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Correspondence: Richard Stillman, Centre for Ecology and Hydrology Dorset, Winfrith Technology Centre, Winfrith Newburgh, Dorchester, Dorset DT2 8ZD, UK (e-mail email@example.com).
1The debate over the interaction between shellfishing and shorebirds is long-running. Behaviour-based models predict how animal populations are influenced by environmental change from the behavioural responses of individual animals to this change. These models are a potential tool for addressing shellfishery problems, but to be of value they must produce reliable predictions using data that are readily available or can be collected relatively quickly.
2We parameterized a behaviour-based model for the oystercatcher population of the Wash, UK, for 1990–99 using data from shellfishery (mussels and cockles), shorebird and climate monitoring schemes. During the 1990s the overwinter mortality rates of Wash oystercatchers varied widely. The model correctly identified the years in which the observed overwinter mortality was either low (1–2%) or high (10–26%) from annual variation in the food supply, oystercatcher population size and temperature.
3Many oystercatchers were observed and predicted to die when only a fraction of the available food was consumed. Within the model at least, this was because interference competition excluded the least dominant birds from part of the food supply and the least efficient foragers died before the food supply was fully depleted. A simplified model, which excluded interference and individual variation, incorrectly predicted that all birds survived in all years. Models that exclude these two components of behaviour will tend to underestimate the effect of mussel and cockle food shortage on oystercatchers. Shellfishery management based on such predictions may cause high oystercatcher mortality rates even though enough food would appear to be reserved for the birds.
4Synthesis and applications. This study shows how a behaviour-based model can be parameterized and predict annual variation in oystercatcher mortality using data routinely collected from the Wash. The principle on which the model is based, that animals behave in order to maximize their chances of survival and reproduction, applies to any system, and the shellfishery, bird and climate data used to parameterize the model are widely available. The model can be used to advise how to manage shellfisheries, by predicting the proportion of the stock that needs to remain unfished in order to maintain low oystercatcher mortality rates.
Human interests often conflict with those of wildlife. In the coastal zone, humans often exploit shellfish populations that would otherwise provide food for shorebirds (Charadrii). Shellfishing removes the large-sized shellfish that are most profitable to birds such as oystercatchers Haematopus ostralegus L. (Zwarts et al. 1996) and may also disturb the birds and force them to feed in less profitable areas or at higher densities, increasing interference competition (Goss-Custard & Verboven 1993). There has been considerable debate over the consequences of shellfishing for the survival of shorebirds, and conversely the effects of shorebird predation on the shellfish stocks remaining for human exploitation (Clark 1993, 1996; Goss-Custard, McGrorty & Durell 1996a). However, it has been difficult to determine the exact impact of current shellfishery practices on birds or to investigate how possible alternative policies would affect their survival.
To help resolve this problem, Goss-Custard et al. (1995a,b), Stillman et al. (2000, 2001) and West et al. (2002) built and field-tested a behaviour-based model. The model predicts the changed intake rates of birds forced by shellfishing to alter their diet and/or to redistribute themselves over resource patches of varying quality (Goss-Custard et al. 2000). It does this using optimal foraging theory and game theory, which are thought to provide a reliable basis for prediction (Sutherland 1996; Goss-Custard & Sutherland 1997). The behavioural responses of model birds to shellfishing are based on decision principles, such as intake rate maximization, that are unlikely to be affected by shellfishing, even if the particular choices made by individuals, and thus their chances of surviving, do change. Model birds are therefore believed likely to respond to current and alternative shellfishing regimes in the same way as real birds.
Stillman et al. (2000) developed this model for the oystercatcher population on the Exe estuary, UK, using data collected between 1976 and 1980. On completion, the model accurately predicted the mortality rate and much of the underlying behaviour of the oystercatcher population, suggesting that it provided a reasonable description of the real system. It also accurately predicted the density-dependent increase in oystercatcher mortality rate during 1980–90, when the oystercatcher population was larger than during 1976–80 (Stillman et al. 2000; Durell et al. 2001). This was evidence that the model could predict accurately for conditions outside the range for which it was parameterized. Although these results were encouraging, this model was parameterized as part of an intensive study of oystercatchers and their food supplies. Such detailed studies are rare, and if they are to be generally applicable such models must be able to produce accurate predictions using data that are already available or that can be collected within a relatively short time span.
