Estimating food consumption of marine predators: Antarctic fur seals and macaroni penguins

Summary

• 1
  Estimating food consumption is central to defining the ecological role of marine predators. This study developed an algorithm for synthesizing information about physiology, metabolism, growth, diet, life history and the activity budgets of marine predators to estimate population energy requirements and food consumption.
• 2
  Two species of marine predators (Antarctic fur seal Arctocephalus gazella and macaroni penguin Eudyptes chrsolophus) that feed on krill in the Southern Ocean were used as examples to test the algorithm. A sensitivity analysis showed that estimates of prey consumed were most sensitive to uncertainty in some demographic variables, particularly the annual survival rate and total offspring production. Uncertainty in the measurement of metabolic rate led to a positive bias in the mean amount of food consumed. Uncertainty in most other variables had little influence on the estimated food consumed.
• 3
  Assuming a diet mainly of krill Euphausia superba, annual food consumption by Antarctic fur seals and macaroni penguins at the island of South Georgia was 3·84 [coefficient of variation (CV) = 0·11] and 8·08 (CV = 0·23) million tonnes, respectively. This was equivalent to a total annual carbon consumption of 0·35 (CV = 0·11) and 0·72 (CV = 0·23) G tonnes year⁻¹. Carbon expired as CO₂ was 0·26 (CV = 0·06) and 0·65 (CV = 0·19) G tonnes year⁻¹ for fur seals and macaroni penguins, respectively. The per capita food consumption varied depending upon sex and age but, overall, this was 1·7 (CV = 0·22) tonnes year⁻¹ for Antarctic fur seals and 0·45 (CV = 0·22) tonnes year⁻¹ for macaroni penguins.
• 4
  The algorithm showed that the seasonal demand for food peaked in both species in the second half of the breeding season and, for macaroni penguins, there was a second peak immediately after moult. Minimum food demand occurred in both species during the first half of the breeding season.
• 5
  As both Antarctic fur seals and macaroni penguins compete for krill with a commercial fishery, these results provide an insight into the seasons and stages of the life cycle in which competition is likely to be greatest.

Introduction

The impact that pinnipeds, such as fur seals, and seabirds have on their prey, and particularly the consequent interactions with fisheries, is a continuing source of debate and controversy in a wide range of large-scale marine ecosystems and for many different species and species groups (Swartzman & Haar 1983; Alverson 1992; Wickens et al. 1992; Livingston 1993; Pascual & Adkinson 1994; Agnew 1997; Best, Crawford & Van der Elst 1997). Many studies have calculated the total prey requirements of predators such as seabirds, seals and whales to provide a regional assessment of the food requirement for maintenance of predator populations (Laws 1977; Croxall, Ricketts & Prince 1984; Doidge & Croxall 1985; Perez & McAlister 1993; Boyd, Arnbom & Fedak 1994; Joiris, Tahon & Holsbeek 1996; Croll & Tershy 1998; Green, Slip & Moore 1998; Wanless, Harris & Greenstreet 1998) or to examine the strength of food web interactions (Punt & Butterworth 1995; Springer, Piatt & van Cliet 1996; Yodiz 1998). With the additional importance of these components of food webs for biogeochemical cycling of carbon (Huntley, Lopez & Karl 1991) and also their utility for constraining oceanic carbon budgets (van Franneker, Bathmann & Mathot 1997; Priddle et al. 1998), there is a need to develop robust methods to investigate the role of predators at the top of marine food chains.

This study developed an algorithm to calculate the food consumptions of Antarctic fur seals Arctocephalus gazella Peters and macaroni penguins Eudyptes chrysolophus Brandt at South Georgia (54°S, 38°W) in the Southern Ocean (Croxall et al. 1988). Both these species are mainly dependent upon Antarctic krill Euphausia superba Dana for food in this region. The algorithm was developed: (i) to provide information about prey consumption in these two species because of their potential interactions with fisheries (Trathan et al. 1998); (ii) to show how large amounts of life-history and bioenergetics information can be synthesized to reduce, or define, uncertainty in the estimates of food consumption by marine predators; and (iii) to examine the sensitivity of estimates of food consumption to uncertainty in these input variables. The algorithm used standard Monte Carlo methods (Manly 1991) to define the level of uncertainty in estimates of food consumption. In this example, parameters were evaluated for a single year, in this case 1991, because this was the last year in which a population survey of Antarctic fur seals was carried out and therefore had the most complete data set in terms of the most critical variables. The algorithm, which has already been applied in the context of food web studies in the Southern Ocean (Priddle et al. 1998; Everson et al. 1999), provided information about total prey consumption, consumption of each dietary item, energy and carbon flux through a predator population and the energy and carbon sequestered within the population.

At its simplest level, the calculation of the gross food requirements of a population is a matter of multiplying the daily ration of an individual, r, by the population size, N, and then scaling up to whatever time scale is appropriate. However, both r and N are difficult to estimate. Moreover, r will be composed of a set of items (the diet) that depends upon the type of individual involved (e.g. reproductive, non-reproductive, adult, juvenile, male, female), and the class composition of N will depend upon when measurements are made. Both r and N are more properly represented as vectors than scalars. Therefore, the basic model being developed in this paper can be represented as a combination of two vectors, n and r, representing the number of individuals in each class and the total ration, given in a common currency such as Joules or moles of carbon, required by each class in a time period t. The total population ration will be:

• (eqn 1)

where the total ration in each time period is being summed over k time periods and I is a scalar. The values within n and r may also vary with time (t) because of changes in the composition of the population and the activity patterns of individuals. Each vector associated with each time interval would need to be derived separately.

