Applying difference equations to wolf predation

Abstract

Parameters for generalized Lotka-Volterra equations, expressed as difference equations, have been estimated from actual data on wolves and their prey. The functional response is represented by a single constant, while the numerical response is expressed as a ratio-dependent limitation on predator abundance. Parameters for the Lotka-Volterra equations were estimated by multiple-regression fits to data on moose (Alces alces) and wolves (Canis lupus) on Isle Royale, and from other sources. Observed prey-predator ratios are highly variable, but much of the variability may arise from nonequilibrium conditions. A multiple-prey model has been developed by assuming that utilization rates vary in proportion to relative current biomass. If analyses are to be useful, the dynamic, nonlinear nature of predator-prey systems requires that a system of equations be developed, along with extensive series of observations of actual abundances of predator and prey.