Counting the bodies: Estimating the numbers and spatial variation of Australian reptiles, birds and mammals killed by two invasive mesopredators

Introduced predators negatively impact biodiversity globally, with insular fauna often most severely affected. Here, we assess spatial variation in the number of terrestrial vertebrates (excluding amphibians) killed by two mammalian mesopredators introduced to Australia, the red fox (Vulpes vulpes) and feral cat (Felis catus). We aim to identify prey groups that suffer especially high rates of predation, and regions where losses to foxes and/or cats are most substantial.

Since British colonisation in 1788, the introduced red fox Vulpes vulpes (hereafter 'fox') and domestic cat Felis catus (hereafter 'cat') have had, and continue to have, major detrimental impacts on Australian biodiversity. These mesopredators are thought to be the primary cause of extinction for at least 20 animal species, and responsible for the ongoing declines of many others (Abbott et al., 2014;Woinarski, Braby, et al., 2019;Woinarski et al., 2015).
In Australia, the management of foxes and cats is a priority conservation concern (Department of the Environment, 2015; Department of the Environment Water Heritage & the Arts, 2008).
Across mainland Australia, there are areas in which broad-scale baiting of foxes (and other wild canids) has been implemented for many years (Robley et al., 2009;Saunders et al., 2010), a smaller number of areas with comparable cat control (e.g., Comer et al., 2020), as well as some relatively small areas where fencing excludes both predators . Otherwise, the vast majority of Australia has no effective management of invasive predators. Without management, the impacts of foxes and cats on Australian biodiversity are likely to be severe, widespread and ongoing.
A recent series of related papers, building on large datasets of dietary studies, have documented the number of species (and their biological traits) of Australian vertebrates killed by cats Woolley et al., 2019), and the number of species (and their traits) of Australian reptile, bird and mammal species killed by foxes (Stobo-Wilson, Woinarski et al., 2021). This allows the complement of species eaten by these two predator species to be compared, and the species eaten by one or both predators to be tallied. These studies have demonstrated a high degree of dietary overlap between foxes and cats in the vertebrate species consumed, but also some differences, with foxes taking, on average, larger prey than cats, highlighting their impacts are both compounded and

complementary.
A parallel set of analyses evaluated the total numbers of individual vertebrates killed annually by cats in Australia Woinarski et al., 2018), including by pet cats . Here, we build upon these recent papers by addressing the following research questions: 1. Does spatial variation in the density of foxes in Australia differ from that of cats?
We predict the density of foxes will vary across their Australian range, and that there will be regions where the density of foxes is higher than cats, and vice-versa 2. What is the estimated number of individual Australian reptiles, birds and mammals killed annually by foxes?
We predict there to be a greater number of individuals consumed by foxes in those regions of Australia where fox densities are predicted to be higher.
3. How does the number and spatial pattern of animals killed by cats compare to that of foxes across Australia?
We predict there to be a greater overall number of individuals consumed by cats relative to foxes due to the greater geographic range of cats. Additionally, we predict there to be a separation of impact between foxes and cats across Australia, with a greater number of individuals consumed by cats in regions of Australia where cat densities are predicted to be higher.
4. What is the combined toll of animals killed by cats and foxes across Australia?
We predict there to be significant cumulative predation pressure by foxes and cats across large regions of Australia.
Our study -the first to quantify the continental-scale death toll imposed by both cats and foxes on vertebrate prey -aims, in part, to help direct management efforts to areas where impacts may be most acute and the benefits of investment may be most substantial. We know of no comparable study at this scale that describes and compares the death toll, across multiple vertebrate prey groups, imposed by two co-occurring introduced predators.

| Background: the fox and cat in Australia
Foxes were introduced to south-eastern Australia from the 1840s (Abbott, 2011), and populations became established from about 1874 (Fairfax, 2019). Foxes now occupy about 6.2 million km 2 (>80%) of mainland Australia, absent only from monsoonal northern Australia. They also occur on about 50 Australian islands (totalling 3,265 km 2 ). In contrast, cats now occur across >99% of mainland Australia and Tasmania (a total area of 7.6 million km 2 ) and are present on about 100 islands (with total area of about 90,000 km 2 ) . Cat introduction and spread preceded that of foxes by about 30-50 years (Abbott, 2008).

