Partial permanence and extinction in an N-species nonautonomous Lotka–Volterra competitive system

In this paper, we first consider a general N-species nonautonomous Lotka–Volterra system. We show that certain average conditions involving the respective averages of the growth rates and the interaction coefficients imply the total persistence of all species. Using this result, we then give computable conditions on the coefficients which imply the ultimate extinction of certain species in a NN-dimensional Lotka–Volterra system.