Partial life-cycle analysis: A model for birth-pulse populations

Matrix population models have become standard tools for the demographic ana lysis of age- or stage-structured populations. Although age-classified (Les lie) matrix models make maximum use of age-specific demographic data, age a t first reproduction, which has been suggested to be an important life-hist ory variable, does not appear as an explicit parameter in these models. Con sequently, the sensitivity of population growth rate to changes in age at f irst reproduction cannot be calculated using standard techniques. Age-speci fic demographic data to parameterize age-structured models are difficult to collect, and models that can be parameterized with partial demographic dat a ("partial life-cycle models") have been developed. Partial life-cycle mod els are based on life-history stages, and these models can also be used to calculate sensitivity of population growth rate to changes in various life- history variables, including ages at first and last reproduction. Here, we present a partial life-cycle model appropriate for situations where demogra phic data are collected immediately after the birth pulse (post-breeding ce nsus). We present methods of parameterizing the partial life-cycle model, a nd derive formulas for calculating the sensitivity of the population growth rate to changes in model parameters, including ages at first and last repr oduction. We analyzed life-table data for several species of mammals using the partial life-cycle model and found that results of our partial life-cyc le model compare favorably with those obtained from the corresponding age-c lassified models.