In this study, we tested whether this behaviour-based model can predict oystercatcher mortality rate in a different site by using data routinely collected on shorebird and shellfish populations and the climate. We parameterized the model for oystercatchers feeding on cockles Cerastoderma edule L. and mussels Mytilus edulis L. on the Wash, UK (52°58′N, 0°19′E; Fig. 1), an embayment in which overwinter oystercatcher mortality rate has varied widely since the mid-1980s and has been linked to variation in the cockle and mussel food supply (Clark 1993, 1996; Atkinson et al. 2003). Although the data required to parameterize the model are widely available, the Wash is one of relatively few sites in which observed data are available to test the model's mortality rate predictions. This is because estimating annual variation in mortality rate requires long-term bird marking programmes and these have only been conducted on a few sites. We explored the consequences for oystercatcher survival of a number of shellfishery management regimes, and showed that regimes that simply consider the total amount of food consumed by the birds may be damaging to the birds even though, superficially, they would appear to be protecting them.
We used a version of the model developed and tested for mussel-feeding oystercatchers in the Exe estuary (Stillman et al. 2000, 2001). The model is individual-based and tracks the foraging location, body condition and ultimate fate of each individual within the population. The food supply is distributed over a number of discrete patches, each of which may differ in the type (prey species), quantity (prey species abundance) and quality (size and energy content of prey species) of food, and the exposure of food through the tidal cycle. During each day, each bird must consume enough food to meet its temperature-related energy demands. It attempts to do this by feeding in those locations and at those times of the day where its intake rate is maximized. Although all individuals decide using the same principle, intake rate maximization, the actual decisions made by each differ. Their individual choices depend on their particular competitive ability, which depends on two characteristics. Interference-free intake rate (IFIR) is the rate an individual feeds in the absence of competition, and measures its basic foraging efficiency. Susceptibility to interference measures how much interference from competitors reduces an individual's intake rate as bird density rises. Survival is determined by the balance between an individual's daily rates of energy expenditure and consumption. Energy expenditure depends on metabolic costs plus any cost of thermoregulation at low temperatures. Energy consumption depends both on the time available for feeding and intake rate while feeding. When daily energy consumption exceeds daily expenditure, individuals accumulate energy reserves or maintain them if a maximum level has already been reached. When daily requirements exceed daily consumption, individuals draw on their reserves. If reserves fall to zero, an individual starves, the only source of mortality in the model and the main source of overwinter oystercatcher mortality in the wild (Goss-Custard et al. 1996b). Stillman et al. (2000, 2001) describe the model in detail and Stillman et al. (2000) perform a sensitivity analysis.
parameterizing the model
The model was parameterized for the seven winters between 1992–93 and 1998–99, and simulated the period from 1 September to 15 March each winter. The model versions for each winter differed in the size of the oystercatcher population, the abundance of cockle and mussel food supplies and the climate. The total number of oystercatchers present each winter was taken as the average monthly maximum recorded during Wetland Bird Survey (WeBS) counts between September and March (for methods see Musgrove et al. 2001). The target body masses of oystercatchers (the body mass that each individual attempted to maintain) were the average monthly masses of birds captured on the Wash (Johnson 1985). Oystercatcher daily temperature-dependent energy requirements and digestive restriction on intake rate were the same as in Stillman et al. (2000). Daily temperatures (mean of daily minimum and maximum) were from Hunstanton on the north-east coast of the Wash, and were obtained from the British Atmospheric Data Centre (BADC; www.badc.nerc.ac.uk).
