1. Routine vigilance is an important component of foraging for many species and can occupy a large proportion of this time. Vigilance can conflict with some aspects of foraging (i.e. searching) and, consequently, has the potential to reduce feeding rates by interrupting foraging behaviours. However, for animals that handle food in an upright posture vigilance can be compatible with this portion of handling and, therefore, any vigilance during this time will incur minimal time-costs to foraging.
2. Several functional response models that incorporate vigilance have assumed that, (i) vigilance preferentially occurs during compatible portions of a foraging routine where no costs are incurred; and (ii) vigilance can be treated as a single discrete block of time related in frequency to the feeding rate, i.e. one vigilance scan per feeding event.
3. To determine whether these assumption are appropriate we measured the vigilance behaviour of four species of granivorous bird, yellowhammer, tree sparrow, linnet and grey partridge, and assessed the quantity of vigilance compared to compatible handling time, the relationship between scan rate and feeding rate and the distribution of vigilance during compatible and non-compatible portions of foraging.
4. The results show that there was frequently enough compatible handling time to accommodate routine vigilance, yet a high proportion of vigilance occurred during non-compatible components of foraging, thus incurring a time-cost. The frequency of vigilance bouts was higher than the feeding rate for three species and, therefore, routine vigilance was not just a by-product of the feeding rate (i.e. one scan per peck). Frequent head-down searching behaviour was recorded during handling suggesting that searching is still a prominent component of foraging even when prey is superabundant.
5. We have shown that the assumptions of previous functional response models might underestimate the effects of vigilance on feeding rate by overestimating the proportion of compatible handling devoted to vigilance. Future functional response models must account for this distribution of vigilance between compatible and non-compatible behavioural states. We derive an example of such a model; however, more experimental research will be needed before we understand the factors that influence the distribution of vigilance.
Several functional response models, i.e. those that predict feeding rate as a function of prey density, have incorporated the effects of routine vigilance and its interaction with handling time. Fortin et al. (2004b) derived a functional response model that demonstrated how ‘spare time’ can result from handling limitations when the encounter rate is faster than the rate of handling and that this ‘spare time’ could be allocated to vigilance. Here it was shown that vigilance often reduced the intake rate of grazing herbivores even when there was adequate time for cost-free vigilance during handling. Several functional response models have explicitly included vigilance as a parameter and have allowed the interaction between vigilance, handling and searching to vary in several ways (Smart, Stillman & Norris 2008; Baker et al. 2010). Smart, Stillman & Norris (2008) allowed the proportion of time spent vigilant to overlap with the total time spent handling and found that vigilance had no effect on the predicted feeding rate. Baker et al. (2010) divided handling time into two components, the head-down approach component that is incompatible with vigilance (Hx) and a head-up processing component that is compatible with vigilance (Hc). A functional response model was derived that allows vigilance to interact with only the Hc portion of prey handling and it was found that when allowing such an interaction vigilance affected the predicted feeding rate when prey density was very low, i.e. ratio of compatible handling to searching was high (Cowlishaw et al. 2004). Thus, the incorporation of vigilance into the functional response model has not predicted the large decreases in feeding rate that might be anticipated. This raises two questions: (i) does vigilance have a limiting effect on feeding rate in these species? and (ii) do these models realistically represent vigilance and its effect on feeding rate?
Such functional response models that have explicitly incorporated routine vigilance have treated vigilance as a discrete block of time (i.e. the proportion of time vigilant) [models 4 & 5 (Smart, Stillman & Norris 2008) and model 2 (Baker et al. 2010)], assuming that the effect of vigilance on feeding rate depends on whether the proportion of time vigilant is greater than the proportion of compatible handling time. Thus, two assumptions are made regarding the properties of vigilance: (i) that vigilance preferentially occurs during compatible portions of a foraging bout where no costs are incurred; and (ii) that vigilance can be treated as a single discrete block of time related in frequency to the feeding rate, i.e. one vigilance scan per prey consumed. Whether such simplifying assumptions are appropriate for these functional response models is questionable especially when considering the assumptions of classic vigilance models, i.e. random initiation of vigilance scans (Pulliam 1973; Bednekoff & Lima 1998). If the assumptions of the classic vigilance models are correct then vigilance scans could be initiated during any portion of a foraging bout with equal probability and, therefore, vigilance is likely to have a greater impact on the functional response than predicted by these functional response models. However, there are apparent differences between these classic vigilance models and the foraging behaviour of many granivorous foragers, most notably the tendency to handle prey in an upright posture. Thus, where the vigilance models assume head-down foraging interrupted by randomly induced head-up vigilance bouts these granivorous foragers tend to move sequentially into a head-up posture after making contact with a seed (i.e. non-random).
