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Keywords:

  • agricultural change;
  • functional response;
  • foraging behaviour

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
  • 1
    Many farmland bird species have undergone significant declines. It is important to predict the effect of agricultural change on these birds and their response to conservation measures. This requirement could be met by mechanistic models that predict population size from the optimal foraging behaviour and fates of individuals within populations. A key component of these models is the functional response, the relationship between food and competitor density and feeding rate.
  • 2
    This paper describes a method for measuring functional responses of farmland birds, and applies this method to a declining farmland bird, the corn bunting Miliaria calandra L. We derive five alternative models to predict the functional responses of farmland birds and parameterize these for corn bunting. We also assess the minimum sample sizes required to predict accurately the functional response.
  • 3
    We show that the functional response of corn bunting can be predicted accurately from a few behavioural parameters (searching rate, handling time, vigilance time) that are straightforward to measure in the field. These parameters can be measured more quickly than the alternative of measuring the functional response directly.
  • 4
    While corn bunting violated some of the assumptions of Holling's disk equation (model 1 in our study), it still provided the most accurate fit to the observed feeding rates while remaining the most statistically simple model tested. Our other models may be more applicable to other species, or corn bunting feeding in other locations.
  • 5
    Although further tests are required, our study shows how functional responses can be predicted, simplifying the development of mechanistic models of farmland bird populations.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Many species of bird associated with farmland have undergone significant declines during the last 30 years (Fuller et al. 1995; Siriwardena et al. 1998; Gregory, Noble & Custance 2004). In large part, this is thought to be due to a decline in food resulting from changes in agricultural practices (Robinson & Sutherland 2002; Newton 2004). It is important to predict the effect of future agricultural change on farmland bird populations and to predict their response to conservation measures. This requirement could be met by mechanistic models that predict population size from the optimal foraging behaviour and fates of individuals within populations (Bradbury, Payne & Wilson 2001).

Mechanistic models have been applied to a range of wading birds and wildfowl (Stillman et al. 2001, 2005; Caldow et al. 2004; Durell et al. 2005), but only one mechanistic model has been developed for farmland birds (Robinson 2003). Robinson (2003) developed a spatial depletion model of seed-eating birds feeding on stubbles, to predict accurately the distribution of birds between habitats and the number of bird days supported. This example shows how mechanistic models could predict and quantify how farmland bird populations may respond to changes in farming practices (Bradbury et al. 2001; Stephens et al. 2003).

A key component of these models is the functional response, the relationship between food and competitor density and feeding rate. It is essential to know the shape of the functional response in order to understand or predict the effect of food shortage on a predator population. While several functional responses have been measured for wading birds (Goss-Custard et al. 2006; Gill, Sutherland & Norris 2001; Gillings et al. 2006), very few have been measured for farmland birds (Kenward & Sibly 1977; Cresswell 1997; Stephens et al. 2003; Stillman & Simmons 2006). These functional responses must be measured, or predicted, in order to ensure that the mechanistic models predict realistically the effect of food shortage on farmland bird populations.

However, farmland birds forage in vegetated habitats, such as weedy stubbles, which makes it very difficult to observe feeding behaviour in the natural environment. Another difficulty of measuring functional responses in the field is that most animals congregate in areas of higher food density, but in order to predict the effects of food shortage it is the response of animals feeding at low food abundance which is most important. Either an experimental system has to be designed in which birds can be observed feeding at a range of food densities or the functional response has to be predicted from behavioural parameters using an appropriate mathematical model (Stillman & Simmons 2006).

The purpose of this paper is to: (i) describe a method for measuring functional responses of farmland birds; (ii) use this method to measure the functional response of a declining farmland bird, the corn bunting Miliaria calandra L.; (iii) derive alternative models to predict the functional responses of farmland birds; (iv) parameterize these models for corn bunting, by measuring behavioural parameters directly, to determine which model predicts the functional response most accurately; and (v) assess the minimum sample sizes for behavioural parameters required to predict the functional response accurately.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

study area

The study site was near Marden (latitude/longitude: 51°31′ N/1°88′ W), on the edge of Salisbury Plain, UK, on an area of set-aside. This region supports intensive arable farming in a landscape with large open arable fields and very few hedgerows. Corn bunting were observed regularly feeding on set-aside and overwintered stubbles surrounding the experimental site. Conservation projects already running in the area had shown that corn bunting would feed readily on patches of seed. Waste grain tailings, supplied by a local farmer, were used to bait the experimental patch (approximately 1 m × 1 m) at the site. These tailings contained small cereal grains and a variety of weed seeds. Grain was replenished at least twice a week to maintain a constant supply.

