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Keywords:

  • depletion model;
  • granivorous passerines;
  • habitat quality;
  • Monte Carlo;
  • over-winter stubble;
  • resource availability;
  • seed survival

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

1.  Reductions in resource availability, associated with land-use change and agricultural intensification in the UK and Europe, have been linked with the widespread decline of many farmland bird species over recent decades. However, the underlying ecological processes which link resource availability and population trends are poorly understood.

2.  We construct a spatial depletion model to investigate the relationship between the population persistence of granivorous birds within the agricultural landscape and the temporal dynamics of stubble field availability, an important source of winter food for many of those species.

3.  The model is capable of accurately predicting the distribution of a given number of finches and buntings amongst patches of different stubble types in an agricultural landscape over the course of a winter and assessing the relative value of different landscapes in terms of resource availability.

4.  Sensitivity analyses showed that the model is relatively robust to estimates of energetic requirements, search efficiency and handling time but that daily seed survival estimates have a strong influence on model fit. Understanding resource dynamics in agricultural landscapes is highlighted as a key area for further research.

5.  There was a positive relationship between the predicted number of bird days supported by a landscape over-winter and the breeding population trend for yellowhammer Emberiza citrinella, a species for which survival has been identified as the primary driver of population dynamics, but not for linnet Carduelis cannabina, a species for which productivity has been identified as the primary driver of population dynamics.

6.Synthesis and applications. We believe this model can be used to guide the effective delivery of over-winter food resources under agri-environment schemes and to assess the impacts on granivorous birds of changing resource availability associated with novel changes in land use. This could be very important in the future as farming adapts to an increasingly dynamic trading environment, in which demands for increased agricultural production must be reconciled with objectives for environmental protection, including biodiversity conservation.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

Patterns of agricultural land use determine the spatial and temporal distribution of key resources, such as nest sites and food supplies, for farmland biodiversity. Changes in land use, whether policy-driven or for socio-economic reasons, can therefore influence demographic rates and population dynamics through consequent changes in resource availability and exploitation. For example, increased annual mortality, linked to the loss of seed-rich habitats such as over-wintered stubble, has been identified as the key demographic mechanism behind the significant and widespread declines of many farmland bird species (Siriwardena et al. 2000).

Despite the importance of the link between resource availability, its exploitation and population trends in agricultural landscapes, surprisingly little is known about these ecological processes in farmland birds. Recent studies have shown that increasing the availability of winter food supplies can increase survival and local abundance (Peach et al. 2001; Hole et al. 2002) and, to some extent, can influence breeding population trends (Siriwardena et al. 2007). However, key questions remain over the necessary levels of resource provision required, both spatially and temporally, to deliver population-level responses. Answers to these questions are particularly needed to inform the design and delivery of effective agri-environment schemes, the main policy tool by which the UK Government will deliver its Public Service Agreement target of reversing the long-term decline in farmland bird populations by 2020.

Spatial depletion modelling, based on optimal foraging theory, provides a method for understanding the mechanistic links between land use, food resources and bird distribution patterns (Stephens et al. 2003). In the approach’s simplest form, depletion of resources caused by the foraging population is assumed to drive changes in their distribution (Sutherland & Anderson 1993) but both resource input (Sutherland & Allport 1994) and other causes of depletion (Percival, Sutherland & Evans 1996) during the modelling period can also be incorporated. Depletion modelling has been successfully used to predict the distribution of birds over a variety of spatial scales in estuarine and grassland systems (e.g. Sutherland & Allport 1994; Percival et al. 1996; Gill, Sutherland & Norris 2001). However, whilst the potential value of this approach in linking field-scale management with landscape-scale consequences for farmland bird populations is clear, it has rarely been applied to agri-environmental issues involving granivorous birds.