There is now considerable evidence to show that the assumptions of classic vigilance models considerably over simplify vigilance behaviour, especially in regards to the randomness of scan initiations (Bednekoff & Lima 1998; Beauchamp 2006; Pays et al. 2010) and the synchronization of vigilance scans between conspecifics (Pays et al. 2007a,b). This might suggest that the timing of vigilance scans and their duration is flexible enough to accommodate vigilance where the costs are lowest. Carrying out vigilance scans only during compatible portions of a foraging bout might not provide the optimum strategy for detecting an approaching predator and therefore a trade-off is likely between reducing the costs of routine vigilance and maximizing the feeding rate. Frequent short vigilance scans have been shown to increase the probability of detecting an approaching predator (Cresswell et al. 2003; Whittingham et al. 2004), but the proportion of time spent vigilant and the mean scan duration do not correlate strongly with predator detection. An increased scan rate appears to correlate with a higher instantaneous intake rate (Gluck 1987; Fritz, Guillemain & Durant 2002; Whittingham et al. 2004) although this is probably a consequence of higher foraging efficiency and not due to the vigilance frequency per se. Thus, the optimum strategy for detecting a predator might be frequent scans of short duration and this might conflict with the frequency and pattern of compatible handling time. Whether vigilance is an important and necessary component in functional response models is of interest because vigilance adds significant complexity to the functional response model. However, if functional response models can be developed that accurately incorporate the effects of vigilance then these models will be have great application to applied conservation issues where the functional response can be used to link resource density to feeding rate and ultimately individual survival (Stephens et al. 2003; Goss-Custard et al. 2006).
Here we aim to assess the assumptions of previous functional response models, specifically the interaction between vigilance and compatible handling time and the temporal distribution of vigilance throughout the foraging bout. We test: (i) the relationship between three measures of vigilance and food density; (ii) whether the amount of time spent vigilant for each peck exceeds the amount of compatible handling time (Hc) and, therefore, whether a time-cost is incurred; (iii) the relationship between the frequency of vigilance scans and the feeding rate to determine whether vigilance scans are a consequence of the feeding rate; and (iv) compare the proportion of time spent vigilant during Hc and non-Hc foraging time and, therefore, whether the assumption that vigilance occurs when its costs are minimized is correct. To address these questions we measured the functional response and the associated behavioural parameters [handling time (Ht (total = Hc + Hx), Hc & Hx), proportion of time vigilant, duration of vigilance scans, frequency of vigilance scans, vigilance during Hc, vigilance during non-Hc] of three species of European granivorous farmland bird (Fig. 1), yellowhammer Emberiza citronella L, tree sparrow Passer montanus L, and linnet Carduelis cannabina L. Additionally, we re-examine the data for grey partridge Perdix perdix L presented in Baker et al. (2010) with the expectation that the majority of vigilance here will occur during the compatible components of foraging as little effect of vigilance on the functional response was predicted by the functional response model in this study. We find that the data from these species do not entirely support the assumptions of previous functional response models incorporating vigilance, and so derive two new functional response models with more realistic assumptions. We discuss the implications of these results for functional response models and especially those that incorporate vigilance.
Materials and methods
Handling time and vigilance: definitions
Holling (1966) defined handling time as a function of the time spent: (i) pursuing and subduing each prey item; (ii) eating each prey item; and (iii) in ‘digestive pause’. Because we will be measuring the foraging behaviour over a short time interval and, therefore, the birds are not likely to be satiated during that time only the first two components of Holling’s definition are appropriate. In this study the first component of handling is termed Hx and can be considered the attack component (the x indicating incompatibility with vigilance). Hx is included as a part of handling because once an attack has begun the forager’s focus is on only a single prey item and thus it can be recorded as the time taken to capture a single prey. The second component is termed Hc and represents the processing and ingestion of each prey item (the c indicating compatibility with vigilance).
