Methods

Population Parameters, Growth, and Biomass

Annual Survival Rate

T. S. McCann's (1985) revision of R. M. Laws's (1960) life tables for male and female southern elephant seals was used to provide statistics on survival rates from birth to 20 years of age (table 6.1). These were based on cross-sectional age distributions from material collected by Laws and from a collection made in 1978. Comparison was made between these survival rates and those for the Macquarie Island stock (Hindell 1991), where longitudinal data have been collected on survival rates of individuals. Estimates of survivorship differed for the two stocks, especially survival rates up to 1 year and in the 5- to 12-year age classes (ibid.). Given that the Macquarie Island stock has been in decline while the South Georgia stock has been stable in recent years (Hindell and Burton

Fig. 6.1
The relationship between nose-tail (N–T) straight length and age for female (dots)
and male (open circles) southern elephant seals. Data were from Laws (1953), and
Gompertz growth models (large dots and solid line for females; large open circles
and dashed line for males) were fitted by least squares regression.
The regression equations were:
female length = 168 + 128 × e(–e – 0.028[age – 4.5])
male length = 202.4 + 264.9 × e(–e – 0.039[age – 39.73])

1987; McCann and Rothery 1988), reduced survival at Macquarie Island would be sufficient to account for this difference. The maximum longevity for a female elephant seal from South Georgia is 21 years (Arnbom et al. 1992), which is close to the 20 years predicted by McCann's life table.

Survival rate estimates for males are less certain than those for females. Males were assumed to become sexually mature at 4 years of age but did not breed until they were > 6 years of age (Laws 1953).

Growth

For the purposes of this analysis, we define the mean size of seals in any age class as the size at the end of the period of reproductive investment each year (the end of the breeding season). For seals < 1 year old, this means from the time of nutritional independence or weaning. Laws (1953) gave the nose-tail curved lengths of male and female elephant seals in relation to age. Curved lengths are about 10% greater than nose-tail straight length, so Laws's data were corrected to the equivalent nose-tail

Fig. 6.2
The relationship between nose-tail straight length and mass for 162 female elephant
seals. The line was fitted by least squares regression (length = 22.61 + 25.33 mass³ ).

straight length and asymptotic growth curves were fitted to the data by least squares regression (fig. 6.1). The predicted values for each age were used as the mean length for a given age (table 6.1). The model overestimated weaning mass of both sexes, so the values given by T. S. McCann, M. A. Fedak, and J. Harwood (1989) were used for this age class.

Recent studies in which females were chemically immobilized (Baker et al. 1990; McCann, Fedak, and Harwood 1989; Boyd, Arnbom, and Fedak 1993) have yielded a relationship between mass and nose-tail length for females (fig. 6.2). This was used to estimate mean mass for each age class of elephant seal (table 6.1). The relationship between mass and length in males described by Bryden (1969b , 1972) was used to calculate the equivalent mass-age relationship for males. The pectoral girth of seals was also estimated using the equations in M. M. Bryden (1969b ) which were subsequently corrected (Bryden 1972; see table 6.1).

Biomass

The number of individuals in each age class was calculated from a pup production of 102,000 (McCann and Rothery 1988), assuming a 1:1 sex ratio at birth (McCann 1985) and a stable population age structure. The biomass of each age class was derived from the product of the

number of individuals in each age class and the mean mass of those individuals (table 6.1). The total body gross energy (TBGE) for that biomass was calculated using the equation provided by J. J. Reilly and M. A. Fedak (1990) derived from body composition analyses of gray seals. We assumed a mean water content of 55% derived from estimates of northern elephant seal, M. angustirostris , water content during lactation and molt (Costa et al. 1986; Worthy et al. 1992). The validity of using the Reilly and Fedak equation on different species was discussed in relation to other work on ringed seals, Phoca hispida (Stirling and McEwan 1975), and was broadly confirmed by I. L. Boyd and C. D. Duck (1991). Estimates of biomass are calculated in metric tonnes; 1 tonne equals 1,000 kg.

Energy Expenditure

The annual cycle of southern elephant seals involves three distinct activities: (1) reproduction in adult seals, (2) molt, and (3) foraging at sea (Laws 1960). Each of these will have a characteristic energy cost depending on the mass, reproductive status, and sex of the seal. An additional cost will be incurred in terms of body growth, which will vary with age, although reversible growth, such as seasonal fattening before breeding or molt, is considered as one of the costs of reproduction or molt in this analysis. The total energy expenditure (E) for an individual southern elephant seal can be expressed as

where ER, EG, EF, and EM are the energy costs of reproduction, growth, foraging, and molt, respectively. ER includes the heat increments of lactation, gestation, and, in the case of males, harem defense and competition for mates. EF includes the heat increments of locomotion and feeding the estimates of assimilation efficiency and duration of foraging. EG includes the energy value of tissue growth but excludes seasonal changes in body reserves.