study species

The UK population of corn buntings fell by 85% between 1970 and 1998 (British Trust for Ornithology; http://www.bto.org.uk). This decline has been attributed to increased rates of adult mortality and evidence suggests that this has been caused by declines in winter food availability brought about by changes in agricultural practices (Donald 1997; Siriwardena et al. 2007).

Corn bunting were chosen as the study species because of their conservation status and because previous work has shown that they could be attracted to an area by providing a concentrated seed source. They were found regularly at the study site in a flock of between 30 and 60 individuals and would return quickly, within 10 min, following disturbance.

experimental platforms

Experiments were run on a purpose-built platform set flush with the surrounding soil. The platform was constructed from a plywood base, covered with a 20-mm thick layer of concrete. This was dyed and textured to produce a substrate which simulated the surrounding soil in appearance and texture. Soil was not used as the experimental substrate because early investigations found that seed left at the end of an experiment could not be removed successfully without removing the substrate itself (using a hand-brush and/or hand-held vacuum). This made it difficult to conduct repeat experiments and caused more disturbance to the birds due to increased time spent at the platform. The concrete substrate enabled seed to be removed quickly, reducing disturbance to the birds, and meant that experiments could be repeated more easily and quickly. The platforms measured 1 m × 1·5 m and the birds were observed within in a central area of the platform 0·5 m × 1 m marked by wooden pegs in the corners. Birds were fed on the platform for 8 weeks before the experiments to enable the birds to become accustomed to feeding on the platforms and to build up numbers in the area.

Corn bunting were presented with seven densities of wheat seed, 125, 250, 500, 1000, 2000, 3000 and 4000 seeds m−2. We did not measure seed densities in the field in which the experimental platform was located, but our range of densities covered the range of weed seed densities (266–860 m−2) found commonly on stubble fields, an important feeding habitat for granivorous farmland birds (Moorcroft et al. 2002). Seed densities of more than 500 seeds m−2 were measured by weight. Seeds were also counted separately for the central area and the boundary area, outside the pegs. This ensured that the seed density within the central area was accurate. Three replicates were performed at each density. Each replicate was filmed for at least 15 min, after which the remaining seed was removed using a hand-held vacuum (Black & Decker version 9·6 Dustbuster; http://www.blackanddecker.com) and replaced with fresh seed for the following experiment. Corn bunting returned to the feeding platforms quickly (usually within 5 min) after the seed had been spread on the platform. As we did not mark our study population individually, we do not know the composition of birds in our experiments or the extent to which replicate experiments attracted the same or different individuals. After the final afternoon experiment, the platforms were covered with a wool-based black garden membrane on top of which grain tailings would be spread. This kept birds attracted to the site throughout the experimental period. When resuming experiments the grain tailings could be removed with the membrane, which kept the platform clean for the following experiments. Experiments were undertaken between February and April 2006 in dry weather conditions between 09·00 and 15·00 h. This gave birds time to feed undisturbed before and after experiments. Experiments were ordered randomly.

Experiments were recorded using a video camera (Canon 3CCD XL1; http://www.canon.com) from a distance of approximately 30 m. The platforms were viewed along their length, with the camera zoom lens adjusted so that the field of view encompassed the 0·5 m width of the central area. This field of view was used because preliminary trials showed that this was the maximum for which the birds’ mandibular movements (used to measure handling time) could be observed.

video analysis

Video of the experiments was downloaded onto a computer and analysed using a purpose-built event recording program, which was used to record different behavioural activities and the position of birds on the platform.