In this study we have tried to quantify the proportion of time a forager spends vigilant in order to predict the impact of this behaviour on the functional response. In order to do this we chose to define routine vigilance behaviour as the time spent with the head in an upright posture with the bill parallel to the ground or at a greater angle. However, this definition is largely taken for practical reasons because it is possible to observe and quantify this behaviour during video analysis. Whilst this posture is likely to signal routine vigilance, several studies have shown that predator detection still occurs in head-down postures, a position that has been defined here as non-vigilant. For example, Lima, Zollner & Bednekoff (1999) showed that dark-eyed juncos Junco hyemalis were still able to detect a simulated predator with their head-down, although over a shorter distance. Bednekoff & Lima (2005) found that these birds preferred to forage in a habitat where their visual field was not obstructed when in a head-down position. However, it is clear that head-up vigilance is the optimum posture for detecting predators as foragers tend to increase the amount of head-up scanning in response to higher predation risk or reduced detection potential (Elgar 1989; Whittingham et al. 2004). Therefore, head-up time is probably the best indicator of the perceived threat and is a good metric of the time-costs incurred by engaging in routine vigilance. The targets of routine vigilance might be either predators or conspecifics and it is possible that these different targets could induce different patterns of vigilance. However, granivorous foragers tend to have short handling times that offer little opportunity for kleptoparasitism or scrounging and thus the benefits of monitoring conspecifics are probably not as important as for many group foraging species [i.e. shorebirds (Stillman, Goss-Custard & Caldow 1997)].
Functional response data
Here we used data from three separate functional responses of three different granivorous bird species, yellowhammer, tree sparrow and linnet feeding on wheat, millet and rapeseed, respectively. In addition, we re-examined one functional response data set presented in Baker et al. (2010) for grey partridges foraging for wheat seeds on bare soil, extracting additional parameters where necessary.
Functional response and vigilance experiments
The functional response experiments were conducted as follows: the linnet (rapeseed) experiment was conducted at Woodborough Hill Farm, Wiltshire, England between the 1st and 3rd February 2006: the tree sparrow experiments were conducted at Easton Farm, Wiltshire, England between the 5th and 7th April 2006; and the yellowhammer (wheat) experiment was conducted at Stanton St Bernard Farm Wiltshire, England between the 22nd March 2006 and the 6th April 2006. The protocol of these experiments closely follows that of Smart, Stillman & Norris (2008) and, to a lesser extent, Baker, Stillman & Bullock (2009) but will be briefly summarized here. The functional response experiments were conducted on plywood and concrete feeding platforms measuring 1 m × 1·5 m and dyed and textured to mimic the surrounding soil. The birds were presented with different densities of scattered seeds (125, 250, 500, 1000, 2000, 3000, 4000 seeds m−2) in a random order and three replicates were carried out for each density. The experiments were conducted between 09:00 and 15:00 h and each replicate was filmed using a Canon 3CCD XL1 video camera (http://www.canon.co.uk) for at least 15 min from a distance of c. 30 m, filming along the length of the platform. Outside the periods of the experiment the platforms were covered and seed scattered on top to keep the birds attracted to the area.
Analysis of functional response & behavioural experiments
The video footage was downloaded onto a PC and analysed using a purpose-built event recorder. During the analysis we were careful to analyse sequences where large groups of birds were foraging on the feeding platforms simultaneously to avoid including the same individual more than once. These sequences were relatively easy to find here as the seed densities used were high and the birds quickly flocked to the platform. Where there were fewer than 15 birds foraging simultaneously on the platform all the birds that engaged in a foraging sequence of >5 pecks (uninterrupted by obviously induced vigilance bouts) were recorded. Where >15 birds were feeding simultaneously on the feeding platform focal individuals were randomly selected from those individuals that engaged in foraging sequences >5 pecks on a previously unused portion of the platform (to exclude significant depletion effects). The feeding rate was measured from the frame before the bird made contact with the first seed until the frame before the bird made contact with the last seed for a minimum of five pecks. Because we are interested in measuring the instantaneous feeding rate, which excludes the digestive processes associated with the long-term feeding rate, sequences were terminated after a maximum of eight pecks.
