Danny Raj M

# Finding out how fish interact

Fish display schooling, a phenomenon where a group of fish stay cohesive and aligned as they collectively move from one location to another. Typically, individual fish are unaware of the group’s collective state and are only capable of limited cognition. Yet, they display *remarkably robust, global coordination* that offers them advantages in foraging and protection against predator attacks. Can one identify the underlying interactions between fish that result in the observed collective behaviour? To answer this question, fish can be brought to a lab and allowed to school in a large tank under ‘controlled’ conditions and imaged using a camera. However, the challenge would be to find out the interactions between fish from the collected data.

**Schooling behavior exhibited by Etroplus suratensis (experiments done in **

__TEELAB__**)**

Fish movement is probabilistic in nature. Each fish turns spontaneously while also trying to align and stay cohesive with its proximate neighbours. Interestingly, the stochastic turning that a fish displays can be modelled *like chemical reactions in a system with small number of molecules*. Every interaction that a fish exhibits can be modelled as a reaction and the corresponding reaction-rate will determine the propensity of the fish to exhibit that interaction. Now the task is to determine the different reactions and their rates from the data collected (of the fish school). However, identifying the 'correct' reaction-model is an impossible task, due to the endless possibilities for the choice of a model. Hence, we need to identify a set of candidate model-families to focus our search for the ‘correct’ model. For this reason, we went back to data.

**Order parameter characterizing the polarization of the school fluctuates as the school moves**

From the fish school data, we computed an order parameter that characterises how well the fish are aligned. The time series of this order parameter was found to be noisy. Surprisingly, we found that this noise, encoded important information regarding the nature of the underlying interactions—the amplitude of the noise was low when the school was ordered and large when it wasn’t. Now, this leads to interesting consequences. An unaligned school, by random chance may get ‘kicked’ to a more aligned state due to large fluctuations. But once the school is more polarised, it remains in a state of order for a longer duration, due to lower amplitude of fluctuations. We observe that *noise gives rise to order!* Analysing the jump moments corresponding to this noise helped us identify a family of 2D voter models that are potential candidates for how the fish interact.

**A schematic of the model identification problem**

Even after we reduced the search space considerably, the model identification problem was still a hard one to solve due to the combinatorially large number of possibilities—different orders of interactions and the several possible combinations of rates of reactions. Hence, *we posed this as an optimisation problem* where we minimised an objective function that quantifies how far the predictions are from the data, while optimising for both the reaction model-type and the corresponding rates. This gave rise to a non-linear programming problem with both continuous and integer variables. Hence, we turned to random-search methods like Genetic algorithms, to solve the optimisation problem. The optimiser identified that *fish must interact with each other one at a time*, in a pairwise manner, to give rise to the observed noise induced order.

__For more information:__

Jitesh Jhawar, Richard G. Morris, U. R. Amith-Kumar, **M. Danny Raj**, Tim Rogers, Harikrishnan R., Vishwesha Guttal, ‘** Noise-Induced Schooling of Fish**’, Nature Physics, 16, 488–493, 2020.

This work was done in collaboration with Dr Vishwesha Guttal and team (TEELAB), Centre for Ecological Sciences, IISc Bangalore – where the experiments were carried out and the project was originally conceived. Website: https://teelabiisc.wordpress.com/