For each experiment, up to 10 birds were selected randomly from the beginning of the experiment to minimize effect of depletion and their behaviour recorded for 30 s, or until they left the platform (minimum 10 s). The potential proportional depletion of seeds at the lowest seed densities was high, but in practice relatively few birds were attracted to these areas, and those that were attracted did not always feed for 30 s. Therefore, we did not take account of potential depletion when analysing our results. The numbers of birds within the experimental arena was recorded every 10 s. For each of the selected birds, feeding rate (seeds consumed s−1), handling time, proportion of time spent vigilant and time spent searching was recorded over the time taken to consume five seeds. Birds fed by pecking a seed from the substrate and then manipulating the seed in their bill before breaking it down and consuming it. This process could be observed for each bird, making it possible to measure feeding rate directly. Handling time was measured as the time taken from pecking for a seed to the time at which mandibular movements ceased. Vigilance time was measured as the time spent in a head-up position, while searching was measured as the time spent with head and/or body tilted down. Corn bunting showed an obvious change in behaviour when they detected a seed, so seed detection distance could be measured from their location when identifying and starting to move towards an individual seed to their location when reaching and pecking at the seed. Detection distance was measured only for birds travelling across the screen using the central pegs as points of reference. Birds not travelling directly across the screen were discounted because of potential errors in measuring accurately the distance travelled. Searching speed was measured at the two lowest seed densities (250 and 125 seeds per m2) from birds travelling across the screen and was calculated as the distance between the point of the previous peck to the point at which they appeared to detect the next seed, divided by the time to travel this distance. Searching speed was measured only at the lowest two seed densities because birds seldom needed to move between two seed captures at higher seed densities, and so searching speed could not be calculated. All distances were estimated by comparison of the screen distance moved by a bird with the screen distance between the pegs at the front and rear of the platform (known to be 0·5 m apart). Searching rate (a) was calculated as by Stillman & Simmons (2006):

  • A = 2 ds,(eqn 1)

where s = searching speed (ms−1) and d = searching distance (m). Searching distance is the maximum distance over which a bird can detect a seed, and so was measured from maximum detection distance. The 2 in this equation accounts for the fact that searching distance was measured in only one direction, but birds can detect seeds both to their left and right.

functional response models

We derived five equations (see Appendices S1–S5 in Supplementary material; Table 1) to describe the shape of the functional response. Model 1 is simply the Holling disk equation (Holling 1965). The remaining models accounted for the fact that some of the assumptions of the disk equation were not met by corn buntings. Model 2 adds vigilance and assumes that vigilance is independent of searching and handling; corn bunting spent some time vigilant, with their heads up, while neither searching nor handling. Model 3 assumes that searching and handling can occur concurrently (when handling occurs head-down) and does not include vigilance; corn bunting were observed frequently handling food while in a head-down, searching position. Model 4 assumes that vigilance and handling can occur concurrently (both head-up), but that searching occurs independently; corn bunting could handle food while being vigilant, as both these behaviours could occur in a head-up position. Model 5 assumes that handling and vigilance (head-up), and handling and searching (when handling is head-down) can occur concurrently, but that searching (head-down) and vigilance (head-up) are independent.

Table 1.  Alternative functional response equations derived in Appendices S1–S5 (see Supplementary material). F = feeding rate (food items s−1), D = food density (food items m−2), a = searching rate (m2 s−1), H = handling time (s per food item), v = proportion of time spent vigilant
ModelAssumptionsFunctional response
1Mutually exclusive searching and handling No vigilanceinline image
2Mutually exclusive searching, handling and vigilanceinline image
3Concurrent searching and handling No vigilanceinline image
4Mutually exclusive searching Concurrent handling and vigilanceinline image
5Concurrent searching, handling and vigilanceinline image

comparing alternative functional response models

We assessed the alternative models by comparing their abilities at describing and predicting the observed functional response. Descriptive ability was measured using non-linear regression (sas; http://www.sas.com) to fit a model to the observed functional response by calculating best-fitting parameter values (searching rate, handling time, proportion of time vigilant). Predictive ability was measured using a model to predict the functional response based on parameter values measured directly from the experiments. Akaike's information criterion (AIC) was used to quantify the goodness-of-fit of each model to the observed data, taking into account the number of parameters in a model.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

shape of the functional response

Feeding rate increased at a decelerating rate with increased seed density (Fig. 1). For seed densities of between 125 seeds m−2 and 1000 seeds m−2 feeding rate was related positively to food density (linear regression, feeding rate = 0·323 + 0·000116 seed density, n = 65, P = 0·019). For higher seed densities, between 2000 seeds m−2 and 4000 seeds m−2, feeding rate was unrelated to seed density (linear regression, feeding rate = 0·543–0·000004 seed density, n = 81, P = 0·829).