Vigilance was defined as time spent with the head positioned so that the bill is parallel to the ground, or at a greater angle. The proportion of time spent vigilance was defined as the proportion of the recorded foraging bout in which the bird was vigilant. The duration of vigilance bouts is the mean duration of all vigilance bouts within a single foraging sequence. The frequency of vigilance is the number of times the head was raised into a vigilant position during the foraging sequence. The time spent vigilance per peck was calculated from the total amount of vigilance during a foraging sequence divided by the number of pecks. The number of individuals feeding within the immediate vicinity of the platform (an area of c. 2 m2) was recorded at each vigilance scan. This represented the core of the flock which can become defuse at the edges and is therefore difficult to define absolutely. The attack portion of handling time (Hx) was measured from the frame at which the bird began moving decisively towards the target prey until the frame before contact was made with the prey item.
The compatible portion of handling time (Hc) was measured from the frame at which the bird made contact with the seed until the frame at which the bird stopped manipulating the seed in its bill. This distinction was chosen because it marks the transition to a state in which the head can be raised without losing the functionality of processing. Once the seed has been seized vigilance can occur without affecting handling whereas prior to this moment any vigilance will decrease the feeding rate. The amount of vigilance that occurred during Hc was recorded and subtracted from the total amount of vigilance during the foraging sequence, which yielded the amount of vigilance during non-compatible foraging activities: these were converted into proportions.
Here we define the end of Hc based on bill movement and consequently assume that handling subsequent to the cessation of bill movement is negligible (i.e. swallowing). This assumption is often made in handling time studies and here we make this assumption based on several lines of evidence. Firstly, using additional data (DJB unpublished) of yellowhammers feeding on millet seeds (length c. 3 mm) we found that the mean time between the end of Hc (cessation of bill movement) and the beginning of the next Hx (attack phase) was not significantly different between yellowhammers feeding on wheat (length c. 6 mm) or millet (t-test, t98 = −0·776, P =0·440). If further processing occurs after manipulation in the bill and before the beginning of the next attack we would expect this to take longer with the substantially larger wheat seeds and this suggests that further processing time is negligible. Furthermore, Zweers (1982) showed using live X-ray imaging that the time taken to pass food into the pharyngeal cavity was very rapid in pigeons Columba livia L and that multiple food items could be consumed before a bottleneck was reached in the pharynx.
To compare the proportion of time vigilant, duration of vigilance and frequency of vigilance to food density we fitted linear mixed-models. The most likely model based on Akaike Information Criterion was a random intercept model with trial as a random factor. For the grey partridge experiment, where each individual bird was individually identifiable, Bird_ID was included as a random factor. Group-size was initially included as an explanatory variable in each model and removed when not significant. The residuals were checked for normality and heteroscedacity to determine whether a transformation was required. Only the duration of vigilance showed a non-normal distribution of the residuals and this was corrected with a log transformation of this response variable (for all three species). The time spent vigilant per peck and Hc per peck were compared by fitting linear mixed-effects model, as above, testing the significance of the intercept = 0 and slope = 1. An identical approach was taken for the relationship between the frequency of vigilance bouts and the feeding rate. The amount of vigilance during Hc and non-Hc was compared using a paired t-test for each species separately. All statistical analysis was completed using R 2·10·0. (R Development Core Team 2009) and the nlme package (Pinheiro et al. 2009).
Food density and vigilance
Feeding rate for each of the three species showed no significant correlation with seed density: yellowhammer (b = 0·00001, t12 = 0·264, P =0·797); tree sparrow (b =0·000001, t13 = 0·456, P =0·656); linnet (b = −0·00002, t12 = −0·528, P =0·607), where b is the slope of the regression model. The proportion of time spent vigilant was not correlated with seed density for yellowhammer (Fig. 2a) (b = 0·0000003, t12 = −0·022, P =0·983), tree sparrow (Fig. 2b) (b =0·00002, t13 = 1·09, P =0·296) and linnet (Fig. 2c) (b =0·00003, t12=1·178, P =0·262). There was no effect of seed density on the frequency of vigilance [yellowhammer (b =0·00003, t12=1·182, P =0·26); tree sparrow (b =0·00003, t13=1·248, P =0·234); linnet (b =0·00004, t12=1·042, P =0·318)] or the natural log transformed duration of vigilance [yellowhammer (b = −0·00006, t12=−1·422, P =0·18); tree sparrow (b = 0·00002, t13=0·707, P =0·492); linnet (b =0·00001, t12=0·471, P =0·646)]. Table 1 shows the mean and 95% confidence intervals for the three measurements of vigilance for all species.
