Density-dependent starvation in a vertebrate without significant depletion


  • J.D. Goss-Custard,

    Corresponding author
    1. Centre for Ecology and Hydrology (CEH) Dorset, Winfrith Technology Centre, Winfrith Newburgh, Dorchester, Dorset DT2 8ZD, UK; and
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  • A.D. West,

    1. Centre for Ecology and Hydrology (CEH) Dorset, Winfrith Technology Centre, Winfrith Newburgh, Dorchester, Dorset DT2 8ZD, UK; and
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  • R.A. Stillman,

    1. Centre for Ecology and Hydrology (CEH) Dorset, Winfrith Technology Centre, Winfrith Newburgh, Dorchester, Dorset DT2 8ZD, UK; and
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  • S.E.A. LE V. DIT Durell,

    1. Centre for Ecology and Hydrology (CEH) Dorset, Winfrith Technology Centre, Winfrith Newburgh, Dorchester, Dorset DT2 8ZD, UK; and
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  • R.W.G. Caldow,

    1. Centre for Ecology and Hydrology (CEH) Dorset, Winfrith Technology Centre, Winfrith Newburgh, Dorchester, Dorset DT2 8ZD, UK; and
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  • S. McGrorty,

    1. Centre for Ecology and Hydrology (CEH) Dorset, Winfrith Technology Centre, Winfrith Newburgh, Dorchester, Dorset DT2 8ZD, UK; and
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  • R. Nagarajan

    1. Centre for Ecology and Hydrology (CEH) Dorset, Winfrith Technology Centre, Winfrith Newburgh, Dorchester, Dorset DT2 8ZD, UK; and
    2. Department of Psychology, University of Exeter, Exeter EX4 4QG, UK
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J.D. Goss-Custard, 30 The Strand, Topsham, Exeter EX3 0AY, UK (


  • 1It is often difficult to quantify the separate contribution of exploitation and interference competition to the starvation of poor competitors yet, in vertebrates, it seems widely supposed that depletion is normally the mechanism underlying density-dependent starvation. This paper presents arguments that density-dependent starvation occurs through interference in wintering oystercatchers Haematopus ostralegus eating mussels Mytilus edulis without prey depletion having a significant influence.
  • 2Exclosure experiments and mussel bed surveys showed that oystercatchers (i) depleted mussel numerical density by up to 25% in their most preferred large prey size classes, but by only 12·1% overall; (ii) reduced mean mussel length by 1·5%; but (iii) had no detectable effect on the thickness of the shells and therefore the availability of mussels to the 60% of oystercatchers that opened mussels by breaking the shell.
  • 3Oystercatcher intake rate did not fall until prey biomass had decreased to very low densities. Depletion was not nearly large enough for mussel biomass to be reduced to this point.
  • 4The flesh content of individual mussels decreased from autumn to spring by 40–50% but oystercatchers did not increase their rate of foraging to compensate. Intake rate declined over the winter because of deteriorating mussel condition; very little was because of depletion.
  • 5Over the current range of population size, the density-dependent functions produced by a behaviour-based individual’s model were the same whether depletion was allowed to occur or not, confirming that depletion played no role in the density-dependent starvation.
  • 6At current population sizes, intake rate was reduced as population density increased only through increased interference, this leading to starvation late in winter when mussel flesh content was low. It was not just the subdominant birds most susceptible to interference that starved, but the least efficient ones as well, even though the density dependence was not due to exploitation competition.


Density-dependent mortality arising directly or indirectly through starvation can be caused by two kinds of competition. In exploitation competition, the food supply is increasingly depleted as the number of competitors increases so that an increasing proportion of poor competitors cannot feed fast enough to survive. In interference competition, an increasing proportion starves because intensifying interference reduces the intake rate of an increasing proportion of poor competitors, even if the food supplies remain abundant. These two mechanisms are not incompatible but it is difficult in empirical studies to quantify their separate contribution to the starvation of poor competitors. Yet we seem to suppose that, in vertebrates, food depletion is usually a necessary condition for density-dependent starvation to occur (Sinclair 1989). This paper describes a case in which density-dependent starvation arises without food depletion having a significant effect on intake rate. Rather, field and modelling studies show that it occurs because intensifying interference as competitor densities rise causes more poor competitors to starve.

The study was on overwintering oystercatchers Haematopus ostralegus L. on the Exe estuary, UK, where the main prey are mussels Mytilus edulis L. supplemented by other bivalve molluscs, Cerastoderma edule L. and Scrobicularia plana da Costa, and by earthworms Lumbricidae over high water. Most oystercatchers arrive in September and remain until spring, when they leave to breed. Most birds that disappear in winter appear to have starved, especially in severe weather when increased bird energy demands coincide with reduced prey availability and quality (Goss-Custard et al. 1996). Over 15 study winters, oystercatcher numbers on the 10 main mussel beds varied between 1181 and 1883 and mortality from starvation was density-dependent (Durell et al. 2000), with above-trend rates occurring in unusually cold and/or windy winters (Durell et al. 2001).