image

Figure 1.  Observed relationship between feeding rate and seed density. The solid circles show the mean observed feeding rate for each seed density (with associated standard deviation). The two lines show the relationship between feeding rate and seed density within the range of seed densities 125 seeds m−2 to 1000 seeds m−2 and 2000 seeds m−2 to 4000 seeds m−2. See text for regression equations which were fitted to the raw data.

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To test whether interference competition was influencing feeding rate, we used multiple regression incorporating the effects of both competitor and seed density on feeding rate. Corn bunting density did not effect feeding rate significantly at either low or high seed densities (low seed density, n = 65, P = 0·459; high seed density, n = 81, P = 0·333), so we concluded that interference competition was insignificant in the experiments.

To test whether time of day was influencing feeding rate, we used multiple regression incorporating the effects of both the time of day at which an experiment was conducted and seed density on feeding rate. Time of day did not affect feeding rate significantly at either low or high seed densities (low seed density, P = 0·630, high seed density P = 0·064).

behavioural parameters

Handling time declined significantly with increasing seed density, but the regression explained only 4·5% of the variation (handling time = 2·06–0·000132 seed density, R2 = 4·5, n = 137, P = 0·013) (Fig. 2a). The proportion of time vigilant did not vary significantly with seed density (proportion of time vigilant = 0·364 + 0·000013 seed density, n = 137, P = 0·101) (Fig. 2b). Detection distance also declined significantly with increasing seed density (detection distance = 0·0337 – seed density 0·000005, n = 377, P = 0·000) (Fig. 2c). Searching distance (equation 1) is calculated from maximum detection distance, so we calculated searching distance (0·075 m) as the 95th percentile detection distance measured in the two lowest seed densities (250 and 125 seeds m−2). We used the 95th percentile rather than the absolute maximum to exclude unusually long detection distances. Searching speed was calculated at the lowest two seed densities as 0·029 ms−1.

image

Figure 2. Observed relationships between (a) handling time, (b) proportion of time spent vigilant and (c) detection distance and seed density. The solid circles show the mean observed value for each seed density (with associated standard deviation). The dashed line in (c) denotes the 95th percentile detection distance for seed densities of 100 and 250 m−2, used to estimate searching distance. See text for regression equations which were fitted to the raw data.

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describing the functional response

Table 2 and Fig. 3 show the fit of each functional response model to the observed data and the best-fitting parameter values.

Table 2.  Comparison of fitted and observed searching efficiency (a) and handling time (H). Models 2, 4 and 5 also included the proportion of time spent vigilant (v), which was set to its observed value, as a fitted value could not derived. Sample size = 146 feeding rate observations; SE: standard error
Modela (± SE)H (± SE)v
10·00415 (0·000922)1·85 (0·0640) 
20·0068 (0·00151)1·13 (0·0390)0·39
30·00266 (0·000350)2·09 (0·0571) 
40·00415 (0·000922)1·85 (0·0640)0·39
50·00264 (0·000288)2·04 (0·0565)0·39
Observed0·00431·780·39
image

Figure 3. Fit of each functional response model to the observed relationship between feeding rate and seed density. The solid circles show the mean observed feeding rate for each seed density (with associated standard deviation). See Table 2 for best-fitting parameter estimates for each model, which were derived from the raw data.

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Significant fits could be obtained only for models 1 and 4, both of which excluded vigilance. The non-linear regression could not calculate best-fitting values for the proportion of time spent vigilant, implying that the observed functional response was not dependent upon vigilance time. In order to fit these models, we set the proportion of time vigilant to the observed value (0·39) and then estimated best-fitting values of searching rate and handling time using non-linear regression. Significant fits were then obtained for all models.

