be used to predict when vigilance might cause a decrease in feeding rate, such that when this ratio is high vigilance has no effect on feeding rate. Searching time is often assumed to be a function of prey density (Stephens & Krebs 1986) and, therefore, if compatible handling time is constant the effect of vigilance on the feeding rate should be negatively correlated with food density. The relationship between food density and vigilance in both birds and mammals appears to be mixed (Beauchamp 2009), however, some results might be influenced by factors other than food density i.e. interference from conspecifics. At high food densities, when handling time is limiting feeding rate, the extent of the overlap between vigilance and compatible handling time is crucial in determining the effect of vigilance on the feeding rate (Smart, Stillman & Norris 2008). Other evidence (Cowlishaw et al. 2004) suggests that when the compatible handling time is short relative to searching time, and vigilance is long, vigilance will begin to limit feeding rate, thus affecting the shape of the functional response.
Smart, Stillman & Norris (2008) developed three separate functional response models that incorporated vigilance, each allowing different overlap between vigilance, searching and handling. However, two different studies (Smart, Stillman & Norris 2008; Baker, Stillman & Bullock 2009) found no improvement in the ability to predict the functional response of a granivorous bird from observed behavioural parameters using these models. This happened because the models assumed that vigilance could occur throughout the whole of handling time, whereas some components of handling (e.g. approaching prey) could be incompatible with vigilance. Consequently, these models overestimated the potential time for cost free vigilance to occur. It is also possible that the food densities used in these studies were not low enough to reduce the searching time to a sufficient degree to observe any effect of vigilance on feeding rate. For these reasons, any effect of vigilance on the functional response may not have been detected in these studies. Fortin et al. (2004) derived a functional response model that could estimate the ‘spare time’ during foraging that could be allocated to vigilance behaviour, however, they did not incorporate vigilance into the functional response model. To address these problems, we have developed a new functional response model that allows the proportion of handling time that is compatible with vigilance to vary. Depending on its parameter values the new model can represent each of the models derived by Smart, Stillman & Norris (2008) [model 1 (Holling’s disc equation) – no vigilance; model 2 – no overlap between handling and vigilance; model 4 – complete overlap between handling and vigilance], as well as the continuum between these extremes.
In this study we have: (i) derived the new functional response model; (ii) measured the functional response and associated behavioural parameters [i.e. total handling (H), the proportion of compatible handling time (p), searching rate (a) and the proportion of time spent vigilant (v)] of a granivorous bird, the grey partridge Perdix perdix L (Fig. 1); (iii) parameterized the new functional response model for grey partridge to predict when vigilance will affect the functional response; and (iv) tested the model on a previously studied species, the chaffinch Fringilla coelebs L, that spends >50% of its foraging time vigilant, to test the implication of higher vigilance on the functional response. If vigilance affects the functional response, there will be a reduction in feeding rate relative to that predicted by a model that excludes vigilance. To maximize the potential to detect an effect of vigilance on the functional response we required a forager that handles food quickly, but still spends a large proportion of its foraging time vigilant. The grey partridge has been show to spend ∼40% of its foraging time vigilant (Watson, Aebischer & Cresswell 2007), which is broadly similar to previously studied granivores (Smart, Stillman & Norris 2008; Baker, Stillman & Bullock 2009), but it handles seeds more rapidly and, therefore, has less potential for cost-free vigilance during handling. Furthermore, we manipulated the searching rate by reducing the lower food densities to levels below those used previously and through altering the habitat structure (Whittingham & Markland 2002; Baker, Stillman & Bullock 2009), i.e. two treatments: bare soil and crop stubble. We discuss the implications of this study for predicting the functional responses of granivorous foragers and in the broader understanding of foraging behaviour.
Materials and methods
Study species and site
The grey partridge is a farmland game bird that predominantly feeds on plant material, including seeds, during the winter (Holland et al. 2006). This species is significantly larger (i.e. grey partridge mass = ∼390 g, corn bunting mass = 42–53 g) than the previously studied finches and buntings, but has broadly similar foraging behaviours, i.e. continuous foraging, visual detection of prey and foraging bouts divided between searching, handling and vigilance. This species has previously been shown to spend ∼40% of its foraging time vigilant (Watson, Aebischer & Cresswell 2007) and preliminary trials found that they handled wheat seeds faster than corn buntings Miliaria calandra L (Smart, Stillman & Norris 2008).
