Lateral diffusion of nutrients by mammalian herbivores in terrestrial ecosystems

Abstract

Animals translocate nutrients by consuming nutrients at one point and excreting them or dying at another location. Such lateral fluxes may be an important mechanism of nutrient supply in many ecosystems, but lack quantification and a systematic theoretical framework for their evaluation. This paper presents a mathematical framework for quantifying such fluxes in the context of mammalian herbivores. We develop an expression for lateral diffusion of a nutrient, where the diffusivity is a biologically determined parameter depending on the characteristics of mammals occupying the domain, including size-dependent phenomena such as day range, metabolic demand, food passage time, and population size. Three findings stand out: (a) Scaling law-derived estimates of diffusion parameters are comparable to estimates calculated from estimates of each coefficient gathered from primary literature. (b) The diffusion term due to transport of nutrients in dung is orders of magnitude large than the coefficient representing nutrients in bodymass. (c) The scaling coefficients show that large herbivores make a disproportionate contribution to lateral nutrient transfer. We apply the diffusion equation to a case study of Kruger National Park to estimate the conditions under which mammal-driven nutrient transport is comparable in magnitude to other (abiotic) nutrient fluxes (inputs and losses). Finally, a global analysis of mammalian herbivore transport is presented, using a comprehensive database of contemporary animal distributions. We show that continents vary greatly in terms of the importance of animal-driven nutrient fluxes, and also that perturbations to nutrient cycles are potentially quite large if threatened large herbivores are driven to extinction.

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 and 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*M^1.191; 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.