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A Common Rule for the Scaling of Carnivore Density

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Science  22 Mar 2002:
Vol. 295, Issue 5563, pp. 2273-2276
DOI: 10.1126/science.1067994

Abstract

Population density in plants and animals is thought to scale with size as a result of mass-related energy requirements. Variation in resources, however, naturally limits population density and may alter expected scaling patterns. We develop and test a general model for variation within and between species in population density across the order Carnivora. We find that 10,000 kilograms of prey supports about 90 kilograms of a given species of carnivore, irrespective of body mass, and that the ratio of carnivore number to prey biomass scales to the reciprocal of carnivore mass. Using mass-specific equations of prey productivity, we show that carnivore number per unit prey productivity scales to carnivore mass near –0.75, and that the scaling rule can predict population density across more than three orders of magnitude. The relationship provides a basis for identifying declining carnivore species that require conservation measures.

Across communities in plants and animals, there is an inverse relationship between population density and body size, such that resource use and availability are driving consistent statistical patterns (1–5). The critical factor is the individual species' rate of resource use. Typically, resource use is identified in general metabolic or physiological terms, as these represent the invariant properties of all biological systems at different levels. The precise measure and form of resource use have only been described indirectly (6–9).

We developed a general model (10) to predict carnivore density relative to resources, expressed as prey biomass and prey productivity (11–14). We tested this model with data from the literature on density of 25 species of carnivores (15–20) and their most common prey (21) (Table 1). For each species, we calculated the average number of carnivores per unit prey biomass (i.e., carnivore number per 10,000 kg of prey). Controlling for prey biomass allows us to account for the wide variation in carnivore density resulting from variation in prey density within species, as well as to make comparisons between species.

Table 1

Summary of carnivore density and prey biomass. The number of carnivores per 10,000 kg of prey biomass was estimated from the ratio of carnivore population density (number per 100 km2) to biomass density (in units of 10,000 kg per 100 km2) of the main prey species averaged for each species. These values were used in Fig. 2A. Minimum and maximum estimates of the carnivore density and prey biomass density obtained for this study are provided (43).

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Within carnivore species, population density is typically positively correlated with prey biomass (Fig. 1). In keeping with the assumption that a species' population density is influenced by individual rates of resource use (4), the number of carnivores supported on a given biomass of prey increases with decreasing body size. Comparing between species, we find a strong negative relationship between the number of carnivores per 10,000 kg of prey and carnivore body mass (Fig. 2A). The relationship takes the form of a power function [number per 10,000 kg of prey = 89.1 × (carnivore mass)−1.05;N = 25, R 2 = 0.83, P< 0.0001]. The exponent does not differ significantly from –1.0 [95% confidence limits, –0.845 (upper), –1.25 (lower); confidence limits for constant, 169 (upper), 47 (lower)] (22–24).

Figure 1

Carnivore density (number per 100 km2) plotted against prey biomass density (in units of 10,000 kg per 100 km2) for different species of carnivores. For the purposes of illustration, we show the slopes of the regression (plotted through the origin) estimated for each species (see text for details): solid circles and solid line, tiger (Panthera tigris); shaded circles and gray line, lion (Panthera leo); open circles and dashed line, leopard (Panthera pardus); asterisks and dotted line, Canadian lynx (Lynx canadensis).

Figure 2

Three measures of carnivore density plotted against carnivore body mass (plotted on a log-log scale): (A) number of carnivores per 10,000 kg of prey, (B) average carnivore density (number per 100 km2), and (C) number of carnivores per unit prey productivity (number per 10,000 kg of prey productivity per year) (see text for details). In (A), the Eurasian lynx is represented by the open circle; excluding this species, the regression is y= 94.54x – 1.03 (R 2=0.86).

Our results depend on controlling for prey biomass. A plot of average carnivore population density (number per 100 km2) against carnivore body mass has considerably more variation than in the biomass-based analyses (Fig. 2B) [number per 100 km2= 197.6 × (carnivore mass)−0.88; N = 25, R 2 = 0.63, P < 0.0001; confidence limits for exponent, –0.59 (upper), –1.18 (lower); confidence limits for constant, 500 (upper), 78 (lower)].