Interference-free functional response

Oystercatcher intake rates [mg ash-free dry mass (AFDM) s−1] were measured in 40 sites located on all the main mussel beds over the winters 1981–82 to 1999–2000. Oystercatcher intake rate depends greatly on prey mass (Zwarts et al. 1996), so prey biomass density, rather than just numerical density, was measured at approximately the mid-point of the 1–2 month period over which, in each site, intake rates were recorded, mainly from October to March. A site comprised several 25 × 25-m squares, marked out with canes. Feeding behaviour data were obtained by direct observation from elevated towers throughout enough exposure periods to accumulate 30–80 5-min observations from mostly unmarked birds using a particular feeding method. Every attempt was made to ensure that observations were representative of all squares and birds in the site.

The lengths of the mussels consumed during a 5-min observation were estimated against bill length by eye, adjusting for observer bias (Goss-Custard et al. 1987). Bird density was measured as the mean number of feeding oystercatchers in the square at the beginning and end of the 5 min. Records with > 2 birds (> 48 birds ha−1), excluding the subject bird, were discarded as interference occurs at higher densities (Stillman et al. 1996). Observations during which birds were attacked by any species of bird were also discarded. Intake rates were therefore free from interference from kleptoparasitism from any species.

In each square of each site, the mussels were sampled using 5–10 randomly located 20 × 20-cm quadrats. The maximum length of each mussel was measured by callipers. Quadratic regressions between loge mussel length and loge AFDM were determined from a sample of 30–50 fresh animals from each site using methods described elsewhere (Cayford & Goss-Custard 1990), and making the error mean square correction on back-transformation from the logarithms.

Intake rates were obtained by summing the AFDM of all mussels consumed during each 5-min observation. Mean intake rate in a site was calculated from all observations across all squares and provided the single datum used in the functional response. The mussel biomass density was obtained by summing the products of the numerical density and AFDM of each 5-mm length class; 30–35 mm, 35–40 mm, etc. Most consumed mussels were 30–60 mm long (Cayford & Goss-Custard 1990. However, as very few Exe mussels exceed 60 mm, the size range > 30 mm (aged 4 years and over) was often used as an equally valid measurement of the food supply.

A single datum in a functional response was obtained from the mean of all the 5-min measurements of intake rate obtained from all the squares in the site, the average standard error being 11·1% of the mean (range 4·6–20·2%). Mussel biomass density was obtained from the mean of all the quadrats taken across all squares in the site. The average standard error of the estimates of numerical mussel density, which was the main determinant of site biomass density (see below), was 13·2% of the mean (range 6·8–21·8%).

Exclosure experiments

Oystercatchers were excluded from plots where overwinter changes in mussel abundance were compared with nearby control areas where oystercatchers fed. The 11 exclosures were on four beds that supported typical densities of oystercatchers: two exclosures on bed 4 in the winters 1981–82 and 1982–83; one on bed 20 in 1983–84; two on beds 20, 30 and 31 in 1990–91. An exclosure was 2–3 m square, 0·5 m high at the centre and 33 cm high along the sides. It consisted of a central post and, along the sides, 1-m long bamboo sticks inserted every 10 cm between four stout corner posts. Synthetic twine criss-crossed around and over the exclosure formed a ‘cat’s cradle’ of twine that was impenetrable to oystercatchers yet allowed tidal access. Two guy ropes at each corner, pegged into the substrate with long stakes, provided strength. Throughout 11 exclosure winters, only one oystercatcher was seen inside.

Exclosures were erected in September or October and mussel density estimated from 20 random quadrats (20 × 20 cm) taken from the central part to avoid edge effects. A similarly sized control area, with a comparable density of mussels, was marked out nearby (< 5 m) and sampled the same way. Exclosures and control areas were sampled again in February or March. Depletion was measured as the relative change in mussel abundance between exclosure and control. Additionally, the overwinter reduction in each year class > 4 years old on all 10 main mussel beds was estimated on eight occasions and depletion measured over the whole estuary (McGrorty et al. 1990).

Wintering Exe oystercatchers ate the larger mussels (Cayford & Goss-Custard 1990). Depletion may therefore not only have affected the numerical density of mussels > 30 mm long, but also their mean size (length), unless any reduction was compensated for by the growth of smaller mussels (McGrorty 1997) or the immigration of larger ones (McGrorty & Goss-Custard 1995). Because intake rate increases with prey size in oystercatchers (Zwarts et al. 1996), the maximum length of all mussels was measured.