Here, we construct a spatial depletion model to investigate the impacts of stubble field and resource dynamics on the distribution and population persistence of granivorous birds in agricultural landscapes. Stubble fields are considered as ephemeral food patches whose availability is dictated by the timing of harvest and the resumption of cultivation, and whose quality (in terms of food resources) is dictated by the crop type grown and associated management. We investigate how temporal changes in resource availability influence the number of bird days a landscape can support and link this to observed breeding population trends.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

Model structure

We defined a model arable landscape consisting of 100 patches, each representing a field, in a 10 × 10 array. Five types of stubble, linseed, oilseed rape, sugar beet, barley and wheat were included in the landscape. Management characteristics for each field, including harvest date, life span, the number of herbicides applied to the preceding crop and whether or not the crop was sprayed with pre-harvest desiccant, were included as input into the model. These data were derived from a field study carried out on 20 farms located throughout and adjacent to the Norfolk Brecklands, UK (Robinson 2003). Stubble life span represented the number of days between harvest and the field being ploughed, reflecting the length of time each field was available as foraging habitat. Outside this time period, it was assumed that fields effectively had a resource density of zero and were not suitable foraging habitat for seed-eaters. The model ran for a non-breeding period of 224 days, corresponding with the time between the harvesting of the first arable fields in mid-July (day 1 = 19th July) and the start of spring (day 224 = 28th February).

The dynamics of four seed types, cereal seeds (represented by barley Hordeum vulgare L.), oilseed rape seeds (Brassica napus L.), linseeds (Linum usitatissimum L.) and weed seeds (represented by knotgrass Polygonum aviculare L.), within fields in the landscape were modelled. All are important potential food resources for farmland birds (Wilson et al. 1999). Initial crop and weed seed densities present in each stubble field immediately after harvest were allocated by randomly sampling with replacement from the distribution of values in the appropriate crop type recorded from a sample of fields in Breckland, UK (Table A1 in Supporting information Appendix S1). Subsequent resource dynamics were driven by additional resource input, via weed seed rain, and resource depletion, via avian and non-avian predation, germination and decomposition. Levels of weed seed rain were estimated based on multiple regression models of data collected from the Breckland field study that included the number of chemical used on the crop, harvest date and whether or not a field was sprayed with broad spectrum herbicide before harvest as predictor variables (see Appendix S1, Supporting information for details).

The model was coded to calculate prey depletion by two model bird ‘ecotypes’ defined on the basis of dietary preferences. The first represented large buntings, which preferentially forage on cereal seeds but also feed on arable weed seeds. The second represented Cardueline finches which avoid cereal seeds but feed on oilseeds and arable weed seeds. Yellowhammers Emberiza citrinella L. and linnets Carduelis cannabina L. were used as respective model species for the two ecotypes. Energy intake rates on each field at each time step were estimated using a modified version of Holling’s disc equation (Holling 1959):

  • image(eqn 1)

where E/T = energy intake rate, ei = energy content (j) of seed type i, = search efficiency (s m−2) for seed type i, = density (m−2) of seed type i and = handling time (s) of seed type i. Seed mass and energy content details were taken from the ECOFLORA data base (Fitter & Peat 1994) and Diaz (1990). Yellowhammers foraging on cereal fields and linnets foraging on linseed and oilseed rape fields were faced with a choice of alternative prey items with differing profitability. Optimal foraging theory states that individuals consume the most profitable prey item to maximize their energy gain until the most profitable food becomes scarce, at which point they forage unselectively (Charnov 1976). Threshold densities, at which it becomes optimal to forage unselectively, were calculated as the density of seeds at which the energy intake rate when selectively foraging on the crop seed fell below the energy intake rate when foraging unselectively on both crop and weed seeds. Using baseline parameters (see below), this was calculated as 0·53 crop seeds m−2 for yellowhammers on foraging on cereal fields and as 1·59 and 2·38 crop seeds m−2 for linnets foraging on linseed and oilseed rape fields respectively. Threshold values were recalculated when search efficiency and handling times were altered as part of the sensitivity analyses.