The ration at any time is more commonly represented as an a × b matrix, R_t, where a is the number of classes of individual and b is the number of items in the diet. This matrix defines a different diet for each class of individual. The cells of this matrix might contain the proportion of the diet in the jth class of individual represented by each dietary item. Most often, this is expressed as a proportional frequency of occurrence of a dietary item and therefore it is necessary to transform the matrix into a common currency such as energy. In this case:

• E_t = R_tc_t(eqn 2)

where E_tis an a × b matrix equivalent to R_t but expressed in units of energy, and c_t is a column (b × 1) vector whose elements are the product of wet mass and mass-specific energy for each prey type. Therefore a more complete model to that given by equation 1 would be:

• (eqn 3)

This shows the energy intake of the total population, which is represented by the sum across all time periods of all energy intakes (that are themselves determined by the diet composition) multiplied by the population size at each time interval. The vector c_t in equation 2 can be replaced by a vector representing the product of wet mass and mass-specific carbon content of each item to give the estimated carbon consumption.

The majority of previous estimates of prey consumption from the total gross energy requirement of a population of predators have been derived by scaling up from measurements of energy expenditure at the level of individuals (Croll & Tershy 1998). Potentially, there is a high degree of uncertainty in these types of estimates because errors (associated with both measurement and because of natural variability) will be additive across all input variables (e.g. metabolic rate, digestive efficiency, growth rate) and multiplicative across population size and time. Except in a few cases (Furness 1978; Shelton et al. 1997; Stenson, Hammill & Lawson 1997; Warren, Shelton & Stenson 1997) this type of uncertainty, together with other uncertainties about the demographic and behavioural features of the life histories of individuals, has not traditionally been incorporated into estimates of prey consumed.

Methods

ALGORITHM STRUCTURE

The main features of the algorithm are illustrated in Fig. 1, which shows the major components requiring data input (shaded boxes) separately from the calculations (unshaded boxes). A listing of the input variables required is given in the Appendix. The algorithm makes use of all available data about the population size, as well as the age (years) and size (mean body mass) structure of the population. The algorithm also incorporates information about time budgets on the scale of the annual cycle and during the breeding season, and the energy expenditure associated with each stage in the annual cycle. Importantly, however, the algorithm can be applied even when not all of the variables listed in the Appendix are known.

Figure 1. Flow diagram of the prey consumption model for marine predators.

The algorithm estimated individual gross energy requirements and multiplied these to provide an estimate of the population energy requirements (equation 1). This energy requirement was then partitioned between different dietary items according to their contribution to the energy budget. This was determined by their energy content and their frequency of occurrence in the diet (equation 3). The calculation was iterated using different plausible values of each of the variables to provide an indication of the degree of uncertainty that exists in the final estimate of food requirements.

ESTIMATION OF ERRORS AND UNCERTAINTY

As shown in Fig. 1, the calculation of food consumption was iterated using randomly selected values from the probability distributions of the input variables. It was assumed there was no correlation between variables and this was based on a general lack of correlations in the empirical data. Each run of the algorithm involved a minimum of 200 iterations because the estimated standard deviation of food consumption had stabilized at this number (Fig. 2). In the context of the present study, the uncertainties associated with estimates of food consumption include those associated with natural variability and with measurement error because the empirical estimates of input variables include both these forms of uncertainty.

Figure 2. Mean (a) and standard deviation (b) annual prey consumption by an Antarctic fur seal population during two runs of the model in relation to the number of model iterations.

All input variables were assigned a statistical error based on their empirical standard errors or on an estimate of the upper and lower boundaries of plausible values for each variable. Where a population mean and standard error were available, the probability distribution was based upon the normal distribution. Where the mean was quoted with an upper and lower 95% confidence interval, the algorithm calculated the distribution based upon standard deviations derived separately for the upper and lower segments of the distribution, thus allowing for probable skewness in some error distributions. In cases where only a range was available then an even probability distribution was used within that range, and when a mode and range were available a triangular distribution was used (Evans, Hastings & Peacock 1993).

ESTIMATES OF FOOD REQUIREMENTS

Food requirements were estimated by calculating the total energy requirements of individuals (Lavigne et al. 1982) of each age, sex and reproductive class in the population and then converting these to a food mass sufficient to sustain the expected gross energy intake. Therefore:

• E_gross = P + E_faecal + E_urinary + E_SDA + E_work(eqn 4)

where P is the production energy, E_gross is the gross energy intake, E_faecal is the energy content of the faeces, E_urinary is the energy in the urine, E_SDA is the energy cost of digestion and E_work is the energy expended in activity. P was estimated from annual growth (allocated evenly through each daily time step except during breeding) and values for the other variables were obtained from the literature. E_SDA and E_work were considered as a single quantity because both are components of field metabolic rate which, for practical reasons, does not normally distinguish between these two forms of energy expenditure. The algorithm was structured so that the daily gross energy requirement of an individual in a particular stage (i) of the annual cycle (EG_i,t) was calculated by the summation of the metabolic costs of particular activities undertaken during the current stage (i) of the annual cycle such that:

• (eqn 5)

In this case, γ_f is the power (watts) generated under activity f, q_f,i is the proportion of time spent in activity f within stage i of the annual cycle, g_i,t is the daily incremental growth (expressed in Joules and assuming that growth only occurred during non-reproductive stages of the annual cycle and that growth was isometric with respect to fat and protein) and d_w,t is the digestive efficiency of the food items w being eaten. The daily ration (r) therefore was defined by EG_i,t divided by the energy density of the prey. This calculation assumed that: (i) animals balance their energy budgets at time scales of less than the cycle duration of the algorithm (normally 1 year for an annually breeding species); and (ii) that all essential nutrients are available within the prey that are eaten.

The following sections of the Methods describe how data concerning these different groups of input variables were assimilated into the algorithm.

PHENOLOGY OF THE ANNUAL CYCLE

It was important for the algorithm to be responsive to changes in the activity budgets of individuals through the annual cycle because different activities have widely varying energetic costs. This was achieved by dividing the annual cycle into logical time periods when animals tended to be involved in different sets, or schedules, of activities. The timing of events, such as reproduction or moult, in the life histories of individuals was simulated from empirical data concerning the annual schedule of behaviour, including the variability around specific dates such as the start and end of breeding in the population. Because both species being considered here breed and moult annually, the duration of the algorithm cycle was set to one year. The step duration of the algorithm was set to one day so there was a possible 365 time-steps in the calculation. Note, however, that this could include time steps > 1 day if the intention was to examine variability across > 1 year.

