Animal movement and resulting tracking data

We simulated movement data using an approach that is strongly related to the ‘stepping-stone’ algorithm, as presented by Avgar et al. [46]. In particular, we simulated 5000 steps of movement on the finest available spatial scale, i.e., on a scale of pixels (in the following termed ‘trip’). For each simulation/trip, the starting location and the location of the attraction centre were chosen randomly within the virtual study area. However, to avoid boundary effects, the starting location was restricted to the 500×500 square in the centre of the area and the attraction centre to the 850×850 square. It was assumed that the boundary was never reached by the virtual track, and boundary-related bias could thus be excluded. For each simulated time step t with location X→t=(X1,X2), the probability of choosing the neighbouring pixel Y→=X→t+1 out of the eight nearest neighbours Z→∈N as the next point was given by

with

where a more detailed motivation of the general structure of this stepping stone algorithm is given by Avgar et al. [46]. Here, N(0,σ_SD) represents a normally distributed random component in animal movement (where new values are drawn for each evaluation of F(.)), i.e., scaling the strength of random movement vs. directed/biased movement in the animal path, quantified by the movement standard deviation σ_SD∈[0,2.5]. We want to point out that σ_SD as well as all following parameters denoted with σ were fixed parameters for each particular simulation, and were varied only across different simulation scenarios (c.f., overview at the beginning of the “Methods” section). σ_ω∈[0,1.0] quantifies the strength of resource selection, while the term μ||Y→−X→t|| with μ=1.8 penalizes larger Euclidean distances to the 4 of the 8 neighbouring pixels within a rectangular grid. Furthermore, σ_α∈[0,0.1] penalizes angular deviations α_att from the direct path between Z→ and the attraction centre (and thus introduces directional bias towards the centre, ‘biased random walk’ [8]), and f(σ_ran,σ_ran2) finally penalizes angular deviations α_pers from the direction of the foregoing movement step via the two constant parameters σ_ran and σ_ran2, thus leading to directional persistence (‘correlated random walk’ [8]). Notably, f(σran,σran2)=σran/1+σran2·∑Z→∈Nhab(Z→)/8) includes the parameter σ_ran∈[0,2.5] for the general strength of directional persistence, but also the parameter σ_ran2∈[0,1.0] antagonizing this effect if local habitat values (averaged over all neighbours) are high. The latter effect thus induced a less-directed and more-random search behaviour in appropriate habitats. Finally, after generating the animal track, a virtual time t was assigned to the locations using equidistant time steps of 1 minute. Some example tracks with varying values for σ_ω,σ_α and σ_ran are given in Fig. S2.

The simulated animal movement data at the spatial pixel scale (c.f., previous subsection) were subsequently reduced to a much coarser temporal resolution, mimicking the data collected by a tracking device. In particular, a total of 300 tracking points were selected with equidistant time points between the tracking points. After selection of the spatio-temporal subset (‘tracking data’) from the raw animal movement data, as described above, spatial measurement error was added, quantified by the parameter Error_spat∈[0,3] depicting the standard deviation of a normally distributed random error separately added to each point and coordinate.