Category Archives: Papers

Two new papers

Two papers I am very fond of just came out.

The first one deals with competition: for decades, we’ve been teaching undergraduate students about the principle of competitive exclusion, showing the simple and appealing notion that intra-specific competition has to exceed inter-specific competition for two species to coexist. Often, however, we fail to mention that this simple rule does not extend to more than two species (guilty as charged).

Can we say anything interesting about the role of intra- and inter-competition in determining the stability of large systems? Turns out that some fairly old results in linear algebra, mixed with more recent advances in random matrix theory,  can be used to write simple conditions for the stability of large competitive communities.

György Barabás, Matthew J. Michalska-Smith & Stefano Allesina
The effect of intra- and interspecific competition on coexistence in multispecies communities
The American Naturalist, 2016

Interestingly, when we have more than two species we can think of how interaction strengths should be arranged to maximize (minimize) stability. Thanks to some very intensive numerical searches, we were able to show that these cases correspond to visually beautiful and ecologically reasonable patterns of interaction strengths:

The second paper takes a new angle to study a very old problem: are modular structures more conducive to stability than random ones? This idea was already put forward by Robert May at the end of his celebrated 1972 paper—yet, a good method to settle this question once and for all was lacking.

We have found a new way to calculate the stability of large random matrices with block structure, showing that rarely modularity has a positive effect on stability:

Jacopo Grilli, Tim Rogers & Stefano Allesina
Modularity and stability in ecological communities
Nature Communications, 2016

One interesting anecdote about this paper: Jacopo and I had been working on it for a while, and had received positive reviews from Nature Communications. However, we didn’t have a way to show that our conjectures were right. At the end of Dec 2015, I was at the Santa Fe Institute for a workshop. I gave a talk on this topic, and Charles Bordenave told me that a friend of his, Tim Rogers, had developed a method that could be used to perform this type of calculation. On Christmas day—thinking that at Christmas everybody’s good—I emailed Tim, asking whether he’d be able to help us out. Come New Year’s Eve and I receive an email from Tim: he had done the calculation, confirming our conjectures exactly!

The method Tim developed is based on quaternionic functions—I believe this is the first paper in ecology to ever mention quaternions in the abstract…


Here come old flat top
He come groovin’ up slowly
He got joo joo eyeball
Come together
Lennon  & Mccartney

We have been working on the applications of random matrix theory to ecology for four years. By now, it is quite clear that the most important challenge ahead is to extend the theory to the case of structured networks (as described here). A new study we just published is a first step in this direction:

 Stefano Allesina, Jacopo Grilli, György Barabás, Si Tang, Johnatan Aljadeff & Amos Maritan
Predicting the stability of large structured food webs
Nature Communications, 2015

In this work, we studied community matrices produced according to the cascade model, in which “big fish eat little fish”. These matrices look like this:

eyeballmatwhere the red squares represent negative coefficients (effects of predators on prey), and the blue ones positive coefficients (effects of prey on predators). These matrices produce a peculiar spectrum, suggestive of an “eyeball”:


In the paper, we derive simple, analytical results that allow us to approximate the spectrum (and hence the stability) of the eyeball.

 I wrote an R package that performs the analysis described in the paper, and published it on github.

PS: Despite the quote from the Beatles above, all I could listen to while writing the paper was Pink Floyd. Maybe because I remember another eyeball I saw a long time ago


In a new paper, Jacopo, Gyuri and I studied the persistence of metapopulations living in a landscape where patches of suitable habitat are scattered randomly.

We found strong connections between metapopulation theory, the mathematics of Random Geometric Graphs, and the physics of disordered systems. You can find the paper here:

Jacopo Grilli, György Barabás, Stefano Allesina
Metapopulation Persistence in Random Fragmented Landscapes
PLoS Computational Biology, 2015

A bit on the backstory: in December 2014, I gave a talk at UC Davis, and, at dinner, Sebastian Schreiber mentioned that if I liked problems involving eigenvalues I should have looked at the classic Hanski & Ovaskainen model. Back in Chicago, Gyuri (who had just started his postdoc) and Jacopo (who was visiting from Italy) thought it would be a good project to jumpstart our collaboration…

More is more (when it comes to abstracts)

In the summer of 2013, I was coordinating a class meant to prime incoming graduate students on what it takes to succeed in graduate school. One session dealt with writing good abstracts. You have heard the usual advice: keep it short and simple, avoid jargon, write it for a general reader, etc.

I thought that it would be fun to test whether following this type of advice increases readership (citations). After a few months, I pitched this idea to my friend James Evans, and we decided to try it out with the help of Cody Weinberger, an undergraduate student in my laboratory.

We collected about 1M abstracts from 8 disciplines, and we tested the impact of following the usual advice on citations, once accounted for obvious factors such as age of the article, journal where it was published, etc. To our surprise, we found that following some of the most common suggestions leads to a significant decrease in citations!

You can read the results here:
Cody J. Weinberger, James A. Evans, Stefano Allesina
Ten Simple (Empirical) Rules for Writing Science
PLoS Computational Biology, 2015


The short article starts with a quote from Boyle’s “Proemial Essay”. Robert Boyle was one of the main proponents of the use of “modern” scientific articles to disseminate science (i.e., instead of books). Amusingly, while describing the advantages of this approach, Boyle already states some guidelines on how the essays should be written: we’ve been told how should we write our science for at least 350 years!

Update: The Chronicle of Higher Education features a Q&A with Cody.

Random matrices in ecology: the challenges ahead

RMT-ProductIn October 2013, I was a speaker at the 29th Annual Meeting of the Society of Population Ecology, held in Osaka, Japan. The invitation came with the possibility of writing an article for a special issue of the journal Population Ecology.


I thought that this would be a great occasion to review the progress my laboratory has made on the study of the stability of large ecological systems. Even better, this article could outline a research program on this topic, listing the main challenges that we are facing.

My former student Si Tang (now pursuing a second PhD in Statistics) and I set to work with this idea in mind. You can now read this hybrid between a review and a list of “grand challenges”:

Stefano Allesina & Si Tang
The stability–complexity relationship at age 40: a random matrix perspective
Population Ecology, 2015

Our hope is that all the challenges we list will be solved by the time May’s 1972 paper turns 50.