For each species the cycle was divided into stages with measured start and end dates (Table 1). The number of stages was defined by the operator. The proportion of individuals that were expected to be in each stage of the annual cycle was calculated for each age class within each sex. Thus, for macaroni penguins with 30 age classes, seven stages in the cycle duration of the algorithm (referred to from here on as the annual cycle) and two sexes, the distribution of individuals within the annual cycle involved the creation of 153 300 data cells showing the proportion of individuals of each age and sex on each day of the year that are in each stage of the annual cycle.

Table 1.  Mean and lower and upper 95% values for metabolic rate (multiple of basal metabolic rate) for each activity. For each metabolic rate the proportion of time spent in that activity is given for each stage of the annual cycle in macaroni penguins (a) and Antarctic fur seals (b). All values are given for males of each species. Where values for females differ from those of males, they are given in parentheses. Dates are in Julian days and are given ± SD

(a)	Metabolic rate			Stage of the annual cycle
Activity	Mean	Lower	Upper	Courtship	Incubation	Brooding	Chick-rearing	Pre-moult	Moult	Winter
Ashore	1·4	1·2	1·6	1·0	0·9 (0·7)	0	0	0	0	0
Brooding	1·3	1·2	1·4	0	0	0·5	0·2	0	0	0
At sea	4·3	3·9	4·9	0	0·1 (0·3)	0·5	0·8	1·0	0	1.0
Moulting	5·0	4·8	5·2	0	0	0	0	0	1.0	0
Start date				303 ± 6 (313 ± 6)	322 ± 6	362 ± 6	21 ± 6	57 ± 10	71 ± 4 (69 ± 4)	95 ± 4 (93 ± 4)
End date				322 ± 6	362 ± 6	21 ± 6	57 ± 10	71 ± 4 (69 ± 4)	95 ± 4 (93 ± 4)	303 ± 6 (313 ± 6)

(b)	Metabolic rate			Stage of the annual cycle
Activity	Mean	Lower	Upper	Winter	Breeding
Ashore	2·7	3·0	3·3	0·1 (0·0)	0·5 (0·2)
At sea	4·5	4·2	4·8	0·9 (1·0)	0·5 (0·8)
Start date				321 ± 15 (341 ± 10)	10 ± 15 (90 ± 15)
End date				10 ± 15 (90 ± 15)	321 ± 15 (341 ± 10)

The duration of stages and the transition between stages was described using two normal distribution functions with mean µ₁ and µ₂ and standard deviation σ₁ and σ₂, respectively. One distribution described the beginning of a stage and the other described the end of a stage. The average duration of the stage, i, was the difference between the mean start date and the mean end date. The distribution of the animals among stages depended on the values of and the duration of the stage. If N_k,j,t is the size of the population of individuals of sex k and age class j during day t of the cycle, then the number of individuals included in a particular stage on any day of the annual cycle will be:

• n_t,i = N_k,j,t · p_i(t, µ₁, µ₂, σ₁, σ₂)(eqn 6)

where p_i(t, µ₁, µ₂, σ₁, σ₂) is normally distributed and provides the expected proportion of individuals in the ith stage of the annual cycle so that:

• (eqn 7)

Rothery & McCann (1987) and Boyd, Walker & Poncet (1996) showed that this could be used to describe the distribution of breeding elephant seals present ashore and, in general, transitions between different stages of breeding cycles in both Antarctic fur seals and macaroni penguins also appear to approximate reasonably well to cumulative normal distributions (Boyd 1989; Davis, Croxall & O’Connell 1989; Duck 1990; Williams & Croxall 1991).

The annual cycle of the Antarctic fur seal was divided into only two stages, breeding and non-breeding, but the timing and duration of these differed between adult males and females (Boyd 1989; Duck 1990; Lunn & Boyd 1993) (Table 1). In adult males, the breeding season began before that of females but was shorter than for females because of lactation. Adult males were assumed not to feed during the breeding season, which is consistent with observation (Boyd & Duck 1991). Only female Antarctic fur seals incurred the energetic costs of parental care.

The annual cycle of macaroni penguins was divided into seven stages. These were courtship, incubation, early chick rearing, late chick rearing (creche), pre-moult, moult and winter (at sea) (Croxall 1984; Davis, Croxall & O’Connell 1989) (Table 1). Males and females were assigned different schedules resulting from the different arrival times at the colony during courtship, and different nest guard duties during incubation and chick rearing. In macaroni penguins, both parents were assumed to provide food to the chick in equal shares (Williams & Croxall 1991) and all birds were assumed to moult, except for chicks of the year. Allowance was made for changes in the timing of moult between juveniles and adults (see the Appendix).

In both macaroni penguins and Antarctic fur seals, juveniles were assumed to skip the stages of the annual cycle associated with reproduction.

PREDATOR POPULATION SIZE AND STRUCTURE

The algorithm required information about population size or total fecundity (chick or pup production) together with estimates of age-specific fecundity (chicks or pups hatched or born per adult female), age-specific annual survival rate and the rate of increase of the population. A population age structure was then obtained from the survival rates by deriving this directly where an estimate of total fecundity was present (e.g. for fur seals; Boyd 1993; Boyd et al. 1995).

Age-specific survival and fecundity rates (together with associated errors around these estimates) of female Antarctic fur seals were obtained from Boyd et al. (1995). The annual rate of increase of the fur seal population (1·10; Boyd et al. 1995) was assumed to lie in the range 1·06–1·14. Total fur seal pup production with probable error around the estimate was obtained from Boyd (1993). Adult male age-specific survival rates were derived from the distribution of age-at-death assuming that all males were recruited to the adult population by age 7 years (Boyd & Roberts 1993). For neither sex was there reliable information about juvenile survival. This was set at a level during each iteration of the model to produce a balanced life table (i.e. balancing birth and death rates with allowance for the rate of increase) and it was assumed to be identical for both males and females. Female age-specific survival rates were used for the 4–7-year-old age classes in the male section of the population as there was no other information upon which to estimate adult male survival rates for these ages.

