Our recent GEB paper on spatial indicators featured with a front cover image

We are delighted that our recent GEB paper on spatial indicators of critical slowing down has been featured with a front cover image (by Stephanie Eby)! This is also the first instance of front cover appearance for our lab’s paper, so we are delighted!



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: https://github.com/tee-lab/spacetime-csd

New paper on financial market crashes and media coverage

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.

Article on “Discovering facts: Finding the longest day with school children” appears in Resonance

Long back, in 2012, I did a very interesting teaching project with primary school children. I also wrote about it in this blog. The same blog article, with some modifications, has been published in Resonance.

Click here for the article (pdf): Discovering Facts: Finding the longest day with school children

For some reasons, there were three footnotes in my article submissions which have been ommitted in the final version. The footnotes were numerically referenced as [1], [2], [3] in the text but what exactly those are got missed out in the final version (my fault to have missed it at the stage of proof). I am posting those below here:

[1] Disclosure: The school is founded by close relatives and friends. You can learn more about it by visiting the website: www.purnapramati.in

[2] A preliminary version of this article appeared in the souvenir of the school in Jan 2013 and has also been put up on my personal/lab blog.

[3] Data for sunrise and sunset for most cities can be downloaded from: http://aa.usno.navy.mil/data/docs/RS_OneYear.php (you need to know Longitude and Latitute of the place) OR http://www.timeanddate.com/worldclock/astronomy.html?n=438

Ecology: Individuals to Collectives – article in Resonance

I would be writing a series for Resonance on some aspects of theoretical ecology, and from the perspective of a physicist turned ecologist!

The first of the series came out two months ago. I copy paste the abstract here, and here is the link to the pdf if you want to read it in full! Do leave a comment or suggest me how you liked the article and what would you like to cover in the series.

“Common people and even scientists think of ecology as a discipline that exclusively studies wildlife and topics related to environmental pollution. My friends both within and outside the scientific community are often baffled when they hear that I am a physicist doing research in ecology. The aim of this series of articles is to emphasize the less known fact that theory and mathematics have been central to ecology since the inception of this relatively young scientific field. In this first article, I will talk about the following three points. First, I will discuss how the emphasis of the basic science of ecology is much broader than its applied aspects involving the conservation of natural ecosystems. Second, I will discuss a fundamental parallel between statistical physics and ecology that arises because both disciplines emphasize macroscopic systems (e.g., magnetic materials in physics or flocks of birds in ecology) as collectives of interacting units that are more than the sum of their constituents. What makes them fascinating is that interactions at small scales typically give rise to unexpected properties at larger scales. Finally, I will discuss how ecology offers a new and rich set of challenges to mathematically trained scientists because of variations among biological organisms and the role of natural selection in shaping ecological systems, both of which have no parallels in the physical sciences.”

Our manuscript on “Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns” published in Plos ONE

Our new collaborative paper (with researchers from five different countries) summarizing methods to detect early warning signals of ecological transitions using spatial patterns has been published in Plos ONE this March. Click here to read the paper.

The paper also comes with an R package to use the methods. Its available from the github: https://github.com/earlywarningtoolbox/spatial_warnings

If you would like to use this toolbox and face any problems, please feel free to contact me:

Story behind the paper: Vasilis Dakos, Marten Scheffer and Stephen R Carpenter organized a fantastic workshop in Santa Fe Institute (New Mexico, USA) and invited a bunch of people who had worked on developing early warning signals. It was two and a half days of extremely interesting discussion and we decided to summarize the methods of early warning signals in two papers.

One paper was to focus exclusively on methods to detect early warning signals in time series data. Vasilis Dakos took the lead and we published a paper in Plos ONE that can be found here. Together with the paper, we also provided an R package so that researchers can use the methods without having to develop their own code. The methods and package can be obtained from the website: www.early-warning-signals.org

A second paper was to focus on the methods for analyzing spatial patterns to detect early warning signals. Sonia Kefi and myself took the lead, and we had to face the challenge of summarizing results for analyzing spatial patterns where the methods have not been not so well developed. Finally, the second paper has also been now published! We now need to make the codes more easily accessible to users.


Theoretical ecology and statistics

There is an interesting post (and lots of discussion in comments section) by Brian McGill at Dynamic Ecology blog on excessive usage of fancy, complicated and unnecessary statistics in ecology literature; he calls this statistical machismo (hat tip: Hari Sridhar, a graduate student in our department). It reminded me of an interesting comment on statistics from a referee on one of my manuscripts. I thought of writing about that, and also more generally about statistics and its role in my field of theoretical ecology.

Before I get to my story, let me say that I couldn’t agree more on the basic point McGill is making that ecologists tend to overuse (perhaps, largely in response to demanding referees) statistics when simple methods would yield equally good results. If you dont have fancy named stats in your publication, referees and editors, especially those of high impact factor journals, may object and ask for more, and likely even reject your paper. Your peers may criticize that you haven’t been rigorous enough. Despite recent debates, fancy and complicated statistics continue to flourish in the ecology literature.

What is the role of statistics in theoretical ecology? Being a theoretical ecologist, at least in principle, I don’t need to use any statistics for my publications. Our aim is to show general ecological principles or develop predictive tools using simple mathematical models. We do this either through analytical calculations where we derive relationships between two ecological quantities, or when we can not derive analytical results, we do numerical simulations to find those relationships. For the former case, statistics is not needed at all. For the latter, since we can do as many simulations as we like, we can obtain relationships where the error bars could be smaller than the thickness of the dots or lines on the plot. In other words, we can live without statistics (but see last paragraph).

Here is my unusual story of referee’s comment on stats during a manuscript review.  As a physics graduate student, I submitted a paper to an ecology journal developing a quantitative method to ‘assess’ ecosystem dynamics, commenting on how it may offer an useful tool for ecologists. In this largely theoretical paper, we showed our claim by analytical calculations and numerical simulations but we had not done any statistics (and I could not have done anything either). Referees in general liked the idea, and here is a comment by one of the referees that you may find interesting: “Authors are physicists, not ecologists; it would be unfair to ask them to do detailed statistical analyses, and that will make paper too long” [1, 2]. I dont know what I thought of that at the comment at that time, but now I find it amusing at first sight but also very reasonable. I will leave it to you for your own interpretation.

Why would a theoretical paper need statistics when I argued above that we can avoid it entirely. Statistics can be very useful, and perhaps essential, to test whether our principles or tools derived from mathematical models work (i.e., provide significant results) even within typical limitations of real ecological data sets.  For example, the ecological data are typically short and not finely resolved. It will have observational errors and we usually lack a full understanding of underlying processes. It was in this context that the referee was talking about statistical analyses in our manuscript. Eventually, after our work and several other related papers suggesting new such tools came out, many papers that exclusively develop and discuss statistical methods for these types of analyses got (and continue to get) published. Clearly, it would have been an overkill to demand statistics for our paper and I am glad referees were with us.

[1] I have made a slight modification to the actual referee comment to shorten an otherwise long sentence.

[2] I am not entirely sure if its okay to quote an anonymous referee’s comments. Any ideas?