Approximately 60% of Exe oystercatchers hammered open mussels by attacking either the dorsal or ventral side, and generally selected the thin-shelled individuals (Durell & Goss-Custard 1984). The remainder stabbed between valves, regardless of shell thickness. Depletion by hammerers may therefore have increased shell thickness in surviving mussels, making it increasingly difficult for birds to find suitable mussels. To test this, shell thickness in 30–50 mussels > 20 mm long, chosen at random from exclosure and control areas, was measured in September–October and February–March, as described in Durell & Goss-Custard (1984), in eight of the 11 experiments. The generality of the exclosure findings were again tested by comparing shell thickness in autumn and spring in eight winters on all the main mussel beds.


This was described and tested in Stillman et al. (2000). In brief, the model follows the location, behaviour and body condition of each individual animal on each day of a simulation from 15 September to 15 March. It uses simple foraging theory to calculate the sizes of mussels eaten on each mussel bed and the interference-free intake rate of birds of average efficiency, and uses game theory to determine where each individual feeds. Although all individuals base their decisions on intake rate maximization, their decisions differ because birds vary in foraging efficiency (FE) and susceptibility to interference (STI). FE is measured in terms of standard deviations (SD) of the mean interference-free intake rate, expressed as a percentage, and allocated to individuals at random from a normal distribution with an SD of 10% or 15%, depending on the feeding method. STI is measured as m, the slope of loge intake rate on loge competitor density. Above a certain threshold density of competitors, m varies between individuals, according to the individual’s age, feeding method and dominance.

The model includes seasonal changes in prey quality and weather and the neap–spring and diurnal cycles. Model birds failing to obtain their energy requirements from mussel beds over low tide feed upshore on other intertidal prey or in fields above high tide. Individual overwinter survival is determined by the balance between daily rates of energy acquisition and temperature-dependent energy expenditure, with excess energy being stored in body reserves. Individuals draw on these reserves when daily requirements exceed daily acquisition, and starve if reserves are all used up.



Numerical density

The overwinter change in the densities of 30–60-mm mussels in the control areas relative to those in the exclosures was the most reliable estimate of depletion because there was some recruitment into this size range through local immigration and growth. So, for example, if exclosure density increased by +3%, whereas density in the control area decreased by −15%, the net change, and so depletion, would be −18%.

The mean net reduction in mussel density across the 11 experiments increased with mussel length, reaching the statistically significant (P < 0·05, 1-sample t-test against zero) values of 14·5% and 25·3% in the 40–50-mm and 50–60-mm size classes, respectively (Table 1a).For all mussels > 30 mm long, the mean net reduction was 12·1%. This was identical to the 7-year average overwinter reduction of 12·1% (SE = 2·7) in the numerical densities, on all the main mussel beds combined, of mussels 4 years and older (> 30 mm long; McGrorty et al. 1990). Oystercatchers depleted mussels by up to 25% in their most preferred size classes, but by only 12% overall.

Table 1.  Summary of the results from 11 exclosure experiments. (a) The density of mussels in each of the three 10-mm length categories (30–60 mm) most used by oystercatchers, with the data for the 20–30 mm category shown for comparison. (b) The mean length of the mussels in the 30–60-mm size range. (c) The thickness of the shells on the dorsal and ventral surfaces of a typical mussel 45 mm long. In all cases, the data at the start of the experiment in autumn are shown for the exclosure and control area, with the subsequent change by spring (February or March) shown as a percentage of the autumn value. The net percentage change shows the percentage change recorded in the control compared with that recorded in the exclosure. Sample sizes are 11 in (a) and (b), but only eight in (c). P = P-value in a 1-sample t-test against zero. SD = standard deviation; SE = standard error
 Exclosure% change by springControl area% change by springNet % change by spring
(a) Density in autumn
Size class (mm)No. m−2 (± SD)% (± SE)No. m−2 (± SD)% (± SE)% (± SE)P
20–30 196·1 (147·5)+0·10 (14·7) 205·1 (132·7)+9·10 (18·80)+9·00 (20·10)0·66
30–40 476·0 (352·0)+2·64 (4·30) 483·9 (311·4)−10·86 (6·63)−13·50 (9·74)0·20
40–50 516·3 (276·4)+0·80 (3·27) 549·5 (306·1)−13·69 (3·67)−14·49 (5·01)0·02
50–60 137·4 (156·8)−0·29 (6·65) 163·5 (161·5)−25·60 (11·10)−25·30 (9·69)0·03
> 301142·0 (646·0)−1·28 (2·04)1211·0 (672·0)−13·36 (4·04)−12·08 (5·17)0·04
(b) Mean length of 30–60 mm mussels
 mm (± SD)% (± SE)mm (± SD)% (± SE)% (± SE) 
   42·41 (2·75)−0·21 (0·68)  42·25 (2·38)−0·31 (0·79)−0·10 (0·73)0·89
(c) Shell thickness of a 45-mm mussel
 mm (± SD)% (± SE)mm (± SD)% (± SE)% (± SE) 
Dorsal side   0·781 (0·096) −2·79 (2·74)   0·780 (0·079)−0·29 (2·26)+2·50 (2·00)0·25
Ventral side   1·045 (0·118)−4·13 (2·14)   1·028 (0·067)−2·35 (0·87)+1·78 (2·78)0·54