There was less information available to allow the development of a demographic model of macaroni penguins. An adult survival rate of 0·8 ± 0·03 (SD) was used together with an annual fecundity rate (proportion of birds breeding in consecutive years) of 0·715 ± 0·07 (SD) (Williams & Rodwell 1992). Data for fledging success (British Antarctic Survey, unpublished data) show that 0·468 ± 0·013 (SD) of chicks fledge from each nest and this was used as the main component of first-year survival. From colony counts (Croxall & Prince 1979) at South Georgia in 1977 the population estimate was 5·4 million pairs compared with 3·0 million pairs in 1991 (British Antarctic Survey, unpublished data). This suggests that the population was declining at a rate of c. 0·97 per annum (range 0·92–1·0). Based on the fledging rate, and assuming a large uncertainty, chick production was estimated at 2·1 million with a possible range of 0·5–2·5 million in 1991. Because there were no estimates of juvenile survival, this number was used, together with the estimated rate of change of the population and the estimated fecundity rate, to derive an age structure by iterating juvenile survival rates to produce a balanced life table. However, with the current data it proved impossible to balance the life table as this would have required juvenile survival rates > 1. For the purposes of this exercise, therefore, juvenile survival rates were set equal to unity. The general effect of this will have been to underestimate the total number of animals in the population.

Populations were stratified according to a class structure that was related to age and sex. This allowed consideration of different behaviours and body sizes in relation to age and sex. For Antarctic fur seals and macaroni penguins, 20 and 30 1-year long age classes, respectively, were used for each sex. In this analysis, the most complete data sets were available for 1991, which is the last year in which the size of fur seal populations were estimated. Therefore, the quantitative estimates of food consumption in the present study are for 1991.

PREDATOR GROWTH AND ESTIMATION OF BIOMASS

Each age class in each sex was allocated a body mass according to the mean and standard deviation of body mass measured empirically at each age. In the case of Antarctic fur seals, data from Payne (1979) were used. Macaroni penguins reach adult body size at fledging. During certain stages of the annual cycle when animals are fasting, body mass is lost as a result of a negative energy balance. The calculation assumed that the mass lost during such periods of fasting had been gained during the previous stage of the annual cycle when feeding had occurred. Thus the algorithm reallocated the energetic requirements of a fasting stage to the required energy gain of the previous feeding stage.

Average biomass for each class was calculated from the product of mass-at-age and numbers-at-age. Energy sequestered in biomass was estimated from standard regressions for the proportion of fat, protein and water in tissues (Antarctic fur seals, Arnould, Boyd & Speakman 1996; phocid pinnipeds, Reilly & Fedak 1990; macaroni penguins, Davis, Croxall & O’Connell 1989). Error was included in these calculations by allowing body water content to vary within the empirical range; 0·58–0·62 for fur seals and 0·56–0·61 for macaroni penguins.

ENERGY FLUX DUE TO METABOLISM

Metabolic rate has been determined empirically for both Antarctic fur seals and macaroni penguins. In Antarctic fur seals, metabolic rates used were associated with (i) presence ashore (Costa & Trillmich 1988; Boyd & Duck 1991) and (ii) being at sea (Costa, Croxall & Duck 1989; Arnould, Boyd & Speakman 1996). Only the metabolic rate for male fur seals at sea has not been measured directly and, in this case, the metabolic rate for females, adjusted for differences in body size, was used. Within the algorithm all metabolic rates were expressed as multiples of basal metabolic rate (BMR).

BMR in fur seals was assumed to vary with mass (M) according to the equation given by Kleiber (1975), and specifically for marine mammals by Lavigne et al. (1986), in which metabolic rate = 293M^0·75 where mass (M) is in kg and metabolic rate is in kJ day⁻¹. Although this equation strictly only applies to interspecific comparisons, the results of metabolic measurements of male and female Antarctic fur seals when ashore show close correspondence when expressed as multiples of BMR, despite a fivefold difference in body size (Costa & Trillmich 1988; Boyd & Duck 1991). This suggests that the power relationship does hold for Antarctic fur seals.

Metabolic rate measurements were available for macaroni penguins for time spent ashore (resting, courtship, at the nest incubating or guarding the chick and during moult) and at sea while foraging during chick rearing (Davis, Kooyman & Croxall 1983; Brown 1984; Brown 1985; Brown 1989; Davis, Croxall & O’Connell 1989).

The allometric equation given by Ellis (1984), in which metabolic rate = 381M^0·72 kJ day⁻¹, was used to relate field metabolic rate in macaroni penguins to multiples of BMR. Both macaroni penguins and Antarctic fur seals can show large (± 30%) changes in body mass during stages of the annual cycle (Croxall 1984; Boyd & Duck 1991). For the purposes of this study it was assumed that this made little difference to overall metabolic rate because most of the metabolic costs will be associated with activity (Boyd et al. 1999). The multiples of BMR used are given for each activity in Table 1.

DIGESTIVE EFFICIENCY, FAECAL AND URINARY LOSSES

Digestive efficiency is the gross energy intake minus the energy lost as faeces expressed as a proportion of the gross energy intake. This was entered as a variable with information about the fat and protein contents of each dietary item. In the case of Antarctic fur seals there are no estimates of digestive efficiency. Therefore, digestive efficiencies for fish and cephalopods from northern fur seals Callorhinus ursinus, harp seals Pagophilus groelandicus and Steller sea lions Eumetopias jubatus (Fadely, Worthy & Costa 1990; Mårtensson, Nordøy & Blix 1994; Rosen & Trites 1999) were used, as were those for krill from crabeater seals Lobodon carcinophagus (Nordøy et al. 1995). These studies showed a high degree of consistency in digestive efficiency among species and, based on them, uncertainty in digestive efficiency was represented as the value defined in the input data set (0·84 for krill, 0·87 for fish) for each prey item ± 0·02 based on an even probability distribution. Similarly, faecal and urinary losses were represented by a 2–8% energy loss (Brody 1945) based on an even probability distribution.