Energy of Reproduction

The metabolic rate, measured by metabolic water production, of female southern elephant seals during lactation was 88 MJ/day (Fedak et al., this volume) or 3.1 times the predicted standard metabolic rate (SMR). The general relationship (SMR = 0.293 W^0.75 MJ/d) between SMR and body mass of mammals has been discussed and confirmed for seals by Lavigne et al. (1986). Energy expenditure on metabolism was 46% of total energy expenditure. This shows that the total energy expenditure of lactation is 6 times SMR, which is in close agreement with measurements made in northern elephant seals (Costa et al. 1986). The mean duration of suckling used to calculate the heat increment of lactation was 23 days for mothers with either male or female pups (McCann, Fedak, and

Harwood 1989; Fedak et al., this volume). Thus, the energy of reproduction for an individual female was obtained from 6 × SMR × 23.

The mean mass of elephant seals at birth was 42.5 kg (McCann, Fedak, and Harwood 1989). The energy density of fetal seals at term has been calculated for ringed seals (9.04 MJ/kg; Stirling and McEwan 1975), harp seals (7.24 MJ/kg; Worthy and Lavigne 1983) and gray seals (5.76 MJ/kg; Anderson and Fedak 1987). The variation in these figures probably reflects species differences in the fat content of pups at birth. We do not know which value is the most appropriate for southern elephant seals, but because some of the ringed seal pups in I. Stirling and E. H. McEwan's study (1975) could have been suckled and this figure may be an overestimate of energy density, we used a conservative value of 6.5 MJ/kg in this analysis. The mass of southern elephant seal placentas is 5 kg, and an energy density of 0.46 MJ/kg (Lavigne and Stewart 1979) was used to calculate total energy content.

There is less information about the energy costs of reproduction in males. The only pinniped studies that have measured energy expenditure showed that breeding male northern elephant seals and territorial male Antarctic fur seals, Arctocephalus gazella , both have metabolic rates 3.3 times SMR (Deutsch, Haley, and Le Boeuf 1990; Boyd and Duck 1991). The competitive mating behavior of these species is similar to the southern elephant seal (McCann 1981). Therefore, we used the same value to calculate the metabolic costs of reproduction in males > 6 years of age. According to McCann (1980), the number of bulls ashore at the breeding grounds increases from September 1 to October 1 and remains roughly stable thereafter until November 18 when the number declines rapidly. We have assumed that they are present from September 14 until November 20 (58 days). The duration of the postweaning fast for pups was 45 days.

Energy of Molt

The energy cost of molt in southern elephant seals was estimated to be 2.4 times SMR (Boyd, Arnbom, and Fedak 1993), which is similar to that measured for adult female northern elephant seals (Worthy et al. 1992). Molting lasts 28 and 40 days on average in adult female and male southern elephant seals, respectively (Ling and Bryden 1981). These values were used to calculate the heat increment of molt in both sexes.

Energy of Growth

The body composition of southern elephant seals shows minor changes at different stages of life (Bryden 1969a ). However, because the scale of these changes is small, we have assumed that growth of body components is proportional to growth in total mass. The annual growth increment of southern elephant seals was calculated from the data on body mass (table 6.1), and the energy increment it represents was calculated using the equation for TBGE provided by Reilly and Fedak (1990).

Energy of Foraging

Activity budgets of seals during the aquatic phases of the annual cycle are based on time depth recorder outputs for southern elephant seals (Boyd and Arnbom 1991; Slip, Hindell, and Burton, this volume). While at sea, adult elephant seals spend 88% of their time diving. Velocities of descent and ascent were 1.64 m/s and 1/44 m/s, which makes sense in terms of empirical measurements of the cost of transport in phocids (Davis, Williams, and Kooyman 1985; Williams and Kooyman 1985). Seventy-four percent of dives had a profile showing that the seals remained at a specific depth for 54% of the duration of the dive. A further 10% of dives had a period when the seals remained at a constant depth before the resumption of a descent phase, and 16% of dives had no period spent at constant depth. Mean dive duration was 17 minutes for each type of dive.

