Statistical Methods for Identifying W olf Kill Sites Using Global Positioning System Locations

Accurate estimates o f kill rates remain a key lim itation to addressing many predator—prey questions. Past approaches for identifying kiU sites o f large predators, such as wolves {Canis lupus), have been lim ited primarily to areas w ith abundant w inter snowfall and have required intensive ground-tracking or aerial monitoring. M ore recently, attem pts have been made to identify clusters o f locations obtained using Global Positioning System (GPS) collars on predators to identify kill sites. However, because decision rules used in determ ining clusters have not been consistent across studies, results are not necessarily comparable. W e illustrate a space—time clustering approach to statistically define clusters o f w olf G PS locations that m ight be w olf kill sites, and we then use binary and multinom ial logistic regression to model the probability o f a cluster being a non—kill site, kill site o f small-bodied prey species, or kill site o f a large-bodied prey species. W e evaluated our approach using field visits o f kills and assessed the accuracy o f the models using an independent dataset. T he cluster-scan approach identified 42—100% o f wolf-kiUed prey, and top logistic regression models correctly classified 100% o f kills o f large-bodied prey species, bu t 40% o f small-bodied prey species were classified as nonkills. A lthough knowledge o f prey distribution and vulnerability may help refine this approach, identifying small-bodied prey species will likely remain problematic w ithout intensive field efforts. W e recom m end that our approach be utilized w ith the understanding th a t variation in prey body size and handling time by wolves wiU likely have implications for the success o f both the cluster scan and logistic regression components o f the technique. (JO U R N A L O F W IL D L IF E M A N A G E M E N T 72(3):798-807; 2008) DOT 10.2193/2006-566 KEYW ORDS Canis lupuSy handing time, kill sites, predation, predator-prey interactions, space-time clustering, wolves. A lth o u g h p redation is recognized as a m ajor factor influencing population dynamics and com m unity structure (Schm itz et al. 1997), there remains substantial dehate surrounding key issues such as lim itation versus regulation o f prey hy predators (Eherhardt et al. 2003), type o f predator functional responses (Ahram s and G inzhurg 2000), im por­ tance o f top-dow n effects on prey populations (Schm itz et al. 2000), and dynamics o f switching in m ulti-prey systems (Ahram s and Allison 1982, Patterson et al. 1998). A practical problem to resolving these issues is adequate quantiflcation o f actual kill rates o f predators (i.e., prey animals killed/predator/unit tim e), w hich requires locating all kill sites made during continuous tim e intervals (Boutin 1992, Boyce 1993, Eherhardt 1997, M arshal and Boutin 1999, E herhardt et al. 2003). Locating kiU sites o f wolves {Canis lupus) is particularly difficult because wolves range over wide areas, hu n t in packs, and have shorter preyhandling times than do some other large predator species (Anderson and Lindzey 2003). Past approaches for locating w o lf kill sites have used either aerial or g round-m onitoring o f radiom arked wolves. F re­ quent (twice daily to every o ther day) relocations o f radiocollared w olf packs via fixedor rotary-w inged aircraft have been used to locate kills, hut this approach is costly and misses kills o f small prey for w hich handling times are typically short (M essier and C rete 1985, D ale et al. 1994, Hayes et al. 2000, Sm ith et al. 2004, Sand et al. 2005). In addition, aerial m onitoring is infeasible in areas w here snow cover is lacking or highly variable, w eather and terrain prevent regular flights, or sightahility is poor due to ̂ E-mail: n'webb@ualbertaxa extensive forest cover. T h e alternative to aerial m onitoring to locate kills during w inter has been continuous snowtracking sessions (H uggard 1993, Kunkel 1997, H ehhlew hite et al. 2004). A lthough ground-tracking has reduced the likelihood o f missing kills, this approach depends on suitable snow conditions and usually results in small samples o f kill sites across packs (Fuller 1989, H ehhlew hite et al. 2004). T hus, current approaches rem ain lim ited hy the need for adequate snow cover, open terrain, and road access and still require substantial financial investm ent to sample even relatively short tim e periods. T h e recent advent o f G lobal Positioning System (G PS) radiocollars for predators provides the potential to locate kill sites w ithout the need for intensive aerial m onitoring or tracking snow (A nderson and Lindzey 2003, Sand et al. 2005, Franke et al. 2006). However, these approaches have been m et w ith variable success, have been thoroughly tested w ith wolves only for large prey species, and may require extensive field visitation to potential kill sites to determ ine kill rates. For example. Sand et al. (2005) estim ated tha t as m any as 32% o f w olf-killed moose {Alces alces) w ould not he included in clusters th a t w ere defined hy their decision rules. Further, characteristics o f m ovem ent behaviors representing kill sites are likely to vary am ong predator species due to differences in predator-handling and resting behaviors and types o f prey killed. As a result, a m ethod th a t is effective for small ungulate prey species and minimizes field visits to potential kiU sites is needed (Anderson and Lindzey 2003, Sand et al. 2005, Franke et al. 2006). O ur objective in this paper is to present a new approach th a t uses a space-tim e clustering algorithm adapted from epidemiology to identify clusters o f w o lf G P S locations and 798 T h e Jou rna l o f W ild life M an ag em en t • 72(3) uses binary and m ultinom ial logistic regression to model the probability o f a cluster being a non-k ill site, kill site o f a sm all-bodied prey species, or kill site o f a large-bodied prey species based on w olf m ovem ent characteristics. W e also investigated w hether site-specific environm ental covariates can improve predictive success. W e assessed the accuracy o f our approach for predicting kill sites using an independent set o f G PS-m ovem ent data and associated clusters collected from wolves in 4 packs.