Model 1, Holling's disk equation, had the best goodness-of-fit to the observed feeding rate (lowest AIC) (Table 3). Furthermore, the fitted searching efficiencies and handling times of model 1 were not significantly different from the observed values (searching efficiency P = 0·858, handling time P = 0·395), evidence that the maximum feeding rate at high food densities is limited by handling time, an assumption of equation 1. However, one of the assumptions of Holling's disk equation is that searching and handling is mutually exclusive, and during experiments birds were observed searching and handling at the same time.

Table 3.  Comparison of Akaike's information criterion (AIC) index and R2 for models using fitted functional response. Sample size = 146 feeding rate observations
 Model 1Model 2Model 3Model 4Model 5
No. of parameters23233
AIC–3·93–3·91–3·77–3·91–3·77
R221·121·17·721·18·8
Adjusted R220·019·56·419·56·8

Model 2 is a derivation of model 1 but includes mutually exclusive vigilance. While both fitted models generated the same relationship between feeding rate and seed density (Fig. 3), the goodness-of-fit of model 2 was slightly poorer as it contained one extra parameter (vigilance) (Table 3). Model 3, which was a derivation of the vigilance-free functional response (model 1) but with concurrent searching and handling, had a poorer goodness-of-fit than model 1 (Table 3). Model 4 included mutually exclusive searching and concurrent handling and vigilance. The fitted model 4 generated virtually the same relationship between feeding rate and seed density as model 1, but had a slightly poorer goodness-of-fit as it included an extra parameter (vigilance) (Table 3). While model 5 provides the most biologically accurate model with concurrent searching, handling and vigilance (observed birds exhibited this concurrent behaviour), it had the poorest goodness-of-fit (Table 3). We concluded that, on statistical grounds, model 1 provided the best fit to the data with the minimum of parameters.

predicting the functional response

The previous section examined how well each model described the functional response when its parameters were estimated by fitting the model statistically to the data. The alternative approach is to measure each parameter directly in the field, and then use these values to predict the functional response.

The functional response was predicted from direct measurements (observations) of searching speed, food detection distance, handling time and proportion of time vigilant (Table 4; Fig. 4). Model 1 had the best goodness-of-fit to the data (Table 4). Model 4 had the second-best goodness-of-fit, predicting the same relationship between feeding rate and seed density as model 1, but using one extra parameter (Table 4). Both these models predicted functional responses very similar to their best-fitting functional responses (Fig. 3), and in neither model did predicted and fitted functional responses differ by more than 0·01 seeds s−1. In comparison with models 1 and 4, the remaining models had poor goodness-of-fit to the data (Table 4); models 3 and 5 over-estimated feeding rates below 2000 seeds m−2, whereas model 2 under-predicted feeding rate across the entire range of seed densities.

Table 4.  Comparison of Akaike's information criterion (AIC) index and R2 for models using predicted functional response. R2 could not be calculated for models 2, 3 and 5 because these models consistently overestimated or underestimated feeding rate. Sample size = 146 feeding rate observations
 Model 1Model 2Model 3Model 4Model 5Model 1 with variable handling
No. of parameters232333
AIC–3·91–2·97–3·40–3·90–3·51–3·83
R219·7  19·7 14·3
Adjusted R218·6  18·0 12·5
image

Figure 4. Relationships between feeding rate and seed density predicted by each functional response model from directly observed values of searching efficiency, handling time and vigilance time. The solid circles show the mean observed feeding rate for each seed density (with associated standard deviation). See Table 2 for observed parameter values.

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The previous predictions assumed that handling time did not vary with seed density, but handling time was observed to be related negatively to seed density (Fig. 2a). To test the influence of variable handling time, we developed an extension of model 1 in which handling time was the observed function of seed density. However, incorporating variable handling time, and hence increasing the number of parameters, decreased the model's goodness-of-fit (Table 4, Fig. 5). This poorer fit was due to the predicted functional response, with variable handling time over-predicting feeding rate at higher seed densities (2000–4000 seeds m−2), and containing an extra parameter. We concluded that the model with a constant handling time provided the best fit to the data.

image

Figure 5. Relationships between feeding rate and seed density predicted by model 1 when handling time is either assumed to be constant or related to seed density. The solid circles show the mean observed feeding rate for each seed density (with associated standard deviation). See text and Fig. 2a for relationship between handling time and seed density.

