Frankenstein matrices: Among-population life history variation affects the reliability and predictions of demographic models.

Population matrix models are routinely used to study the demography of wild populations and to guide management choices. When vital rates are unknown for a specific population or life history stage, researchers often replace them with estimates from other populations of the same species. Such 'hybrid' matrices might ignore among-population life history variation and lead to incorrect inferences. In this study, we examined the real-world effect of using hybrid matrices on demographic inference and management decisions, using a large dataset on yellow-bellied toad (Bombina variegata) populations, an amphibian species whose life history depends on human land use. We estimated stage-specific survival and recruitment for 18 populations across different habitat types. We then assessed how estimated population growth rates and elasticities changed when population-specific vital rates were replaced by estimates from other populations, chosen randomly or based on habitat, demographic or geographic proximity. The use of hybrid matrices mixing demographic estimates from different populations and habitats biased predictions. The mean bias was relatively minor even when sampling randomly across all populations, because our large dataset represented the whole range of life histories and errors cancelled out on average. However, borrowing estimates from geographically close or demographically similar populations substantially reduced the risk of extreme errors. Borrowing from populations from similar habitat types could also reduce bias, but results varied depending on the exact habitat types concerned. Our study illustrates how habitat-specific among-population variation in life history affects the reliability of population matrices commonly used in evolutionary demography, ecology and conservation. When the use of hybrid population matrices cannot be avoided, their creation can be informed by additional information about ecological or demographic patterns, helping reduce bias. When such information is not available, we recommend that studies should consider the whole space of parameter estimates (the complete range of estimates available), thus transparently describing the true uncertainty surrounding demographic estimates.