| Numbers of animals killed by foxes: approach and assumptions
The approach taken to estimate the number of individual animals killed by cats in Australia has been described previously Woinarski et al., 2018).
We used similar methods to estimate the number of reptiles, birds and mammals killed by foxes. The approach comprised the following steps: (i) prediction of spatial variation in fox density across Australia; (ii) compilation of existing data from studies that report the frequency of occurrence (FOO) of taxonomic groupings (prey groups) of animals in fox dietary samples (i.e., the proportion of dietary samples that contain a specified item), and then modelling spatial variation in FOO; (iii) assessment of the numbers of individual animals (of particular prey groups) in fox dietary samples that contain that prey group and (iv) a discount for the number of food items that appear in fox dietary samples, but were likely scavenged (i.e., as carrion) rather than killed by the fox.
We do not estimate tallies of the numbers of frogs taken by foxes, given that these have been recorded in relatively few fox dietary samples, and because their digestibility makes scat samples an unreliable method for interpreting the extent of predation on frogs  Broadly, our analytical approach assumes that the annual number of individual animals of each prey group killed by foxes at a location can be estimated from the product of the density of foxes at that location, the average number of individuals of that prey group in a single fox stomach at that location and the number of days in a year. We then assumed that these local estimates can be summed to derive national estimates. There are several assumptions underlying, or caveats qualifying, this procedure: 1. All animals in fox dietary samples were killed by the fox that consumed them. This assumption may lead to some overestimation in the kill rate by foxes because foxes will consume pre-killed animals (carrion). In response, we develop and apply a discount factor for animals consumed as carrion (see later section).
2. Foxes consume all animals that they kill. This assumption may lead to an under-estimation in the kill rate because foxes frequently surplus kill [i.e., do not consume animals they kill, as has been reported many times for foxes in Australia (Abbott et al., 2014;Short et al., 2002)].
3. What is present in a fox scat or stomach represents what is eaten by a fox in the preceding 24 h, and hence can be expressed as the daily kill rate by that fox, following the logic used in analogous cat dietary studies (e.g. Murphy et al., 2019). Based on studies of the passage rate of food items in the fox digestive tract (e.g., Witt, 1980), this assumption is likely to be highly conservative, with digestion rate of most prey types typically being <24 h. However, some prey items may be cached for later consumption or consumed over several days, such that the presence of that prey item in a fox dietary sample may not mean that the animal was killed within the 24-h period preceding sample collection (Macdonald, 1976).
4. Fox density and the incidence of any prey group in fox diets at any site are temporally invariant. However, fox density at any location varies seasonally (due to highly seasonal reproduction), and in some parts of Australia, fox density changes in response to control programmes and to rainfall patterns (and the consequential variation in prey abundance) . Furthermore, the diet of foxes also varies seasonally or with rainfall conditions (Green, 2003;Green & Osborne, 1981;Pavey et al., 2008;Wilson & Wolrige, 2000), between sex and age groups (Forbes-Harper et al., 2017) and in response to pest control programmes (that reduce fox and/or prey abundance) (Newsome et al., 2014;Roberts et al., 2006). Hence, there may be temporal variation in the take of prey groups by foxes at any location. However, there is no systematic bias in this respect in the set of our compiled studies: the constituent studies included sampling across one or many seasons, and with or without control programmes (although such information is not always stated in the studies themselves), and our modelling across studies does not include any factors relating to seasonal condition or management. 5. We assume that eggs are detected in proportion to the number consumed. Many studies have demonstrated high rates of predation by foxes on clutches of reptile and bird eggs and have concluded that, for some reptile and bird species, the major impact of fox predation is likely to be through predation of eggs (Thompson, 1983). However, eggs were likely to be severely under-recorded in the fox dietary studies we collated because they are highly digestible and thus difficult to discern in fox stomachs and scats, and because foxes often only consume egg contents (Dawson et al., 2016;Spencer et al., 2021). Consumption rates of eggs will therefore be under-estimated in our data collation and reporting.