For penguins fed on krill, total faecal and urinary losses have been estimated to be 0·26 of gross energy intake (Davis, Croxall & O’Connell 1989), and a range of 0·2–0·3 with an even probability distribution was used in this study.

DIET

Diet was measured for Antarctic fur seals using scat analysis during the summer season of 1991 (Reid & Arnould 1996). Although fish was a prominent feature of the diet from scats in this year, fish prey may be overrepresented in the diet because of the inherent biases in scat analysis (Croxall 1993). It was assumed that fish formed 10% by wet mass of the diet of fur seals and that the remainder was made up of krill. The proportion by mass of each major item in the diet of macaroni penguins is given in Table 2.

Table 2.  Variance in total food consumption by male and female Antarctic fur seals associated with each variable, when present in the model as the only variable with uncertainty, expressed as a proportion of the total variance in food consumption. Also shown is the sensitivity of the total food consumption by females to a change by 10% in the values of the input variables. In this case a negative value shows when the direction of change in food consumption was opposite to the direction of change in the value of the variable

Model number	Variable	Proportion of total variance explained		Sensitivity (Δ%)
		Male	Female
1.	Offspring production	0·146	0·156	10
2.	Rate of population increase	0·090	0·006	−  4
3.	Start/end of stages in the annual cycle	< 0·001	< 0·001	–
5.	Activity-specific metabolic rate	0·006	< 0·001	8
4.	Age-specific annual survival rate	0·302	0·403	30
6.	Rate of brood loss	< 0·001	< 0·001	< 1
7.	Heat increment of reproduction	< 0·001	< 0·001	< 1
8.	Duration of parental care	< 0·001	< 0·001	1
9.	Growth efficiencies of protein and lipid	< 0·001	< 0·001	< 1
10.	Parent–offspring food transfer efficiency	< 0·001	< 0·001	< 1
11.	Birth/hatching mass	< 0·001	< 0·001	< 1
12.	Weaning/fledging mass	< 0·001	< 0·001	2
13.	Age-specific mass	0·003	< 0·001	5
14.	Body composition	< 0·001	< 0·001	2
15.	4–10 combined	0·013	0·011	–
16.	1 and 4	0·868	0·758	–

Subsamples of krill carapaces in scats were used to determine the portion by size of the krill population exploited by fur seals. This allowed examination of the impact of predation on each size class of prey. The frequency distributions of krill lengths were derived from carapace lengths using the general relationship between total length and carapace length (both expressed in mm) given by Hill (1990). The krill length distribution was translated into a krill wet mass (g) distribution using the allometric equation defined as wet mass = (3·85 × 10⁻⁶) × length^3·20 (Morris et al. 1988). Different age classes of krill were treated as separate items in the diet.

Almost all empirical information about diet expresses each item as a proportion of total wet mass consumed. This differs from the total energy consumed because different items have different energy contents. The daily gross energy requirement of each sex (EG_k,t; equation 5) was allocated so that:

• (eqn 8)

where I_k,w,t is the daily mass consumed of item w by sex k, p_k,w,i is the proportion of item w in the diet by wet mass for each sex during stage i, and e_w is the mass-specific energy content of the item. In this case, diet was only defined separately for each sex and was assumed not to differ among different age classes mainly because there were no empirical data to support such a split. Mass-specific energy content was obtained from the literature. For krill, proximate lipid, protein and fat composition (Clarke 1980) was used, assuming energy densities of protein and lipid to be 18·00 and 39·34 kJ g⁻¹. For this analysis krill protein and lipid contents of 10% and 4%, respectively, were used but the current version of the algorithm has the capability of allowing these energy densities to vary in relation to age and sex class of the prey, and this can be included when more detailed information is available. Energy values for fish were obtained from Cherel & Ridoux (1992) and Perez (1994). In this analysis, there was no discrimination between fish species high in fat (e.g. myctophids) and non-fatty fish species. Instead, an average value of 5 kJ g⁻¹ was used. A value of 4 kJ g⁻¹ was used as the energy density of squid (Croxall & Prince 1982; Clarke, Rodhouse & Gore 1994).

SENSITIVITY ANALYSES AND STATISTICS

The contribution that each of the input variables made to explaining the variance around each of the estimates of food consumption was assessed. This was done by comparing the statistical error around the results from the algorithm, when it was applied using the estimate of error around all the input variables, with the results when error was only applied to individual input variables when the remainder of the variables were held constant. In addition, for metabolic rate, the effects of biases in the estimate, both in terms of the statistical error around the mean estimate and in terms of the value of the mean, were investigated. This was achieved by varying both the mean and the error around the mean independently of one another and by comparing the estimated food consumption in each case.

The effect of varying each of the input variables independently was also examined. This was done by increasing or decreasing the variable by 10% and then comparing the percentage change in the magnitude of the estimated food consumption.

All means were quoted with plus and minus 1 SD or with their coefficient of variation (CV).

USE OF CARBON AS A CURRENCY

The above description was based upon the use of energy as the currency. Growth, body composition and metabolism were also expressed in terms of the use made of lipid and protein substrates. Carbon sequestered in biomass was estimated from standard regressions for the proportion of fat, protein and water in tissues (Antarctic fur seals, Arnould, Boyd & Socha 1996; macaroni penguins, Davis, Croxall & O’Connell 1989) and assuming that protein is 52·9% carbon by mass and that lipid is 77·6% carbon by mass. For metabolism, it was assumed that animals metabolized only lipids while they were fasting but that, while feeding, they metabolized substrates in the same proportions as they were present in the diet.

