Jitesh defended his thesis titled “Intrinsic noise in collective dynamics” – where he theoretically and empirically investigated how stochasticity plays a very counter-intuitive role and creates order!
The thesis was reviewed by Prof Martin Evans (Dept of Physics, Edinburgh, UK) and Prof Malay Banerjee (Dept of Math, IIT Kanpur)! We thank them for their very constructive comments and their valuable time.
As you can see, although this work is from CES and we look at fish schools, it was reviewed by physicists/mathematicians! This is because there are lots of links between physics and schooling fish.
Jitesh is continuing as a short-term post-doctoral fellow in the lab. He will soon join Max Planck Institute for Collective Behaviour in Konstanz for his postdoctoral work on honey bees and collective cell migration.
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.
I am super delighted to share this — somewhat belated — news that Sumithra Sankaran has defended her PhD thesis on 7th December 2018. Sumithra’s thesis was on understanding how local interactions, spatial patterns and ecosystem stability are related. Needless to say, Sumithra gave a fabulous presentation and the examiners (including external examiner Prof Partha Sarathi Dutta from IIT Ropar, Department of Mathematics) were super impressed.
It is worth noting – especially for prospective students to our lab – that Sumithra was formally trained in zoology and wildlife biology. Because of her exceptional interest in theory, she did a thesis in theoretical ecology involving fairly involved mathematical calculations, e.g., mean-field models, stochastic differential equations and their analyses via Fokker-Planck equations, cellular automata models. Finally, testing her predictions of theory with empirical data – which required another suite of skills in analysing remotely-sensed data, statistics, and making sense of results in light of theory!
Do check some of her papers here,here, here and here. There are two more being prepared.
Congratulations to Sumithra – its been so much fun collaboratingworking with you – which I hope we will continue!
HUGE congratulations to two lab members (now, unfortunately, former lab members) — Sabiha Majumder and Jaideep Joshi – for the successfully defending their thesis.
Sabiha Majumder defended her thesis on 26th February 2018. She joined IISc as an Integrated PhD student in the Department of Physics. Her Physics adviser was Prof Sriram Ramaswamy and with us she worked on “Multiple stable states and abrupt transitions in ecosystems”. She made some extremely important contributions to our understanding on patterns and dynamics ecosystems with multiple stable states, whether we can anticipate them via measuring simple quantities from field data, and whether we can even estimate threshold/critical points of such ecosystems.
Sabiha has joined as a postdoctoral fellow at Crowther Lab at ETH-Zurich. All the best for her future work. She will be badly missed in our lab.
Jaideep defended his thesis on 30th January 2018. He joined IISc as a PhD student at CES and worked on some deeply insightly theoretical aspects of the evolution of cooperation in spatial systems. Apart from working with me, he also established his own collaborations as part of his thesis. After his PhD, he has joined as a postdoctoral researcher at Divecha Centre for Climate Change, IISc with prof Sukumar of CES. All the best to Jaideep for his future endeavours!
As I mentioned in the previous post, our postdoc is attending Ecological Society of America Annual Meeting in Portland this week. In addition, our lab had presence in various other international conferences and workshops this summer.
Four PhD students from our lab presented their work at the conference “Mathematical models in ecology and evolution” (MMEE) held at London in July 2017.
Jaideep Joshi, final year student who has already submitted his thesis, presented his work on “Demographic noise and the evolution of tag-based cooperation”.
Sumithra Sankaran, finishing her 4th year of PhD, presented her work on “Demographic noise promotes bistability in ecosystems”
Jitesh Jhawar, finishing his 3rd year of PhD, presented his work on “Role of stochasticity in the dynamics of fish schools”
Aakanksha Rathore, finishing her 2nd year of PhD, presented her work on “Spatial dynamics of Blackbuck herds”
Three of the students, Sumithra, Jitesh and Aakanksha, also attended BES organised one day symposium on movement ecology in London.
After the conference, Aakanksha went to visit Dr Colin Torney at University of Glasgow.
Jaideep went on to Puerto Rico to attend a workshop on tropical forest ecology.
Student trips were supported by funds from Indian Institute of Science (MHRD) and a grant from Royal society to visit Dr Torney’s lab.
Our friends from France, Sonia Kefi and two of her group members Miguel Berdugo (currently a student of Prof Fernando Maestre in Spain and soon moving as a postdoc with Sonia) and Angeles Mayor (a postdoc with Sonia) visited Bengaluru for about a week. They enjoyed the tree festival Neralu and other small fun events in the town.
Of course, we all met them to have exciting discussions and how to take our collaboration forward. Here is a group picture at a cafetaria.
We 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’
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.
We had very good interactions with scientists at NRSC. We discussed our requirement of high resolution data of various ecosystems for our research work for which they offered lot of support. We hope to build strong collaborations with the ISRO scientists.
Congratulations to Sumithra Sankaran who won a best poster award for her poster on ‘Characterising vegetation of semi-arid ecosystems’. She presented her modelling work on based on simple cellular automata models and how one can use spatial metrics of remote sensing data to infer ecological features underlying the system.
Dr Sonia Kefi, a researcher from the CNRS Montpellier and two of her students, Alex Genin and Miguel Berdugo, are visiting our lab for two weeks from 27th Nov to 10th Dec 2015. Our labs are collaborating on developing mathematical models of patterned ecosystems, especially the vegetation of semi-arid ecosystems.
Discussions over tea and mist
Priya kicks off the meeting!
No, thats not right.
Sumithra writing stuff
Alex and Sumithra in deep disccussions!
The three visitors from France and the three folks from our lab (me, Sumithra and Sabiha) went to a tea estate resort near Conoor in Tamil Nadu, away from the distraction of Bengaluru, to assess the progress we have made so far on our projects. We also had a guest – Krishnapriya Tamma, a PhD student from NCBS (Dr Uma Ramakrishnan’s student) who gave a fantastic talk on her superb phd thesis. It was a great scientific meeting discussing a number of ideas.