New Paper by Jitesh Jhawar et al — Noise-induced schooling of fish in Nature Physics

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):

This is the FIRST experimental work of our ‘theory-lab’. Obviously, this is exciting.

This blog is based on the thread I created on twitter. Here is the screenshot of the paper! @iiscbangalore

View image on Twitter

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]

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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.

View image on Twitter

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.]

View image on Twitter

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.

View image on Twitter

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!

View image on Twitter


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.

With generous support by @DBTIndia @serbonline @IndiaDST.

I will stop here!! There is quite a bit of technical stuff in Methods and Supplementary Materials.


New paper by Sumithra Sankaran et al: Inferring resilience from spatial patterns in ecosystems

This blog post was created based on my twitter thread, attempting to explain some aspects of the new paper by former students Sumithra Sankaran, Sabiha Majumder and Ashwin – published in Methods in Ecology and Evolution.

It looks really pretty in the formal formatted version 🙂

Before I go further, we are so happy that there is Kannada Abstract to this paper! I will do a Kannada thread as well later.

Thanks to Kolleagala Sharma @kollegala for the help with Kannada abstract. Incidentally, the paper came out on Nov 1st!

Some background: Many ecosystems can ‘suddenly’ switch states, also called regime shifts or tipping points. This can happen in semi-arid vegetation, mussel beds, lakes, corals, etc. Therefore, we want to know which ecosystems are prone to sudden tipping.

An ideal way to find this is to perturb the ecosystem & measure how it returns. But this is difficult & in many cases, such a perturbation may cause the tipping! So this is not even desirable.  

A paper in Nature 2007 proposed that we may infer stability by measuring properties of spatial patterns. Specifically, they focused on semi-arid vegetation. Here is an image from Google Earth, in Rajasthan. Note that not all clusters of plants are of same size.

Basically, they argued that the resilient (or stable) ecosystems do not have any ‘typical size’ of clusters. Broadly, they claimed that cluster-size distribution and its properties can inform us about ecosystem resilience. 

Mathematically, this means that the frequency distribution of cluster sizes is a power-law. Power-laws are fascinating because their mean & variance are infinitely large!

This is in quite a contrast to distributions we regularly use – like Gaussian/normal or exponential. 

To make this clear, we show a graph in the paper tries to explain how power-laws are fundamentally different from normal or exponential decay functions.

Power-laws have a large tail, and hence you are likely to find very large-sized patches in such systems.

These are not just mathematical fantasies! Many empirical systems do show power-law distribution of clusters.

Here is Figure 1 from our paper with empirical examples of power-law clustering.

Does it mean they are highly stable ecosystems? There were several follow up studies, that found mixed evidence to this overall claim.

That’s the background to Sumithra’s work. 

The main result from Sumithra’s work is that the above-proposed link between resilience and cluster-size distribution is NOT robust. So it’s a NEGATIVE result!

To show this, she used a simple computational model of ecosystems  

Here is a pictorial representation of the spatial-model.

The model itself is directly taken from a statistical physics paper (Lubeck, J Stat Phys 2006) but with ecological interpretation thrown in!

Sumithra showed that power-law cluster-size distribution can occur even when systems are very close to tipping points. Hence, power-laws are not indicators of ecosystem resilience. Here is a conceptual diagram and result that explains the results.

Power-law cluster-sizes are also studied extensively in the context of ‘percolation’ in the physics literature. We showed that power-law cluster-size distribution in our ecology models relates to percolation of physical systems! 

We also talk about what else can be measured to infer resilience. There are more technical aspects! Because this paper uses ideas from many areas – ecology, physics, math, computer simulations and statistics of fitting distributions – we explain many technical aspects. 

Finally, I must say that handling Editor Dr Hao Ye at Methods in Ecology and Evolution gave extensive comments that really helped the clarity and presentation of the manuscript.

If you came this far, thanks!! 