An example of the importance of controlling for prey biomass can be seen by comparing the European badger (Meles meles) (15) and the coyote (Canis latrans) (19), both of which weigh about 13 kg. These species differ in average population density by a factor of almost 20, but this is due to a nearly 40-fold difference in the prey biomass density available to these species. Our biomass-based estimate of population density differs by a factor of only 1.6 (Table 1).

Previous studies have pointed out that density estimates of different-sized species may be confounded by sampling area (25,26). Although the density values for carnivores and their prey may both be influenced by the sampling area, it is unlikely that this factor would bias our estimates of the predator-prey relationships in a way that would influence the overall allometric relationship shown inFig. 2A. In addition, previous analyses of wolf population data (27) (Table 1) found that the inclusion of sampling area in a multiple regression model did not substantially improve the model fit.

Ultimately, predator populations are sustained by population productivity rates of their prey rather than by standing biomass. Estimates of turnover on a population-by-population basis are not available, but biomass-based population productivity measures have been estimated in relation to body mass (11–13). We expected that the number of carnivores per unit prey biomass would vary with (carnivore mass)−1.0 and that the carnivore number per unit productivity would vary with (carnivore mass)−0.75 (10). We plotted the average ratio of carnivore number per unit productivity (number per 10,000 kg per year) against carnivore mass (Fig. 2C). This relationship has an exponent not significantly different from –0.75 [number per unit productivity = 56.2 × (carnivore mass)−0.66;N = 24, R 2 = 0.70, P< 0.0001; exponent confidence limits, –0.48 (upper), –0.85 (lower); confidence limits for constant, 101 (upper), 31 (lower)] (28). These findings support the notion that there is no systematic variation in prey productivity between carnivore species, and that carnivore density is constrained by metabolic rates and prey abundance.

We selected species that provide a range of body sizes, habitats, and feeding strategies; these include an invertebrate-feeder [the European badger (15)] and vertebrate hunter specialists [e.g., the African lion (Panthera leo) (16), leopard (Panthera pardus) (16, 17), and polar bear (Ursus maritimus) (18)]. Despite the wide variation in species' ecology, we find remarkable consistency in the average population density in relation to prey biomass and carnivore mass. However, some of the residual variation in population density can be explained in terms of species' biology. For example, interspecific predation and competition is a major factor influencing carnivore population density (29). African wild dogs (Lycaon pictus) and cheetahs (Acinonyx jubatus) can be found at lower densities in areas where prey are very abundant because of the abundance of competing lions and spotted hyenas in these areas (30, 31).

Clearly, all species are influenced to some degree by competition with other carnivores, and this must contribute to the variation found in density estimates across populations. Furthermore, the temporal responses of carnivore density to changes in prey may be somewhat related to turnover rates in different-sized prey (29). Lynx (Lynx canadensis) and coyotes (Canis latrans) feeding primarily on smaller prey such as rodents and hares show more rapid functional responses than do larger carnivores such as Isle Royale wolves (Canis lupus), which require 3 to 5 years to respond to population changes in moose numbers (29). As more data become available, our predictive model should be refined to quantitatively show the effect of these ecological differences in species abundance.

Allometric scaling, frequently used in biology to extrapolate trait values for species that are relatively unknown, is increasingly being applied to the prediction of population numbers for rare, endangered, and threatened species (32–34). Scaling studies that control for key ecological variables (such as resource availability) may provide an important framework for identifying species that deviate from expected values because of other ecological processes. The data on the Eurasian lynx cited in this study provide an example (Fig. 2A). This species is rare relative to the estimated prey biomass availability (35–37). One population was recently reintroduced and both populations have been exposed to poaching, possibly contributing to the relatively low densities at these sites.

Mammalian carnivores are often uniquely characterized by fine-tuned relationships with their prey (38–40). It appears that carnivores are closely tied not only to prey size (14) but also to prey biomass. Carnivore populations and species are now rapidly dwindling in numbers. At least 90 carnivore species are currently listed as threatened or endangered (41). Our results show that prey density is a fundamental determinant of carnivore density both within and between species. Given that carnivore population density has been identified as a predictive factor influencing extinction risk (42), prey density is critical to the future of stable carnivore populations.

  • * To whom correspondence should be addressed. E-mail: chris.carbone{at}ioz.ac.uk

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