Mean size

Across the 11 experiments, neither the changes in mean length in both the exclosures and control areas nor the net reduction in mean length of 0·1% were significantly different from zero (Table 1b). Across the 10 main mussel beds, the 7-year average reduction across all beds combined for the mean length of mussels 4 years and older was 0·6 mm (SE = 0·2), or 1·5% (SE = 0·4) of the September mean of 42·2 mm (SE = 0·5), a statistically significant (P = 0·012, 1-sample t-test) but small reduction. The exclosure experiments and estuary-wide surveys both showed that depletion had only a very small effect on mean mussel size within the oystercatcher size range.

Shell thickness

Two-thirds of hammering birds were dorsal hammerers (J.D. Goss-Custard, unpublished information). Of the c. 20% of the largest and most preferred (> 40 mm long) mussels removed by oystercatchers, dorsal and ventral hammerers would therefore have removed c. 8% and 4%, respectively. Assuming that oystercatchers only took the mussels with the thinnest shells, we estimated the increase this would have caused in the mean shell thickness of mussels remaining on the beds, from a sample of 509 45-mm mussels collected from bed 30 in the winter 1995–96. Shell thicknesses on the dorsal and ventral sides were normally distributed and unrelated to each other; birds using each technique would have attacked different mussels. Based on this sample, removing the 8% with the thinnest shells on the dorsal side and the 4% with the thinnest shells on the ventral side would have increased mean shell thickness by only 3·5% and 1·1%, respectively. As oystercatchers do not only take the very thinnest shells (Durell & Goss-Custard 1984), the real impact on shell thickness would have been even smaller.

Mean shell thickness across the eight experiments did not increase between autumn and spring in either control areas or exclosures but decreased non-significantly by up to 4% (Table 1c). The small net increase in shell thickness between control areas and exclosures (+2·5% and +1·8% on dorsal and ventral sides, respectively) was not significantly different from zero.

Similarly small changes occurred on the main mussel beds over seven winters. The mean overwinter increases in the dorsal and ventral shell thicknesses, respectively, of 50-mm mussels across all beds were only 0·0005 mm (SE = 0·0092, n = 69) and +0·0014 mm (SE = 0·0103, n = 70), neither being significantly different from zero (P = 0·96 and 0·89, 1-sample t-test). But because some mussel beds attracted dorsal hammerers while others attracted ventral hammerers, and some attracted both, the data were re-analysed using just those beds where birds of the feeding method in question were common. On beds where dorsal hammerers were numerous, mean dorsal shell thickness actually decreased non-significantly (P = 0·31, 1-sample t-test) by 0·0106 mm (SE = 0·0104, n = 53). Where many ventral hammerers fed, mean ventral shell thickness decreased non-significantly (P = 0·28, 1-sample t-test) by 0·0139 mm (SE = 0·0128, n = 46). Thus, neither the exclosure experiments nor estuary-wide surveys detected a significant increase in shell thickness resulting from overwinter depletion by oystercatchers.


Interference-free intake rate did not fall until mussel biomass density reached extremely low values (Fig. 1). Asymptotic hyperbolic functions, forced through the origin, were fitted, this being an appropriate equation for describing a relationship of this shape. In stabbers and ventral hammerers, intake rate remained at asymptote until prey biomass fell to < 2 g AFDM m−2. In dorsal hammerers, this happened at 18·5 g AFDM m−2, but, with only one datum at low prey densities, this is certainly an overestimate.

Figure 1.

The functional responses of oystercatchers that stab into mussels (a) or hammer through the shell on either the dorsal (b) or ventral (c) sides. The lines show the fitted asymptotic hyperbolic functions, the gradients of which in (a) and (c) are virtually vertical.

Prey biomass density would therefore have to be depleted to extremely low levels for intake rate to be affected by exploitation competition. The mean September biomass density of mussels > 30 mm on the 10 main mussel beds combined over the eight years of McGrorty et al.’s (1990) study was 350 g AFDM m−2 (SE = 46·7). Even 25% depletion would have left biomass density well above that at which intake rate fell below asymptote. This was true even for the bed with the lowest biomass of 99·5 g AFDM m−2 (SE = 12·9). Depletion was therefore not large enough for significant exploitation competition to have occurred.