| Fox density analysis
We developed a fox density layer by building a predictive model based on a dataset of 437 published and unpublished observations of fox density (ten from highly modified environments) spread across the fox's Australian range ( Figure S1b). A variety of methods were used to estimate density, but the most common were spotlighting, track counts and counts of active dens (used for 70%, 9% and 6% of density observations, respectively). The fox density estimates included areas with and without fox control. However, given that our aim was to predict fox density across Australia, and we do not have a spatial layer describing area with and without fox control across Australia, we simply included both subsets of data in the analysis. To avoid pseudoreplication, density estimates from the same location were averaged, reducing the dataset to 44 spatially distinct density estimates, including six from highly modified environments ( Figure S1b). To analyse the fox density data, we took the same approach as that used by Legge et al. (2017) for modelling cat density across Australia.
We used least-squares linear regression models incorporating all combinations of six climatic and environmental variables, determined for each location, giving a total of 64 models. The variables were mean annual temperature (Australian Bureau of Meteorology, 2016a), mean tree cover within a 5-km radius (Hansen et al., 2003), topographic ruggedness within a 5-km radius (Jarvis et al., 2008), distance from the coast (distance from coast was used instead of the island [yes/no] variable that was used in the original complementary cat analysis), mean human population density within a 5-km radius (Australian Bureau of Statistics, 2014) and vegetation disturbance within a 5-km radius (Australian State of the Environment, 2017) (see Table S1 for a detailed description of each parameter). Mean annual rainfall (Australian Bureau of Meteorology, 2016b) was originally considered as a predictor variable, but preliminary analysis highlighted that this variable was strongly correlated with vegetation cover (r > .7) and moderately correlated with several other variables (r > .5), so it was ultimately excluded from analyses. We log 10 -transformed distance to coast and human population density. Fox density was log-transformed prior to analysis to ensure normality of model residuals.
Models were evaluated using Akaike's information criterion corrected for small samples sizes (AIC C ). The final model was based on multi-model averaging of the entire candidate set, with each model weighted according to the Akaike weight (Burnham & Anderson, 2003).
The final model was used to predict fox density across the fox's distributional range at 1 km 2 resolution ( Figure S1). Note that the fox is largely absent from far northern Australia, and to demarcate the northern range limit we used fox presence records, based on specimens or sightings, from the Atlas of Living Australia (ALA) database (www.ala.org.au), following Stobo- . For the mainland, we identified bioregions (Department of Sustainability Environment Water Population & Communities, 2013) in which the fox is present (i.e., bioregion has recent [post-1970] fox records), and added islands where the fox is known to occur based on the database of Legge et al. (2018).
To estimate the total population of foxes in Australia, we predicted density for every 1 × 1 km cell across the fox's distributional range and then calculated the sum of the estimates across all cells.
We characterised the uncertainty of the total fox population by bootstrapping the dataset 10,000 times and recalculating the population based on each random selection of the data. We report the 2.5% and 97.5% quantiles for the 10,000 bootstrapped values of total predicted population.

