Non-linear relationships between human activities and wolf-livestock depredations

Abstract

Livestock depredations present real and perceived threats to property and human livelihood, undermining carnivore conservation and management. Considerable research has been aimed at identifying factors influencing depredations but contradictory relationships indicate our predictive ability still needs improvement. Previous approaches have relied primarily on linear correlation modeling not considering that some factors may promote and limit depredations across the range of observed conditions. We investigated relationships between wolf (Canis lupus) depredations of livestock and indices of human activity in Michigan’s Upper Peninsula (UP), USA. Using binomial generalized linear models at three spatial scales (site scale, radius [r] = 0.9 km; area of mean 50% wolf core area [core area scale], r = 4.4 km; and 95% wolf territory area [territory scale], r = 9.0 km), we tested the hypothesis that the relationship between depredation probability and indices of human activity is nonlinear, and that the greatest probability of depredations occurs at an intermediate level of conditions. Across spatial scales we found support for quadratic relationships between cattle density, human density, and proportion of agricultural lands with the occurrence of wolf-livestock depredations (n = 260). We also demonstrated that at the wolf territory scale, increased road density reduced the probability of depredations. Using test data, model prediction accuracy for estimating depredations was 90% (n = 28) at the land section scale and 84% (n = 26) at the core area scale. We provide demonstrative use of non-linear modeling to evaluate factors influencing depredations robust to wolf and prey distribution and abundance.