A two-sex population dynamics model with strong parental care

Abstract

We present a two-sex age-structured population dynamics deterministic model taking into account parental care of offspring. The model includes a weighted harmonic mean-type pair formation function and neglects the spatial dispersal and separation of pairs. Each sex has pre-reproductive and reproductive age intervals. All adult (of reproductive age) individuals are divided into single males, single females, and permanent pairs. All pairs are of two types: pairs without offspring under parental care at the given time and pairs taking child care. All individuals of pre-reproductive age are divided into young (under parental care) and juvenile (offspring who can live without parental care) groups. It is assumed that births can only occur from couples and after the death of any of the pair partner all offspring under parental care are killed. The model consists of six integro-partial differential equations subject to the conditions of the integral type. A class of separable solutions is studied for this model in the case of time-independent vital rates and a system for macromoments evolving in time is derived in the case of age-independent vital ones.