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!!