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. Equilibrium density of the resources is provided being minimal. Thus maximum energy influx into the population is gained. Search algorithm of evolutionary values of puberty, age and maximal longevity of individuals belonging to the consumer population is proposed. Analytic dependence of maximal longevity on environmental factors and some other parameters are found. Aging is considered to be mechanism leading to death while individual approaches evolutionary optimal longevity.