Fig. 2.
a The accessibility space (G τ) of an animal at time τ (i < τ < i + 1), where movement begins at known fix location a i and ends at known fix location a i+1, is the intersection of the forward disc (D i,τ) and past disc (D i+1,τ). The union of the G τ, for all τ, is then the PPA; which by definition is an ellipse. b The joint accessibility space (G AB τ) of two animals (A and B) at time τ (i, j < τ < i + 1, j + 1),, where movement begins at known fixes a i, b j, and ends at known fixes a i+1, bj+1 respectively, is the intersection of G A τ and G B τ