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…