Population dynamics of deer

Abstract

We modelled a population of white-tailed deer and determined the optimal harvesting patterns. Since the deer naturallay fall into three distinct groups—fawns, does, and bucks—we used a three-dimensional system of difference equations to model the sizes of the three groups at yearly intervals. We include arbitrary harvesting terms in each equation which were to be chosen in order to maximize the total value of the harvest over a long period of time. We assumed that the mortality rates of each group were proportional to their sizes. The total yearly food supply remained constant. We used actual data to estimate realistic ranges on the parameters in the model. We defined the value function of the harvest as a weighted sum of the harvested deer and the live deer. We then used an iterative linear programming method to optimize this value function in order to determine an optimal harvesting pattern over a period of twenty years. Under normal conditions, we found that it is best to harvest mostly bucks, some does, and no fawns. We discovered that a “buck law”—a law which prohibits hunting anything but bucks—is not an optimal way of harvesting the deer. We examined the results for different values of the mortality parameters and found them to be the same. Therefore, our solution appears to be stable with respect to environmental conditions.