The work required to transport a body through seawater is given by

where CD is the coefficient of drag, V is the velocity, r is the average water density (1.027 × 103 kg/m³ for the Southern Ocean, data from British Antarctic Survey), A is the maximum cross-sectional area, and L is the distance. This is an extended form of the equation of drag (Williams 1987). Estimates of CD will depend on the shape and size of the seal. Values of CD measured for seals range from 0.06 to 0.09 (Williams and Kooyman 1985; Feldkamp 1987), but these are for gliding seals, and it is well known that the drag associated with active swimming is greater. Furthermore, an average adult female elephant seal (length 3.0 m) has a Reynolds number (Re) of 4.3 × 10⁶ , which is close to Re = 5 × 10⁶ for turbulent flow at a velocity of 1.5 m/s. This suggests that most elephant seals are close to the boundary of turbulent flow. Put together, this suggests that the CD for southern elephant seals is greater than measured values for other species would suggest. Therefore, a value of 0.12 was used in the calculation.

T. M. Williams, G. L. Kooyman, and D. A. Croll (1990) showed that harbor seals, Phoca vitulina , had a swimming efficiency (power output as a percentage of power input) that varied with velocity but was approximately 10% at 1.5 m/s.

Using the parameters given in table 6.1, we calculated the average cost of transport for the South Georgia elephant seal population. This assumed that most elephant seals forage in a way similar to the small sample for which detailed measurements are available. It also assumed that nonbreeders continued to forage during the breeding season but that all seals molted on land.

For harp seals, the heat increment of digestion was estimated to be 17% of the gross energy intake (Gallivan and Ronald 1981), and for harp seals and northern fur seals, the assimilation efficiency was estimated to be 90%

of gross energy intake (Keiver, Ronald, and Beamish 1984; Fadely, Worthy, and Costa 1990) on a diet of fish. There is no information for elephant seals, so we have used these figures in our calculations of the heat increment of foraging.

Diet Composition and Population Energy Consumption

It has been difficult to obtain an accurate measure of the diet of southern elephant seals at South Georgia mainly because it has not yet proved possible to measure diet at the foraging grounds. We have to rely on stomach samples obtained from elephant seals at the breeding and molting areas, which can be many hundreds of kilometers from the foraging areas (Fedak et al, this volume). Laws (1956) examined 139 stomachs, of which 108 contained no food; of the remainder, 24 contained squid and 9 fish. Laws (1977) therefore suggested that the diet of southern elephant seals consisted of 75% squid and 25% fish by weight. P. G. Rodhouse et al. (1992) have described the cephalopod prey, from samples obtained by stomach flushing, and confirmed that squid made up the greatest proportion of the diet. No fish remains were discovered, but fish are probably underrepresented in stomach flushes because of their rapid rate of digestion. Therefore, we have little justification for departing from Laws's overall figure for diet composition. In addition, we have to assume for the present that diet measured from stomach lavaging is broadly indicative of overall diet, although the analysis presented here also provides an indication of what amounts of different types of prey would be taken if the proportions of squid and fish departed from those suggested by Laws (1977).

Energy densities vary considerably between different species of squid, so the squid diet was divided into three parts: (1) muscular squid, (2) gelatinous squid, and (3) cranchiid squid, which have a leathery mantle. The classification of each species plus its representation by percentage mass of squid in the diet is given in table 6.2. Energy values were assigned following A. Clarke et al. (1985). We assumed that fish taken were a mixture of myctophids and notothenids. Although there is no evidence that southern elephant seals feed on myctophids, they are dominant among species of shoaling fish in the parts of the water column in which elephants seals apparently feed (Hindell 1991; Boyd and Arnbom 1991), which suggests that they are potential prey. Energy densities of myctophids are in the range of 7–8 MJ/kg (Cherel and Ridoux 1992), and we have used a value of 7.5 MJ/kg. The energy density of other fish species was assumed to be 4 MJ/kg (ibid.).

The total biomass of each item consumed in the diet was calculated from the gross energy requirement of the population (GE), so that

where I1_m , I2_m , . . . , ln_m denote the mass of each item in the diet and I1_e , I2_e , . . . , ln_e denote the energy value (MJ/kg) of each item. This equation was solved for the mass of each item from knowledge of the proportion by mass of each item in the diet. Therefore,

where r1, r2, r3, and so on were the ratios of In_m to the mass of the other items in the diet.