Appendix to: Correlated velocity models as a fundamental unit of animal movement: synthesis and applications

The UCVM (figure 1A) has no mean velocity component (μ(t) = 0) and a real, non-negative relaxation parameter α. Defined as α = 1 τ , τ represents a characteristic time scale of auto-correlation [1, 2]. The parameter β has units of velocity × time−1/2 which makes it difficult to interpret biologically. However, the mean squared speed of the UCVM is given by η2 ≡ lim t→∞ 〈 |v(t)|2 〉 = β2τ , such that it can be written