Temporally‐indexed multi‐species density impact functions: Quantifying timing and impact of invasive predators on seabird breeding success

Abstract Conserving threatened bird species often requires effective predator suppression strategies, particularly on islands where introduced predators pose significant threats. However, to be effective, predator suppression requires an understanding of the nature and timing of predator impacts, often within the context of a multi‐predator assemblage that requires simultaneous management. Density‐impact functions provide a framework to quantify the relationships between predator abundance and impact but are currently limited to a single species with invariant impact. Here, we expand density impact functions to a multi‐species assemblage with temporally varying impacts, applying them to a case study of rat ( Rattus spp.) and mustelid ( Mustela spp.) predation on a burrowing seabird species. We calibrate these impact functions using data collected over 2 years and across 14 grey‐faced petrel ( Pterodroma gouldi ) colonies in northwestern New Zealand. We found that nest success is negatively affected by increased abundance of Norway rat ( Rattus norvegicus ) and stoat ( Mustela erminea ) during the early chick rearing stage. Surprisingly, despite equal or greater predator abundances, we found no relationship during the egg‐laying and late chick rearing stages. Our temporally indexed multi‐species density‐impact functions allow us to identify key predators and management periods in the breeding cycle, thereby recommending an effective strategy for restoring and conserving a threatened species. Our results provide empirical evidence that a burrow‐nesting procellariid species can be successfully conserved in invaded ecosystems, highlighting a valuable conservation strategy for several globally threatened procellariids on such islands.