This is an extended version of my Nobel Lecture, delivered on December 8, 2021. I will
recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe …

Rich out-of-equilibrium collective dynamics of strongly interacting large assemblies emerge
in many areas of science. Some intriguing and not fully understood examples are the glassy …

From tropical forests to gut microbiomes, ecological communities host notably high numbers
of coexisting species. Beyond high biodiversity, communities exhibit a range of complex …

We compute the typical number of equilibria of the generalized Lotka-Volterra equations
describing species-rich ecosystems with random, nonreciprocal interactions using the …

The worldwide loss of species diversity brings urgency to understanding how diverse
ecosystems maintain stability. Whereas early ecological ideas and classic observations …

The eigenvalue spectrum of a random matrix often only depends on the first and second
moments of its elements, but not on the specific distribution from which they are drawn. The …

A central concern of community ecology is the interdependence between interaction
strengths and the underlying structure of the network upon which species interact. In this …

In this Letter, we explore the dynamics of species abundances within ecological
communities using the generalized Lotka-Volterra (GLV) model. At variance with previous …

The composition of ecological communities varies not only between different locations but
also in time. Understanding the fundamental processes that drive species toward rarity or …

We consider the generalized Lotka–Volterra system of equations with all-to-all, random
asymmetric interactions describing high-dimensional, very diverse and well-mixed …