The interplay of ecological and evolutionary dynamics: immigration, extinction, and chaos (and DMFT?)

"Ecological and evolutionary dynamics are intrinsically entwined. On short timescales, ecological interactions determine the fate and impact of new mutants, while on longer timescales evolution shapes the entire community."

 Spatiotemporal ecological chaos enables gradual evolutionary diversification without niches or tradeoffs       Aditya Mahadevan, Michael T Pearce, and Daniel S Fisher

Understanding this interplay is "one of the biggest open problems in evolution and ecology."

New experimental techniques for measuring the properties of large microbial ecosystems have stimulated significant theoretical work, including from some with a background in theoretical condensed matter physics. For an excellent accessible introduction see:

Understanding chaos and diversity in complex ecosystems – insights from statistical physics

This is a nice 2.5-page article by Pankaj Mehta at the Journal Club for Condensed Matter. He clearly introduces an important problem in theoretical ecology and evolution and describes how some recent work has provided new insights using techniques adapted from Dynamical Mean-Field Theory, which was originally developed to describe strongly correlated electron systems. 

Here are just a few highlights of the article. It may be better to just read the actual article.

Fifty years ago, Robert May "argued that the more diverse an ecosystem is (roughly defined as the number of species present), the less stable it becomes." He derived this counter-intuitive result using a simple model and results from Random Matrix Theory. This is an example of an emergent property: qualitative difference occurs as a system of interacting parts becomes sufficiently large.

"One major deficiency of May’s argument is that it does not allow for the possibility that complex ecosystems can self organize through immigration and extinction. The simplest model that contains all these processes is the Generalized [to many species] Lotka-Volterra model (GLV)".

"Despite its simplicity, this equation holds many surprises, especially when the number of species is large".

Another case of how simple models can exhibit complex behaviour.

One special case is when the interactions are reciprocal – how species i affects species j is identical to how species j affects species I. "In the presence of non-reciprocity the system can exhibit complex dynamical behavior including chaos." Understanding this case was an open problem until the two papers reviewed by Mehta. For a detailed but pedagogical introduction see:

Les Houches Lectures on Community Ecology: From Niche Theory to Statistical Mechanics, Wenping Cui, Robert Marsland III, Pankaj Mehta

This is relevant to understanding the origin of the fine grained diversity observed in sequencing experiments of microbial ecosystems.

Aside: de Pirey and Bunin "derive analytic expressions for the steady-state abundance distribution and an analogue of the fluctuation-dissipation theorem for chaotic dynamics relating static and dynamics correlation functions."

"Using a DMFT solution, they derive a number of remarkable predictions... in the chaotic system the species fall into two groups: species at high abundances and species at low abundances near the immigration floor. de Pirey and Bunin show that even in the chaotic regime, the number of high abundance species in the ecosystem will always be less than the May stability bound. This result is quite surprising since it suggests that ecosystems self-organize in such a way that the high abundance species still follow May’s diversity bound even when they are chaotic."