Uncertainty propagation in matrix population models: Gaps, importance and guidelines

Abstract

Matrix population models (MPMs), which describe the demographic behaviour of a population based on age or stage through discrete time, are popular in ecology, evolutionary biology and conservation biology. MPMs provide a tool for guiding management decisions and can give insight into life history trade‐offs, patterns of senescence, transient dynamics and population trajectories. These models are parameterised with estimates of demographic rates (e.g. survival and reproduction) and can have multiple layers of underlying statistical analyses, all of which introduce uncertainty. For accurate and transparent results, this uncertainty should be propagated through to quantities derived from the MPMs, such as population growth rates (λ). However, full propagation is not always achieved, leading to omitted uncertainty and negative consequences for the reliability of inferences drawn. We summarised the contemporary standards regarding demographic rate uncertainty reporting and propagation, by reviewing papers using MPMs from 2010 to 2019. We then used reported uncertainties as the basis for a simulation study to explore the impact of uncertainty omission on inferences drawn from the analysis of MPMs. We simulated four scenarios of demographic rate propagation and evaluated their impact on population growth rate estimates. Although around 78% of MPM papers report some kind of uncertainty in their findings, only half of those report uncertainty in all aspects. Additionally, only 31% of papers fully propagate uncertainty through to derived quantities. Our simulations demonstrate that, even with moderate levels of uncertainty, incomplete propagation introduces bias. Omitting uncertainty may substantially alter conclusions, particularly for results showing small changes in population size. Biased conclusions were most common when uncertainty in the most influential demographic rates for population growth were omitted. We suggest comprehensive guidelines for reporting and propagating uncertainty in MPMs. Standardising methods and reporting will increase the reliability of MPMs and enhance the comparability of different models. These guidelines will improve the accuracy, transparency and reliability of population projections, increasing our confidence in results that can inform conservation efforts, ultimately contributing to biodiversity preservation.