Understanding the constraints dominant predators impose on subordinate species is important for predicting ecosystem dynamics and anticipating outcomes of predator management. Subordinate predators may avoid dominant predators in time or space, making it difficult to quantify antipredator behaviours unless joint spatiotemporal analyses are used. Here, we tested whether an invasive dominant predator (red fox Vulpes vulpes) alters the spatiotemporal activity of an invasive subordinate predator (feral cat Felis catus). We collated records of both species from 3,667 camera-traps deployed experimentally across two regions of south-eastern Australia with simplified predator guilds. Foxes were poison-baited in some landscapes within each region. We used generalised additive models to quantify changes in predator spatiotemporal activity across geographic space, vegetation types, human footprint and (artificially manipulated) gradients of dominant predator activity. Foxes and cats had similar diel activity patterns when averaged across all sites, however there was important differentiation at a finer scale cats did not reduce their spatial activity but shifted diel patterns when localised fox activity was high. Cats were crepuscular on average. However, across dry vegetation types of both regions (where foxes were nocturnal), cats shifted to diurnal behaviour with increasing fox activity. In contrast, fox activity was relatively consistent throughout the daily cycle in the wet forest; here cats avoided dawn when fox activity was high. Changes in cat diel activity patterns may facilitate spatial coexistence between these two invasive predators, potentially shifting feral cat impacts onto different native prey. It is well-appreciated that predator activity varies spatially and fluctuates throughout the daily cycle. However, our study demonstrates that diel activity patterns also vary across space, likely mediated by both landscape-context and fear. Dominant predator avoidance in time appears to be spatially dynamic a key nuance which is overlooked when simply comparing the average activity overlap between two species.

We compiled data from multiple smaller-scale camera-trap studies, each designed to experimentally assess mammal responses to fox control. Overall, we collated 5,449 and 2,202 independent detections of foxes and cats, respectively (separated by at least 30 minutes) from 172,052 camera-trap nights. We collated camera-trap data across two regions in south-west Victoria, Australia: the Glenelg region and Otway Ranges. In broad sections of each region, government land managers conduct ongoing targeted lethal fox control for biodiversity conservation. All camera-trap deployments consisted of a Reconyx (Holmen, Wisconsin) brand camera-trap (white or infrared flash), attached to a tree or a metal picket, facing a lure.

Analyses were conducted in R version 4.1.3 [@R]. We first used lorelograms to identify the minimum interval to approximate independence; this indicated that discarding repeat detections of a species within 30 minutes was sufficient to reduce temporal autocorrelation. To account for day length variation across space and time, we extracted sunrise and sunset times for each camera-trap deployment using the 'maptools' R-package and adjusted detection times to be relative to sunrise and sunset using the average double anchoring approach described by @vazquez2019comparing. We then built a dataframe consisting of a row for each hour of the day (0-23), for every camera-trap deployment (n = 3,667), recording the total number of 'independent' fox and feral cat detections within each hour across the camera-trap survey. We modelled the total number of independent detections of each predator per hour for each camera-trap deployment (response variable) with generalised additive mixed-effect models implemented in the 'mgcv' R-package.