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In this paper we seek necessary and sufficient conditions for the permanence and the global asymptotic stability of a positive equilibrium for a Lotka-Volterra system with two delays. ᮊ 1999 Academic Press G 0, and , are continuous functions. Obviously, we can take ␤ G 0 2 Ž . without loss of generality. We assume that 1.1 has a positive equilibrium U

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In this paper, we consider population survival by using single-species stage-structured models. As a criterion of population survival, we employ the mathematical notation of permanence. Permanence of stage-structured models has already been studied by Cushing (1998). We generalize his result of permanence, and obtain a condition which guarantees that population survives. The condition is applicable to a wide class of stage-structured models. In particular, we apply our results to the Neubert-Caswell model, which is a typical stage-structured model, and obtain a condition for population survival of the model.

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