New paper by Gokul and Athmanathan (UG students): Fission-fusion dynamics in heterogeneous populations

Very happy that a very cool paper led by two former UG students of the lab – Gokul Nair and Athmanathan – is now published!

Screenshot 2019-03-14 at 11.11.26 AM


Gokul Nair, Athmanathan Senthilnathan, Srikanth Iyer, and Vishwesha Guttal, 2019, Fission-fusion dynamics and group-size dependent composition in heterogeneous populations, Physical Review E99, 032412, arXiv:1711.06882 [nlin.AO], Data and codes,  Download PDF. 


This is the first analytical model of fission-fusion dynamics in heterogeneous systems. Previous studies had looked at only homogeneous populations. We make interesting predictions: smaller groups are likely to be homogeneous while larger groups will be heterogeneous.

I really enjoyed working with these students and also with Prof Srikanth Iyer, who is a professor of Mathematics at IISc. My collaboration with Srikanth started with this project when we jointly advised Athmanathan, a UG student majoring in Math at IISc, for his UG project (Sept 2014- May 2015). While Athma formulated the model and got preliminary results, Gokul Nair (a UG physics Major from IISc) carried this on during his free-time, resolved many tricky mathematical issues, did more simulations and finally wrote the paper.

Although the paper is quite mathematical (perhaps most mathematical of all my papers so far), many sections are written in a way that is accessible to nonspecialists (you can easily skip mathsy parts without losing the essence – that was the attempt of our writing). I hope you will read and enjoy it!

New book-chapter by Jitesh Jhawar et al: A first principle derivation of models of collective behaviour that account for finite group size

I am really pleased that a new publication – a first book chapter from lab and first paper of 2019 – is now out! Its led by Jitesh Jhawar, a final year PhD student in our lab and in collaboration with Richard Morris – a former postdoc at NCBS.

Jitesh Jhawar, Richard Morris, and Vishwesha Guttal, 2019, Deriving mesoscopic models of collective behaviour for finite populations, In Handbook of Statistics Vol 40: Integrated Population Biology and Modeling  (edited by Arni Srini Rao and C R Rao), Part B, 551-594. DOI:;  Pre-print from Arxiv;  Codes and data on github.  Download PDF

Collective behaviours of animal groups are often modelled via agent-based simulations. They are relatively difficult to tract analytically. The main highlight here is that we present two analytical methods that are used in the literature (statistical physics and physical chemistry); we compare which method offers ease of model construction.

A second point worth highlighting is that most analytical methods often assume that group/population sizes are infinitely large. The methods we present accounts for the fact that real animal groups are finite in size and individuals interact with each other in inherently probabilistic ways! The resulting scale of description is also referred to as mesoscopic — a term that appears in the title of the book chapter.

The mesoscopic descriptions yield very counter-intuitive results,; for example, noise can actually facilitate collective order!!! Read the chapter for more details.

The writing style we have adopted is pedagogical so that even undergraduate students from physics and mathematics can understand the methods presented here.

Finally, I also want to highlight that the first author of the paper – Jitesh Jhawar – did his bachelor and masters degrees in Biotechnology – but in this chapter, he uses mathematical techniques like Fokker-Planck equations, Langevin equations, Ito Calculus, etc! So even biology background students can learn hard-core mathematical/theoretical biology if you really love doing theory! 



New paper by Jaideep Joshi: Demographic noise and cost of greenbeard can facilitate greenbeard cooperation

We are delighted to announce a new paper from the lab!

Jaideep Joshi and Vishwesha Guttal, 2018, Demographic noise and cost of greenbeard can facilitate greenbeard cooperation, Evolution, DOI:

This is the second paper of our former PhD student Jaideep Joshi. Fantastic work, involving some hard-core analytical and simulational work to address an interesting problem on the evolution of greenbeard cooperation.

Congratulations to Jaideep!

While you are here, you must also check the previous paper of Jaideep on how mobility promotes cooperation, published last year in Plos Computational Biology.