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number of parameter replicates required

We used bootstrap resampling to derive the relationships between sample size and the accuracy of measuring handling time, vigilance time, detection distance and searching speed. To do this, n samples were drawn at random from the observed data for one behavioural parameter and the mean value of the behavioural parameter calculated. Samples were not removed from the set of samples after being selected randomly, so could be sampled more than once within the sample of n (i.e. we used sampling with replacement). This was repeated 1000 times to generate a frequency distribution of means derived from a sample size of n, from which the mean, 5th and 95th percentiles were calculated. Even though accuracy continued to increase with increased sample size, the analysis showed that the best compromise between accuracy and effort occurred between 15 and 50 repeat measurements of the main behavioural parameters. This compares to the 150 repeat measurements which we used to build the functional response models.

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

This paper shows that the functional response of a declining farmland bird can be predicted accurately from a few behavioural parameters: searching speed, food detection distance and handling time. These parameters can be measured more quickly than the alternative of measuring the functional response directly.

The functional responses and behaviour of other farmland birds could be measured using our methodology, as well as the effects of variables such as seed size and type. The platform substrate was modified to mimic the colour and topography of the surrounding soil while allowing for repeatable experiments with limited disturbance to the birds between experiments. The ‘substrate’ could also be modified to examine the effects of habitat structure, such as the effect of stubble height on feeding rate (Butler, Bradbury & Whittingham 2005). Our experiment does not mimic situations in which seeds are buried, partially covered or still attached to plants, and so further studies are required to determine functional responses under these conditions.

Errors would have occurred in measuring detection distance if behaviour was less clear or if we had assessed incorrectly when a corn bunting detected food. However, corn bunting showed a clear change in behaviour when moving towards food, so detection distance could be measured. It is likely that detection distance could be measured similarly for other declining farmland birds. It may not always be as easy to measure distances travelled as in the present study, but a range of techniques are available, such as correlating distance travelled with time, counting paces or measuring distance travelled across a video screen (Poole, Stillman & Norris 2006). As in this study, it may be necessary to feed birds low densities of seed, as birds may make only very small or no movements in areas of high food density.

The functional response of corn bunting consuming wheat has been measured previously (Robinson 1997), with an estimated handling time (2·0 s) very similar to this study, but a lower estimated searching rate (0·0007 m2 s−1). Differences in the visibility and availability of wheat on the experimental substrate may explain the difference between these searching rates. Further studies measuring functional responses on a range of substrate types are required to test these hypotheses.

Interference did not influence feeding rate in our experiments, but in systems in which it does occur (e.g. Dolman 1995) it can reduce feeding rate at high competitor density. This is more likely to occur where food is highly aggregated (Johnson, Grant & Giraldeau 2004; Vahl et al. 2005), handling time is long (Stillman et al. 2002a) and prey is mobile (Yates, Stillman & Goss-Custard 2000). When interference competition is significant it is important to incorporate it into the functional response. The strength of interference can also be predicted from behavioural parameters (Stillman et al. 2002b).

Handling time declined significantly at higher seed densities. This may be because at high seed densities birds spend less time manipulating and breaking down individual seeds, as there is a plentiful supply of other seeds. At low seed density they may increase handling time to break down the seeds and increase digestibility to maximize energy gain per seed, as there are fewer seeds available. However, the magnitude of the change in handling time was relatively small, and incorporating the observed variation in handling time into a functional response model did not improve the fit to the observed data.

Handling time limited feeding rate in this study, but this is not always the case (Goss-Custard et al. 2006). Feeding rate may be limited by gut processing rate (Jeschke, Kopp & Tollrian 2002), perceptual constraints (Goss-Custard et al. 2006) or changes in prey selection (Stillman & Simmons 2006). In this study, a possible reason for handling time limiting feeding rate may be that corn bunting visited experiments only to feed. While not feeding, birds flew to nearby cover. It is likely that the birds minimized the amount of time feeding on the ground (exposed to predation), flying back to cover before they became satiated. This is in contrast to wading birds, which do not have a functional response limited by handling time (Goss-Custard et al. 2006), possibly because these species remain on the ground not only while feeding but also while performing other activities (e.g. resting to digest food). This implies that other farmland birds species (e.g. tree sparrow Passer montanus L., yellowhammer Emberiza citrinella L. and cirl bunting Emberiza cirlus L.) that minimize time away from cover may be expected to have a functional response limited by handling time. However, grey partridge Perdix perdix L., an open farmland species, which remains on the ground whether feeding or performing other activities, may be more similar to waders and have a functional response that is not limited by handling time.

