Stable population analysis in periodic environments

A discrete time model is developed for periodic survivorship and maternal frequency rates. The Leslie matrix is subdivided by an additional variable representing time of birth (season of birth in the example presented) to accommodate both age-specific and time-specific variations in vital rates. Thus, in contrast to the standard time-invariant model, significant periodic alterations in age-specific birth and death rates are explicitly accounted for and may realistically include observed recurrent changes, such as zero or reduced birth rates during unfavorable seasons, etc. Conditions for stability of the extended projection matrix are developed and are shown to be analogous to those of the Leslie model. The periodic model is applicable to populations with overlapping generations in seasonal environments.