Large carnivore hunting and killing of domesticated livestock represents one of the most common triggers of human-carnivore conflict globally (Mizutani, 1999; Frank et al., 2005; Maggi et al., 2014). Within this context, people who have experienced livestock losses will often retaliate against those carnivores perceived to be responsible or in an effort to prevent future livestock losses (Kissui, 2008; Hazzah et al., 2009; Goldman et al., 2013; Dickman et al., 2014; Lichtenfeld et al., 2014; Kahler and Gore, 2015). Termed “livestock depredation,” this driver of conflict has been exacerbated by increasing population growth, range expansion, and meat dependency among the global human population (Naughton-Treves et al., 2003; Treves and Karanth, 2003; Ripple et al., 2014). Today, >75% of the world's large carnivore species are experiencing population declines, and retaliatory killing in response to depredation is one of the primary threats to the conservation of these species (Treves and Karanth, 2003; Linnell et al., 2012; Inskip et al., 2013; Chapron et al., 2014; Ripple et al., 2014). Given the importance of this issue, much research has been devoted to documenting the biotic and abiotic conditions that correlate with carnivore depredation of livestock (Miller, 2015; Montgomery et al., 2018a,b).

Typically, this research seeks to develop predictions capable of optimizing the implementation of interventionist activities meant to decrease carnivore attacks on livestock (Treves et al., 2011; Meena et al., 2014; Miller, 2015). There are a number of models used to predict spatial patterns in carnivore depredation of livestock, which are often referred to as risk models. These models generally fall into one of three categories including correlation modeling, spatial interpolation, and spatial associations (Miller, 2015). Correlation modeling and spatial interpolation inherently test for associations between depredation incidents and the landscapes in which they occur (Hebblewhite et al., 2005; Northrup et al., 2013). Spatial association analyses, in contrast, test for spatial autocorrelation among depredation locations independent of the landscape (Baruch-Mordo et al., 2008; Dale and Fortin, 2014; Peeters et al., 2015). Across the three categories, the models developed to predict carnivore depredation of livestock are all informed by the principles of spatial autocorrelation (Miller, 2015). Thus, if spatial patterns in depredation are spatially autocorrelated then the number of carnivore-killed livestock should exhibit clustering at close distances and dispersion with increasing distance. The calculations of clustering or dispersion are carried out via a comparison of the data to a completely spatial random pattern (Aldstadt, 2010; Chakraborty, 2011; Diggle, 2014).

As such, prior to predictive model fitting, diagnostic tests, including the calculation of spatial autocorrelation, should be assessed (Baruch-Mordo et al., 2008; Chakraborty, 2011; Miller, 2015). If tests of this type are not assessed or described in risk mapping of carnivore depredation of livestock, it is unclear whether measured spatial patterns in these data conform to the principles of spatial autocorrelation. It might be more challenging to derive applied management actions from the outputs of spatial risk models if patterns in carnivore depredation of livestock are not statistically different from random. Correspondingly, this would hamper the implementation of interventions built from those models.

Here we conducted a series of diagnostic tests, typically carried out prior to predictive spatial modeling, to determine the degree of spatial autocorrelation evident in carnivore depredation of livestock data. Our objective was to explicitly assess the assumption of spatial autocorrelation. In doing so, we hope to draw conclusions about important considerations in future depredation risk modeling studies, to increase the efficacy of the management and intervention efforts that are based on such models. As there are multiple possible approaches to testing for spatial autocorrelation within a data set, and given that these tests are rarely described in the risk mapping literature, we used a triangulation approach to further verify our results. We applied three diagnostic tests (the ordinal spatial scan statistic, the Bernoulli spatial scan statistic, and the Getis-Ord local spatial statistic) of spatial autocorrelation to our depredation data. We discuss the results of our analysis for spatial modeling of carnivore depredation data and the interventionist activities that are typically associated with this research. Spatially autocorrelated patterns of livestock depredation are used to inform predictions of future predation risk, and management efforts to reduce this risk. Therefore, the ecological inferences that derive from such analyses have important implications for the optimization of activities that are meant to alleviate conflict between humans and carnivores.

