Table 1.
Allometric fits for behavioral and physiological phenomena used in the calculation of diffusivity†.
Figure 1.
Allometric relations between bodymass M and population density, metabolic rate, mean longevity, daily displacement, home range, and range length.
Figure 2.
Allometric relations between bodymass M and animal-mediated nutrient diffusivity, Equations [3] and [4] in the main text.
Solid lines are estimates calculated using scaling arguments, dashed lines as a fit to primary data. Circles show diffusivity by way of excreta, crosses show diffusivity by way of bodymass.
Figure 3.
Diffusion into granitic region of KNP.
Upper panel shows geometry of the simulated transect, with an inset to show the initial and boundary conditions of a transect across the substrate gradient in the absence of herbivore diffusion. Lower panels show phosphorus stocks in edible vegetation under a succession of herbivore removals, varying from Φ varies from 7 km2/year (estimate prior maximum) to 2 (present-day estimate) to 0.075 (estimate in the absence of herbivores >100 kg). A. P dynamics under an upper estimate of K = 0.0013/year; B. P dynamics under a lower estimate of K = 0.00013/year. Additional parameter values set to Po = 875 kg P km−2, G = 0.5 kg P km−2 year−1.
Figure 4.
Estimates of herbivory and nutrient diffusivity in Kruger National Park by mammalian herbivores >1 kg in KNP.
(a) Potential rates of consumption based on population density and metabolic demand. The mean rate of herbivory per taxon is 927 kg/km2 or 0.37% of the biomass standing crop. (b) cumulative rate of herbivory across body mass (c) nutrient diffusivity Φ, using observations of component terms (where possible – black points) and allometric scaling (8.672*M1.191; red points). (d) cumulative nutrient diffusivity Φ across body mass, based on direct observations of component terms, and allometric scaling of component terms.
Figure 5.
Global distribution of terms in herbivore diffusion of nutrients.
(a) nutrient diffusivity Φ = DQ/αB, (b) change in Φ if all threatened species are lost.
Figure 6.
Global distribution of terms in herbivore diffusion of nutrients.
(a) movement diffusivity D, (b) percent consumed biomass Q/αB, (c) total animal biomass (ie Σ mass * population), (d) nutrient diffusivity Φ = DQ/αB, (e) edible biomass αB, (f) number of mammalian herbivores >1 kg.