At the start of each day, a specified number of birds were introduced into the model landscape, regardless of whether they had survived the previous day (see below). Potential energy intakes were calculated for each available field and birds were allocated to the field where their energy intake rate was maximized. If more than one field met this criterion birds were evenly distributed between them. A field was considered unavailable if the maximum achievable energy intake rate was insufficient to meet the daily energy requirements of a single bird. Seed depletion due to birds was calculated as the product of the rate of energy intake and the number of birds occupying the field. The model calculated seed depletion and potential energy intake rates on an hourly basis and birds were re-distributed each hour accordingly. Seed rain and seed depletion due to other sources were simulated on a daily basis. Model output represented the total number of birds using each crop type in the last hour of each day. For the population to persist to the end of a given day there had to be sufficient resources available within the landscape for all birds to realize their daily energy requirements so the model output was used to calculate the number of bird days a landscape could support. It is important to note that resource availability within the landscape could increase from one day to the next if, for example, levels of weed seed rain outweighed levels of seed depletion or if additional fields became available due to crop harvesting. A specified number of birds were introduced to the model landscape each day, regardless of whether the population had persisted to the end of the previous day, to account for these potential increases in resource availability. If the population had failed to persist on the previous day and resource availability had not increased, there would still be insufficient food in the landscape to support the population and model output for the final hour of the day would again be zero. However, if levels of seed rain or changes in stubble area meant that sufficient resources were available for all birds to realize their daily energy requirements, the population would persist through the day and this would be reflected in the model output. An overview of the model is shown in Fig. 1 and the full Matlab model code (http://www.MathWorks.com) is provided in Supporting information Appendix S2.

image

Figure 1.  Flow diagram showing the structure of the mechanistic model.

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Parameter estimation

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

Foraging rates, seed depletion and population persistence were strongly influenced by four parameters in the model but the confidence with which these parameters could be estimated varied considerably.

  • 1
    The daily energy requirement of individual free-living yellowhammers and linnets could be estimated with reasonable confidence using allometric relationships based on body size (Walsberg 1983).
  • 2
    The specific handling times of birds feeding on the four seed types included in our model were not known but linear regression analysis, based on reported handling times for a range of passerine species feeding on different seed types (Holmes 2002; Stephens et al. 2003) and including seed length, bird body mass and a bill shape index (bill length/bill depth) as predictor variables, was used to estimate them with some degree of confidence (see Appendix S1, Supporting information for details).
  • 3
    The estimated search efficiencies of passerines feeding on seeds are highly variable, both within and between species. We used the mean search efficiency of passerines feeding on seeds reported in Holmes (2002) and Stephens et al. (2003) for both bird ecotypes feeding on all seed types (see Appendix S1, Supporting information for details) but only low levels of confidence could be associated with this estimate.
  • 4
    Daily survival rates for weed and crop seeds in arable landscapes are poorly understood. To identify the most appropriate baseline seed survival parameter values, we incorporated a calibration exercise into the model validation (see below). We assumed that daily survival rates for each seed type would lie between 0·85 and 1·0 (Holmes 2002) and explored all combinations of survival rates within this range to determine which resulted in the best model fit. We assumed that the survival probability was constant in space and time. All other parameter values were held constant for this calibration (see Table 1).
Table 1.   Parameter estimates used for model validation and sensitivity analyses. Linnets were used to represent the Cardueline finch ecotype and yellowhammers to represent the large bunting ecotype
ParameterBaseline estimateRange explored
Both ecotypes
 Search efficiency (m2 s−1)0·07020·00702–0·702
 Daily seed survival probability  
  Oilseed rape0·930·85–1·0
  Linseed0·930·85–1·0
  Cereal seed0·990·85–1·0
  Polygonum aviculare0·950·85–1·0
Linnet ecotype
 Daily energy requirement (kJ)77·54−50% to +50%
 Handling time (s)  
  Oilseed rape3·07−20% to +20%
  Linseed6·91−20% to +20%
  Polygonum aviculare5·99−20% to +20%
Yellowhammer ecotype
 Daily energy requirement (kJ)103·25−50% to +50%
 Handling time (s)  
  Cereal7·26−20% to +20%
  Polygonum aviculare3·53−20% to +20%

