Abstract
In this paper, we first derive an equationfor a single species population with two age stages and a fixedmaturation period living in the half plane such as ocean andbig lakes.By adopting the compact open topology, we establish some a prioriestimate for nontrivial solutions after describing asymptotic propertiesof the nonlocal delayed effect, which enables us to show thepermanence of the equation. Then we can employ standard dynamical system theoretical arguments to establish the globaldynamics of the equation under appropriate conditions. Applyingthe main results to the model with Ricker's birth function andMackey-Glass's hematopoiesis function, we obtain threshold resultsfor the global dynamics of these two models.
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