The AFDM of mussels of standard length decreased linearly overwinter by almost half (Fig. 2). Yet surprisingly, oystercatchers did not increase their foraging rate (i.e. searching for and handling mussels) to compensate. This was shown by recalculating intake rates and mussel biomass densities across all sites in Fig. 1 using a standard AFDM–length relationship that removed any differences due to site, month and year. This was the average of 102 relationships obtained from all the main mussel beds and throughout the period September to March across 14 winters, and was:

Figure 2.

The overwinter decrease in the ash-free dry mass (AFDM) of mussels 45 mm long. The data are the means of predictions for a mussel 45 mm long from allometric equations relating mass to length, these being obtained monthly from six mussel beds over the winter 1982–83, 10 mussel beds over 1997–98 and one mussel bed over 1994–95; vertical bar = 1 SE.

inline image

where A = AFDM in mg and L = length in mm. This removed the influence on both intake rate and prey biomass of the 40–50% overwinter decline in flesh content and, in effect, measured the volume of the shells consumed. The ‘volumetric intake rate’ would have increased through the winter if birds compensated for the decline in prey flesh content by foraging more intensively.

The volumetric functional responses were almost identical to those based on site-specific AFDM–length relationships (cf. Fig. 3a and Fig. 1); dorsal and ventral hammerers were combined because they were so similar (Fig. 1). Hyperbolic asymptotic functions forced through the origin were fitted (not shown in Fig. 3a) and the effects of (i) a dummy 0/1 variable representing stabbing and hammering birds (‘SH’), and (ii) the number of days elapsed since 1 August (‘DAYS’) were explored by multiple regression. While the effect of SH was highly significant ( P < 0·01), that of DAYS was far from being significant (P > 0·5). For the purposes of presentation, the residuals of the multiple regression of the hyperbolic asymptotic function and SH alone are plotted against the number of days elapsed since 1 August (Fig. 3b). This shows clearly that the birds did not increase their consumption rate of mussel ‘volume’ to compensate for the reduced flesh content of individual mussels.

Figure 3.

(a) Volumetric functional responses of stabbing (solid circles) and hammering (open circles) oystercatchers obtained by using a standard allometric equation across all sites to calculate the ash-free dry mass (AFDM) of mussels from their length when estimating both intake rate and prey biomass density. (b) The residuals from fitting, by multiple regression, an asymptotic hyperbolic function and a dummy 0/1 variable representing stabbing and hammering birds to the volumetric functional responses plotted against the numbers of days elapsed since 1 August.


This result meant that intake rate was likely to depend closely on the AFDM of consumed mussels, which in turn would depend on the flesh content of the mussels present. With the site-specific AFDM–length relationships, intake rate was indeed closely related (r2 = 48%) to the mean AFDM of the consumed mussels (Fig. 4a), which, in turn, was related (r2 = 42·5%) to the AFDM of the mussels present (Fig. 4b).

Figure 4.

(a) The dependence of intake rate on the mean ash-free dry mass (AFDM) of the mussels consumed by stabbing (solid circle) and hammering (open circle) oystercatchers, and (b) the dependence of the AFDM of consumed mussels on the mean AFDM of the mussels > 30 mm long on the mussel bed.

However, the axes in Fig. 4 are not independent because the same length–AFDM equations were used to estimate the values in both. To avoid this difficulty in Fig. 4a, we used two independent measurements that, combined with SH, determined the mass of consumed mussels. These were (i) loge mean length of consumed mussels (CONLEN), which measures absolute mussel size, and (ii) DAYS, which measures their flesh content; the small standard errors in Fig. 2 show that, in comparison with the seasonal decline, between-site and between-year variations in AFDM were small. In a linear multiple regression, intake rate was negatively related to DAYS (P < 0·001) and positively related to CONLEN (P = 0·044) and was higher in hammerers (P < 0·001); none of the two-way interaction terms was significant (P = 0·332–0·602). At 45·3%, r2 was almost the same as in Fig. 4a, suggesting that much of the variation in intake rate was indeed related to the mass of the mussels consumed. As for Fig. 4b, linear multiple regression showed that the AFDM of consumed mussels was, in turn, negatively related to DAYS (P = 0·012) and positively related to the mean loge length of mussels on the bed (BEDLEN) (P < 0·001), while hammerers ate the larger mussels (P = 0·004); none of the two-way interaction terms was significant (P = 0·582–0·682). At 39·1%, r2 was only a little less than that in Fig. 4b. Therefore much of the variation in the mass of consumed mussels, and thus intake rate, was related to the mussels on the bed.