| Fox diet analysis: variation in FOO
We compiled data from 89 studies of fox diet in Australia (with several studies including multiple sites, such that the total number of sites with samples was 168) that reported the FOO of reptiles  (Table S2). These studies were widely spaced across the geographic range of the fox in Australia and sampled diverse environments ( Figure S1a). Some studies excluded empty stomachs from FOO calculations; where this was the case, we recalculated FOO to apply to all collected samples. We also noted whether the dietary sampling was from fox scats or fox stomachs as previous studies have indicated that different prey groups (e.g., birds, livestock) are more likely to be detected in fox stomachs than in fox scats (Cavallini & Volpi, 1995;Fleming et al., 2021). Note that this collation of fox dietary studies has also largely been used by Fleming et al. (2021) to describe characteristics of the diet of foxes in Australia, and more details of the collated dataset are described in that paper. Prior to modelling, we followed the protocol for data exploration provided by Zuur et al. (2010). All continuous predictor variables were centred and standardised by deducting the mean and dividing by twice the standard deviation (Gelman, 2008).
For each fox diet study site, we determined the values of the six climatic and environmental variables described above to assess their effects on the FOO of animals in fox diet samples. To accommodate the potentially different detectability of animals from scat versus stomach samples, we also considered the proportion of dietary samples that were from scats (cf. stomachs) in each study, as a predictor variable.
We used generalised linear models (GLMs), within the binomial error family, to examine geographic variation in the FOO of each prey group in the diet of foxes. The response variable was the proportion of fox diet samples (scats and/or stomachs) containing the prey group. Using the binomial error family, the GLMs incorporated lower precision from observations based on a small number of samples. We examined a set of 128 candidate models representing all combinations of the seven explanatory variables described above (temperature, vegetation cover, ruggedness, distance to coast, human population density, vegetation disturbance, proportion of scat samples). Models were evaluated using a second-order form of Akaike's information criterion (QAIC c ), which is appropriate for small sample sizes and over-dispersed data (Burnham & Anderson, 2003). There was evidence of strong overdispersion, so we used the 'quasibinomial' error structure to estimate coefficient standard errors and confidence intervals. We applied model averaging to the entire candidate set to account for model uncertainty, with each model weighted according to its Akaike weight. We identified highly influential variables by calculating relative variable importance (RVI), defined as the sum of Akaike weights for all models containing a given predictor variable. Variables with a RVI value ≥0.73 (equivalent to an AIC c difference of 2; Richards, 2005) were retained in the best model, which was used to identify the most influential predictor variables and visualise variable effects. Model averaged coefficients from the entire candidate set were used to predict the FOO of each prey group in fox diets across Australia.
The proportion of scat samples was retained as a variable here only if it was found to have a negative influence on the prey groups FOO (i.e., the prey group was less likely to be detected in scat than in stomach samples).
Four fox diet studies for island sites were included in analyses (three studies from Phillip Island and one from Bennison Island; see Figure S1a). We modelled the FOO of all prey groups in fox diets both including and excluding these islands to ensure that island sites did not bias the results. We found that including island sites did not alter the most influential predictor variables identified for any of the prey groups and therefore retained all sites in our analyses (see Table   S3).

| Fox diet analysis: variation in number of individual prey animals, and proportions of native species, within samples
In 18 studies that analysed fox stomachs only, tallies were given for the number of individual reptiles in those samples that contained reptiles. We found a significant positive correlation between the FOO for reptiles and the number of individual reptiles identified in fox stomachs and therefore used the predicted FOO of reptiles in fox stomachs to estimate the number of individual reptiles in those diet samples that contained reptiles, using a linear least-squares regression model (log 10 [individuals − 0.99] ~ log 10 [frequency]) (see Figure S4a). Of the fox dietary studies that reported the species of reptiles consumed (n = 47), none reported consumption of introduced reptile species. Hence, our fox predation tallies assume all reptiles killed were native.
In 21 studies that analysed fox stomachs only, tallies were given for the number of individual birds in those samples that contained birds. We found no significant relationship between the FOO of birds and the number of individual birds in fox stomachs across these studies, so we used the mean number of individual birds within fox stomach samples across studies (1.2 birds) to estimate the number of individual birds in diet samples that contained birds.
For the studies in our collation that also reported on the species of birds occurring in fox scats or stomachs (n = 38), we calculated the proportion of native and of introduced birds (relative to all birds) in those samples. Note that far more fox dietary studies reported simply on the occurrence of 'birds' in samples rather than on the species of bird consumed, so our fox predation tallies report on overall consumption of birds rather than breaking this tally down to groups of bird species.
In 22 studies that analysed fox stomachs only, tallies were given for the number of individual mammals in those samples that contained mammals. There was a significant positive correlation between FOO of mammals and the number of individual mammals identified in fox stomachs. We therefore used the predicted FOO of mammals in fox stomachs to estimate the number of individual mammals in those diet samples that contained mammals, using the same approach described above for reptiles (see Figure S4b).

