Modeling high-frequency position data of large herbivores with a phase-state model

Understanding the rules and factors that drive the foraging behavior of large herbivores is important to describe their interaction with the landscape at various spatial scales. Some unresolved questions refer to landscape–behavioral interactions that result in oriented or random search in seasonally changing landscapes. Remotely sensed position data indicate that herbivores select local patches of heterogeneous landscapes depending on a complex host of dynamically varying animal and environmental conditions. Since foraging paths consist in successions of relatively short steps, increasing the frequency at which position information is acquired would contribute to entangle the mechanisms resulting in herbivores’ foraging paths. We addressed the question whether herbivores would obtain information at a patch scale that would modify their distribution at a landscape scale based on directed movement or navigation ability. We considered a set of 100,000 high-frequency (1min intervals) position data of several free-ranging sheep (Ovis aries) at a seasonal-varying range (Patagonian Monte, Argentina) and observed their movements at landscape and at single vegetation patch scales. At a landscape scale, we inspected the spatial co-variation of seasonally varying forage offer and ewes’ movement speeds. At a patch scale, we developed a phase-state (P-S) model of movement cycles based on the occurrence of behavioral phases along foraging paths, and fitted it to the observed daily time series of ewes’ movement speeds. Ewes were preferentially distributed in areas with high forage offer during periods of low forage availability and the reverse occurred during the season of high forage availability. Parameters of the model of activity cycles amenable to control by ewes (duration of speed phases, time elapsed between speed cycles) did not covariate with forage offer, but varied significantly among ewes. The shape (kurtosis) parameter of the model of movement cycles, one which is unlikely under ewes’ control, co-varied significantly with spatial forage offer but did not differ among ewes. We conclude that ewes allocated foraging time along a series of similar movement efforts irrespective of forage availability at small patches. Average forage scarcity at multi-patch level increases the ratio of searching to feeding time. This results in apparent selective time allocation to richer forage areas but does not imply evidence for oriented movement at a landscape scale. We advance a behavioral-based definition of forage patches and discuss its implications in developing foraging theory and models. The P-S model applied to high-frequency position data of large herbivores substantially improves the interpretation of the factors controlling their time allocation in space with respect to previous models of herbivore spatial behavior by discriminating among behavioral-based and environmentally induced components of their movements.