The IFIR of oystercatchers was calculated from a hyperbolic functional response:
where B= biomass density of mussels or cockles [gash-free dry mass (AFDM) m−2] within the size range consumed by oystercatchers (mussels 20 mm; cockles 15 mm), a= maximum IFIR and b= biomass at which intake rate is 50% of maximum. The values of a and b were estimated from a wide range of studies of cockle- and mussel-feeding oystercatchers (J. D. Goss-Custard, unpublished data). The value of b was estimated from those studies in which intake rate was measured across a range of prey density. The value of a was measured from those studies in which intake rate was measured when prey density was well above b and hence measured maximum intake rate. Regression analysis showed that a varied with prey type (cockle or mussel), oystercatcher feeding method (stabbing or hammering) and the average size of the prey:
where w= mean ash-free dry mass (mg) of prey within the size range consumed by oystercatchers. Oystercatcher feeding method was incorporated as individual birds tend to specialize in one method and because it influences intake rate (Hulscher 1996). Stabbing oystercatchers open shellfish by forcing their bill between the gapping shell valves, while hammering oystercatchers open shellfish by breaking a hole in the shell (Hulscher 1996). In contrast to a, b was unrelated to characteristics of the prey or feeding method and so the average value measured across all studies was used (b = 0·35). Predicted intake rates were higher when shellfish were more abundant and larger.
The strength of interference between mussel-feeders using either the hammering or stabbing feeding technique was calculated using the same procedure as Stillman et al. (2000). The percentage of stabbers in the population (65%) was calculated from the bill tip shape of birds caught by the Wash Wader Ringing Group between 1991 and 1999 (for methods see Durell, Goss-Custard & Caldow 1993). The strength of interference between cockle-feeders was based on the relationships observed at low cockle abundance in Triplet, Stillman & Goss-Custard (1999). The individual variation in foraging efficiency and assimilation efficiency of mussels and cockles were the same as in Stillman et al. (2000). Also as in Stillman et al. (2000), we assumed that cockles were consumed less efficiently at night than during daylight but, based on new evidence (Sitters 2000), we assumed here that the efficiency of consuming mussels was the same during the night as during the daytime.
The abundance of shellfish within 5-mm size classes in September each year was derived from data routinely collected by the Centre for Environment, Fisheries and Aquaculture Science (CEFAS) and the Eastern Sea Fisheries Joint Committee (ESFJC). Each September the abundance of cockles (≥ 15 mm) and mussels (≥ 20 mm) on natural and laid beds below the 4-m Chart Datum contour (Fig. 1) was surveyed from a boat. Data were unavailable for some beds in some years. These were estimated using the most likely values based on observations on adjacent beds or on the same bed in previous or subsequent years, using interpolation or mean values where appropriate. Up to 10 cockle beds (Breast, Daseley’s, Gat, Herring Hill, Holbeach, Inner Westmark Knock, Mare Tail, Roger/Toft, Stubborn Sand and Wainfleet/Wrangle/Friskney), six wild mussel beds (Inner Westmark Knock, Mare Tail, Daseley’s, East Gat, West Gat and South Gat) and five mussel lays (Tofts, Thief, Scotsmans, Pandora and Le Strange) were used in the model (Fig. 1). Each cockle or mussel bed was represented as a single patch in the model. As no data were available from the Wash, we used published values of the mortality rates of mussels (Stillman et al. 2000) and cockles (Stillman et al. 2001) due to factors other than oystercatchers, the length vs. ash-free dry mass (AFDM) relationship in mussels (Stillman et al. 2000; bed 4) and cockles (Zwarts 1991), the decline in flesh quality through winter in mussels (Stillman et al. 2000) and cockles (Stillman et al. 2001) and the energy density of shellfish (Stillman et al. 2000). Mussel and cockle beds were assumed to be exposed for 6 h during each low tide period (M. G. Yates, personal observation). The amount of shellfish removed from each size class by fishing each year was also estimated by CEFAS and ESFJC. In the model these quantities were removed from the total stock at the start of simulations as most fishing was early in winter. Most mussel and cockle fishing on the Wash occurs from boats at high tide and we assumed in the model that shellfishing did not disturb the birds.