Model validation and sensitivity analyses

We constructed a model arable landscape using data on land use and management collected during the 2000/2001 and 2001/2002 winters from 168 stubble fields on 20 farms located throughout and adjacent to Breckland, UK, covering an approximate landscape area of 100 000 ha (Robinson 2003). Each patch in the 10 × 10 array was assigned crop and management characteristics equivalent to those of a surveyed field, maintaining the relative proportions of stubble types observed. The average field area was 10·7 ha and the total stubble area modelled was 1124 ha. This comprised 118·3 ha linseed, 301·1 ha oilseed rape, 163·8 ha sugar beet, 240·7 ha barley and 300·1 ha wheat. The specified number of birds introduced into the landscape each day was altered every 2 weeks according to the total number of yellowhammers and Cardueline finches (linnet, greenfinch Carduelis chloris L., goldfinch Carduelis carduelis L.) counted on two-weekly surveys undertaken across the 20 study farms between July 2000 and February 2001 (see Appendix S1, Supporting information for details). The bunting ecotype potentially represents both yellowhammer and corn bunting Miliaria calandra L. but no corn buntings were recorded on our surveys. Whilst the model is largely deterministic, initial weed and crop seed densities were randomly allocated to fields by sampling with replacement from the range of appropriate values so25 iterations of every simulation were completed. Variation between iterations was low so we present only the average daily number of birds on each stubble type within each two weekly period across iterations throughout the paper.

As detailed above, we first used this landscape to derive optimal seed survival estimates. Oilseed (i.e. both oilseed rape and linseed), cereal seed and weed seed survival rates were varied in combination and the impact on model fit was assessed by comparing observed and predicted bird numbers on each stubble type. For each ecotype, we calculated the proportion of available birds that were incorrectly allocated over the course of the model period and the optimal set of survival estimates was selected as the combination that resulted in the lowest average misclassification rate across the two ecotypes. The best model fit was achieved with daily survival rates of 0·93, 0·99 and 0·95 for oilseeds, cereal seeds and weed seeds respectively and these were subsequently used as baseline parameter estimates (Table 1). We compared log-transformed observed and predicted bird numbers on each stubble type at two-weekly intervals over the winter using correlation analysis and checked for systematic bias in predictions using paired t-tests. Log-transformed data were used to reduce bias due to heteroscedasticity, i.e. where absolute deviations are larger in more highly used crop types.

Monte Carlo sensitivity analyses were then carried out to investigate the effect that variation in key parameter values had on model predictions and to critically examine the robustness of predictions. As above, the modelled Breckland landscape was populated with the total number of yellowhammers and Cardueline finches counted on each two-weekly survey but this time parameter estimates for daily energetic requirements, handling time, search efficiency and seed survival were each randomly sampled from a range of possible values (Table 1) over 1000 model simulation runs. The proportion of misclassified birds in each ecotype was calculated for each model run and Generalised Linear Models, specifying a quasibinomial error structure and logit link (Crawley 2007), were used to explore the influence of each parameter on model fit.

Linking population persistence over winter with breeding population trends

To provide population relevance to the model output, we explored the model’s capacity to characterize landscape quality in terms of population persistence and link over-winter resource availability with observed breeding population trends. These analyses were based on resource availability and population trends in the 525 1 × 1 km squares covered by the Breeding Bird Survey (BBS) and Winter Farmland Bird Survey (WFBS). From these, we identified every square that had at least three BBS records of yellowhammer and/or linnet between 1994 and 2007 and had a complete survey record from the WFBS, three visits in each of the winters of 1999/2000, 2000/2001 and 2002/2003 (Gillings et al. 2008). First, we used General Linear Mixed Models to analyse BBS count data to estimate yellowhammer and linnet trends in each of these squares between 1994 and 2007. We then constructed three model landscapes for each square, one for each winter, using WFBS habitat data to define stubble field dynamics based on the availability of linseed, oilseed rape, sugar beet, barley and wheat stubbles recorded on each visit (see Supporting Information Appendix S3). The crop and stubble management characteristics assigned to each crop were based on data collected from the Breckland region and used in the model validation process above. We populated each landscape with 100 individuals of each ecotype, this density of birds was considered high enough to allow discrimination between landscapes in terms of resource availability and population persistence without being so high that resource availability in any landscape was insufficient for populations to persist. We completed 25 iterations of each simulation and calculated the average daily number of birds on each stubble type within each two-weekly period across iterations and winters for each square.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