Results

SENSITIVITY TO CHANGES IN INPUT VARIABLES

The proportion of the variance in food consumption attributable to each variable in the algorithm provided a measure of the relative contribution that each makes to the uncertainty of the final estimate of food consumption. Using the example of the Antarctic fur seal, reasonable estimates of the variables and their ranges showed that there was a large skew in the contribution that each variable made individually to the uncertainty in the final result (Table 2). Most of the physiological and morphological variables, when represented by their empirical range of values, contributed < 0·1% to the overall variance (Table 2). Only metabolic rate appeared to be more important. When considered as a group, morphological and physiological variables contributed only 1–2% to the total variance (Table 2, model 15). In contrast, the variables that were associated with demographic processes, including offspring production, annual age-specific survival rate and the population rate of increase, contributed most to the overall variance. As a group, these three variables contributed 75–87% to the total variance (Table 2).

Similar results were obtained for an analysis of changes associated with varying each input variable independently. In the analysis in Table 2, a direct linear relationship between the magnitude of the variable was only found for offspring production. Errors in the measurement of metabolic rate and mass were also likely to lead to large errors in the estimation of food consumption. Errors in the estimate of population rate of increase were also relatively important but overestimation of this variable led to a reduction in the estimated food consumption. However, the largest effect was associated with the estimation of annual survival rate, in which a 10% change caused a 30% change in the estimated food consumption. This shows that the uncertainty surrounding the estimate of food consumption was considerably more sensitive to the variables used to express the total population size than to virtually any other variables.

Nevertheless, it is also possible that the range of uncertainty associated with some physiological variables is not well represented by the data that are currently available. This may be the case for metabolic rate in which small sample sizes (mainly of adult females during lactation in the case of Antarctic fur seals and breeders in the case of macaroni penguins) have been used. As expected, increasing the 95% confidence intervals associated with the estimate of field metabolic rate caused an increase in the standard deviation of the estimated food consumption (Fig. 3a) such that a doubling of the 95% confidence intervals led to a c. 10% increase in the SD of the food consumption. Doubling of the 95% confidence intervals also led to a 5–8% increase in the estimate of mean food consumption (Fig. 3a). Doubling of the field metabolic rate (FMR) led to a roughly equivalent change in the estimate of mean food intake, and a three- to four-times increase in the standard deviation. Therefore, estimates of food consumption appear to be more sensitive to changes in the mean FMR than in the error associated with the mean, except that increasing error led to overestimation of the mean food intake.

Figure 3. Mean and standard deviation of annual prey consumption by an Antarctic fur seal population in relation to the range of the error term associated with the mean field metabolic rate (a) and in relation to variation in the mean itself (b). The mean FMR was 4·5 × predicted BMR.

An important feature of this sensitivity analysis (Table 2) is that variables appear to act synergistically to increase the overall variance of the estimate to exceed the sum of all the individual variances. This can be seen from model 16 (Table 2). Offspring production and survival rate, when examined individually, contributed 15–40% of the total variance but, when considered in combination, they contributed 75–87% of the variance.

TOTAL POPULATION FOOD CONSUMPTION

Based on a diet principally of krill or other similar crustacean prey with a similar energy density, the calculation gave a total annual food consumption by Antarctic fur seals of 3·84 million tonnes (CV = 0·11). This food intake was divided roughly equally between males (1·99 ± 0·14 million tonnes) and females (1·85 ± 0·07 million tonnes). Based on the probability of the food consumption of males exceeding that of females, these estimates for the two sexes were not significantly different (P > 0·05). For macaroni penguins the total annual food consumption was 8·08 million tonnes (CV = 0·23). The mass of food eaten by female macaroni penguins did not differ significantly from that of males (3·99 ± 0·69 million tonnes for males; 4·10 ± 0·93 million tonnes for females; t = 2·59, d.f. = 198, P < 0·01). Total annual food consumption by the Antarctic fur seal and macaroni penguin populations at South Georgia was 11·93 million tonnes (CV = 0·16).

The total annual carbon consumption was 0·35 ± 0·04 G tonnes and 0·72 ± 0·16 G tonnes for fur seals and macaroni penguins, respectively. The total annual energy intake was 1.16 × 10⁴ ± 0·11 × 10⁴ GJ and 2.41 × 10⁴ ± 0.42 × 10⁴ GJ for fur seals and macaroni penguins, respectively. Carbon expired as CO₂ was 0·26 (CV = 0·06) and 0·65 (CV = 0·19) G tonnes year⁻¹ for fur seals and macaroni penguins, respectively.

GROSS EFFICIENCY

The gross efficiency (energy ingested that contributes to growth) of Antarctic fur seals was only 1·4%, and it was only 0·26% for macaroni penguins. Equivalent values for efficiency expressed in terms of carbon ingested as a percentage of carbon present in tissues was 1·3% for fur seals and 0·25% for macaroni penguins.

EFFECTS OF AGE ON FOOD CONSUMPTION AND per capita FOOD CONSUMPTION

The per capita food consumption varied depending upon sex and age (Fig. 4) but, overall, this was 1·7 (CV = 0·22) tonnes year⁻¹ for Antarctic fur seals and 0·45 (CV = 0·22) tonnes year⁻¹ for macaroni penguins. Information about growth and age-specific survival and fecundity rates was sufficient in Antarctic fur seals to allow the estimation of the age-specific food requirements. More than half the food consumption by both male and female fur seals was attributed to individuals < 5 and < 6 years of age, respectively. Most males and females were sexually mature by 6 and 4 years of age, respectively, and this shows that 62% of food is consumed by sexually immature individuals. Of the total population food requirement, 5·4% was attributable to the raising of pups but, on average, 19·7% of food consumption by adult females was allocated to raising pups.

Figure 4. Mean (± SD) mass of prey consumed in relation to age for the whole Antarctic fur seal population (a), assuming that krill is the major item of prey, and also expressed as the mean prey consumed per individual (b). The results are given separately for the two sexes and the histogram shows the food consumption (both absolute and per capita) that is required to raise a pup.