Table 1. The mean (± 95% confidence intervals) estimate of three measures of vigilance for each of the three species of granivorous passerine included in this study. There was no significant effect of prey density on each of these behavioural parameters and therefore this data was pooled to estimate the overall mean
Proportion time vigilant
Frequency of vigilance scans
Duration of vigilance scans
Can routine vigilance be accommodated during Hc?
We compared the mean time spent vigilant (s) for each peck during an individual foraging sequence with the mean Hc (s) for the same foraging sequence to determine whether routine vigilance could be accommodated into the compatible portion of handling (Hc) subsequent to each peck. Table 2 shows the results for the linear regression of time spent vigilant against Hc testing for the intercept=0 and the slope=1. For yellowhammer (Fig. 3a) the intercept was significantly different from zero suggesting that the time spent vigilant was consistently greater than the amount of Hc. Both tree sparrow (Fig. 3b) and grey partridge (Fig. 3d) spent significantly less time vigilant per peck than the amount of Hc: for grey partridge these results are consistent with Baker et al. (2010). The linnets (Fig. 3c) spent more time vigilant per peck than Hc when the duration of Hc was short, however, this difference decreased as the amount of Hc per peck increased until vigilance was shorter than Hc for Hc values over 1 s per peck.
Table 2. The linear regression coefficients and significance tests of the intercept=0 and the slope=1 for the mean time spent vigilant and the mean compatible handling time (Hc). There was no effect of food density on vigilance across the densities used in this analysis so the data was pooled
Intercept = 0
Slope = 1
Intercept = 0
Slope = 1
Intercept = 0
Slope = 1
Intercept = 0
Slope = 1
How is routine vigilance distributed during foraging?
Although it often appears that time spent vigilant is approximately the same or less than the Hc portion of handling it does not necessarily follow that this vigilance is distributed entirely within Hc. Figure 4 and Table 3 shows that the frequency of vigilance scans is often higher than the feeding rate and therefore multiple vigilance scans occur for each feeding event (i.e. a single peck). For yellowhammer, tree sparrow and linnet the frequency of vigilance scans tends to be greater than the feeding rate, although for the latter two this effect diminishes as the feeding rate increases. For grey partridge the frequency of vigilance is consistently lower than the feeding rate suggesting multiple pecks between vigilance scans. Here the frequency of scans appears to be consistent regardless of the feeding rate.
Table 3. The linear regression coefficients and significance tests of the intercept=0 and the slope=1 for the frequency of vigilance against feeding rate. There was no effect of food density on vigilance across the densities used in this analysis so the data was pooled
Intercept = 0
Slope = 1
Intercept = 0
Slope = 1
Intercept = 0
Slope = 1
Intercept = 0
Slope = 1
The proportion of vigilance during compatible and non-compatible components of foraging (Fig. 5) were not significantly different for yellowhammer (paired t-test, t59=0·693, P =0·491) and linnet (paired t-test, t92=−1·884, P = 0·063), but was significantly greater in the compatible component (Hc) for tree sparrow (paired t-test, t82=6·978, P <0·001) and the incompatible component (non-Hc) for grey partridge (paired t-test, t127=−18·498, P < 0·001). Figure 6 shows the proportion of Hc spent in a head-down posture, characterized as searching behaviour, for each of the four data sets and it can be seen that for three of the species (tree sparrow, linnet and grey partridge) greater than 50% of Hc is spent searching.