Validation and sensitivity analyses

The observed distribution of buntings and finches between crop types and that predicted by the model when baseline parameter values were set are shown in Fig. 2. Very few yellowhammers were recorded on linseed or sugar beet stubbles in the field study (linseed: maximum count = 4, total counted = 6; sugar beet: maximum count = 2, total counted = 7) and the model predicted zero use by the bunting ecotype (Fig. 2a,c respectively). Comparison of log-transformed observed and predicted yellowhammer numbers generated highly significant correlation coefficients of 0·73, 0·91 and 0·64 for oilseed rape, barley and wheat stubbles respectively (< 0·01 in all cases) and there was no significant bias in predicted levels of use according to paired t-tests (oilseed rape: = 0·12; barley: = 0·1; wheat: = 0·27). The number of linnets observed using wheat stubbles over the season was relatively low and the model predicted zero use (see Fig. 2j). Comparison of log-transformed observed and predicted linnet numbers gave correlation coefficients of 0·65 (< 0·01) for linseed, 0·79 (< 0·01) for oilseed rape, 0·77 (< 0·01) for beet and 0·21 (> 0·3) for barley stubbles. Paired t-tests on log-transformed data showed no significant bias in the use of linseed (= 0·37), sugar beet (= 0·7) or barley stubbles (= 0·87). The use of oilseed rape stubbles by linnets over the course of the winter was significantly under predicted (= 0·04).

image

Figure 2.  Comparison of observed (closed circles) and predicted (open squares) bird numbers in difference stubble types for each 2-week period: yellowhammers – (a) linseed, (b) oilseed rape, (c) sugar beet, (d) barley, (e) wheat; Cardueline finches – (f) linseed, (g) oilseed rape, (h) sugar beet, (i) barley, (j) wheat. Dashed lines show temporal variation in stubble area availability (ha) for each crop type.

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The sensitivity analyses showed that the distribution of both yellowhammers and linnets between stubble types was strongly influenced by daily seed survival estimates but model predictions appeared robust to variation in parameter values for energetic requirements, search efficiency and handling time (Table 2). For the yellowhammer ecotype, model fit was dictated by the specified daily survival rate of cereal seeds and weed seeds whilst for the linnet ecotype, it was dictated by the specified daily survival rate of oilseeds and weed seeds.

Table 2.   Results of General Linear Models, specifying quasibinomial error structure and logit link function, exploring the influence of parameter estimates on misclassification rates for yellowhammer and linnet ecotypes. Parameter estimates were each randomly sampled from a range of possible values (Table 1) over 1000 model simulation runs
EcotypeParametertP
Yellowhammer(Intercept)−12·89<0·001
Cereal seed survival12·52<0·001
Oilseed survival1·390·16
Weed seed survival9·68<0·001
Search efficiency0·060·95
Handling time−0·740·46
Daily energetic requirements−0·740·46
Linnet(Intercept)12·74<0·001
Cereal seed survival0·990·32
Oilseed survival−19·33<0·001
Weed seed survival−3·45<0·001
Search efficiency1·490·14
Handling time0·610·54
Daily energetic requirements1·050·29

