Iteroparous reproduction strategies and population dynamics

Asymptotic relationships between a class of continuous partial differential equation population models and a class of discrete matrix equations are de rived for iteroparous populations. First, the governing equations are prese nted for the dynamics of an individual with juvenile and adult life stages. The organisms reproduce after maturation, as determined by the juvenile pe riod, and at specific equidistant ages, which are determined by the iteropa rous reproductive period. A discrete population matrix model is constructed that utilizes the reproductive information and a density-dependent mortali ty function. Mortality in the period between two reproductive events is ass umed to be a continuous process where the death rate for the adults is a fu nction of the number of adults and environmental conditions. The asymptotic dynamic behaviour of the discrete population model is related to the stead y-state solution of the continuous-time formulation. Conclusions include th at there can be a lack of convergence to the steady-state age distribution in discrete event reproduction models. The iteroparous vital ratio (the rat io between the maximal age and the reproductive period) is fundamental to d etermining this convergence. When the vital ratio is rational, an equivalen t discrete-time model for the population can be derived whose asymptotic dy namics are periodic and when there are a finite number of founder cohorts. the number of cohorts remains finite. When the ratio is an irrational numbe r, effectively there is convergence to the steady-state age distribution. W ith a finite number of founder cohorts, the number of cohorts becomes count ably infinite. The matrix model is useful to clarify numerical results for population models with continuous densities as well as delta measure age di stribution. The applicability in ecotoxicology of the population matrix mod el formulation for iteroparous populations is discussed. (C) 2001 Society f or Mathematical Biology.