This study was conducted on the rearing fields at the Game & Wildlife Conservation Trust, Fordingbridge, Hampshire, in southern England. Twenty-five 8-week-old grey partridges were purchased from Heart of England Farms (Warwickshire, UK) on 18th September 2008 and were divided up into five random groups of five birds, individually colour-ringed [Flat coil (FC) size 3 (8 mm)] and placed into housing pens. Outside of the experimental period (i.e. 14:00 until 08:30) the birds were fed ad libitum food (until 12 weeks of age a high protein pellet Keepers Choice Mini Rearer and subsequently Keeper’s Choice Maintenance Pellets and wheat) and throughout the experiments they had constant access to water. The birds were attended daily by experienced game keepers to assure they remained in good health.
Each group was housed in two interconnected pens, constructed from 3 × 1·5 m prefabricated wooden framed wire mesh panels, one used for housing and the other for the experiments. The 3 m2 pens were arranged in a 5 × 2 grid, with an interconnecting hatch between the front and back pen. The pens were roofed with a fine mesh and each had a door to provide access. During the experiments the birds were unable to see the birds in neighbouring pens as groups not being studied were shut temporarily in the housing pens. The housing pen had a grass surface, two sources of shelter (tree branches and a wooden ledge) and a water supply. Each experimental pen was fitted with a black ground sheet to remove any natural sources of food and to allow any spilt food to be swept up. A 1·5 m2 experimental platform, built from three 1 × 0·5 m plywood boards attached to a wooden frame, was placed centrally in each pen. The stubble platforms were constructed similarly, but with the addition of stubble stems glued in place. The stubble stems were spaced 10 cm apart along each row and 25 cm apart between neighbouring rows and the stubble was cut to a height of 13 cm. This height (Butler, Bradbury & Whittingham 2005a) was chosen to reflect values found naturally, however, the spacing was chosen from field tests to provide maximum physical obstruction without directly impeding the bird’s movement, i.e. without pushing the stubble over.
The functional response was measured across eight seed densities (5, 10, 15, 25, 50, 100, 200, 400 seeds m−2) with one replicate per group of birds for each of the seed densities above 25 seeds m−2. At high densities, once on the feeding platform the birds spread out to forage simultaneously on undepleted sections of the platform. However, at low densities (≤25 seeds m−2) the first few individuals to start feeding on the platform would quickly consume all the available seeds. Therefore, several replicates were required to film all the individual birds foraging at these densities. This was repeated for both the bare soil and stubble treatments. The food was removed from each pen one hour before the start of each experiment at the beginning of the day, with the first experiment starting at 09:30, thus giving the birds some time to feed before the experiment. This was important for both the welfare of the birds and because we did not want to measure the feeding rate of starving birds, which would represent an extreme condition. There was a 1-h interval between each experiment throughout the study in order to maintain a consistent level of hunger. Four replicates were conducted on each pen per day, with each replicate taking not more than 4 min. The seed densities and treatments were fully randomized for each group throughout, but in order to maintain even spacing between the replicates the group order was randomly chosen anew each day.
For each replicate, 1125 cm3 of pre-sieved soil was spread evenly across the platform, giving a depth of 5 mm; onto this the appropriate number of wheat seeds were randomly scattered. Wheat seeds were chosen for the experiment as they had been used previously to measure the functional response of a granivorous passerine (Smart, Stillman & Norris 2008), but were known to be handled more rapidly by grey partridge. The birds were filmed from a Canon XL1 video camera (http://www.canon.co.uk) placed 1·5 m from the front edge of the platform (outside of the pen) and at a height of 1 m above the platform. Filming was started immediately upon set up and continued until each bird had made six or more (three or more at <25 seeds m−2) consecutive pecks or until significant depletion of seeds had occurred across the whole platform. At all densities, we were careful to focus on foraging bouts that occurred on previously unused portions of the platform so that depletion would not affect the observed feeding rate. Very few aggressive interactions were observed between the birds throughout the experiments, with all individuals feeding undisturbed on the experimental platform.
The videos were downloaded and analysed using a purpose built event recorder that allows frame by frame viewing. The feeding rate was measured from the frame before the first peck until the frame before the last peck for a minimum of six pecks at seed densities above 15 seeds m−2 and a minimum of three pecks for the lowest two densities, although most recorded foraging bouts were longer. Handling time was divided into two components based on the compatibility with vigilance. The incompatible component (Hx) was measured from the time at which the bird began moving towards the target seed, shown by a distinct change in behaviour, to the frame before contact with the target. The compatible component (Hc) was measured from contact with the target seed until the seed was consumed. The proportion of compatible handling time (p) was calculated in relation to the total handling time (H), i.e. Hx+ Hc.
