Disordered systems in community ecology: a tutorial

Matthieu Barbier 

A basic fact of community ecology is that most ecosystems are comprised of many species and processes. Mathematical models trying to capture these ingredients and explain empirical phenomena usually face the problem of having vast numbers of unknown parameters and uncertain assumptions. It is not obvious when such mathematical models can truly be quantitatively predictive, or even conceptually helpful -- to this day, this branch of ecological theory carries a heavy burden of proof. This document is an informal introduction to disordered systems in community ecology, an approach inspired by statistical physics, whose starting point is trying to capture a few central ecological processes or mechanisms and replacing many other unknown details by some form of randomness. The challenge comes in two parts: synthesizing observable phenomena into general(-ish) concepts that can be given mathematical counterparts of this kind, and understanding said mathematical objects enough to make them usable (e.g. predictive or explanatory). The first part requires conceptual effort from theoretical ecologists, a lot of which happens either before writing any equation, or going back to reality after all the math is done. Physics-inspired thinking and tools help with the second part, guiding modelling choices and revealing their consequences more robustly than standard explorations through numerical simulations. My hope with this manual is to help people on each side better understand the broader picture and how to concretely work on this challenge, at least in the context of the specific approach I have been using, which I think has a lot of potential for connecting and synthesizing a sizable fraction of existing work and questions in theoretical community ecology. My hope with this manual is to help people on each side better understand the broader picture and how to concretely work on this challenge, at least in the context of the specific approach I have been using, which I think has a lot of potential for connecting and synthesizing a sizable fraction of existing work and questions in theoretical community ecology. My hope with this manual is to help people on each side better understand the broader picture and how to concretely work on this challenge, at least in the context of the specific approach I have been using, which I think has a lot of potential for connecting and synthesizing a sizable fraction of existing work and questions in theoretical community ecology. My hope with this manual is to help people on each side better understand the broader picture and how to concretely work on this challenge, at least in the context of the specific approach I have been using, which I think has a lot of potential for connecting and synthesizing a sizable fraction of existing work and questions in theoretical community ecology. My hope with this manual is to help people on each side better understand the broader picture and how to concretely work on this challenge, at least in the context of the specific approach I have been using, which I think has a lot of potential for connecting and synthesizing a range of existing work and questions in theoretical community ecology.