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

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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. © 2008 The Authors.

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