Because biomass density is the product of numerical density and mean mussel mass, it is surprising that the functional responses were flat over such a wide range of prey biomass. This could only have arisen if (i) variations in numerical density accounted for most of the variation in biomass density, and (ii) numerical density and mean mussel mass were unrelated. Both expectations were confirmed. As measured by standard partial regression coefficient (sprc) in a linear multiple regression of mussel biomass density against numerical prey density and mean prey mass, variations in numerical density (sprc = 1·0203, P < 0·001) were much more important than variations in mussel mean mass (sprc = 0·1954, P < 0·001) in accounting for variations in biomass density across the 40 sites for which data were available. Mussel mass and numerical density were poorly related (r2 = 5·6%, P = 0·076). Consequently, intake rate varied independently of not only mussel biomass density of the mussels but also numerical density across a wide range (Fig. 5).

Figure 5.

Intake rate of stabbing (closed circle) and hammering (open circle) oystercatchers in relation to the numerical density of mussels > 30 mm long.


Using data from all sites, intake rate declined over the winter (Fig. 6). In a linear multiple regression (r2 = 41·6%), intake rate declined with DAYS (P = 0·001) and was higher in hammerers (P < 0·001); the interaction term was not significant (P = 0·411). This decline was due to the overwinter decline in mussel flesh content because neither of the other two contributors to intake rate, mussels consumed s−1 (feeding rate) or their mean length (CONLEN), decreased over winter. In linear regressions, feeding rate was unrelated to DAYS, whether on its own (P = 0·847) or with SH (P = 0·862). The non-significance of SH meant that the difference in intake rate between feeding methods was due to the different sizes of mussels consumed. In multiple regressions, which also included SH, neither CONLEN (P = 0·363) or BEDLEN (P = 0·668) was related to DAYS. There was therefore no overwinter decrease in the rate mussels were taken or in the lengths of mussels either present on the bed or consumed by oystercatchers. Rather, intake rate declined because mussel flesh content declined.

Figure 6.

The intake rate of stabbing (solid circles) and hammering (open circles) in relation to the number of days elapsed since 1 August.

This finding implies that, where mussels have low mass, the functional response asymptote would be low compared with sites with high prey mass. This was tested by distinguishing between sites where consumed mussels had high (> 650 mg AFDM) or low (< 500 mg AFDM) mean mass. These functional responses were again flat across most of the range but differed in mean level, this being significantly higher (P = 0·0002, 2-sample t-test) in sites with high mean prey mass (Fig. 7). The effect on intake rate of the overwinter reduction in mussel flesh content could therefore be visualized as intake rate dropping down a series of asymptotes at successively lower levels, without ever reaching the inflexion point along any one response at which it falls below the current asymptote.

Figure 7.

The functional responses of hammering oystercatchers in sites where the mass of consumed mussels exceeded 650 mg ash-free dry mass (AFDM) (open circles) and in sites where it was less than 500 mg AFDM (closed circles).


The only evidence that depletion affected intake rate was the 1·5% overwinter decrease in the mean length of > 30-mm mussels, from 42·2 mm to 41·6 mm. From equation 1, the mean (standardized) AFDM of the mussels would have decreased by 3·9%, from 484 to 465 mg AFDM. This is very small compared with the 40–50% overwinter reduction in mussel flesh content.

The effect of these decreases on intake rate can be estimated from the data in Fig. 4a, from which:

inline image

where IR = intake (mg AFDM s−1), CM = mass (mg AFDM) of consumed mussels and SH = feeding method (stabbers = 0, hammerers = 1). Using the typical autumn mass for consumed mussels of 650 mg AFDM, equation 2 predicts that a prey mass decrease of 3·9% due to depletion would have reduced intake rate by 2·3% between September and March in stabbers and 2·0% in hammerers. In contrast, the predicted decrease in intake rate resulting from a 45% reduction in mussel flesh content would have been 25·8% and 21·9% in stabbers and hammerers, respectively. On the assumption that both estimates are affected to a similarly small extent by the non-independence of the x and y variables in equation 2, intake rate decreased by an order of magnitude more through the loss of mussel condition than through depletion.


The conclusion that depletion played little role in causing the density dependence of the starvation was supported by simulations with the behaviour-based individual’s model. The model calculates the numbers of each 5-mm length class taken daily by oystercatchers and deducts them from the numerical density present at the start of that day. However, depletion can be prevented by stopping this deduction while retaining the daily reduction in mussel flesh content.

The model generates a density-dependent starvation function by running simulations across a range of September oystercatcher numbers. Over the present-day range (1200–1900 birds), the function was the same whether or not depletion was allowed (Fig. 8). When depletion was allowed, the model predicted the birds would remove 11·4% of the mussels > 30 mm, which agreed well with the observed depletion of 12·1%. Preventing depletion had no discernible effect on the density-dependent starvation function at current population sizes.

Figure 8.