| Discount for consumed items scavenged (i.e., consumption of carrion) rather than killed
Foxes frequently consume carrion (see Appendix S1 and references therein). To account for potential consumption of carrion in our calculations, we used an expert elicitation approach to estimate the proportion of each taxonomic group in fox dietary samples that were likely taken as carrion. We report only estimates of the number of animals killed by foxes (i.e., the total estimated consumption less the proportion taken as carrion).

| Estimates of tolls taken by foxes
To spatially represent the estimated number of animals killed per fox per day, we multiplied the modelled FOO of each prey group in fox diets across Australia by the number of individuals in fox diet samples containing that prey group, discounting the number of animals estimated to be consumed as carrion. We then multiplied this by the modelled density of foxes across Australia, and then by 365.25 (days in a year), to provide a spatial representation of the estimated number of animals killed by foxes per km 2 per year. We summed this rate across the extent of the fox's distributional range in Australia to derive the total number of animals killed by foxes.
We followed the approach of Murphy et al. (2019) to characterise the uncertainty of the estimated total number of animals killed by foxes, using bootstrapping. Bootstrapping is an appropriate approach because we needed to propagate errors from a number of analytical steps. Hence, we simultaneously bootstrapped (10,000 times -which was the maximum feasible given computational constraints) the underlying datasets: (i) fox density; (ii) frequency of the prey group in fox samples and (iii) the mean number of individuals of that prey group in fox diet samples containing that prey group. For each random selection of these underlying data, we recalculated the total number of animals killed. We report the 2.5% and 97.5% quantiles for the 10,000 estimates of the total number of animals killed.
We also include the uncertainty associated with the estimate of the proportion of animals consumed as carrion. We did this by sampling a normal distribution and then applying an inverse-logit transformation to the realised value (to constrain the values [of proportion consumed] between 0 and 1). By adjusting the mean and standard deviation of the underlying normal distribution, we ensured that the median and 10% and 90% quantiles of the final values (constrained between 0 and 1) closely matched the best guess and upper and lower standardised credible intervals.

| Comparison of tolls of animals taken by foxes and cats
The recent analyses of the numbers of animals killed by cats in Australia Woinarski et al., 2018) considered three components of the overall Australian cat population: pet cats, feral cats in highly modified environments (e.g., urban areas) and feral cats in largely natural environments [as defined by Legge et al. (2017)]. A comparable subdivision is not used in our assessment of fox diet because foxes are not kept as pets, and because we included parameters relating to habitat modification in our modelling. We compare tallies (and spatial variation in these tallies) of animals killed by foxes with those killed by (i) feral cats from largely natural environments and (ii) feral cats (in natural and modified environments) as well as pet cats, with the latter component based on an updated estimate of the numbers of animals killed by Australia's pet cats .
We did not include a discount term for the proportion of animals consumed by cats that were taken as carrion, because many studies have shown that cats take much less carrion than do foxes (Christensen et al., 2013;Forsyth et al., 2014;Read et al., 2016).
Nonetheless, cats do some scavenging (e.g. Cunningham et al., 2018;Fleming et al., 2020), so our cat tallies may be marginal overestimates in this regard.

| Fox density and population size cf. cats
We found a significant negative relationship between fox density and mean annual temperature, and a significant positive relationship between fox density and human population density (see Table   S4, Figure S2). The best-supported model of fox density had high model fit (R 2 = .66; Table S4; Figure S3). Areas that have the highest predicted density of foxes include the coastal belt across southeastern Australia, south-western Australia and parts of coastal South Australia (Figure 1a). In contrast, cat density (in years of average rainfall) is less variable across their extensive Australian range ( Figure 1b). Based on spatially modelled density, we estimate that there are 1.7 million foxes in Australia, at an average density of 0.27 km −2 , compared with 6.6 million cats (comprising 2.1 million feral cats in natural landscapes, also at average density of 0.27 km −2 , 0.7 million feral cats in highly modified landscapes and 3.8 million pet cats; Table 1) .