Blanchard & Fritz (2007) emphasized the importance of distinguishing between routine and induced vigilance, as the latter had significantly more affect on the feeding rate. Here we consider routine vigilance only and any feeding bout that was interrupted by an obvious external stimulus was excluded from the analysis. Vigilance was defined by the head being in upright position with the bill parallel to, or directed away from the ground. Although it has been previously demonstrated that birds can remain partially vigilant whilst foraging (Lima & Bednekoff 1999), this is difficult to quantify. By using this definition, we are measuring the vigilance of the birds when they are fully vigilant, which gives a good measure of their perceived threat levels. The proportion of time spent vigilant (v) was calculated as the proportion of time displaying vigilant behaviour during the foraging bout. The frequency of vigilance was measured as the number of times the head was raised into a vigilant position during each foraging bout. The length of vigilance bouts was measured as the mean time spent with the head in a vigilant position for each bird. Searching time measures the amount of time an individual spends searching for a food item before detection. Here we define searching time as the time spent with the head angled below 90° regardless of the posture (upright or head-down), and we include both stationary and active searching under this definition: this was measured from the frame at which searching resumed until the frame before detection. Most detection events occur to either side of the bird’s head and so detection events are characterized by a sudden change in direction and often an increase in speed.
Both attack distance and searching speed required an accurate measure of the distance moved by the birds across the screen. This was accomplished by importing a screen capture of the start and finish position of the bird into Photoshop CS4 (http://www.adobe.com). A 15 × 15 cell grid layer was placed over the top of the video images and the grid was warped using the perspective tools to fit over the shape of the platform. The coordinates of the bird’s position on the platform could now be accurately read from the grid with an error of ±3·1%, as calculated using a model bird moving between random coordinates on a 1·5 m2 platform. The attack distance was defined as the distance between the target seed and the bird at the point that movement towards the seed was initiated. Searching speed was calculated from the movement along a straight line when the bird was actively searching. For both maximum attack distance and search speed only the lowest three seed densities were used as movement becomes less frequent at higher seed densities. The ability to detect food items can be influenced by many environmental factors, including the distance to the prey item, the ambient lighting conditions, contrast of prey with background, as well as forager specific factors, such as height and visual acuity. Thus, searching rate is the most complex of the behavioural parameters to quantify and several models have been derived that incorporate estimations of many of these complex factors. However, we choose to define searching rate based upon a simple model with parameters that can be easily quantified, which gives an approximate estimation of the area searched by the forager. The area searched is approximately twice the maximum distance over which food items were observed to be taken (i.e. the bird can search over the same distance on either side), multiplied by the distance travelled: thus, a =2ds, where d = attack distance and s = searching speed (Fortin et al. 2004; Stillman & Simmons 2006).
Alternative functional response models
The Holling’s disc equation (Model 1) describes a type II functional response using just three parameters, a = searching rate, H = handling time and D = food density, and assumes that searching and handling are mutually exclusive events:
Model 2 (see Appendix S1 for derivation) is a new functional response model that incorporates both the proportion of time spent vigilant (v) and the proportion of handling time that is compatible with vigilance (p). In this functional response model, handling and vigilance can be mutually exclusive or compatible behaviours, and any degree of overlap between p and v is reflected in the predicted feeding rates.
These models were parameterized using the observed behavioural values (Table 1) for grey partridge foraging on wheat seeds in both bare soil and stubble treatments. The models were compared using Akaike Information Criterion (AIC).
Table 1. The mean observed behavioural parameter values (±95% confidence in-tervals) used to parameterize models 1 and 2 to predict the functional responses of grey partridge foraging for wheat seeds in two habitat treatments; bare soil and stubble. For many of these behavioural parameters there was no significant difference between the two treatments and, therefore, these data were combined before analysis (– indicates that the parameter mean was calculated using the combined data and estimate applies to both treatments)
To account for the hierarchical structure of the data, i.e. individual birds within groups, we used linear mixed effects models (LME) to analyse the relationship between each behavioural parameter and the seed density. The optimum random effects structure for all the behavioural parameters was found to be a random intercept for both the individual bird and the group. There was a consistent violation of homogeneity of variance in the behavioural parameters across the seed densities. One likely source of this heterogeneity of variances is due to the birds having more options in their foraging rate at high densities, i.e. they can forage at their maximum rate or choose to forage more slowly, whereas at low densities they are restricted in their foraging rates by the searching rate. Transformations of the response variable were not sufficient to remove this heterogeneity and, therefore, we allowed for a different variance structure per seed density (‘varIdent’ in R nlme package).
