Partial life cycle analysis: a model for pre-breeding census data

Matrix population models have become popular tools in research areas as div erse as population dynamics, life history theory, wildlife management, and conservation biology. Two classes of matrix models are commonly used for de mographic analysis of age-structured populations: age-structured (Leslie) m atrix models, which require age-specific demographic data, and partial life cycle models, which can be parameterized with partial demographic data. Pa rtial life cycle models are easier to parameterize because data needed to e stimate parameters for these models are collected much more easily than tho se needed to estimate age-specific demographic parameters. Partial life cyc le models also allow evaluation of the sensitivity of population growth rat e to changes in ages at first and last reproduction, which cannot be done w ith age-structured models. Timing of censuses relative to the birth-pulse i s an important consideration in discrete-time population models but most ex isting partial life cycle models do not address this issue, nor do they all ow fractional values of variables such as ages at first and last reproducti on. Here, we fully develop a partial life cycle model appropriate for situa tions in which demographic data are collected immediately before the birth- pulse (pre-breeding census). Our pre-breeding census partial life cycle mod el can be fully parameterized with five variables (agc at maturity, age at last reproduction. juvenile survival rate. adult survival rate, and fertili ty), and it has some important applications even when age-specific demograp hic data are available (e.g., perturbation analysis involving ages at first and last reproduction). Wr have extended the model to allow non-integer va lues of ages at first and last reproduction, derived formulae for sensitivi ty analyses, and presented methods for estimating parameters for our pre-br eeding census partial life cycle model. We applied the age-structured Lesli e matrix model and our pre-breeding census partial life cycle model to demo graphic data for several species of mammals. Our results suggest that dynam ical properties of the age-structured model are generally retained in our p artial life cycle model, and that our pre-breeding census partial life cycl e model is an excellent proxy for the age-structured Leslie matrix model.