| Reptiles
The mean FOO of reptiles in fox dietary samples was 10.3%. FOO of reptiles in fox diets significantly increased with mean annual temperature (standardised beta coefficient ± standard error [SE], 0.84 ± 0.34) and decreased with vegetation cover (−1.19 ± 0.37) and vegetation disturbance (−0.77 ± 0.30; see Figure 2a, Figure S5). The best model for FOO of reptiles in fox diets had an R 2 of .49.
We estimate that 88 million reptiles (95% confidence interval [CI]: 49-170 million) are killed by foxes across Australia each year, with 85 million of these in predominantly natural landscapes. These figures exclude the 4% of reptiles that are estimated to be consumed by foxes as carrion. This estimate of reptiles killed by foxes is less than a fifth of the total estimated to be killed by feral and pet cats across Australia each year (609 million reptiles; Table 1, Figure 3).

| Birds
The mean FOO of birds in fox diet samples was 14.4%. FOO of birds in fox samples was significantly lower when sampling comprised a greater proportion of scats than stomachs (standardised beta coefficients ± SE for proportion of scats: −0.43 ± 0.14). The FOO of birds in fox diets significantly increased with vegetation disturbance (0.44 ± 0.11) and mean annual temperature (0.73 ± 0.12) and was higher close to the coast (−0.85 ± 0.11; Figure 2b; Figure S6). The best model for the FOO of birds in fox diet had an R 2 of 0.54.
We estimate that 111 million birds (95% CI: 51-176 million) are killed by foxes across Australia each year, of which 93% are native. These figures exclude the 7% of birds that are estimated to be consumed by foxes as carrion. The estimate of birds killed by foxes is less than a third of the number estimated to be killed by feral and pet cats across Australia each year (399 million; Table 1, Figure 3).

| Mammals
The mean FOO of mammals in fox dietary samples was 70.0% when considering all mammals, 39.5% for native mammals and 37.1% for introduced mammals. The FOO of native mammals in fox diets increased with vegetation cover only (standardised beta coefficients ± SE 1.34 ± 0.15; Figure S7). Conversely, introduced mammals were less likely to occur in fox diets as vegetation cover (−1.11 ± 0.15) and human population density increased (−0.61 ± 0.18) and were more likely to occur in fox diets as vegetation disturbance increased (0.73 ± 0.22; Figure S7). Introduced mammals were also significantly less likely to be detected in fox dietary studies that predominantly used scat (rather than stomach) samples (−0.68 ± 0.25). The best models for FOO of native and introduced mammals in fox diets had  Table 1).
Of the mammal subgroups identified in fox diets, rodents had the greatest FOO (22.4%), with an almost equal representation of native rodents (FOO 10.9%) and introduced rodents (FOO 11.6%) ( Figure S8a,b). A total of 129 million rodents (95% CI: 90-311 million) are estimated to be killed by foxes each year from natural landscapes (Figure 3). Of this total, around 43% (55 million, 95% CI: 31-147 million) are native. This is only 20% of the number of native rodents estimated to be killed by feral cats each year (268 million).
Like cats, lagomorphs were the second most frequently occurring mammal subgroup in fox diets (FOO 19.0%), with 114 million (mostly European rabbits) estimated to be killed by foxes each year (95% CI: 46-259 million) ( Figure S8c). This tally is about half that estimated to be killed by feral cats (201 million). The other main introduced prey group was livestock (FOO 12.9%; Figure S8d). Livestock was the only mammal subgroup that was significantly less likely to be detected at a site as the proportion of scat samples increased (standardised beta coefficient ± SE −1.16 ± 0.24). After accounting for the 74% of livestock estimated to be consumed by foxes as carrion, we estimate foxes kill 38 million livestock animals (95% CI: 4-122 million) across Australia each year; we had no comparable estimate for cats.