The model only included specific details of the mussel and cockle food supplies below the 4-m contour as only these were part of the regular shellfishery survey. Relatively few birds feed above the 4-m contour at low tide, suggesting that this is a less important feeding area than that below 4 m (Goss-Custard, Jones & Newbery 1977). However, upshore feeding areas can be important to bird survival because they are exposed for longer and hence can provide supplementary feeding when downshore areas are covered by the tide. Upshore areas were incorporated into the model as a single patch, exposed 1 h earlier and covered 1 h later (8 h exposure period) than the shellfish beds below the 4-m contour. The supplementary patch represented the food potentially obtained from alternative prey species or mussels and cockles above the 4-m contour. For simplicity, depletion and interference were assumed to be insignificant on this patch, meaning that birds feeding on the patch had a constant intake rate throughout the course of winter. The actual intake rate achieved from the upshore during each year was unknown and so simulations were run with a range of possible values. The purpose of the upshore patch was to provide a source of supplementary food that could be exploited if birds were unable to meet their requirements by feeding on the shellfish beds. Birds were not able to survive by feeding solely on the upshore patch.
The behaviour, physiology and energetics of birds in the model were calculated from general relationships derived in other sites. Stillman et al. (2000) demonstrated the sensitivity of the predicted mortality rate to variation in these parameters. The major Wash-specific parameters were the number of birds arriving in September, the target body mass of birds, daily temperature, the assumed intake rate of birds feeding in upshore areas and the abundance of cockles and mussels below the 4-m contour. Of these, upshore intake rate and shellfish abundance are the parameters about which most uncertainty exists. Upshore intake rate was unknown and shellfish abundance was not measured in all patches in all years. Therefore, a range of simulations was run to determine the sensitivity of the model's predictions to variation in these parameters across their full potential ranges.
The range of intake rates on the supplementary upshore patch was chosen using a combination of data from the Wash and other estuaries. An intensive survey of the Wash during 1985–86 showed that cockles were more numerous and larger below the 4-m contour, the average biomass density was 4·63 g AFDM m−2 above and 15·86 g AFDM m−2 below the contour, and the mean AFDM was 123·4 mg above and 365·5 mg below the contour (M. G. Yates, unpublished data). The predicted asymptotic intake rate was therefore about 1·3 mg AFDM s−1 above and 2·2 mg AFDM s−1 below the contour (calculated from mean AFDM using equation 2). These were the maximum intake rates at the start of winter ignoring any effects of depletion, interference or loss of prey quality, each of which would be expected to reduce the average intake rate achieved over the course of winter. Furthermore, these data were collected before the major declines in the shellfish populations on the Wash and so are upper estimates of the shellfish densities present during the 1990s. The average overwinter intake rate from upshore areas has been measured as 0·67 mg s−1 in the Exe estuary (Stillman et al. 2000) and the Baie de Somme, France (P. Triplet, unpublished information) and 0·87 mg s−1 in the Menai Straight, Wales (R. W. G. Caldow, unpublished information). Additionally, the average overwinter intake rate from terrestrial habitats has been measured as 0·52 mg s−1 in the Exe estuary (Stillman et al. 2000) and Menai Straight (R. W. G. Caldow, unpublished information). These intake rates incorporated any depletion or loss of prey condition during the course of winter. We therefore considered that an intake rate of about 0·67 mg s−1 approximated the expected overwinter average value. Given that the precise upshore intake rate on the Wash was unknown and may have varied between years, we ran simulations with a range of alternatives to determine the model's sensitivity to this parameter. Simulations were run in which the average overwinter mortality rate was either lower than (0·33 mg s−1), equal to (0·67 mg s−1) or higher (1·00 mg s−1) than the average recorded on other sites. An extreme assumption is that no food is present on the upshore, and so we also ran simulations in which the intake rate on the upshore was zero.