A functional response model with uniformly distributed vigilance
Based on the results of this analysis showing that vigilance is consistently distributed between compatible handling time and non-compatible searching time we have derived two simple functional response models that includes vigilance, allow this vigilance overlap with the Hc component of handling only and distribute vigilance uniformly between compatible handling and non-compatible searching (see Appendix S1, Supporting information, for derivation).
where F is the feeding rate (preys−1), a is the searching rate (m2 s−1), D is the prey density (prey m−2), Hx is the incompatible handling time (s), Hc is the compatible handling time (s) and v the proportion of time spent vigilant. By assuming that compatible and incompatible handling times are a fixed proportion of the total handling time a further simplified model can be derived
where Ht is the total handling time (prey s−1), and P the the proportion of handling time that is compatible with vigilance. Model 2 might be generally more applicable due to its simplicity, but model 1 will be important where the Hx and Hc components vary with prey density (Baker et al. 2010) and such variation can be incorporated directly into model 1.
Figure 7 shows how the predictions of models 1 and 2 (which here produce identical predictions) differ from the Holling’s disc model (Holling 1959) when parameterized using behavioural parameters representative of the passerines used in this study (i.e. c. 40% of time spent vigilant, c. 4 : 1 ratio of Hc : Hx (unpublished data – although varies with species and prey) and a searching rate of 0·03 m2 s−1 [i.e. Baker, Stillman & Bullock 2009)]. Allowing vigilance to be distributed uniformly between compatible handling time and incompatible searching time causes a lower estimate of feeding rate compared to the predictions of the Holling’s disc model (parameterized similarly) and the vigilance model from Baker et al. (2010) This latter model predicts a similar fit to the disc model except at very low densities and is not shown in Fig. 7 as the differences are not discernable on the graph at this scale.
The results of this study showed that the time spent vigilant per peck was consistently less than the compatible (Hc) component of handling for the tree sparrow and grey partridge, greater than Hc for linnet and yellowhammer. For linnet the time spent vigilant was on average greater than the Hc component of handling when Hc was low, suggesting compatible handling time was often of insufficient duration to accommodate the required vigilance. For the tree sparrow and grey partridge these results suggest that the negative consequences of routine vigilance could be avoided by accomplishing vigilance during the compatible component of foraging. However, for all species a high proportion of this vigilance occurs subsequent to food handling (Fig. 5) and, therefore, incurs a time-cost even though there is adequate time available to accommodate vigilance with little cost.
There was considerable time spent in a head-down posture (i.e. not fully vigilant) for all species observed here and it is this activity that appears to displace vigilance from the compatible portion of foraging to an incompatible portion (Fig. 6). Additionally, multiple scans per peck were observed for three species (Fig. 4) suggesting that head-up vigilance was conflicting with head-down behaviour, possibly searching. However, at asymptotic feeding rates searching time is expected to tend to zero as prey is superabundant so it appears surprising that handling is interrupted with any head-down behaviour. This head-down time could be interpreted as selective-searching behaviour, i.e. choosing the best morsel of food (Greig-Smith & Crocker 1984), and there is some evidence that increased choice can reduce the rate of decision making in foraging animals (Hutchinson 2005). For grey partridge the majority of vigilance appears to occur during non-compatible portions of the foraging bout, which might be due to short Hc times resulting from their ability to swallow seed whole, using their gizzard to crush the seed after ingestion (Hrabar & Perrin 2002): grey partridge spent c. 95% of Hc in a head-down searching posture. A head-down posture may also allow for the monitoring of conspecifics for possible scrounging opportunities or to avoid aggressive interactions. However, such behaviours are more likely to be important when food resources are limited and their distribution is clumped, thus increasing the potential reward for time spent observing other foragers rather than searching.
The observed pattern and distribution of vigilance might be due to a trade-off between vigilance and selective-searching that still maximizes intake rate by reducing time wasted on unsatisfactory food items. It is unlikely that the short-term feeding rate of these species are constrained by digestive limits as each individual increases its predation risk by foraging in the open and should try to minimize its time spent in a high predation risk environment (Bednekoff & Houston 1994; Brown 1999). This can be achieved by maximizing the feeding rate whilst on the foraging patch (Lima 1985) and retreating to cover when time-costs allow (Lima & Valone 1986; Valone & Lima 1987). Whilst it would still be optimal to be vigilant only during Hc and search only once handling had ended, frequent short scans appear to increase the probability of detecting an approaching predator (Cresswell et al. 2003) and could help optimize foraging behaviour towards the rapidly changing demands of the local environment (i.e. competition from conspecifics) and, therefore, might provide a benefit over a single scan. Fritz, Guillemain & Durant (2002) found that the instantaneous intake rate was reduced less when vigilance was divided into frequent short scans rather than a single scan of the same cumulative duration. The optimum routine for searching, compatible handling and vigilance could be explored further in simulation models and would be expected to vary considerably depending on the predation risk and food availability (i.e. Bednekoff & Houston 1994).