| Toll of Australian fauna taken by foxes and cats
Collectively, we estimate 697 million reptiles, 510 million birds and 1,435 million mammals are killed by foxes and cats across Australia each year (Table 1), with the greatest predation pressure in urban and peri-urban areas (Figure 4) where cat and fox densities are greatest. However, there are contrasting patterns of spatial variation in tolls of animals taken beyond urban areas, with more animals eaten by foxes than by cats in south-eastern and south-western Australia, and by cats in other regions (Figure 4b).

| DISCUSS ION
Here, we provide the first estimates of the toll (and its spatial variation) of wildlife taken by foxes at a continental scale. Our evaluation allows for a direct comparison to the toll taken by another co-occurring introduced predator, the cat. Such tolls help contextualise the relative predation threats imposed by both species (Loss et al., 2012)  Note: Values relating to foxes are from this study. Values relating to cats have been sourced from Legge et al. (2017), , Woinarski et al. (2018), Murphy et al. (2019) and Legge et al. (2020). Confidence intervals for the estimated number of animals eaten by cats were not provided by the original sources and therefore have not been provided here. Note that FOO values and tallies are not given for minor mammal prey groups (FOO < 5%).
TA B L E 1 Density and population estimates for foxes, feral cats and all cats (including feral and pet cats) throughout Australia, with mean frequency of occurrence (FOO) of all major prey groups, and the estimated numbers eaten for all major prey groups 2019). In addition, this information can help determine spatial priorities for such management (Januchowski-Hartley et al., 2018).
A key component of our estimate of tolls is the population size (and its spatial variation) of the two predator species. We found that the density of foxes varies markedly across their Australian range, with highest densities in urban areas and in temperate areas of southern mainland Australia and lower densities in warmer and tropical regions.
In contrast, feral cat density varies less across their near ubiquitous Australian range . On average, cats are more abundant than foxes outside of forested and temperate areas in Australia.
Our national population estimate for foxes (1.7 million) is much lower than a previous estimate of about 7 million (McLeod, 2004); we attribute this discrepancy to the earlier estimate being based on far fewer studies that were mostly in temperate, urban and/or forested areas where fox density is appreciably higher than in their more extensive arid and semi-arid range (Forsyth et al., 2019;McLeod, 2004).
Foxes are opportunistic omnivores (Cagnacci et al., 2003;Saunders et al., 2010), and the pattern observed here of spatial variation in FOO of different prey groups in fox diet is likely to at least partly reflect spatial variation in the abundance of those prey groups, a result consistent with a national Australian study , and regional Victorian study (Davis et al., 2015). This is similar to patterns of spatial variation in FOO displayed by cats in Australia with, for example, reptiles also forming a larger proportion of cat diet in arid and semi-arid Australia . Much of the difference between the two predator species, in terms of the spatial variation in the relative numbers of prey killed, likely also reflects variation in the relative densities of the two predators. Hence, on average, foxes kill more animals than do cats in south-eastern Australian temperate forests (where they are more abundant than cats), but kill fewer animals in the rest of Australia (where foxes are less abundant).
For most prey groups, the Australian fox population kills many fewer individual animals than do cats. This is a consequence of several F I G U R E 2 Model projections of the frequency of occurrence of (a) reptiles, (b) birds, (c) native mammals and (d) introduced mammals in fox diets throughout Australia. Solid black line indicates the Tropic of Capricorn and hatching indicates areas outside of the fox's distributional range The estimated total number of animals, by taxonomic group, killed by foxes (dark grey) and feral cats (light grey) each year in largely natural landscapes across Australia, and (b) the proportion of that total killed by foxes compared to feral cats factors: (i) cats occur over a larger area (7.6 million km 2 cf. 6.2 million km 2 ), resulting in a larger total population of feral cats (2.8 million cf. 1.7 million foxes); (ii) there is an additional component of the Australian cat population, pet cats, that adds considerably to the total toll taken by cats ; (iii) much more of the fox's dietary intake is derived from carrion, so they do not need to make as many kills as cats; (iv) although vertebrates are staples in fox diet, as omnivores they also supplement their diet with more invertebrates and plant material than do cats  which are obligate carnivores; (v) although there is extensive overlap between foxes and cats in the vertebrate species eaten, foxes tend to take larger prey items than do cats (Stobo-  and so obtain the same volume of food with fewer kills and (vi) birds and reptiles occur less frequently in fox diets than in cat diets. The disparity in numbers of animals killed by foxes relative to cats varies across prey groups, and for a few groups (notably possums and macropods), foxes kill more individuals than do cats. For possums, this is probably because their abundance is highest in areas where fox abundance is generally higher than that of cats; for macropods, this difference may be because foxes are more capable than cats of taking larger animals (e.g., Banks et al., 2000).
