It was a really short visit, but we all really enjoyed how they used elegant mathematical and data-driven approaches to understand socio-ecological systems.
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!!
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!
Congratulations to Sumithra – its been so much fun collaboratingworking with you – which I hope we will continue!
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 E14, Data 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.
Our postdoc Krishnapriya Tamma is currently in Portland, USA attending Ecological Society of America’s Annual meeting.
She will be presenting her work titled “Inferring critical points from spatial ecological data”. This is a joint work with PhD student Sabiha Majumder and Sriram Ramaswamy, both from Physics Department, IISc.
Her presentation is scheduled for Friday, 11th August at 8:20am. If you are attending ESA, do go to her talk!
Congratulations to Dr Krishnapriya Tamma for the National-Post Doc Fellowship from SERB to work in our lab.
Krishnapriya will work on analysing various remotely sensed images of vegetation to understand and to predict tipping point phenomena natural forests across the world.
Priya Tamma is not really new to our lab. She was already on a postdoctoral position in our lab from April 2016. This fellowship gives her additional three years to continue her work. This will also allow her to pursue newer directions of research apart from primary focus areas of our lab. Apart from global scale analyses of vegetation, she is deeply interested in understanding biogeography, ecosystem patterns and conservation issues n North-Eastern India.
Before joining our lab, Priya Tamma did her PhD from our neighboring institution NCBS, in the lab of Prof Uma Ramakrishnan, on biogeography of Himalayan region. Check our her Google scholar profile to see her interesting publications.
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’
(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: https://github.com/tee-lab/spacetime-csd
Our new paper showing “Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk” is out in PLoS ONE!
Nature India carried out a very nice article on our work, written by Mr Varma. National University of Ireland, Galway issued a press-release (an initial draft of which was written by Rajashree of Science Media Centre, IISc). and featured it on their website. Here is a media article at Deccan Herald, but whats written there just does not make sense.
This work was done in collaboration with Dr Srinivas Raghavendra, an economist at the National University of Ireland, Galway. We started the work sometime in mid-2012. Nikunj Goel, a Physics undergraduate student at IISc, joined this work in early 2014 and did enormous contributions to the manuscript. Quentin Hoarau, an undergraduate itern from CNS, France, was also a co-author on the manuscript.