Linking population persistence over winter with breeding population trends

The model predicted that as resource availability, calculated as the average area of stubbles recorded across visits and winters within a square, increased so the total number of bird days supported over-winter, averaged across the three landscapes defined for each square, also increased (yellowhammer ecotype: = 0·78, N = 150, < 0·001; linnet ecotype: = 0·68, N = 163, < 0·001). There was also a significant positive relationship between the predicted number of yellowhammer days supported over-winter and yellowhammer breeding population trends (F1,150 = 8·78, < 0·005). However, there was no such relationship between the predicted number of linnet days supported over-winter and linnet breeding population trends (F1,150 = 2·12, > 0·15). To assess whether temporal variation in over-winter resource availability was important in driving breeding population trends, we grouped squares according to whether they had a declining or stable/increasing population trend and compared the predicted number of bird days for each 2-week period over the winter for each group (Fig. 3). The predicted total number of yellowhammer days supported by squares with stable/increasing yellowhammer populations was significantly higher than that predicted for squares with declining populations (= 2·23, d.f. = 148, < 0·03). Furthermore, the predicted number of yellowhammer days supported by squares with stable/increasing populations was higher than that predicted for squares with declining populations for every 2-week period of the winter, significantly so in 5 of the 15 periods (Fig. 3a). There was no significant relationship between the predicted number of linnet days supported by squares with stable/increasing breeding populations and that predicted for squares with declining populations over the winter (> 0·4) nor for any 2-week interval (> 0·12 in all cases, Fig. 3b).

image

Figure 3.  Average number (±1 SE) of (a) yellowhammer and (b) linnet bird days supported by squares with either declining (dashed line) or stable/increasing (solid line) breeding population trends for each 2-week period over winter. Significant differences between the predicted number of bird days in squares with stable/increasing population trends and those with declining population trends in a given 2-week period are highlighted (t-test, *< 0·05, **< 0·01).

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

Our resource depletion model appears capable of predicting both the spatial and temporal distribution of finches and buntings amongst patches of different stubble types in an agricultural landscape. This suggests that the model captures the key drivers of foraging decisions and can be used to assess the relative value of stubbles as foraging resources. The model also appears capable of assessing the relative value of different landscapes for granivorous birds. For both the yellowhammer and linnet ecotype, increasing resource availability in a landscape increased the predicted number of bird days it could support. There was a significant positive relationship between the predicted total number of bird days supported during the non-breeding season and observed breeding population trends for yellowhammers but not for linnets.

The difference in the relationship between predicted bird days supported over-winter and breeding population trends for yellowhammers and linnets reflects the differences in the reported drivers of the population declines both species have experienced over recent decades. Demographic models of population trends suggest that changes in survival are sufficient to explain the decline in yellowhammer populations (Siriwardena et al. 2000), with the loss of over-winter food resources linked to reduced survival (Siriwardena, Calbrade & Vickery 2008). All things being equal, we would therefore expect population trends to be more positive in squares where resource availability is higher and, consequently, the probability of survival likely to be greater. Indeed, WFBS data have previously been used to show that yellowhammer trends are less negative in squares with more cereal stubble available, with approximate stability being achieved when the average area of cereal stubble over three winters is more than 15 ha (Gillings et al. 2005). This is supported by our results; we show that the predicted number of bird days supported by a landscape increases with resource availability and that observed breeding population trends are higher in squares predicted to support a higher number of bird days over-winter. This suggests that the predicted number of bird days supported by a landscape is positively related with survival probability. In contrast, demographic models suggest that changes in productivity are sufficient to explain the decline in linnet populations (Siriwardena et al. 2000). Therefore, whilst we would also expect the predicted number of days supported by a landscape to increase with increasing resource availability, we would not expect predicted number of bird days to be related to linnet breeding population trends because over-winter survival is not currently the key determinant of the population trajectory.

