Fig 5.

(a) Definition of the pair distance d and pair angle θ between two fish. (b, c, e, f) Joint probability density of pair distance and pair angle for all pairs of fish. (d) Qualitative expectations for schooling and shoaling fish. For a school, short distances and small relative angles yield a peak in the bottom left corner. For a shoal, short distances and a wide range of angles yield a vertical band on the left side. For a group that does neither, we expect the distribution to spread over the entire available range of distances and angles. (b, e) Groups of surface fish exhibit close proximity and tight angles indicative of strong schooling. (c, f) Groups of Pachón cavefish exhibit neither schooling nor shoaling. The dashed lines show the expectation for fish following the wall. Comparable probability densities are shown for all group sizes and populations (including Tinaja and Molino) in S1 Fig.