Our new paper in Nature Physics led by the recently minted PhD from our lab – Jitesh Jhawar & with a fabulous collaborative team of Richard Morris, Danny Raj, Amith-Kumar, Harikrishnan & Tim Rogers!
Here is the link to read the paper (FREE): https://rdcu.be/b2pgG
Some background: We have seen collective motion in birds, mammals, fish, insects, microbes, etc – all fascinating patterns.
Each individual has only limited local information about surroundings. Yet they show these fascinating patterns. 2/n
So a question that many of us are interested is: what types of interactions produce these fascinating patterns?
This has been a question of substantial work over the last few decades, and we provide some new insights here. 3/n
To answer this broad question, physicists and computer scientists have built mathematical and computational models since 1980’s.
They show that organisms don’t need complex rules to exhibit collective motion. 4/n
For example, in the classic Vicsek model (PRL 1995), particles follow a simple rule: move in the average direction of their neighbours. This simplistic rule produces a highly-ordered collective motion.
[Pic below is Fig 1 of Vicsek et al 1995 PRL]
The first main result from our study is related to the above context — whats the rule that fish follow? We show that in a species called karimeeen (Etroplus suratensis) (i) fish just copy the direction of a (nearby) random fish, or (ii) they turn a bit randomly. 6/n
We call this rule a ‘pairwise copying’ — which is relatively simpler than the Vicsek-class of models which assume that organisms average the direction of neighbours and turn towards them. 7/n
Ours is not the first paper to show that real organisms behave differently compared to Vicsek-like models. In fact, fish school studies by @JHerbertread, @GTheraulaz etc also show a similiar simpl rule of interactions in other fish species. 8/n
That brings me to the second main result- also the title of the paper: We show that schooling in this fish is a rare empirical example of a phenomenon well studied in non-equilibrium stat physics: ‘noise-induced phase transitions’. But what is this? Let’s dig in a bit 9/n
So this is what we do in terms of experiments and analyses to make the connection with the physics theory. We use karimeen (Etroplus suratensis) — a popular edible fish in western coast of southern India and put them in a fish tank.111
So this is what we do in terms of experiments and analyses to make the connection with the physics theory.
We use karimeen (Etroplus suratensis) — a popular edible fish in western coast of southern India and put them in a fish tank.
We maintain shallow water, so that fish are effectively in a two-dimensional system. This makes tracking of fish movement relatively easy.
[This is from fig 1 of our paper.]
Here is a short video showing fish in the tank. Our experiments has 15 and 60 fish.
From video tracks of how fish, we calculate “polarisation M” – which measures how well aligned are fish with each other.
We then plot this quantity as a function of time. Crucially, we retain all information — not just mean but also how fluctuations are occurring over time.
From such a time series of the polarisation, we construct a stochastic differential equation!!!
I think this is one of the coolest part of the paper – because unlike most papers that intuitively derive a model or equation, here we let the data talk!
In simple words, this equation tells that i. when fish are ordered, even random things that they do, like copy one other, doesn’t change the overall behaviour very much ii. when the fish are moving in a misaligned state, the fluctuations are actually high.214
Therefore, when the fish are not well aligned with group members, the noise grows larger, eventually ‘kicking’ the group from one state — random swimming — to a different state — schooling!!!
This video (based on simulation of the model) makes the point on how noise is high in the disordered state, and pushes the group towards higher alignment.
I will stop here!! There is quite a bit of technical stuff in Methods and Supplementary Materials.