Interestingly, our results suggest that food availability in early/mid-winter might be an important determinant of over-winter survival and breeding population trend. Whilst the predicted number of bird days was higher in squares with stable/increasing population trends than in squares with declining population trends throughout the winter, the difference was only significant in September and October (Fig. 3). The mechanisms underlying this result are unclear; it may represent a direct cause-and-effect relationship linked, for example, to differences in achievable body condition and consequences for survival, or be indicative of differences in the quality of stubbles that survive to the end of the winter or the dynamics of stubble availability after the third visit. This result requires further exploration as it is in contrast to other studies which have proposed that late winter food resources are the critical determinant of over-winter survival and breeding population trends for many seed-eating passerines, including yellowhammers (Siriwardena et al. 2008).

Our model is based on relatively simple ecological theory and makes a number of simplifying assumptions when describing underlying ecological processes, resource availability and dispersion rules. These assumptions are broadly associated with either foraging behaviour or habitat management and highlight key areas for further research. We discuss the likely consequences of these assumptions for model predictions below.

Foraging assumptions

Although we used linnets, yellowhammers and Polygonum aviculare as model species, our ecotypes and the food resources they exploit in the model represent a range of different bird and arable weed species. Furthermore, barley seeds were used to represent both barley and wheat seeds in the model whereas, in reality, the energy content and handling time of wheat and barley seeds are likely to differ (Perkins, Anderson & Wilson 2007). Our model also assumes that stubble fields are the only source of winter food for granivorous birds. However, other types and sources of food, such as game feed, wild bird covers and recently sown fields, are likely to exist in the agricultural landscape for at least some of the period modelled and to make some contribution to ensuring population persistence over-winter (e.g. Brickle & Harper 2000). We acknowledge that our simulations of the BBS/WFBS data are unlikely to reflect the true carrying capacity of the landscapes in early autumn; the increase in predicted number of bird days supported in early autumn (Fig. 3) simply mirrors the increasing availability of stubble fields as crops are harvested. However, we are confident that the predicted declines in the number of bird days supported by landscapes later in the winter reflect true declines in carrying capacity driven by the loss of winter food resources, driven in turn by the temporal dynamics of stubble field availability and a decline in the availability of other seed sources (Siriwardena et al. 2008).

The model also assumes that birds have perfect knowledge of patch quality throughout the landscape, that they can assimilate the full energetic content of any seeds they eat and that they will continue foraging even after their daily energetic requirements have been surpassed. These are unlikely to be accurate reflections, with the influence of the omniscient-foraging assumption on distribution depending on the size of the modelled landscape, becoming less realistic as landscape size increases. Energy assimilation efficiency will be influenced by seed chemistry and any digestive bottlenecks that may exist (Diaz 1996; Van Gils et al. 2005) and foraging behaviour by factors such as the dynamic trade-off between predation and starvation risk (Van Der Veen 2000). Whilst both of these are likely to influence the rate of resource depletion in the model, the extent of any effect is unknown, particularly as these two assumptions may well counteract each other. However, the likely impacts of variation on distribution are expected to be broadly equivalent to changes in daily energetic requirements explored in the sensitivity analyses.

The model does not account for potential interference competition. Whilst the aggregated distribution of seed-eating birds in stubble fields suggests that food availability is the primary driver of distribution patterns (Moorcroft et al. 2002; Hancock & Wilson 2003), there is some evidence that interference competition can occur in seed-eating birds (Dolman 1995) and that such interactions can drive starvation mortality in the absence of prey depletion (Goss-Custard et al. 2001, 2002). We also know that birds are sensitive to factors such as stubble structure and boundary features when selecting where to forage (Moorcroft et al. 2002; Butler, Bradbury & Whittingham 2005). In practice, these factors might make some fields unavailable to foraging birds, even though the model would allow their use if the level of resources present was sufficient to meet the daily energy requirements of a single bird.

Management assumptions

Food resources in the landscape are strongly influenced by the management characteristics associated with different crops. Herbicide applications and the timing of harvesting affect the levels of seed rain into stubbles whilst the dates of harvesting and cultivation affect the dynamics of stubble field availability. There is likely to be considerable regional variation in crop management practices due to factors such as prevailing weather conditions and soil type but for all our models we have used the average management characteristics recorded during the Breckland field study because equivalent data from other regions of the UK are not available. We also assumed that stubble recorded at V3 of WFBS surveys remained available until the end of February. In reality, food resources in the landscape are likely to continue declining until the start of the breeding season in April with a steep decline in stubble area in mid-late February ahead of the establishment of spring crops.