The range of shellfish abundance below the 4-m contour was derived from estimates of the accuracy of shellfish stock assessments on the Burry Inlet, UK, Traeth Lafan, UK, and the Dee estuary, UK, as no suitable data were available for the Wash. Although the precision of shellfish stock assessments varied between years in these sites, on average the 95% confidence interval of shellfish density was approximately 50% of the mean shellfish density (A. D. West, unpublished information). Simulations were therefore run in which shellfish density was either 50%, 100% or 150% of the mean value estimated on each patch.
testing the model
The model was tested by comparing its predicted oystercatcher mortality rate each year with the overwinter mortality rate estimated from dead recoveries of individually marked oystercatchers from catches made by the Wash Wader Ringing Group (using the Cormack–Jolly Seber method in the program mark; White & Burnham 1999; Atkinson et al. 2003).
observed annual variation in shellfish stocks and oystercatcher mortality
During the 1990s there was considerable variation in the sizes of the mussel and cockle stocks (Fig. 2a); cockle abundance varied from 35 to 6269 tonnes AFDM and cockle area from 4909 to 8388 ha, while mussel abundance varied from 123 to 482 tonnes AFDM and area from 92 to 157 ha. Mussel beds were smaller but had a higher biomass density, 62–546 g AFDM m−2 compared with 1–16 g AFDM m−2 on cockle beds. Mussel lays had a higher biomass density (mean 466 g−2) than natural mussel beds (mean 147 g AFDM m−2). The quantity of mussels and cockles removed by shellfishing also varied considerably between years, although only a small proportion of the available stocks were removed most years (Fig. 2a) and, in effect, the wild mussel beds were closed to fishing during this period due to a large crash in previous years. The shellfish stocks were lowest during 1992–93, 1995–96 and 1996–97. both in terms of the total stock available at the start of winter and the amount remaining after shellfishing.
The total population of oystercatchers decreased during the 1990s from around 20 000 in 1992–93 to around 10 000 in 1998–99 (Fig. 2b). There was also considerable variation in the overwinter mortality rates (Atkinson et al. 2003). Overwinter mortality rates were considerably higher during 1992–93, 1995–96 and 1996–97, 10–26%, than in the remaining years, c. 1% (Fig. 2b). Higher mortality rates were therefore observed in years when the shellfish stocks available to birds were smaller.
predicted annual variation in mortality
During the 4 years of low observed overwinter mortality (0·5–1·5%), the model predicted less than 10% mortality in each year even if no food was available above the 4-m contour (Fig. 3a,b). In the years of high observed mortality (10–26%), predictions varied widely depending on the intake rate birds achieved from the supplementary upshore patch. The model also predicted that the body condition of birds was lower in the years in which observed mortality was higher. Virtually no mortality was predicted if an intake rate of 1 mg s−1 was assumed on the upshore, but up to 70% was predicted if no supplementary feeding was possible (Fig. 3a). The model therefore correctly distinguished between the years of low and high observed mortality. The predicted and observed mortalities were related to the size of the shellfish stock at the start of winter relative to the number of birds arriving in September (Fig. 3b). If more than 40 kg AFDM of shellfish was available per bird at the start of winter, predicted and observed mortalities were low. If less than 30 kg AFDM was available per bird, predicted and observed mortalities were high. Overall, the most accurate predictions were produced with an upshore intake rate of 0·67 mg AFDM s−1 (i.e. the average overwinter value recorded in other sites, see above); the average predicted mortalities were 17·1% and 0·1% in the years of low and high food abundance, respectively, compared with observed values of 16·8% and 1·4% (Fig. 3b).
