A jump persistent turning walker to model zebrafish locomotion

Abstract

Zebrafish are gaining momentum as a laboratory animal species for the investigation of several functional and dysfunctional biological processes. Mathematical models of zebrafish behaviour are expected to considerably aid in the design of hypothesis-driven studies by enabling preliminary in silico tests that can be used to infer possible experimental outcomes without the use of zebrafish. This study is motivated by observations of sudden, drastic changes in zebrafish locomotion in the form of large deviations in turn rate. We demonstrate that such deviations can be captured through a stochastic mean reverting jump diffusion model, a process that is commonly used in financial engineering to describe large changes in the price of an asset. The jump process-based model is validated on trajectory data of adult subjects swimming in a shallow circular tank obtained from an overhead camera. Through statistical comparison of the empirical distribution of the turn rate against theoretical predictions, we demonstrate the feasibility of describing zebrafish as a jump persistent turning walker. The critical role of the jump term is assessed through comparison with a simplified mean reversion diffusion model, which does not allow for describing the heavy-tailed distributions observed in the fish turn rate.

Leadership emergence in a data-driven model of zebrafish shoals with speed modulation

“…Similarly to recent efforts on the so-called persistent [8,39] or jump persistent [40] turning walker, the model uses two coupled stochastic differential equations (SDEs) in time t, one for the forward speed U (t), and one for the turning (angular) rate Ω(t)…”

Design of a modular robotic system that mimics small fish locomotion and body movements for ethological studies

“…It is also known that zebrafish can bend their caudal peduncle up to very high angle (up to p rad) with high angular velocities (up to 4.2 rad s À1 ). 21 Therefore, we designed an actuated lure able to emit such tail beating stimulus. While the beating of the tail could have been generated passively using the water flow generated by the motion of the lure, we developed an actuator inside the lure to actively control the tail beating.…”

“…For instance, in a study by Mwaffo et al, 21 fish locomotion is modeled using a jump persistent turning walker model motivated by the sudden and drastic changes in zebrafish locomotion in the form of large deviations in turn rate. Zienkiewicz et al 22 used a stochastic model to reproduce zebrafish locomotion in a confined environment.…”

Analysis of Pairwise Interactions in a Maximum Likelihood Sense to Identify Leaders in a Group

“…Self-propelled particle models can range from the simplest, where the individuals orient themselves in the general direction of their neighbors (Vicsek et al, 1995;Vicsek and Zafeiris, 2012), to more complex models where interactions include collision avoidance, attraction, and alignment (Aoki, 1982;Couzin et al, 2002Couzin et al, , 2005. Data-driven models that incorporate detailed individual dynamics along with species-specific interactions (Gautrais et al, 2009(Gautrais et al, , 2012Kolpas et al, 2013;Borzí and Wongkaew, 2015;Mwaffo et al, 2015aMwaffo et al, , 2017Zienkiewicz et al, 2015a,b;Collignon et al, 2016) provide an even more realistic setup to create such roles and test methods for identifying leaders.…”