Fig. 1. Temporal relationship of real fish (RF) pairs.
A 2D trajectories of two RF swimming together for 10 s and a graphical explanation for obtaining the important temporal parameters by locating the timing of the burst (beat timing). The beat timing signal was obtained from the speed over time. Dots denote the time the fish started a bout, when a local minima occurred in the speed profile. These time points define the bout duration T, and for pairs, the beat timing difference τ. B Occurrences (probability density function; PDF) of mean swimming speed for individuals when their conspecific was in close proximity ( < 4 cm) or far away ( > 10 cm). C The correlation function Cij between 2 RF normalized with the number of sample windows for pairs swimming close (blue), far (red) or for shuffled pairs generated by randomization (yellow; randomizing the entire dataset 100 times, resulting in 100 different curves; see the methods section for more details). Thick lines show single curves from pooled data, and thin, semi-transparent curves show data separately for each pair. D Occurrences (PDF) of bout durations.The distribution f0, which was derived from times when the pairs were close, is the naturally occurring distribution that was used in our model (see later; Fig. 2B). E Heatmap showing the relative occurrences of the beat timing difference τ and bout duration T. If a relationship exists and T is a function of τ, then that defines a phase response curve (PRC). y = 2x is shown for reference as a dashed red line overlaid on the heatmap (left). For comparison, we show the resultant heatmap when we create shuffled pairs by randomizing (right).