The total food consumption by both male and female fur seals declined initially and increased gradually with increasing age until a peak was reached at 4 and 3 years of age for males and females, respectively. Total food consumption was greater for the male than the female fur seal population until age 8 years, with the maximum difference occurring at age 5 years (Fig. 4a). The food consumption of individual males was greater than for females throughout the age range (Fig. 4b) and reached an asymptote of c. 3·8 and c. 1·9 tonnes year⁻¹ for males and females, respectively. The costs of rearing a pup involved the need for an individual mother to eat 0·45–0·61 tonnes of additional food.

SEASONAL CHANGES IN FOOD CONSUMPTION

The inclusion of detailed information about the different phases of the annual cycles and about the different activities during those phases allowed the seasonal changes in food consumption to be resolved (Fig. 5). This shows that the lowest levels of population food demand tend to occur in the early summer (November–January; Fig. 5), when breeding occurs and many adults are ashore. Increasing demand through the breeding season in fur seals is because of the increasing number of males that return to sea to feed after the mating season and because of gradually increasing demand from pups for food (Fig. 5a). The subsequent decline in food consumption by fur seals was caused by a combination of mortality (mainly of juveniles), reduced demand from males after recovering from fasting during the mating season, and reduced demand of mothers when pups wean and their food requirements are met by direct feeding (which is more efficient than lactation).

Figure 5. Mean (± SD) daily food consumption by Antarctic fur seals (a) and macaroni penguins (b) throughout the year based on a diet consisting mainly of krill.

In the case of the macaroni penguin (Fig. 5b), the large number of adults ashore during the breeding season is the main cause of low levels of food consumption, but the apparently slower increase in food consumption through the breeding season compared with the fur seal occurred because of the progressive increase in the number of birds returning ashore to moult through the second half of the summer (January–April). There was an acute decline in food consumption at the transition between fledging of the young and moult in the adults. Thereafter, the relatively high metabolic rates of macaroni penguins when they are at sea, combined with birds never returning to land during the winter (April–November), meant that a relatively high food consumption was required through the winter to sustain the population (Fig. 5b).

SIZE-SPECIFIC PREDATION

The estimated size-specific biomass of prey species consumed by fur seals and macaroni penguins reflects the frequency distribution of these species in the diet after correction for energy content (Fig. 6a). However, this can also be translated into an actual number of individuals consumed (Fig. 6b).

Figure 6. A comparison between the diet of Antarctic fur seals (a) and macaroni penguins (b) during 1991 based upon the total biomass consumed and the total number of individual krill eaten from each size class. These diets assumed that summer measurements of diet were representative of diet at other times of year.

Discussion

This study examined the food consumption by fur seals and macaroni penguins at South Georgia. The estimates of food consumption are most sensitive to uncertainty in demographic variables but consumption by these predators can normally be estimated with a CV of < 0·3, even when there is a relatively large uncertainty associated with many demographic variables. Morphological and physiological variables have a relatively minor role in this type of bioenergetics calculation for these species. Indeed, in the case of the species examined in the present study it may not even be necessary to know these in detail because they could be estimated from allometric equations. The additional uncertainty associated with this approach would be unlikely to add substantially to the overall uncertainty associated with the estimate of food consumption.

The importance of carrying out sensitivity analyses has been recognized in similar studies (Furness 1978; Shelton et al. 1997; Warren, Shelton & Stenson 1997; Croll & Tershy 1998) and these have also concluded that estimates of population energy flux and prey consumption are most sensitive to the variables representing population size. Although this result is not surprising, the present study adds to this by quantifying the relative sensitivity to different variables and providing a method for computing confidence intervals around estimates. However, the present study also does not distinguish between uncertainty associated with measurement errors and environmental stochasticity. Overall, the importance of these results is that, for each predator, it should be possible to parameterize the algorithm with all available data and, where empirical data do not exist for that species, to substitute data, particularly about physiological rather than demographic variables, from related species or by using a best guess with appropriately wide confidence intervals. Running the algorithm will then show how sensitive the final result is to uncertainty in different variables.

A number of tests can be conducted to examine the accuracy of the results. For example, dividing of the total population food consumption by the number of individuals in the population shows average daily food consumption by Antarctic fur seals (Fig. 4) and macaroni penguins (mean = 1·2 kg day⁻¹) that is close to that calculated for similar predators of krill by Croll & Tershy (1998). Overall, the results from the algorithm are consistent with expectation in terms of the resultant gross efficiency of individuals (Humphries 1979), the total annual food consumption by individuals, especially in relation to age or body size, and the per capita metabolic heat production (Costa, Croxall & Duck 1989; Davis, Croxall & O’Connell 1989).

There are at least two important features of this approach to estimating food consumption by pinnipeds and seabirds that can be developed from this algorithm. These are: (i) to integrate a dynamic approach into the algorithm in order to examine changing patterns of prey consumption as a result of changes in population size and structure; and (ii) to place the calculated food consumption in a spatial context so long as the section of a population using a specific region is known. Dynamic (spatial and temporal) models of prey consumption, together with associated levels of uncertainty, are a logical extension to current approaches to examining the population dynamics of pinnipeds and seabirds and their potential impacts upon prey species (Butterworth et al. 1995; Punt & Butterworth 1995). Coupling the algorithm developed in the present study with physiologically based models of starvation duration (Øritsland & Markussen 1990) in the context of variable prey densities may also provide a means of predicting predator population responses to changes in food distribution and abundance. In addition, the algorithm presented here has the potential to partition the impacts of predators both between different prey species and between different age/length classes of those species (Fig. 6). This presents an opportunity to provide a direct link between estimating the impact of predators and age- or size-structured models of the prey population.