There was no relationship between any of the vigilance measures and seed density despite some previous expectation of a trend (Smart, Stillman & Norris 2008; Beauchamp 2009; Baker et al. 2010). However, Beauchamp (2009) suggests that there is unlikely to be a significant correlation between vigilance and food density when the functional response is flat, as they were here. Group-size has been shown to have a negative correlation with vigilance, usually attributed to the ‘many eyes’ hypothesis (Pulliam 1973; Powell 1974) or the dilution effect hypothesis (Roberts 1996) and this has the potential to confound the results of vigilance studies where group-size varies. However, we found no effect of group-size on any of the measures of vigilance, which might be because the group sizes were fairly constant throughout the experiments. There has been much discussion of the reverse effect, where food density would confound the results of experiments on the effect of group-size on vigilance, i.e. both feeding rates and group-size might increase with prey density and are expected to have opposing effects on vigilance, thus cancelling out any observed effect (Elgar 1989; Beauchamp 2009). However, the results here suggest that the potential for any confounding effect are minimal where the foragers are feeding at their asymptotic rate. The lack of a relationship between seed density and feeding rate is likely to be because the seed densities were not low enough. As shown by the grey partridge data presented here the feeding rates only show a significant decline at quite low prey densities and this is largely a consequence of the easy foraging scenario presented in these experiments. In wild conditions food items are likely to be more difficult to find (i.e. partially buried) and the decrease in feeding rates would occur at higher densities; however, these conditions are difficult to replicate consistently in experimental conditions.
These results suggest that current functional response models that include vigilance are over simplifying the relationship between vigilance, handling and searching. It appears that searching is still an important component at high densities, at least in some circumstances (Fig. 6), and there has been no attempt to incorporate this additional searching parameter into these models. This appears to be important because additional searching displaces some of the vigilance from Hc into non-compatible components of foraging and thus incurs time-costs. To-date functional response models with vigilance assume that feeding rate will be maximized and do not consider the optimum pattern and distribution of vigilance. In most conditions animals are not foraging under time-constraints (Wolf, Hainsworth & Gill 1975; Bednekoff & Lima 1994; Ronconi & Burger 2008), even though they may want to reduce the time spent on open ground, and there will be a trade-off between feeding rate and vigilance (Brown 1999; Inger et al. 2006; Aubret, Bonnet & Bradshaw 2007). Future functional response models need to account for this additional head-down to time during Hc and assume that some vigilance will occur during non-compatible foraging. Here, we derived two such models that assume a uniform distribution of vigilance between Hc and searching and showed the effect on the predicted feeding rate (Fig. 7). An approach such as this might predict observed functional responses more accurately than previous models that assume vigilance occurs preferentially during compatible handling time.
The effectiveness and utility of mechanistic functional response models lies in their simplicity and we must be careful not to incorporate more complexity than is necessary (Cox et al. 2006). Whether routine vigilance is a necessary component of the functional response models for these species is still open to debate because routine vigilance can always be reduced in response to time constraints (Brown 1999). To address these questions we require empirical studies of long-term feeding rates when foragers are experiencing time constrains to understand how these constraints affect vigilance and whether vigilance is necessary to predict feeding rates in the most critical circumstances, i.e. when starvation risk is high. However, vigilance can have an effect on foraging behaviour when prey is plentiful as predation risk, and consequently vigilance, can affect the spatial distribution of foragers as they try to optimize the trade-off between feeding rate and predation risk (Whittingham & Evans 2004; Duriez & Ferrand 2005; Cresswell 2008). Functional response models that include vigilance might provide a useful tool to explore such effects.
We would like to thank the landowners for allowing access to their farms for the behavioural experiments. The comments of two anonymous referees helped improve an earlier draft of this manuscript and were greatly appreciated. DJB was funded by a Natural Environment Research Council (NERC) studentship grant.