The effect of density‐dependent catastrophes on population persistence time

Abstract

Summary There has been increasing recognition that catastrophes are an important factor in modelling threatened populations. However, density dependence has generally been omitted from models of threatened populations on the assumption that this omission yields conservative predictions. We explore the significance of including density‐dependent catastrophes in models of threatened populations. Using an analytical model, we show that density‐dependent catastrophes have a significant effect on population persistence, decreasing mean persistence time at large population sizes and causing a relative increase at intermediate sizes. We illustrate our results with empirical data from a disease outbreak in crabeater seals Lobodon carcinophagus and show that intermediate population sizes have the longest predicted persistence times. The pattern we found is qualitatively different from previous results on persistence time based on density‐independent models, in which persistence time increases with population size to an asymptote. Synthesis and applications. This study has important implications for the conservation of species that may experience density‐dependent catastrophes, such as disease outbreaks or starvation. Our results indicate that small and intermediate sized populations may contribute disproportionately to species persistence. Thus populations that have been dismissed as ‘marginal’ may actually be important for conservation. In addition, culling may increase the persistence of populations that experience density‐dependent catastrophes.