Fig. 2: Computational model of surface activity.
From: Fish shoals resemble a stochastic excitable system driven by environmental perturbations
a, We categorized the behaviour of individual fish into three fundamental states: swimming near the surface for respiration (\({{{\mathcal{S}}}}\)), fast diving (\({{{\mathcal{D}}}}\)) and underwater hovering with subsequent slow resurfacing (\({{{\mathcal{U}}}}\))24. b, Comparison between snapshots obtained from the empirical videos and the numerical simulations. c, Surface-activity signal \({{{\mathcal{A}}}}{(t)}\) computed using the model shown in a. d,e, Characteristic time distributions for the inter-spike times τ1 (d) and the spike-duration times τ2 (e). f, Distribution of cluster areas P(a), which is statistically consistent with a power law (black dashed line) with exponent αa = 2.3. g, Plots of the surface-activity signal \({{{\mathcal{A}}}}{(t)}\) for three different sets of parameters, highlighted with different markers in h. h, Average neighbour correlation function \({\langle c(\omega ,\,\theta ,\,{\mu }^{\star })\rangle }_{t}\) showing a maximum at the critical region. The blue cross indicates the location of (ω⋆, θ⋆). i, Plots of \({\langle c({\omega }^{\star },\,\theta ,\,{\mu }^{\star })\rangle }_{t}\) and \({\langle c(\omega ,\,{\theta }^{\star },\,{\mu }^{\star })\rangle }_{t}\) to visualize the maximum when changing variables θ and ω. The plots in b–f were generated using numerical simulations and the parameters ω⋆, θ⋆ and μ⋆. For details, see the section Model implementation in Methods.