This study shows that while corn bunting broke some of the assumptions of Holling's disk equation (model 1), it still provided the most accurate fit to the observed feeding rates while remaining the most statistically simple model tested. The differences in goodness-of-fit between alternative models were sometimes very small, being determined largely by the number of parameters in models. One reason for this is that many of the models had equivalent fits to the data for seed densities over 1000 m−2, and differed only in a minor way at lower seed densities. Model 4 had an equivalent fit to model 1, but was rejected as a poorer model on statistical grounds because it contained an extra parameter for vigilance. However, vigilance can sometimes occupy much more time than in our experiments, and so it may be argued that on biological grounds model 4 is the most appropriate model. For example, in situations where birds experience a high perceived predation risk, a resultant increase in vigilance time may affect the proportion of time available for foraging and hence affect feeding rates (Lima & Bednekoff 1999; Stillman & Simmons 2006). In systems where the proportion of time spent vigilant limits time available for searching, model 4 should be used. The alternative models provided a relatively poor fit to the corn bunting functional response, but may describe the functional responses of other farmland birds more effectively.

Our models assumed that birds attempted to spend a constant proportion of the time vigilant, irrespective of other factors. However, vigilance time may also depend on factors such as flock size, distance from cover, location within a flock and the time for which a patch has been occupied. These factors were not included for simplicity, but their importance could be investigated by measuring functional responses over a range of environmental conditions likely to influence vigilance behaviour.

In order to predict the effect of food shortage on the survival of seed-feeding birds, feeding rate at low seed densities must be measured or predicted. A limitation to achieving this with wild birds is that birds will tend to avoid areas (e.g. feeding platforms) containing very low seed densities. In the present study, the lowest density at which corn bunting would feed on the platform was 125 seeds m−2. However, the results of the present study can still be used to predict feeding rate at lower seed densities because these will fall between the rate measured at 125 seeds m−2, and a feeding rate of 0 seeds s−1 that will occur at a density of 0 seeds m−2. Feeding rates at low seed densities can also be predicted from the observed handling time and searching rate, assuming that these parameters do not change greatly at these seed densities.

This study develops the methods used in Stillman & Simmons (2006) and shows that the functional response of a declining farmland bird can be predicted accurately from a few behavioural parameters. These parameters, searching speed, food detection distance and handling time, can be measured more quickly than the alternative of measuring the functional response directly. The advantage of this technique is that it potentially requires fewer observations from birds feeding in a smaller range of food densities. This approach could be used to develop functional responses for a range of declining farmland birds in a range of situations. These functional responses could be used to develop mechanistic models to predict how possible changes in farming practice, driven by new agricultural policies, affect farmland bird populations. Before this can be achieved further studies are required to determine how food type, habitat structure, substrate type and bird species influence functional responses, and how applicable are functional responses derived under experimental conditions to natural field conditions.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

We would like to thank all landowners for allowing us access on to their farms, especially Tim Carson and John Stradling. We are very grateful to Andy West for providing the bootstrap resampling program, and to two anonymous referees for providing valuable comments on the manuscript. The work in this paper was funded by the Natural Environment Research Council.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Appendix S1. Derivation of vigilance-free functional response with mutually exclusive searching and handling (model 1).

Appendix S2. Derivation of functional response with mutually exclusive searching, handling and vigilance (model 2).

Appendix S3. Derivation of vigilance-free functional response with concurrent searching and handling (model 3).

Appendix S4. Derivation of functional response with mutually exclusive searching and concurrent handling and vigilance (model 4).

Appendix S5. Derivation of functional response with concurrent searching, handling and vigilance (model 5).

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