During the years of low observed mortality, predicted mortality was not sensitive to variation in the abundance of shellfish below the 4-m contour (Fig. 4a,b). Virtually no mortality was predicted even if the total abundance of shellfish was reduced by 50%. In contrast, during the years of high observed mortality, predicted mortality was influenced by variation in shellfish abundance (Fig. 4a,b). In each year, the predicted mortality rate was reduced to nearly zero if shellfish abundance was increased by 50%, but increased greatly if shellfish abundance was increased by 50% (Fig. 4a). Although the model's predictions were sensitive to variation in shellfish abundance it still distinguished between the years of low and high observed mortality.
amount of shellfish required to maintain low oystercatcher mortality rates
Ideally, shellfishery management needs to allocate correctly the proportions of the total stock that should be harvested by shellfishing, left for dependent shorebird populations and left as stock for future years. The simplest way of calculating the proportion of the stock required by the birds would be to multiply the number of birds present by the amount of food each requires to survive winter. Shellfishing could be regulated to ensure that at least this quantity of food remains unfished. However, such a policy can potentially cause high mortality rates of oystercatchers even though surplus food appears to be available. On the Wash each bird consumed 9 kg AFDM of shellfish during winter, but up to 26% of birds were observed to die when twice this amount was available at the start of winter (Fig. 5a). Many birds were dying before all the food supply was used up.
To test why this was the case we compared the predictions of two versions of the model. The individual behaviour-based model used here also predicted that birds should die before the food supply was exhausted (Fig. 5a). We developed a simplified model that excluded interference and individual variation but included all the remaining components of the model (e.g. storage of energy reserves, annual variation in food supply and temperature, tidal exposure of feeding patches and seasonal declines in prey energy content). This simplified model was similar to spatial depletion models, behaviour-based models that exclude interference, individual variation and the storage of energy reserves (Sutherland & Anderson 1993). The simplified version of the model predicted that no birds should die in any year (Fig. 5b), even with no feeding on the upshore. This model only predicted mortality when the entire food supply was used up. This demonstrates that it was the presence of interference and individual variation in the model that caused birds to die before the food was exhausted. Interference excluded less dominant individuals from some of the food supplies, and individuals of lower foraging efficiency starved before the food supply was depleted to the point at which individuals of average efficiency died. This suggests that recommendations of appropriate shellfishery management must consider these aspects of oystercatcher biology.
using the model to advise shellfishery management
The model predicts the mortality rate of birds over the winter from the amount of food present in autumn minus the amount removed by shellfishing and other factors over the winter. It can therefore be used on an annual basis to predict how the food supply affects oystercatcher mortality rate. The previous results suggest that a policy guideline of not letting the shellfishing stocks after shellfishing fall below c. 40 kg AFDM bird−1 would maintain low oystercatcher mortality rates.
The model can also be used to advise shellfishery management by predicting the most efficient way of providing a new food source to reduce oystercatcher mortality rates. One management option to reduce oystercatcher mortality rates is to dredge mussels from deep waters and lay them in the intertidal area to provide an extra feeding area. New beds could be laid either above (upshore) or below (downshore) the 4-m contour and a fixed biomass of mussels could either be laid at high density over a small area, or low density over a large area. We used the model to determine how the laying of an extra mussel bed could have reduced the mortality rate of oystercatchers during 1992–93, the year with the highest observed mortality (Fig. 6). In the simulations, mussels laid above the 4-m contour were exposed for 8 h instead of 6 h but were assumed to contain only 90% of the flesh of mussels below the 4-m contour, as mussel flesh content varies with shore level (Goss-Custard, West & Durell 1993). Mussel density in the high density simulations was set to the average density on mussel lays during 1992–93. Mussel density in the low density simulations was set to the average density on natural mussel beds during 1992–93, which had lower mussel densities than the mussel lays.
Both the location and density of the new mussel lay were predicted to influence by how much oystercatcher mortality rates were decreased. An addition of 600 tonnes AFDM of upshore, low-density mussels was predicted to reduce the oystercatcher mortality rate to 1%, the approximate rate observed in the years of high shellfish abundance (Fig. 6). In contrast, the equivalent quantity of mussels added to a downshore bed only reduced mortality to about 26% or 12%, depending on whether the mussels were laid at high or low densities, respectively (Fig. 6). The same quantity added to an upshore, high-density bed reduced mortality to about 5% (Fig. 6). Even though the low-density, upshore lay was assumed to contain mussels of lower quality than the low-density, downshore lay, this was outweighed by it being exposed for longer, and so it reduced oystercatcher mortality to a greater extent. The high mussel density lays were smaller than the low mussel density lays (see above) and so oystercatcher density was also higher on these lays. As a result, increased interference competition between oystercatchers meant that fewer birds could feed on high-density lays and so these lays reduced oystercatcher mortality to a lesser extent than the low-density lays.