The seasonal variability in consumption (Fig. 5) suggests that, on average, the susceptibility of individuals to competition with fisheries may be greater during the winter than during the summer. Declines in consumption of food during the summer are associated with time spent fasting ashore during breeding and the reduced energy expenditure associated with a relatively low level of activity. Nevertheless, this analysis did not consider the varying spatial demand for food in relation to season. In winter, animals may be dispersed over a larger range (Boyd et al. 1998) so that the demand for food may be more dispersed. This could reduce potential competition with fisheries that are mainly concentrated at South Georgia (Trathan et al. 1998). In summer, demand for food will be greatest in the vicinity of the breeding colony so that competition with fisheries could increase in the summer and this could result in reduced population productivity (Mangel & Switzer 1998). However, at present the krill fishery at South Georgia occurs in the winter (Everson & Goss 1991), thus reducing the potential for competition with fur seals and penguins during the critical reproductive stages of the annual cycle.

Variations in total food consumption by the population of fur seals in relation to age suggest that reduction in food availability is likely to have its greatest effect on juveniles and the young, relatively productive, age classes (Fig. 4). However, this would appear to be mainly caused by the greater relative numbers of these individuals in the population because per capita food consumption in these younger age classes was less than in the older age classes (Fig. 4b). The lower per capita food requirements of females compared with males, and also between young and old individuals, suggest that these different groups will need to forage on different prey densities and may have different sensitivities to reduction in prey availability. Adult male fur seals are likely to be most vulnerable to reduction in mean prey density although, unlike females, they do not have to forage within a restricted radius of the breeding colony in the summer season when females are generally supporting pups (Boyd et al. 1998).

This study has shown that the annual prey requirements of Antarctic fur seals and macaroni penguins are in the order of 11·9 million tonnes, with an approximate range, based upon the 95% confidence intervals, of 6·4–17·4 million tonnes. The diet of macaroni penguins in winter is not known, although for Antarctic fur seals it appears that krill can form an important component of the diet (Reid 1995). The last published estimate of krill standing stock for the region of the Scotia Sea, which includes the region around South Georgia, came from a survey in 1980 which suggested there was a krill standing stock of 35·8 million tonnes (CV = 0·14; Trathan et al. 1995). There are, in addition to Antarctic fur seals and macaroni penguins, other avian (especially other penguins, and prions) and marine mammal (especially baleen whales) predators in the region that are mainly dependent upon krill. Even given the wide error range in the current estimate of krill consumption by fur seals and macaroni penguins at South Georgia, overall, this suggests that predators in the region could be responsible for a substantial part of the annual mortality of krill at South Georgia.

The same krill survey (Trathan et al. 1995) suggested there was a krill standing stock around South Georgia in the order of 1·5 million tonnes. The results of this study suggest that, even if predators are only present in the region around South Georgia during the summer, a high rate of influx of krill into the region is required, or that there is a particularly high rate of growth of krill at South Georgia, in order to sustain the fur seal and macaroni penguin populations in the region. Another independent analysis of the food requirements of breeding seabirds at South Georgia (Croxall, Ricketts & Prince 1984) suggested a similar discrepancy between food requirements and the standing stock of krill.

An important deficiency in current methods for estimating food consumption by marine predator populations is the difficulty of estimating the diet matrix (R_t, equation 2) and its associated uncertainty. In the current study, a highly simplified diet matrix was used with no added uncertainty. Diet analysis has several unquantified elements that contribute to uncertainty (e.g. errors in prey species/type composition, unknown levels of sampling bias, errors in the estimation of prey size from hard parts; Croxall 1993) which, if they had been included in the present analysis, could have added to the degree of estimation error on the food consumption. The small range of species involved in the diet of the predators being examined in the present study will have reduced the effect of errors in the estimation of prey species composition. While there are ways of tackling specific types of uncertainty in diets, such as uncertainty in the prey size distribution (Hammond & Rothery 1996), others types of uncertainty that relate particularly to the different degree of representation of prey species in scat or crop samples, and obtaining a representative range of samples from the various classes within the predator population (e.g. male, female, adult, juvenile), remain to be solved.

Even considering these caveats, this study has demonstrated, for two krill predators in the Antarctic, how an algorithm provides an opportunity to examine the overall consumption of prey by marine predators. Using different input data sets, it would be possible to develop this on a regional basis from current knowledge of the movements and distributions of predators (e.g. based on satellite tags; Boyd et al. 1998; McConnell et al. 1999). Such an approach could be used to quantify spatial, temporal and ecological overlap with fisheries.

Acknowledgements

This study would not have been possible without the assistance of many individuals who were involved in the collection of data about fur seals and macaroni penguins at Bird Island, South Georgia, over the past two decades. I thank all these people and, in particular, Professor John Croxall for encouraging the development of this study.

Appendix

Input variables required for the algorithm (variables in bold are those that require error distributions).

1. Population fecundity/young produced each year

2. Rate of population increase

3. For males and females separately tabulation of:

(i)       Field metabolic rates (multiples of basal metabolic rate)

(ii)     Proportion of time spent in each metabolic rate in each stage of the annual cycle

4. Julian date when the annual cycle begins

5. For males and females separately tabulation of:

(i)       Start and end dates for each stage of the annual cycle

(ii)     Type of stage:

Breeding/non-breeding

Feeding/no feeding

(iii) Proportion of mortality occurring in each stage

6. Rate of brood loss during chick/pup rearing in each stage of the annual cycle

7. Start and end dates of brood loss

8. Number of stages to jump should the brood be lost

9. Presence or absence of male parental care

10. Heat increment of reproduction, e.g. added costs of pregnancy or egg production (MJ)

11. Mass at birth/hatching (kg)

12. Mass at weaning/fledging (kg)

13. Duration of parental care (days)

14. Growth efficiency of protein

15. Growth efficiency of lipid

16. Parent–offspring food transfer efficiency

17. Type of animal (pinniped or seabird)

18. Moulting:

Number of the stage at which moult occurs

Maximum number of days to offset moult (e.g. in juveniles which may moult at a different time to breeding adults)

Number of years over which to apply the offset

19. For males and females separately, tabulation of age-specific survival and fecundity rates, and mass

20. Heat increment of feeding

21. For males and females separately, tabulation of information about each species or age/size class of food item to include:

Proportion fat by wet weight

Proportion of protein by wet weight

Digestive efficiency proportion in diet at each stage