Box 3 Familiarity function in SSFs
From: Identifying signals of memory from observations of animal movements
Movement ecologists have described familiarity with different parts of the landscape that animals experienced using familiarity covariates, which we formalize via a familiarity function, f \(.\) Including an exponential familiarity function allows the attractiveness of different locations to be governed by both environmental and familiarity covariates within the traditional SSF framework (\({e}^{{\beta }_{w}r(s)}\cdot {e}^{{\beta }_{f}f\left(s\right)}={e}^{{\beta }_{w}r\left(s\right)+{\beta }_{f}f(s)}\)). Examples of familiarity covariates include occurrence distributions (ODs) reflecting the intensity of past space use in the study area, time since last visit (TSLV), migratory distances between current and previously used paths, and angular covariates used to capture bias toward previously used migratory ranges: | Â |
\(p({s}_{t}|{H}_{t-1};{\beta }_{m},{\beta }_{w},{\beta }_{f}) = \frac{k({s}_{t}|{H}_{t-1};{\beta }_{m}) \cdot w({s}_{t};t,{\beta }_{w}) \cdot f({s}_{t};t,{\beta }_{f})}{\sum_{{s}' \in U} k({s}'|{H}_{t-1};{\beta }_{m}) \cdot w({s}';t,{\beta }_{w}) \cdot f({s}';t,{\beta }_{f})}\) | (3) |
\(f\left({s}_{t};t,{\beta }_{f}\right)=\{{e}^{{\beta }_{f} \cdot f({s}_{t})}\}\) | (4) |