Log10 transformations to the explanatory variable seed density were required for some of the models (feeding rate, H, Hx,Hc and search time) where there was a clear violation of linearity. To achieve normal errors, the response variables of H, Hx and Hc and search time were Log10 transformed, the frequency of vigilance and duration of vigilance were square-root transformed (+0·5 to account for zero values) and the proportion of time spent vigilant was arcsin transformed. The initial fixed factors included in the analysis were seed density, habitat, sex, time-of-day and the interaction between seed density and habitat. Most of these terms were not significantly related to the response variable and, therefore, only significant results are reported. Where habitat did not significantly affect the behavioural parameters (Figs 3 and 4) the data from both treatments were combined before plotting.
The (log) feeding rate of grey partridge was positively correlated with (log) seed density (LME, F1,261 = 148·32, P < 0·0001), but the presence of crop stubble had no effect (LME, F1,260 = 0·177, P = 0·674) (Fig. 2).
The total handling time (H) was negatively correlated with (log) seed density (LME, F1,261 = 82·406, P < 0·0001) (Fig 3a–c). The two components of handling time were both negatively correlated with (log) seed density, Hx (LME, F1,261 = 199·542, P < 0·0001) and Hc (LME, F1,261 = 20·681, P < 0·0001), but the approach time had a much higher F-value. The presence of crop stubble had no effect on H (LME, F1,260 = 0·706, P =0·402), Hx (LME, F1,260 = 0·0692, P =0·793) or Hc (LME, F1,260 = 2·025, P =0·1559).
The proportion of time spent vigilant (v) was negatively correlated with seed density (LME, F1,261 = 14·901, P < 0·0001), as was the frequency of vigilance bouts (LME, F1,261 = 19·135, P = <0·0001), but the duration of vigilance bouts was only weakly correlated with seed density (LME, F1,261 = 4·819, P = 0·029) (Fig. 3d–e). The presence of crop stubble had no effect on v (LME, F1,260 = 0·02, P =0·889), the frequency of vigilance bouts (LME, F1,260 = 2·503, P =0·115) or the duration of vigilance bouts (LME, F1,260 = 0·016, P =0·899).
The maximum attack distance was negatively correlated with seed density (LME, F1,84 = 9·649, P = 0·0026) and was also significantly affected by the presence of crop stubble (LME, F1,84 = 19·375, P < 0·0001). The search time (Fig. 4) was negatively correlated with (log) seed density (LME, F1,261 = 89·768, P < 0·0001), but the searching speed was not affected by seed density at the lowest three densities (LME, F1,89 = 0·285, P = 0·5947). The presence of crop stubble did not affect these two behavioural parameters: search time (LME, F1,260 = 1·669, P = 0·1975) and searching speed (LME, F1,88 = 0·0141, P = 0·9058).
Predicting the functional response from behavioural parameters
Models 1 and 2 were parameterized using the observed behavioural parameters (Table 1) and their predictions of the functional responses were compared. Vigilance was found to only affect the functional response at seed densities <3 seeds m−2 in both treatments, shown by a reduction in the predicted feeding rate, but as this was below the seed densities used in the experiment model 2 has a lower AIC and an identical R2 value to model 1 (see Table 2). This suggests that vigilance is starting to affect the functional response, but under these experimental conditions the effect is only slight. To understand how variation in the key behavioural parameters of p and v affects the feeding rate, and how these relationships are themselves affected by food density, we plotted the feeding rate calculated using model 2 against the proportion of time spent vigilance (v) and the proportion of compatible handling time (p) (Fig. 5) at three seed densities (5, 25 and 200 seeds m2). The values for parameters a and H were the mean observed values from the bare soil treatment. These figures indicate that at low seed densities, with even moderate values of p and v, vigilance should begin to affect the functional response of these birds.
Table 2. The Akaike Information Criterion (AIC) comparing the ability of models 1 and 2 to predict the observed functional response
The Akaike weights (Aw) are used to compare the likelihood of each model relative to the other (Edwards et al. 2007).