The disparities in numbers of animals killed by foxes and cats suggest important differences in the relative impacts of these two predators. Such differences can help set broad management priorities; for example, to direct fox control efforts especially to areas where the toll from foxes is greater than that from cats. However, we note that the modelling on which we base our estimates of total numbers of animals killed is continental in scale, and that there will be much nuance in local conditions, not readily described in our broad-scale assessment. Furthermore, our tallies mostly group taxonomically related prey species, while predation impacts may fall especially on some individual wildlife species, including those whose attributes render them relatively poorly adapted to sustained predation. For example, detailed studies and experimentation have demonstrated that, in some areas, foxes, but not cats, take an unsustainable toll of clutches of some turtle species (Spencer & Thompson, 2005;Spencer et al., 2016), even though across most of Australia, we found that cats take far more reptiles than do foxes. This example also serves as a caveat that our analyses probably under-estimate the consumption of reptiles (and birds), because digested eggs leave little trace in fox stomachs or scats.
Notwithstanding our interest in the comparison between foxes and cats in relative kill rates, the cumulative or compounded impact of these two species is of more conservation concern. Across their vast overlapping range, these two predators are collectively exert- interactions between these two predators can complicate the conservation outcomes (Marlow et al., 2015). These examples demonstrate that the predation pressure imposed by cats and foxes is likely unsustainable for many Australian animal species in many regions, but with well-planned, targeted management, that pressure can be significantly reduced or even removed. be sustainable for many species, but the predation pressure falls inequitably across species  and some native vertebrate species may be incapable of sustaining even low rates of predation .
Our estimates of the numbers of animals killed annually by foxes can also be counterpointed with total population estimates F I G U R E 4 (a) The estimated total number of animals (including only reptiles, birds and mammals) eaten by foxes and cats combined each year throughout Australia, and (b) the proportion of this total that is attributable to fox predation; dashed line indicates where the number of animals eaten by foxes versus cats is relatively equal (50% although Saunders et al. (1995) noted the proportion of lambs taken by foxes in some areas was much higher (10-30%). In this case, our likely over-estimate may be because we under-estimated the proportion of livestock consumed as carrion, and that larger animals (including livestock) killed by foxes are likely to be eaten over multiple days.
In addition to improved knowledge of the population size and its spatial variation for two nationally important threats to biodi- Our focus in this study is on the number of animals killed by these two introduced predators, and its biogeographic patterning. But we recognise that assessing the relative conservation impact of such rates of mortality is complex. The impacts of cats and foxes may be compensatory rather than simply additive, as many studies have shown interactions between these two predators (Glen & Dickman, 2005;Molsher et al., 2017;Ritchie & Johnson, 2009). Adding to the complexity, there may be some situations where fox and/or cat predation may provide an element of conservation benefit, such as where such predation constrains the abundance of introduced pest species (Courchamp et al., 1999). The losses attributable to predation by cats and foxes should not be viewed in isolation, as the impacts of cat and fox predation interact with (and compound and are compounded by) many other threatening processes, including habitat fragmentation, fire and grazing pressure (Graham et al., 2013;Hradsky, Robley, et al., 2017;Legge et al., 2019).
Our results demonstrate that the magnitude of fox and cat predation on Australian wildlife is substantial, and there is justification in maintaining and expanding strategic and targeted programmes aimed at reducing the numbers and hence predation pressure of these two introduced species.

ACK N OWLED G EM ENTS
The data collation, analysis and preparation of this paper were sup-

CO N FLI C T O F I NTE R E S T
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are openly available