Collective behaviour of fish in the presence and absence of flow

Emergence of in-line swimming patterns in zebrafish pairs

“…There are several additional directions for the potential improvement of the model, which include: (i) the development of a dynamic model for the speed in the form of a stochastic different equation, similar to that of Zienkiewicz et al. (2015a,b) to overcome the approximation of constant speed and include additional mechanisms of social interaction; (ii) the extension to hydrodynamic interactions with walls in the tank and background water currents toward an improved understanding of the transition from in-line to side-by-side swimming as a function of the flow speed (De Bie et al., 2020); and (iii) the extension of individual differences in the stability analysis that could help explain the modulatory role of fish body size on schooling and shoaling (Karakaya et al., 2020; Reebs, 2001).…”

“…Another swimming pattern that is often considered in the literature is side-by-side swimming (De Bie et al, 2020;Kato et al, 2004;Laan et al, 2017;Perna et al, 2014), where the fish swim parallel to each other with Δx(t) = −d sin c and Δy(t) = d cos c . For the present model, this swimming pattern does not constitute a nominal solution: hydrodynamic interactions will have an equivalent effect as alignment and attraction, thereby causing the fish to approach one another.…”

“…Predicting the behaviour of a zebrafish pair requires the time integration of (1) and (6). While the general mathematical treatment of this system may not be feasible, important insight can be gathered by examining its linearized dynamics about salient configurations that have previously been documented (De Bie et al., 2020; Kato et al., 2004; Laan et al., 2017; Perna et al., 2014; Sadaat et al., 2021). To further simplify the problem, we assume the two fish to be identical, such that , , , , , , and .…”

“…Going beyond numerical simulations, we offer analytical insight into the model by elucidating the stability of in-line swimming. This swimming pattern has been experimentally and numerically studied in the technical literature on collective behaviour with multisensory cues, but its stability has never been analytically investigated (De Bie et al., 2020; Kato et al., 2004; Laan et al., 2017; Perna et al., 2014; Sadaat et al., 2021).…”

Use of multimodal sensory cues in predator avoidance by wild-caught zebrafish shoals

“…The software provided us a tracking accuracy in the range of 70%-99% and thus, using an assisting software, ‘idPlayer’, we manually corrected these videos to improve this accuracy to almost 100%. After this, tracks were smoothed using a moving average of 10 (de Bie et al 2020) and using MATLAB (R2021a) we plotted the velocity profile of each fish at a temporal resolution of 25 frames per second (details of calculation of velocity has been provided in the Supplementary Material). The mean velocity of the shoal was then calculated using the velocity of each individual.…”