Two dimensional searching paths exhibit fractal distribution that change with food availability (Normalized Difference Infrared Index, NDII)

•Temporal sequences of foraging searching paths are indicator of food availability.•Searching paths exhibiting a fractal distribution that changes with food availability.•When food is abundant searching paths distribution approaches to a random distribution.•When food is scarce searching paths approaches to an auto-correlated distribution.•Two dimension fractal distribution accurately characterize searching path complexity. Monitoring grazing activity and grasslands productivity has a great interest for the understanding of the feedback processes that regulate dynamic and conservation of grasslands. In this study we examined the spatiotemporal patterns of free foraging sheep and cattle (no shepherd) to understand how the two species adapt to the changes in food availability and quality in alpine and subalpine pastures during the summer. We used two vegetation indices derived from Sentinel 2 imagery (S2A) to characterize grassland: Normalized Difference Vegetation Index (NDVI) and Normalized Difference Infrared Index (NDII). We hypothesized that sheep and cattle would show different spatiotemporal displacement patterns, which would also change over time with phenology of pasture. We tested this using movement data of tagged sheep and cattle with satellite GPS collars. Animals are yearly free ranging in the studied alpine and subalpine pastures since June to end of September, when they are moved to the shelters. According with optimal searching strategy we predicted that displacement distribution would approach to a random searching path when the forage is more nutritive and abundant, i.e., when livestock have just arrived to their summer pastures. As the summer advances, animals would change their searching paths to an auto-correlated random walk, because pastures lose nutritional quality and consequently food availability is smaller, also due to animal consumption in the grasslands. Our results confirmed that hypothesis and showed that average NDII, a proxy of both pasture quality and time of green-up in the summer pastures, influenced the spatiotemporal patterns during grazing activity of free ranging livestock. We provided the first demonstration of two dimension searching path exhibiting a fractal distribution that changes with the availability of food and the intrinsic characteristic of the forager species, i.e., diet selection. The use of temporal sequences of foraging animals can be useful as indicator of food availability for free ranging animals th