The model used in this paper was developed for oystercatchers feeding on mussels in the Exe estuary and was able to predict accurately density-dependent mortality of oystercatchers in that system (Goss-Custard et al. 1995a,b; Stillman et al. 2000). However, the Exe oystercatchers have been the subject of a long-term study (Goss-Custard 1996) and, although only a small part of the overall research was used to parameterize the model, some of the data used in the Exe model are not usually available in other areas. To be of applied value such behaviour-based models must be able to produce reliable predictions using existing data or data that can be collected within a relatively short time scale. The present paper shows that variation in oystercatcher mortality rate on the Wash was predicted using data routinely collected by shellfishery, shorebird and climate monitoring schemes. Apart from their numbers and target body masses, no new data were needed for oystercatchers, as their optimal foraging behaviour and physiology were assumed to be the same as that observed in other areas.
Overall, the most accurate predictions were produced when birds were assumed to achieve an intake rate of 0·67 mg AFDM s−1 when feeding on the upshore supplementary patch. This is also the average overwinter upshore feeding rate recorded on a range of other sites, so is likely to be a realistic average value. However, it is probable that the quality of the upshore areas varied between years, and so the overwinter intake rate that birds were able to achieve probably also varied. Variation in upshore intake rate may explain some of the differences between predictions and observations. For example, with an upshore intake rate of 0·67 mg AFDM s−1 the model underestimated mortality in 1992–93 and overestimated mortality in 1996–97. This may have arisen because the real birds had a lower upshore intake rate during 1992–93 (causing more to starve than predicted) and a higher rate during 1996–97 (allowing more to survive than predicted).
On the Wash, both observed and predicted oystercatcher mortality rates were high in years when the abundance of shellfish at the start of winter was below 40 kg AFDM bird−1. Importantly, this was well above the amount (9 kg AFDM) actually consumed by each bird during winter. Individual variation and interference between oystercatchers caused this threshold shellfish abundance to be higher than the actual amount consumed. A simplified model, excluding individual variation and interference, incorrectly predicted that no birds should have died on the Wash, as the food supply was never completely used up. Interference occurs between mussel-feeding oystercatchers (Goss-Custard 1980; Stillman et al. 1996) and, when prey are scarce, cockle-feeding oystercatchers (Triplet, Stillman & Goss-Custard 1999; but for a case in which interference is not detected see Norris & Johnstone 1998), and individual oystercatchers vary in their foraging efficiency and susceptibility to interference (Caldow et al. 1999). Interference means that some birds are excluded from part of the food resource, and individual variation in foraging efficiency means that some die before the food supply is exhausted. Similarly, Goss-Custard et al. (2001) showed that interference caused density-dependent mortality in Exe estuary oystercatchers when less than 25% of the available mussel food was consumed. If behaviour-based models do not incorporate individual variation and interference, and these are important components of the system being modelled, then they will underestimate the impact of food shortage on animal populations (Goss-Custard et al. 2002). Basing shellfishery management on the predictions of such ration models could lead to high mortality rates of oystercatchers even if surplus food appears to be available.
The threshold food abundance below which mortality rates increase is likely to depend on a number of factors other than interference and individual variation (Fig. 7). Both the amount consumed by each bird and the threshold food abundance are likely to be higher in estuaries with a colder climate, as birds will need to consume more to meet their thermoregulatory needs. Disturbance, either from shellfishing or other human activities, will have a similar effect to interference by preventing birds from feeding in certain areas. The threshold is likely to be higher in estuaries in which interference is stronger, individual variation higher, disturbance greater and the shellfish losses due to factors other than the birds greater. The importance of the strength of interference and individual variation is likely to depend on the feeding conditions for birds, such as the proportion of mussels and cockles, and the densities of these shellfish and other alternative prey. The amount of disturbance will depend on the shellfishing method and the amount of other human activities. Predictions are required for a wider range of estuaries to determine the relative importance of these factors on the threshold food abundance for low oystercatcher mortality.
