Asymptotic Behavior of an Age-Structured Population Model and Optimal Maturation Age

AbstractA continuous age-structured population model with two population groups, juveniles and adults, and with a dynamics for the resource, is considered. The only density dependence is through a uniform increase of the death rates. A complete description of the asymptotic behavior of the population dynamics system is obtained showing under natural hypotheses the existence of a nontrivial (“ecological”) equilibrium which attracts any initial nonzero population with nonzero initial amount of resources. Assuming that the offspring production rate is an increasing function of the maturation age, the evolutionarily stable value of this variable is briefly discussed