Bias in population growth rate estimation: sparse data, partial life cycle analysis and Jensen's inequality

Demographic matrix models have become an integral part of population viability analysis for threatened and endangered species, but their use is often limited by data availability. A common solution to this problem is to assume constant annual rates within a multi‐year stage. Partial life cycle analysis (PLC), which incorporates only juvenile and adult stages, is a noteworthy example of this approach because it has been described in the literature as a reliable approximation of age‐structured populations. However, we predict from Jensen's Inequality that the required lumping of age classes leads to over‐ or underestimation of population fitness when survival rates are truly age‐dependent. We illuminate this problem by comparing fitness estimates from Leslie matrix and PLC models for theoretical populations having different levels of age‐dependence in their survival rates. We also propose a modification of the PLC approach to address this problem and demonstrate its applicability using data from a published long‐term study of red deer Cervus elephas .