Spatial scaling of allometry for terrestrial, mammalian carnivores

A regression slope of -0.75 between log₁₀ density and log₁₀ body mass is thought to express equivalence of energy conversion among species' populations of similar taxonomic and trophic status. Using larger sample sizes than the usual 1-3 density estimates per species, we estimated a regression slope of -0.71 for terrestrial mammalian carnivores. We investigated the sampling variation in this estimate, and those derived from smaller intra-specific subsets, using 1000-iteration bootstrap analyses to obtain 90% confidence intervals. As expected, these widened as random subsets were reduced in size, but always contained the postulated -0.75. However, log₁₀ density also declined as 3/4 of the log₁₀ spatial extent of study area, and study area accounted for virtually all of the variation in density that was previously thought due to body mass. We removed the effect of study area by using the species-specific regression models between density and study area to predict density at a common scale of 400 km². These common-scale densities regressed against body mass with a slope of -0.16, but separated into body mass classes less than and greater than 11 kg, they produced slopes that were not significantly different from zero. We show that the allometry of density could be a case of circular logic, whereby body mass has influenced the investigator's choice of study area, and the resulting scale-dependent densities are related back to body mass. To test the allometry hypothesis, the effect of study area on density estimates needs to be removed. This requires conducting larger-scale studies of the smaller-bodied species so that all species compared are represented by an average study area that is near the common scale. Furthermore, study sites need to be selected and designed to represent more than the local detail in species' density.