Previous studies have shown that the proportion of time spent vigilant in some granivorous bird species can be as high as 60% (Baker, Stillman & Bullock 2009) and, therefore, it is possible that for these species vigilance will affect the functional response at low food densities. Setting the values of a and H to those reported for chaffinches in Baker, Stillman & Bullock (2009) and comparing the values of p given v = 0·578 or 0·598 (chaffinches, bare soil and stubble treatment, respectively) suggests that vigilance should affect the predicted functional response at all values of P <0·916 or ≤1, respectively (see Appendix S1, equation 24), at a seed density of 25 seeds m−2. To test this hypothesis, we re-analysed video data for the functional responses of chaffinches in bare soil and stubble treatments, published previously in Baker, Stillman & Bullock (2009), calculating the value of p. As there was no effect of treatment (bare soil or stubble) on p (lm, F1,205 = 2·114, P =0·148) we used the mean of the combined data (P =0·903) to calculate the feeding rate using model 2. We found that the feeding rates predicted using model 2 differed from that of model 1 at food density <25 seeds m−2, the lowest seed density used in this study, in bare soil treatment and <42 seeds m−2 in the stubble treatment (Fig. 6). This indicates that vigilance could affect the predicted functional response at low food densities in a forager with high vigilance, even when p is high.
We have developed a functional response model (model 2) that can account for the effect of vigilance on feeding rate when the proportion of time spent vigilant begins to exceed the proportion of handling time that is compatible with vigilance (Hc). When v =0 and p ≥0 the model predicts a response without vigilance (identical to the Holling’s disc model). When v ≥0 and p =0 the model predicts a functional response with mutually exclusive vigilance and handling. When v ≥0 and p =1 the model predicts a functional response with completely overlapping vigilance and handling. When parameterized using values for a, H, v and p for a granivorous bird, the grey partridge, measured under experimental conditions, the model indicated that vigilance should have an effect on the functional response, but only at very low food densities (<3 seeds m−2). However, simulations of the effect of vigilance on feeding rate at different seed densities show how the potential for vigilance to affect feeding rate (i.e. the values of p given v) increases as the proportion of time spent vigilant increases. To test this we parameterized model 2 for a species, the chaffinch, with a higher value of v and found that vigilance reduced feeding rates at higher food densities and had a larger effect in the stubble treatment.
These results show that when parameterized using observed behavioural parameters vigilance can have an effect on the functional response of a granivorous bird, especially at low food densities or in obstructed habitats where searching rates are lower. The proportion of time spent vigilant (v) measured for grey partridges in this study was lower than expected (Watson, Aebischer & Cresswell 2007), most likely caused by using intensively reared captive birds (Beani & Dessi-Fulgheri 1998), and consequently this mitigated the impact of the low Hc. Assuming that the other parameters will remain unchanged, the value of v (i.e. v = ∼0·4) observed in wild grey partridges (Watson, Aebischer & Cresswell 2007) would increase the effect of vigilance on the functional response. However, extrapolating these conclusions from captive grey partridge to wild birds is not productive given the uncertainty about the values for the remaining behavioural parameters in wild birds. The effect of vigilance on the functional response of wild chaffinches (Fig. 5) suggests that vigilance can be an important limiting factor in the functional response of wild birds and, therefore, is likely to impact on their foraging behaviour when food resources are low. The presence of crop stubble was predicted to increase the effect of vigilance on the functional response by reducing the searching rate. Although, this was found to have occurred in the chaffinch study no effect was found with the grey partridges, suggesting that the stubble did not sufficiently reduce the searching rate for an effect to be observed.
The impact of vigilance on a forager may not always manifest itself in reduced feeding rates as individuals could adjust other behaviours, i.e. through patch choice or joining a larger groups of foragers, in order to maximize their feeding rates and minimize their predation risk (Whittingham & Evans 2004; Jones, Krebs & Whittingham 2006; Beauchamp 2009). Butler et al. (2005b) showed that switching to a more obstructed patch only occurred once the ratio of the food densities between the two patches had exceeded a threshold, when the benefit of foraging in a more risky environment had exceeded the risk, i.e. increased feeding rate at the expense of vigilance. In experiments with no option of patch switching, as food density decreases, any effect of vigilance on foraging behaviour is likely to be displayed through a reduction in feeding rate, as reported here. We found no significant difference between the vigilance parameters in the two treatments; however, the stubble was primarily used to provide a physical obstruction to reduce the searching rate and, therefore, may not have been high enough to change the vigilance behaviour.
