Dynamics of biological community of the "resource--consumer" type considering age structure of consumer population is described by a system of differential equations with special derivatives. On the basis of such a model, a competition model for non-crossing populations with different individual development rates is elaborated. It is shown that only a population with development rates maximizing the Malthusian function (reaching zero value at the equilibrium state of the system) is able to survive under competition for food resources.
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