Coexistence for more than two species

One of the main obsessions in the laboratory is to build robust ecological theories for communities composed of many species.
This is especially important in competitive systems—much of our  understanding in this area descends from the analysis of the dynamics of two competitors.
In a new review published this week in Nature, Jonathan Levine, Jordi Bascompte, Peter Adler, and yours truly provide a roadmap for extending these considerations to systems with more than two species.
Interestingly, certain mechanisms, such as higher-order interactions and intransitive competition, can only be studied in high-dimensional systems.
You can read the paper here:

Jonathan M. Levine, Jordi Bascompte, Peter B. Adler & Stefano Allesina
Beyond pairwise mechanisms of species coexistence in complex communities
Nature, 2017

Here’s the “Outlook”:

In this Review, we suggest that coexistence mechanisms that emerge only in systems with more than two competitors exert a largely unexplored control over the maintenance of diversity in species-rich communities. We also highlight that when studying more than two competitors, ecologists necessarily confront an ecological network. However, it remains largely unknown how the structure of the network influences coexistence. The sparseness of evidence results from the intractability of empirically evaluating competition between many species and the technical difficulties that are inherent in tightly coupling theory to data. Despite these challenges, there are compelling reasons to deepen our understanding of these more complex mechanisms of coexistence. Armed with advances in data-driven modelling and network analyses that have been developed for multitrophic systems, ecologists are well-positioned to determine, for at least some species-rich communities, how much of the coexistence results from mechanisms that emerge only in diverse systems. Few other questions in ecology have such great potential to radically shift how we think about the maintenance and fragility of biodiversity.

15 years in science

Hard to believe, but I’ve been working in science for fifteen years! Many things have happened since I started my PhD in Antonio Bodini’s lab in Parma, but I still have fun doing my job, and I am extremely grateful for the fantastic students, postdocs and colleagues who have been working with me through the years. The anniversary calls for a song!

studying large matrices and their eigenvalues
teaching to code and to despise p-values
watching your students give excellent talks
these are a few of my favorite things

reviewing good papers that are bright and novel
writing nice code to implement a new model
having a coffee with my lab and friends
these are a few of my favorite things

finding a method to do something crazy
I will keep searching until I turn lazy
sending proposals before they are due
these are a few of my favorite things

when the grant bites
when reviews sting
when I’m feeling mad
I simply remember my favorite things
and then I can start over

Last week, I was at the National Gallery in DC, and I’ve stumbled upon the painting that is featured as the first slide of most of my talks. I think it’s a perfect metaphor of science: the reality is out there, we have a small window to observe it, and we want to compose a simplified picture to understand what is going on. May I’ll still be happy to peer through the window in 2032!

Me and one of my favorite paintings!
Me and one of my favorite paintings!

Tips jar

In lieu of a laboratory meeting, we typically chat over coffee at the Smart Museum of Art every morning. Recently, they introduced a “vote with your tips” mechanism in which you can choose between two alternative tip jars. On Jacopo’s birthday, these were the options:

IMG_20160722_092846

Looking for a postdoc

With Gyuri leaving for Sweden, the laboratory is short of a postdoc. I am therefore looking for a new postdoc who could start in late 2016 or early 2017. Here below I past the ad I am circulating.

Postdoctoral position — Allesina Laboratory, University of Chicago

The Allesina laboratory at the University of Chicago is looking for a postdoc, starting in late 2016 or early 2017. The interests of the laboratory include ecological networks (food webs, mutualistic, competitive networks), community ecology, and theoretical ecology in general. The focus of the lab is on the development of new mathematical, statistical and computational methods for the analysis of ecological systems. More information on the research interests can be found here. A list of recent publications from the laboratory is here.

The candidate should have a strong mathematical background, be well-versed in statistics, and fluent in at least one of the programming languages used in the laboratory (C, python, R). Knowledge of Linux, Git, LaTeX, and SQL is a plus. Candidates with a background in mathematics or physics are also encouraged to apply.

To apply, please send an email including a CV, a brief description of research interests and experience, and the name of two letter writers to Stefano Allesina (sallesina@uchicago.edu).

Note: Gyuri Barabas and Matthew Smith will be at ESA Annual Meeting. If you are attending and are interested in this position, make sure to contact them to hear about life in the laboratory.

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…