The model predicted the most efficient way of creating a new mussel lay in order to reduce oystercatcher mortality rate in a year of low shellfish abundance to that observed in years of high shellfish abundance. The fewest mussels were required when they were laid in a new upshore, low-density mussel lay. The equivalent quantity of mussels reduced mortality to a much lesser extent if they were used to make high-density or downshore mussel lays. This prediction arose because upshore lays were exposed for longer and interference was less intense on low-density, and hence large, mussel beds. Whether this prediction holds for other situations depends on: (i) the relative time for which upshore beds are exposed; (ii) the relative quality of upshore compared with downshore mussels; and (iii) oystercatcher population size and hence the strength of interference on high-density, small beds, compared with low-density, large beds.
One example of how the model can be used to advise shellfishery management is provided here, but many others exist. Although mussels and cockles are currently dredged from the Wash at high water when the birds are roosting, this was not always the preferred method of harvesting and the model can incorporate the disturbance to birds caused by other fishing methods that are used elsewhere at low tide (West et al. 2003). The model can be used to compare the effects on birds of harvesting a fixed quantity of shellfish using fishing methods that cause different amounts of disturbance (Stillman et al. 2001). In this study we have concentrated on the effect of shellfish abundance on birds, but shellfishery managers will also want to know the effect of birds on the amount of stock available to harvest (Bell et al. 2001). The model continuously tracks the quantity of shellfish stock as it is depleted by birds, shellfishing or other factors, and so can be used to predict the proportion of the stock consumed by birds (Goss-Custard et al. 2002). Simulations could be run to determine how the amount of stock consumed by birds is related to the bird population size, the density and size of shellfish beds and the availability of alternative food supplies.
On the Wash only shellfish beds below the 4-m contour are surveyed as shellfishing is concentrated in this area. However, the predicted oystercatcher mortality rates were very sensitive to the quality of feeding areas above the 4-m contour, and the creation of a new upshore mussel bed reduced oystercatcher mortality rate to a greater extent than an equal size downshore bed. Upshore areas are important because they are available to birds for longer, allowing them to compensate if their intake from the better-quality downshore is not sufficient to meet their requirements. More precise predictions could have been made if the food supply above the 4-m contour had been monitored. In many other areas, shellfishery surveys do cover all of the main shellfish beds, including those upshore, and so will estimate the entire shellfish food supply.
Although this study has been restricted to the interaction between shellfish and oystercatchers, the general principle on which the model is based applies to any system. Likewise, the relationships shown in Fig. 7 do not need to be restricted to the quality of shellfish beds. Provided that sufficient data are available, or can be collected, the model can be used to assess the quality of any food supply, in terms of whether it is sufficient to maintain high body condition and low mortality rate. The required data are the quantity, quality and distribution of the food supply, the time for which feeding areas are available and the numbers of birds present.
In this study we have shown that an individual behaviour-based model, developed for one oystercatcher population, can be used to advise shellfishery management for a different population using data routinely collected on many shellfisheries. Importantly, the model incorporated interference competition and individual variation, without which it would have greatly underestimated the impact of food shortage on the oystercatcher population.
We are grateful to Andy South and an anonymous referee for helpful comments on the manuscript, and to the Wash Wader Ringing Group for allowing access to their data. The Wetland Bird Survey (WeBS) is funded by a partnership of the British Trust for Ornithology, the Wildfowl and Wetlands Trust, the Royal Society for the Protection of Birds and the Joint Nature Conservation Committee (the last on behalf of English Nature, Scottish Natural Heritage and the Countryside Council for Wales, and the Environment and Heritage Service in Northern Ireland). We would also like to thank the volunteers for their effort in counting waders on the Wash.