Phase Dependent Population Growth Models

Growth of biological populations is phase dependent; individuals can give birth to offspring only after reaching a ‘maturity age’. Assuming that the life time of an individual consists of two phases, we study the implication of phase dependence in deterministic and stochastic population growth models. By taking the first phase to be of constant duration in the deterministic model an explicit expression for the size of the population is derived. Developing a birth and death process in which the birth and death rates are age and phase dependent, an explicit expression for the mean number of individuals has been obtained in the case when the death rate is constant. Two particular cases of the model are also discussed.