The density-dependent function obtained from the behaviour-based individual’s model of the Exe estuary oystercatcher population with depletion either allowed (closed circle) or not allowed (open circle) to occur. The closed triangles show the function obtained when mussels do not lose flesh content over the winter and depletion is allowed. The means of three simulations are shown. The vertical dashed lines show the present-day range in population size.

However, the average mean lengths of the mussels remaining in March across all 10 mussel beds at the median oystercatcher population size of 1550 birds differed significantly (P < 0·001, paired sample t-test) between the depletion and no depletion simulations but the difference was very small, the means being 38·3 mm (SE = 1·5) and 38·6 mm (SE = 1·4), respectively. The model thus predicted that depletion reduced the mean length of mussels by 0·8%, reasonably close to the observed value of 1·5%.

The two starvation functions diverge increasingly, however, at higher September population sizes, with higher mortality rates occurring with depletion than without (Fig. 8). Depletion now affects rather more the sizes of mussels remaining on the beds at winter’s end. With 7500 birds in September, for example, the mean lengths of mussels > 30 mm long in March across all beds were 36·9 mm (SE = 1·6) and 38·6 mm (SE = 1·4) with depletion and without depletion, respectively (P < 0·001, paired sample t-test). At this higher population size, depletion would reduce mussel length by 4·6%.

Figure 8 also illustrates the importance of the loss in mussel condition to oystercatcher survival. With depletion, but without individual mussels losing mass from September to March, mortality remains density-dependent but occurs at a much lower rate.


The characteristics of animals that die can help understand how mortality occurs. It is not known whether an individual efficient at consuming mussels is equally efficient eating supplementary prey. But given the relationship between diet and bill-tip form (Sutherland et al. 1996), this is perhaps unlikely and, as in previous simulations, was assumed not to be so (Stillman et al. 2000).

As an example, Fig. 9a shows the FE and STI of starving and surviving stabbing birds in simulations with 5000 birds. The probability of surviving was estimated as a logistic regression against STI and FE. The line shows the values of STI and FE giving a 50 : 50 chance of surviving. It is a diagonal, showing that starving birds had both low FE and low STI. The lines at higher population sizes were parallel to that at 5000 birds but higher (Fig. 9b). In all cases, the G-statistic, which tests the overall significance of the discrimination, was highly significant (G = 208·3, 353·3 and 598·8 at 5000, 10 000 and 15 000 birds, respectively; P < 0·001), as were the contributions that both STI and FE made in predicting which birds died (P < 0·001). The greater STI of the birds that starved as population density increased reflects the greater impact of interference on intake rate at higher population densities.

Figure 9.

(a) The characteristic of model stabbing birds that either survived (crosses) or starved (circles) in simulations with 5000 birds. The lines show the logistic regression predictions for which the values of susceptibility to interference (STI) and foraging efficiency (FE) gave a 50 : 50 probability of birds being alive or dead. (b) The logistic regression lines for populations of 5000 (solid line), 10 000 (dashed line) and 15 000 (dotted line). FE is the interference-free intake rate as a percentage of the mean. STI is the slope of the logarithm of intake rate against the logarithm of competitor density; STI refers to the beginning of the winter, before interference intensifies as the feeding conditions deteriorate (Stillman et al. 2000).


Exe oystercatchers removed by spring 12% of > 30-mm mussels present in autumn, but up to 25% of the most preferred large mussels, a rate similar to that in the Oosterschelde (Meire 1996). However, their functional responses were flat across a wide range of prey biomass density, and depletion had little effect on intake rate. However, model results showed that this conclusion only applies at present-day population sizes. Exploitation competition would begin to affect intake rate at two–three times present population levels. The greater depletion rates would then approach the average of 50% (SD = 19·3) found by Dolman & Sutherland (1997) across 24 vertebrates, although whether rates in that sample are typical of vertebrates, or only of cases where depletion was considered large enough to study, is unclear.

Depletion did reduce the mean length of mussels but the effect on intake rate would have been so small (< 3%) that the birds would probably not have detected any decrease (Stillman et al. 2000). Nor is there any evidence that depletion much affected the mean shell thickness of mussels, confirming Meire’s (1996) finding for Oosterschelde ventral hammerers. While many more exclosures might have detected the small net increase in shell thickness (1–3·5%) expected from depletion, the very large samples of autumn–spring comparisons from all mussel beds over 8 years provided no evidence of this. If depletion did cause mussel shells on the main feeding areas to be thicker by the winter’s end, it was undetectably small.

