We describe a new method for estimating the area of home ranges and constructing utilization distributions (UDs) from spatial data. We compare our method with bivariate kernel and alpha-hull methods, using both randomly distributed and highly aggregated data to test the accuracy of area estimates and UD isopleth construction. The data variously contain holes, corners, and corridors linking high use areas. Our method is based on taking the union of the minimum convex polygons (MCP) associated with the k-1 nearest neighbors of each point in the data and, as such, has one free parameter k. We propose a "minimum spurious hole covering" (MSHC) rule for selecting k and interpret its application in terms of type I and type II statistical errors. Our MSHC rule provides estimates within 12% of true area values for all 5 data sets, while kernel methods are worse in all cases: in one case overestimating area by a factor of 10 and in another case underestimating area by a factor of 50. Our method also constructs much better estimates for the density isopleths of the UDs than kernel methods. The alpha-hull method does not lead directly to the construction of isopleths and also does not always include all points in the constructed home range. Finally we demonstrate that kernel methods, unlike our method and the alpha-hull method, does not converges to the true area represented by the data as the number of data points increase.

1. The reintroduction of grey wolves Canis lupus (L.) to Yellowstone National Park provides a natural experiment in which to study the effects of a keystone predator on ecosystem function. 2. Grey wolves often provision scavengers with carrion by partially consuming their prey. 3. In order to examine how grey wolf foraging behaviour influences the availability of carrion to scavengers, we observed consumption of 57 wolf-killed elk Cervus elaphus (L.) and determined the percentage of edible biomass eaten by wolves from each carcass. 4. We found that the percentage of a carcass consumed by wolves increases as snow depth decreases and the ratio of wolf pack size to prey size and distance to the road increases. In addition, wolf packs of intermediate size provide the most carrion to scavengers. 5. Applying linear regression models to the years prior to reintroduction, we calculate carrion biomass availability had wolves been present, and contrast this to a previously published index of carrion availability. Our results demonstrate that wolves increase the time period over which carrion is available, and change the variability in scavenge from a late winter pulse dependent primarily on abiotic environmental conditions to one that is relatively constant across the winter and primarily dependent on wolf demographics. Wolves also decrease the year-to-year and month-to-month variation in carrion availability. 6. By transferring the availability of carrion from the highly productive late winter, to the less productive early winter and from highly productive years to less productive ones, wolves provide a temporal subsidy to scavengers.

The Greater Yellowstone Ecosystem in the northern Rocky Mountains provides the context for a natural experiment to investigate the response of consumers to resources with differing spatial and temporal dispersion regimes. Grey wolves (Canis lupus) and human hunters both provide resource subsidies to scavengers by provisioning them with the remains of their kills. Carrion from hunter kills is highly aggregated in time and space whereas carrion from wolf kills is more dispersed in both time and space. We estimated the total amount of carrion consumed by each scavenger species at both wolf and hunter kills over 4 years. Species with large feeding radii [bald eagles (Haliaeetus leucocephalus) and ravens (Corpus corax)], defined as the area over which a consumer can efficiently locate and integrate resources, dominated consumption at the highly aggregated hunter kills whereas competitively dominant species [coyotes (Canis latrans)] dominated at the more dispersed wolf kills. In addition, species diversity and the evenness of carrion consumption between scavengers was greater at wolf kills than at hunter kills while the total number of scavengers at hunter kills exceeded those at wolf kills. From a community perspective, the top-down effect of predation is likely to be stronger in the vicinity of highly aggregated resource pulses as species with large feeding radii switch to feeding on alternative prey once the resource pulse subsides.