The relationship between food density and v found here shows that the birds were spending more time vigilant at low food densities, which is contrary to some previous studies on granivorous birds (Smart, Stillman & Norris 2008; Baker, Stillman & Bullock 2009), but predicted when foragers are time constrained (Beauchamp 2009). Although it is possible that the birds perceive the limited time available for foraging on the platform as a time constraint this is uncertain as they were accustomed to receiving ad libitum food outside of the experimental period. A more likely explanation is that the higher proportion of time spent vigilant at low densities is a consequence of the longer observed compatible handling times at these densities. These similar, but non-linear, negative correlations were found for all the handling time parameters and might have been missed in other studies that used higher food densities. The negative correlation between seed density and the Hx component of handling time was expected as this component includes the time taken to approach the target food item, which is negatively correlated with density. However, the negative correlation between seed density and Hc was not expected as we anticipated that the time take to process a food item would be independent of its density. It is possible that food is processed more carefully when it is less abundant as the scarcity of the resource makes its full exploitation more important. Furthermore, the birds could use some of this handling time to scan for other prey items. However, the corresponding increase in vigilance suggests the birds occupy this additional handling time with further vigilance.
Both models were able to predict the functional responses from observed behavioural parameters very successfully, and, despite the low R2 values, the models capture both the shape of the observed response and the asymptote. The low R2 values are a consequence of the large variability in the observed feeding rate, which is to be expected in a behavioural study, but are similar to those achieved for corn bunting foraging on wheat (Smart, Stillman & Norris 2008). From this study, it is not possible to determine how well model 2 captures the shape of the functional response once vigilance starts to limit the feeding rate as this point was always reached at or below the food densities measured in these experiments. This could be studied experimentally if the values of v and p could be manipulated so that the effect of vigilance could be observed at higher densities. Suggestions for achieving this might include: matching the background colour to the prey colour to make the prey less conspicuous; using uneven surfaces or a courser grained substrate; using larger foraging areas with lower food densities; using smaller prey items; and using dummy predators or predator calls.
Although model 2 was derived and tested around the foraging behaviour of granivorous birds its potential should be considered for all species that forage for discrete immobile prey items and have short handling times relative to the time spent vigilant. The assumptions of the model should not limit its utility to any particular taxonomic group, but more importantly the foraging behaviour of the subject should be considered before applying the model. Examples might include: grey squirrels Sciurus carolinensis foraging for seeds and nuts (Makowska & Kramer 2007) and samango monkeys Cercopithecus mitis erythrarchus foraging for fruit (Cowlishaw et al. 2004). The functional response model developed by Fortin et al. (2004) to describe the foraging cost of vigilance in mammalian grazers/browsers has broad similarities to model 2 presented here. However, functional response models for these forager types might not be directly applicable to granivorous foragers due to the behavioural adaptations of foragers to these food resources, i.e. the possibility of multiple bites from one resource (Spalinger & Hobbs 1992) and of cropping further bites whilst still handling (Fortin et al. 2004). These extra complexities mean that functional response models derived for grazers/browsers often include parameters that are unnecessary when applied to granivorous foragers (Spalinger & Hobbs 1992; Hobbs et al. 2003; Fortin et al. 2004).
Here we have shown that vigilance can affect the predicted functional response of a granivorous bird and have derived a new functional response model that can predict when such effects should be observed. Understanding the effects of vigilance on the functional response will be important if we are to fully understand the foraging decisions and patterns that are observed in the wild. For mechanistic models that use functional responses to link population level demographic processes to environmental parameters (Butler et al. 2010) the incorporation of vigilance may have significant consequences for predicting the distribution of foragers and patterns of resource depletion. Perceived differences in predation risk between patches is likely to cause some patches to be avoided when food is abundant resulting in an uneven depletion of resource across the landscape. Some patches will maintain higher densities of food that can be exploited, at higher predation risk, when resources elsewhere are exhausted. This model will provide a useful tool for exploring the implications of vigilance on larger scale ecological processes and for developing mechanistic models for conservation management.
We are especially grateful to Matt Ford and Chris Davies for looking after the birds throughout the experiment. We would like to thank Etienne Sirot and two anonymous referees for their comments on an earlier manuscript. D.J.B. was funded through a Natural Environment Research Council studentship grant.