(New) Paper on dryland ecosystem transitions and coverage in Deccan herald

Although I have tweeted quite a bit about this paper, I have been rather slow to announce this paper on this blog.

Chen Ning, Kailiang Yu, C Jayaprakash, Vishwesha Guttal, 2018, Rising variability, not slowing down, as a leading indicator of a stochastically driven abrupt transition in a dryland ecosystem, The American Naturalist, 191: E1 E14Data and Codes via Dryad. 

In this paper, we conduct an empirical test of early warning signals in a dryland ecosystem in China. This was based on a very cool email-collaboration with Chen Ning, a graduate student at that time.

The empirical analyses closely match with results of one of my PhD thesis paper with Prof C Jayaprakash, who is also a coauthor on this paper.

Suma from Gubbi Labs wrote this really nice popular article for Research Matters and it was also picked up by Deccan Herald, a very prominent English newspaper in South India !!!!


New paper: Friendship across species borders: factors that facilitate and constrain heterospecific sociality

Check out this new paper by Hari Sridhar, an INSA postdoctoral fellow in our lab.

Hari Sridhar and Vishwesha Guttal, 2018, Friendship across species borders: factors that facilitate and constrain heterospecific sociality, Phil. Trans. Royal Society of London B, 373: 20170014.

Hari did some fabulous work on mixed-species flocks during his Ph.D. thesis, advised by my colleague Kartik Shanker. Hari continues that trend with another piece of fundamental contribution to the field. I am quite lucky to have been involved with him on this and had lots of new things to learn from him on the topic. The main proposal of the paper is nicely captured in the abstract:

Our understanding of animal sociality is based almost entirely on single-species sociality. Heterospecific sociality, although documented in numerous taxa and contexts, remains at the margins of sociality research and is rarely investigated in conjunction with single-species sociality. This could be because heterospecific and single-species sociality are thought to be based on fundamentally different mechanisms. However, our literature survey shows that heterospecific sociality based on mechanisms similar to single-species sociality is reported from many taxa, contexts and for various benefits. Therefore, we propose a conceptual framework to understand conspecific versus heterospecific social partner choice. Previous attempts, which are all in the context of social information, model partner choice as a trade-off between information benefit and competition cost, along a single phenotypic distance axis. Our framework of partner choice considers both direct grouping benefits and information benefits, allows heterospecific and conspecific partners to differ in degree and qualitatively, and uses a multi-dimensional trait space analysis of costs (competition and activity matching) and benefits (relevance of partner and quality of partner). We conclude that social partner choice is best-viewed as a continuum: some social benefits are obtainable only from conspecifics, some only from dissimilar heterospecifics, while many are potentially obtainable from conspecifics and heterospecifics.

This is published as part of theme issue on “Collective movement ecology” – a must read for everyone interested in movement ecology.


New paper: Jaideep Joshi’s paper on mobility and cooperation

We have a bunch of papers from the lab that I haven’t time to announce on the website (but I do active tweet about them!). Here, I briefly post about the first thesis chapter of Jaideep Joshi is now published in Plos Computational Biology. It’s a really cool theory paper on mobility can actually promote cooperation.


(The above picture is from Figure 1 of the manuscript Joshi et al 2017, Mobility can promote the evolution of cooperation via emergent self-assortment dynamics, PLoS Computational Biology, 13(9): e1005732).

The way we set up the problem is that can we have cooperation in mobile organisms if we exclude well known mechanisms that facilitate the evolution of cooperation. Yes, indeed, we can find cooperation via emergent assortment of cooperators. This paper shows this counter-intuitive using heavy simulations of active or self-propelled particles, simulations of passive particles in turbulent media, and an analytical theory. All of it packed into a single paper.