Between 2009 and 2013 we collected a total of 170 records from 113 bomas, including 119 confirmed livestock depredation events. Just under half of the bomas surveyed (44.2%, n = 50 of 113) experienced no livestock depredation activity (“no depredation”), 41.6% (n = 47) experienced 1–2 depredation events (“low intensity”), and the remaining 14.2% (n = 16) experienced three or more events (“high intensity”; Table 1). Close to 90% (n = 107) of depredation events were by spotted hyenas, with only 4.2% (n = 5) by leopards, 2.5% (n = 3) each by lions and black-backed jackals, and 0.8% (n = 1) by cheetahs. Hyenas killed livestock at low and high intensity, whereas the other species were only responsible for low intensity depredation at any given boma (Table 2).

Via the application of three different model diagnostic approaches, we detected little evidence of spatial patterning in the intensity of carnivore depredation of livestock data. All three statistical methods identified just one primary hot spot consisting of only 18 bomas (15.9% of those studied) located in a cluster north of Tarangire National Park (Figures 3–5). Thus, in terms of the intensity of livestock depredation events, the majority of our study site did not differ from a completely spatial random pattern. This result suggests that there may be some other processes, potentially ecological or methodological in form, influencing or obscuring the spatial patterns of livestock depredation in this region. Without an understanding of such processes, and incorporation of that knowledge into spatial pattern analyses of this nature, the ability to develop accurate predictive models for human-carnivore conflict will be limited. Here, we discuss the potential processes that could inform this observed spatial randomness.

We had anticipated that patterns in livestock depredation would be non-random, indicating the presence of behaviorally-grounded carnivore hunting strategies similar to those observed in wild prey predation by the same species. This assumption was supported by previous research showing that the risk of livestock depredation by hyenas increased with vegetative cover (Kolowski and Holekamp, 2006) and depredation risk from lions was significantly higher near riverine habitats (Abade et al., 2014). Nevertheless, the majority of the spatial patterns of livestock depredation events examined here exhibited spatial randomness even though extensive research has documented that large carnivores do not pursue wild prey randomly (Hopcraft et al., 2005; Hayward, 2006; Hayward et al., 2006; MacNulty et al., 2007). As an example, previous research has shown that lions preferentially hunt in areas of semi-dense vegetation and cover, such as tall grasses and open shrublands (Elliott et al., 1977; Scheel, 1992; Spong, 2002; Hopcraft et al., 2005; Fischhoff et al., 2007). This pattern is likely due to the fact that lions are primarily ambush-style predators, relying on vegetation that can hide their presence from prey species until the last possible moment while not restricting their view of potential prey individuals (Hopcraft et al., 2005; Valeix et al., 2009). Similarly, leopards prefer to hunt in areas with moderate woody plant cover, such as open mixed woodlands (Balme et al., 2007). However, substantially less is known about the behaviors of these carnivores in relation to encountering domestic prey. This is particularly true at the household scale (i.e., the scale of bomas; Montgomery et al., 2018a). It remains unclear however, the extent to which hunting behaviors of lions, leopards, or hyenas for wild prey might apply to the selection of livestock for depredation. Therefore, it is possible that the carnivores, in fact, respond to potential livestock prey in the boma randomly.

It is also likely that human presence and activity at the boma contributed to the inherent randomness in the spatial patterns in carnivore depredation of livestock. Livestock husbandry practices, the structural integrity of bomas, as well as cues of human presence including noises, lights, the presence of dogs, and many other elements can be deterrents to large carnivores (Ogada et al., 2003; Frank, 2010; Loveridge et al., 2017). Thus, humans have a capacity to intentionally or inadvertently disturb large carnivores intending to kill livestock at the boma. However, the exact combination of factors that might best deter advancing carnivores has not yet been identified. Importantly, our assessment was focused only on known attacks of livestock, not the other stages of the depredation process (Macarthur and Pianka, 1966; MacNulty et al., 2007; i.e., carnivore search and pursuit of livestock in the boma). To assess how human behavior influences the probability of attack, the rates at which carnivores encounter bomas and do not attack must be calculated. Within wild prey systems, encounter rates are one of the primary determinants of predation intensity (Hebblewhite et al., 2005; Balme et al., 2007). We identify the study of the rates at which carnivores encounter livestock at the boma and do not attack as a productive area of future research.

Finally, the spatial randomness that we observed may also be attributable, at least in part, to noise in the data collection system. Such noise would include issues in sampling, translation, misreporting of depredation events, or spatio-temporal dimensionality. For instance, we considered depredation data from 2009 to 2013, and collapsing the temporal extent of the data could have obscured fine scale temporal dynamics in the depredation patterns. Many studies have shown the importance of temporal resolution in revealing and predicting the mechanisms driving spatial patterning (Elliott et al., 1977; Van Orsdol, 1984; Stander and Albon, 1993). Examining the temporal dynamism associated with these data is part of a separate analysis in which we discovered strong effect of seasonality, with attacks being 2.84 times more likely to occur in the wet season than the dry season, aligning with a similar influence of seasonality found by Kuiper et al. (2015); Kissui et al. (2019). Additionally, our data showed substantial year-to-year variation in hyena depredation patterns (Kissui et al., 2019).

Our study emphasizes the importance of conducting model diagnostic tests of spatial autocorrelation in depredation risk models. Such tests provide the framework for meaningful application of conflict intervention efforts (Baruch-Mordo et al., 2008; Chakraborty, 2011; Miller, 2015). As the principles of spatial autocorrelation underlie the majority of risk model analyses (Chakraborty, 2011; Miller, 2015), without explicit examination of the autocorrelative patterns within the depredation datasets, the results may be misrepresentative of the processes occurring on that landscape. Spatial randomness may indicate that there is no clustering of livestock depredation events, when that result may in fact be due to the presence of other processes that exhibit spatially random patterns at the spatial or temporal scale of assessment. Consideration of such factors is essential for effective application and interpretation of livestock depredation risk models.

The outputs of these risk models are used to identify high-priority locations in which to apply conflict intervention or mitigation efforts around the world, thus informing preventative action to maximize impact and minimize cost (Marucco and Mcintire, 2010; Treves et al., 2011; Miller, 2015). Notably, the exact processes at play may differ depending on the ecological community, human culture, and environmental characteristics of the study location. However, the range of alternative spatial processes identified here are representative of the diversity of factors that should be considered within these examinations. Therefore, such diagnostic approaches can be applied to other study systems to inform subsequent examinations of biotic and abiotic correlates of carnivore depredation of livestock. Without refined understanding of the potential sources of spatial randomness, the model output may not be well-aligned with the implementation of interventions meant to reduce depredation. This misapplication of intervention efforts could result in higher livelihood costs for local communities, increased rates of retaliatory killing of carnivores, and overall increase in conflict between the two (Dickman, 2010; Inskip et al., 2013). Such concerns are not limited to the East African system in which this study is situated, but are relevant to any location experiencing human-carnivore conflict over livestock depredation. The widespread and urgent nature of this threat underscores the necessity of effective use of all available resources and tools, and livestock depredation risk models are a valuable contribution to this effort (Treves et al., 2011; Miller, 2015; Miller et al., 2015). With attention to spatial processes such as those identified here, they are more likely to provide accurate management-relevant predictions of livestock depredation, thus increasing the impact of research-informed conservation efforts and the management practices derived therein.

The datasets generated for this study are available on request to the corresponding author.

The data examined herein was approved by the Tanzanian Committee on Science and Technology (COSTECH) and the Tanzanian Wildlife Research Institute (TAWIRI) and all requisite research permits were received. This study was carried out as part of the Tarangire Lion Project's long term monitoring program, did not comprise of any direct, or indirect interactions with wildlife, and did not collect any personal information from participating individuals. Thus, no additional ethics approvals were required.

All work within this manuscript is original research carried out by the authors. BK developed the original research design and field data collection. CH prepared the data for analysis, carried out the analysis, and drafted the article. RM contributed to the spatial analysis of the data and editing. All authors contributed substantially to the writing and proofing of the article, and read and approved the final submitted version.