The expectation that the shells of surviving mussels would thicken as oystercatchers removed the thin-shelled ones was based on the assumption that shell thickness does not change from autumn to spring. This assumption may be false because recent data indicate that the shell thickness of individual mussels does vary during winter (R. Nagarajan, unpublished information). In response, hammering oystercatchers take thicker-shelled mussels when these predominate and thinner-shelled ones when they are abundant (R. Nagarajan, unpublished information), as do captive oystercatchers (Sutherland & Ens 1987). Present evidence therefore suggests that, within limits, hammerers raise or lower the threshold thickness of the shells they attack according to what is on offer, although presumably with consequences for the risk of bill breakage and energetic costs (Meire 1996). But at present population sizes, there is no evidence that depletion affected intake rate in hammering oystercatchers by changing shell thickness. The similarity in the overwinter change in intake rate in hammerers and in stabbing birds, which select mussels independently of shell thickness (Durell & Goss-Custard 1984), is consistent with this conclusion.

Rather, intake rates decreased because the flesh content of individual mussels declined by 40–50%. Model simulations showed that, without this, mortality rates would have been much lower, although still density-dependent. As mussels lose flesh over the winter because of reduced phytoplankton food supply (Bayne & Worrall 1960), the rate of decline in mussel flesh content, and thus in oystercatcher intake rate, was presumably independent of bird density.

It is nonetheless surprising that intake rate did decline over the winter because birds did appear to have spare foraging time in which to raise their intake rates. Across all sites and independently of the stage in the winter, stabbing and hammering oystercatchers spent only 56·3% (SE = 2·2) and 67·4% (SE = 2·2), respectively, of their foraging time ‘handling’ mussels (i.e. pecking at and attacking mussels, either successfully or unsuccessfully). The remaining time was spent walking with head aloft, the birds apparently searching visually for prey to attack. Contrary to the assumption made in the ‘disc’ equation for the type II functional response (Holling 1959), the asymptotes were clearly not limited by all the foraging time being used in handling mussels, a conclusion also reached for a captive oystercatcher eating Scrobicularia (Wanink & Zwarts 1985). Holling (1959) recognized that factors other than handling time can determine the asymptote, one alternative being a digestive constraint. But although gut processing rate in oystercatchers does limit consumption over a tidal cycle (Kersten & Visser 1996), it is most unlikely to have limited the instantaneous intake rate over the 5-min observation periods. First, oystercatchers eating shellfish elsewhere have intake rates up to twice those on the Exe (Zwarts et al. 1996; Norris & Johnstone 1998). Secondly, Exe oystercatchers did not increase their volumetric intake rates by the end of winter, despite the rates then being considerably below autumn rates; they could presumably have ingested flesh at a higher rate in spring, but did not do so. Thirdly, the consistently lower asymptote in stabbing birds compared with hammerers implies that gut constraints did not limit their intake rate at most stages of the winter.

The factors determining the functional response asymptote in Exe oystercatchers remain to be discovered, as in some other birds (Caldow & Furness 2001). One possibility is that oystercatchers may have traded-off the risks of ingesting parasites against the energetic gains of increasing their intake rate, as argued for oystercatchers selecting cockles of different sizes (Norris & Johnstone 1998). Thus, if the numbers of parasites per mussel remained constant, or even increased, over the winter as the flesh content declined, oystercatchers may have become increasingly selective against the increasing density of parasites in the flesh, and thus rejected an increasing proportion of mussels. However, this is unlikely as the probability of an Exe oystercatcher rejecting an encountered mussel (as defined in Stillman et al. 2000) did not increase over the winter (J.D. Goss-Custard, unpublished information), as would be expected if they had become increasingly selective. Furthermore, the low intake rate on mussel beds in late winter caused large numbers to eat earthworms Lumbricidae above high water (Caldow et al. 1999), where their chance of ingesting damaging nematode worms was probably high (Goss-Custard et al. 1996). Restraining intake rate over low water would merely have resulted in increased exposure to risk of infection from other parasites at high water. As an alternative speculation, we propose a hidden component of searching that adds a time expenditure, x, to every mussel that is attacked, so that the asymptote was limited not by handling time alone but by handling time + x. Research is now testing this hypothesis.

Our interpretation of how density-dependent starvation occurred in mussel-eating Exe oystercatchers is as follows. As population density increased, average intake rate was reduced through increased rates of interference, this leading to starvation towards the end of winter when the mussel condition was poor. However, it was not just the subdominant birds that were most susceptible to interference that starved, but the least efficient ones as well. A bird of low efficiency, by definition, had a relatively low intake rate even when competitors were scarce. They therefore started from a low base, especially towards the end of winter after the mussels had lost nearly half their flesh. Interference reduced the intake rate of the most susceptible animals at a proportionate rate as competitor density increased (Stillman et al. 1996). Thus, with two competitors of equal susceptibility to interference but differing foraging efficiency, the less efficient one starved first as population density increased, even though the density dependence was due almost entirely to interference rather than to exploitation competition.


We are grateful to Ralph Clarke for statistical advice and to Paul Dolman and two referees for commenting valuably on the manuscript.