Insight into the relative importance of different killer whale food resources can be obtained through energetic/demographic bookkeeping; knowing only the abundance, field metabolic rate and consumption efficiency of the predator; and the abundance, caloric value and the life history (i.e. age-specific fertility, mortality and growth) of the prey (). Employing simple demographic modelling approaches (Caswell 2001
; Morris & Doak 2002
) and energetic-needs calculations, this information can be used to conduct feasibility analyses for specific dietary scenarios, thus moving debate from poorly supported conjectures over whether or not some consequence of a food-web interaction occurred to assessments of whether or not it could have occurred and if so how easily. ‘No’ answers are especially powerful because they permit the rejection of hypotheses ().
Figure 3 Species and measurements used in the feasibility analyses based on their demography and energetics. (Predator: killer whales (abundance, field metabolic rate, consumption efficiency); prey: sea otter; pinnipeds; large cetaceans; small cetaceans (life (more ...)
Figure 4 Graphical representation of sustainability analyses. The horizontal axis depicts the proportion of the maximum sustainable mortality that would have to be consumed by transient killer whales to support the number of animals depicted on the vertical axis. (more ...)
We first used this approach to show that killer whale predation could have caused the excess deaths needed to drive the sea otter and pinniped declines with only small changes in dietary composition or the number of predators (Estes et al. 1998
; Williams et al. 2004
). Because this is a ‘yes’ answer, the process is open to alternative interpretations.
We have also used demographic/energetic modelling to ask whether changes in great whale populations due to human exploitation could have resulted in substantial differences in killer whale food resources in the North Pacific (Doak et al. 2006
). Here, we expand this approach to ask what kinds of transient killer whale dietary scenarios are consistent with sustainable prey populations, and in particular whether the current transient killer whale predator–prey system is sustainable without the predation/consumption of large whales. In addition to information on gross caloric value, life history and population abundance identified above, the essential variables in these calculations are (i) the species and life stages of prey that are attacked and eaten by killer whales, (ii) the fraction of prey deaths that result from predation, (iii) the prey tissue types that are eaten, (iv) the caloric values of these tissue types, and (v) the proportion of the carcass (or tissue type) that is consumed. Inherent in the last variable are limitations in meal size and processing rates of killer whales.
We will begin by determining how many transient killer whales could be sustained on various dietary scenarios involving only the great whales and end by asking whether or not the smaller marine mammals were sustainable in the face of killer whale predation following the decline of great whale food resources.
Because full demographic schedules (birth and death rates by age or age class) have not been accurately estimated for any large whale population, we instead relied on three commonly used summaries of life-history patterns that have been estimated for most great whales: age at maturity; ‘natural’ (non-anthropogenic) adult mortality rate; and inter-birth interval. As described in Doak et al. (2006)
, we used these rates to assemble a simple two-stage (juvenile and adult) demographic description for each of the major great whale species in the North Pacific: blue; Bryde's; fin; grey; minke; sei; humpback; bowhead; northern right; and sperm whales. These 10 species represent the majority of great whale numbers in the North Pacific now and in the past. In addition to the demographic rates, estimates of total mortalities rely on population estimates, which we obtained from Pfister & DeMaster (2006)
Seven species of small marine mammals are common in our region of interest: harbour seal; harbour porpoise; sea otter; beluga whale; northern fur seal; Steller sea lion; and Dall's porpoise. While several species of ice seals (spotted, ringed, ribbon and bearded), and the Pacific walrus, also approach our region, they are unlikely to be major food resources for killer whales in the Aleutian region and we therefore do not include them in our analyses. For each of the other species, we created an age-dependent, two-sex demographic model. For the harbour seal, we could rely on the data from Pitcher (1990)
for survival and growth estimates. For all other species, empirical data on demographic rates are partial and, for survival rates, often inconsistent. Therefore, we used the allometric relationships for survivorship in Trites & Pauly (1998)
to approximate size-specific survival rates for each species and used information in various chapters of Perrin et al. (2002)
to obtain reproductive rates. Along with the estimates of abundance (, from Pfister & DeMaster 2006
), these demographic schedules can provide both current and historical estimates of the production of dead animals.
Table 1 Current and historical estimates of small marine mammal abundance in the North Pacific Ocean and southern Bering Sea. (Data from Pfister & DeMaster (2006)).
While we used the basic demographic models just outlined to make production estimates from current numbers, predicting historical production rates requires an additional set of assumptions. Since marine mammal stocks were presumed to be more or less stable prior to industrial exploitation, demographic rates must have been different from those currently estimated. However, which rates differed and by how much is unknown. At one extreme, it is possible that fecundities were unaffected by reductions in numbers (see Mizroch & York 1984
), but mortality rates were considerably higher than currently estimated. This pattern of density-dependent effects would yield the maximum production of dead animals for a stable population of a given size. Conversely, as the numbers increase survival might be unaffected, but fecundities lowered to achieve population stability. This would result in the minimum number of deaths for a given stable population size. Since both extremes and many mixed responses to density are known in mammals, we modified all our population models in two ways, by reducing only fecundity or reducing only survival. We then used these two types of models in conjunction with historical population estimates to arrive at an estimated numbers of deaths.
We next calculated the number of killer whales that could be supported from the sustainable number of great whale or small mammal deaths. We assume that adult male killer whales require 287 331
, while females require approximately 193
(these figures account for assimilation efficiency: Williams et al. 2004
). For small marine mammals, we made the simple assumption that all of each carcass is consumed, and used a standard estimate of 2.5
for all species. Thus, the conversion of a predated animal into food is quite simple.
For great whales, the situation is more complex, with the conversion of dying whales into killer whale food depending on several factors. First is the composition of the tissues actually consumed. Although detailed data on the caloric content of whale tissues are not available, we use information on both whale tissue and other mammals to estimate that whale tongues provide 2.07
, a mixture of whale meat and blubber has approximately 2.5
and blubber alone has approximately 4.0
(Williams et al. 2004
). Second, we need to specify which animals are predated commonly enough to be worth considering. We considered two patterns, which reflect familiar ideas about the preferences of killer whales: (i) only juvenile whales (and adult minkes) are predated, and since a mixture of blubber and meat would be consumed, the average energy gain is 2.5
and (ii) juveniles and minkes are consumed (2.5
), as are tongues (2.07
) and blubber (4.0
) of adults, but only a limited amount of blubber is used (up to the mass of the tongues for all baleen whales, and up to 1000
kg for sperm whales). Third, even a predated whale may provide relatively little food for killer whales, if only a few animals can feed upon the carcass before it sinks. Owing to sinkage, in the different model runs we conservatively assume that each killer whale can feed either once or twice on a great whale kill, thus constraining maximum input per kill for each individual killer whale to 125
kg for adult females and 186
kg for males (estimated from the data provided by McBain, Sea World and the proportional metabolic needs of males and females). Documented group sizes of hunting killer whales range from 5 up to 35 (Reeves et al. 2006
), so we ran the calculations with pack sizes of 10, 20 or 30 animals feeding at once on each prey individual.
Finally, for all prey species, we have no quantitative data on the fraction of dying animals that are predated. Because we have no good information on this for any prey species, we ran estimates of each group of prey (large whales versus small marine mammals) for predation-caused/scavenged deaths that range from 5 to 50 per cent. We summarize many of our analyses over this range to emphasize its key importance in driving our results.