Simple density-dependent matrix model for population projection

A matrix model based on a discrete time form of the logistic equation and the Leslie matrix model was developed for density-dependent population growth; the model is simpler and more easily applied than the model developed by Liu and Cohen in 1987 using a different discrete time form of the logistic equation. The new model requires no additional parameters, matrices, or mathematical functions, and it links life tables, the exponential growth equation, the logistic growth equation, and Leslie's matrix. The new model possesses the same qualitative dynamical behavior as both the model developed by Liu and Cohen and the discrete time logistic equation; it exhibits stable points, cycles, and chaos. It easily can be modified to include features developed for the logistic equation such as time lags. The model was applied to describe the growth of a white-tailed deer population introduced into a fenced reserve.