Here is a nice summary of this work written by Ananya from Research Matters, a popular science communication webpage:

Classically, it has been argued that cooperative interactions evolve mostly among genetic relatives or individuals in close-knit environments – like the lions or the buffaloes. There is also the factor that these animals are mobile and often split and merge depending on the availability of food. What, then, could be the motivation for cooperative interactions to emerge among such dynamic groups that are not genetically related?

“Much of the earlier research on cooperation thought that mobility was a hindrance to the evolution of cooperation. This is because mobility allows defectors to invade and destroy clusters of co-operators, which are necessary for cooperation to sustain”, says Mr. Joshi. In their study, published in the journal PLOS Computational Biology, the researchers have considered two scenarios for mobility – one, where the individuals move through self-propulsion such as fishes and birds, and second, where the individuals move due to the flow of the medium they live in such as microbes.

The study demonstrates that, rather than hinder it, mobility can help animals evolve cooperation to form groups even among unknown individuals without any kinship. “Our study is like a thought-experiment, but aided by sophisticated theoretical and computational tools. However, our model can easily be adapted to real systems by incorporating features specific to those systems. These could include cancer cells, quorum sensing bacteria, mixed species bird flocks, or even grouping mammals such as spotted deer, baboons and elephants”, signs off Dr. Joshi.

Our new paper testing theory of spatial indicators of ecological transitions published in Global Ecology and Biogeography


geb12609-toc-0001We are happy to announce that our new paper on testing theory of spatial indicators of critical slowing down and ecological transitions has appeared in the online early version of the journal Global Ecology and Biogeography. The paper was highlighted via a cover image (left) taken by Stephanie.

Congratulations to Amit Agrawal (former project assistant of our lab) and Sabiha Majumder (PhD student) for their first research publication! This project began during conversations between Stephanie Eby, Andrew P. Dobson and myself. That was back in 2010, when I was a post-doc at Princeton. They had this excellent high resolution data that made sense in the context of a theory paper from my thesis in 2009.

So what is this paper about? 

Ecosystems like clear lakes or forests can abruptly collapse to ‘unhealthy’ states like toxic-turbid lakes or deserts with low vegetation. Our lab uses ideas from physics of phase transitions (e.g., water boiling to become vapour) to develop statistical tools of early warnings of such abrupt transitions. For example, two papers of my PhD thesis (Guttal and Jayaprakash 2008 and 2009) were on developing such tools to analyse time series and spatial data from ecosystems. The underlying theory is now popularly known as ‘Early warning signals of critical transitions’, “Theory of Critical slowing down”, etc.

In this paper, we were testing such tools using spatial data of large scale ecosystems. There were earlier efforts to test these quantitative tools, but mostly in simple laboratory conditions or controlled lake experiments.

Specifically, we test the prediction that the following metrics show stronger signatures of transitions ‘before a collapse of an ecosystem’

(A) Spatial variance (proposed in Guttal and Jayaprakash, 2009)

(B) Spatial skewness (proposed in Guttal and Jayaprakash, 2009)

(C) Spatial autocorrelation (proposed in Dakos et al 2010)

(D) Spatial spectra (proposed in Carpenter and Brock 2010).

This graph below shows how theoretical predictions and real data match.


There were a few subtle and insightful aspects related to analysing this dataset. First, we didn’t have an ideal dataset, so we had to make an approximation called ‘space-for-time substitution’ to compare theory with real data. We justified this approach using a model. Second, the data were discrete-state (occupied/unoccupied), unlike what the models typically assumes continuous variables (like biomass density) in each of the above papers. We developed a data preprocessing method called coarse-graining, inspired from the physics literature. We thought the method to be sufficiently important and hence the details of the method will be published separately. Analysing this dataset has motivated various thesis chapters in our lab’s PhD student Sabiha Majumder, who is from Physics department and works jointly with me and Prof. Sriram Ramaswamy.

I should add that reviewers gave detailed comments that helped the manuscript a lot. This was also our first manuscript where we used services of Axios.

All codes and some data associated with this manuscript are available on our Github page: