Age structured matrix predation model for the dynamics of wolf and deer populations

A matrix predation model similar to Volterraʹs predation model was developed and applied to study predation of the wolf (Canis lupus) on a white tailed deer (Odocoileus virginianus) population. The Leslie matrix enables an age structured predation model to be stated with just two equations that are similar to the Volterra equations but with parameters that can be estimated from available life history data. The wolf and deer population dynamics with the matrix model were the same damped oscillations observed with the scalar differential equation model, but with the matrix model the changes in age structure are obtained. Addition of random environmental variation to survival of fawns resulted in continuing cyclic fluctuations in both deer and wolf. A sensitivity analysis showed that the dynamics of the populations were sensitive to mortality of wolf pups, and that fluctuations in both the wolf and deer populations could be reduced with removal of wolf pups.