Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.

Reindeer habitat selection under the risk of brown bear predation during calving season

The depredation of semi-domesticated reindeer by large carnivores reflects an important human-wildlife conflict in Fennoscandia. Recent studies have revealed that brown bears (Ursus arctos) may kill substantial numbers of reindeer calves (Rangifer tarandus tarandus) in forest areas in Sweden. Several authors have suggested that predation risk is an important driver of habitat selection in wild Rangifer populations where predation is a limiting factor, but little is known about these mechanisms in semi-domesticated populations. We examined the habitat selection of female reindeer in relation to spatial and temporal variations in brown bear predation risk on the reindeer calving grounds and evaluated the simultaneous responses of brown bears and reindeer to landscape characteristics. We used GPS data from 110 reindeer years (97 individuals) and 29 brown bear years (19 individuals), from two reindeer herding districts in the forest area of northern Sweden. Our results did not indicate that reindeer alter their behavior in response to spatiotemporal variation in brown bear predation risk, on the scale of the calving range. Instead, we suggest that spatiotemporal behavioral adjustments by brown bears were the main driver of prey-predator interactions in our study system. Contrasting responses by brown bears and reindeer to clear-cuts and young forest indicate that forestry can influence species interactions and possibly yield negative consequences for the reindeer herd. Even if clear-cuts may be beneficial in terms of calf survival, logging activity will eventually cause greater abundance of young regenerating forest, reducing available reindeer habitats and increasing habitat preferred by brown bears. Domestication may have made semi-domesticated reindeer in Fennoscandia less adapted to cope with predators. Areal restrictions, limiting the opportunity for dispersion and escape, possibly make the calves more susceptible to predation. Also, a generally higher population density in semi-domesticated herds compared to wild populations can make dispersion a less efficient strategy and the reindeer calves easier prey. Overall, the lack of ability of the reindeer females to reduce brown bear encounter risk on the scale of the calving range is probably an important reason for the high brown bear predation rates on reindeer calves documented in our study areas.