Despite these simplifying assumptions, the good correspondence between observed and predicted distribution patterns implies that this ecological complexity must play a relatively minor role in determining the distribution of birds between crop types over time in our study landscape under the prevailing ecological conditions we defined. The model also appears to be relatively robust to uncertainty in functional response and energy requirement parameter estimates, with little evidence that alternative parameter value choices would significantly improve model fit. This supports our mainly evidence-based approach to parameterizing the depletion model. However, repeated measurements of search efficiencies on a range of seed types in the field would aid our understanding and prediction of the ways in which these vary; using average search efficiencies for markedly different seed sizes was not ideal. Model predictions were most sensitive to uncertainty in daily seed survival probabilities, about which we have currently have very little knowledge. For this reason, we felt justified in using a calibration exercise to fit our model rather than an evidence-based approach and the values identified do make ecological sense; the relatively low survival estimate for oilseeds is likely to reflect the fact that these seeds tend to germinate rapidly when on the soil surface after harvest (Lutman 1993). It is important to note that the daily seed survival values we identified were based on the optimum fit between observed and predicted bird distribution within the Breckland region and we had to make the assumption that these values were appropriate for all BBS/WFBS squares in our second analysis. However, daily seed survival rates are driven by a number of factors, such as germination, decomposition and depletion by non-avian predators, which are likely to be context dependent. Further assessment and quantification of seed survival in a range of landscapes and regions are likely to improve the model’s predictive accuracy. Our results emphasize the importance of understanding and accurately defining resource dynamics within the agricultural landscape for predicting bird distribution and population persistence. Further development and integration of our model with models of resource dynamics, in terms of both stubble field availability (e.g. Annetts & Audsley 2002) and weed seed rain (e.g. Freckleton & Watkinson 1998) will therefore be highly beneficial.

Conclusion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

Our model shows that patterns of avian distribution and population persistence in an agricultural landscape can be explained by relatively simple resource dynamics. The model can be used to assess the relative value of resource patches within and across landscapes and to link over-winter resource availability with breeding population trends. It could therefore make a valuable contribution to the debate over the quantity and quality of resources required to deliver stable or increasing population change and be used to inform the design and implementation of agri-environment schemes. By altering land use and management parameters, the model can also be employed to predict population responses to changes in resource availability associated with novel future changes in land use and management (Bradbury et al. 2001; Stephens et al. 2003) and to explore potential mitigation measures which could be introduced alongside such changes to offset any detrimental impacts. This could be very important in the future as farming adapts to an increasingly dynamic trading environment (Mattison & Norris 2005), in which demands for increased agricultural production must be reconciled with objectives for environmental protection, including biodiversity conservation.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

This research was funded under Defra project BD1628 and by National Environment Research Council and Biotechnology and Biological Research Council PhD studentships. We are grateful to the thousands of volunteers who have contributed to the BBS and the WFBS. The BBS is jointly funded by the British Trust for Ornithology, the Joint Nature Conservation Committee (JNCC, on behalf of the Countryside Council for Wales, English Nature, Scottish Natural Heritage and the Council for Nature Conservation) and the Royal Society for the Protection for Birds. The WFBS was funded under a partnership between the BTO and JNCC. We would like to thank participating farmers for aiding fieldwork and providing crop management data and the editors and two anonymous referees for valuable comments on an earlier version of the manuscript.

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  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Parameter estimation
  6. Results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. References
  11. Supporting Information

Appendix S1. Mechanistic modelling of seed-eating birds in an arable landscape: Fieldwork and model parameterisation.

Appendix S2. Matlab code for seed-eater model.

Appendix S3. BBS/WFBS stubble dynamics and management characteristics.

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