Box 1 Step-Selection Analyses (SSAs)

Step-Selection Analyses (SSAs) model the conditional probability, \(p\left({s}_{t} | {H}_{t-1};{\beta }_{m,}{\beta }_{w}\right),\) of finding an individual at a location \({s}_{t}\) at the time t given a set of previously visited locations, \({H}_{t-1}\), using a selection-free movement kernel, \(k\left({s}_{t} |{H}_{t-1};{\beta }_{m}\right),\) which describes how animals would move in the absence of habitat selection, and a movement-free habitat-selection function, \(w\left({s}_{t};t,{\beta }_{w}\right),\) which describes the animals’ preferences for certain environmental features (e.g., variables representing resources, risks, and or other conditions; [62]):

\(p({s}_{t}|{H}_{t-1};{\beta }_{m},{\beta }_{w}) =\frac{k({s}_{t}|{H}_{t-1};{\beta }_{m}) \cdot w({s}_{t};t,{\beta }_{w})}{\int_{{s}'\in U} k({s}'|{H}_{t-1};{\beta }_{m}) \cdot w({s}';{\beta }_{w}) ds'}\)

(1)

\({H}_{t-1} = {s}_{t-1},{s}_{t-2}, \ldots, {s}_{t-i}, \dots, {s}_{0}\)

(2)

\({\beta }_{m}\) contains parameters in the step-length and turn angle distributions \({{(\beta }_{m1 },...,\beta }_{mq})\), and \({\beta }_{w}\) contains resource-selection parameters that quantify the attractiveness of different locations using a vector of selection coefficients (\({{\beta }_{w1 },...,\beta }_{wp})\) for each environmental covariate \({{(r}_{1}({s}_{t}),...,r}_{p}({s}_{t}))\). \({s}{\prime}\in U\) describes all the locations within the spatial domain \(U\). To calculate a step length, sl, two locations are required \(,({s}_{t}, {s}_{t-1})\). Similarly, a turning angle, ta, is calculated using the current and the past two locations \(({s}_{t}, {s}_{t-1},{ s}_{t-2})\).