Collective dynamical regimes predict invasion success and impacts in microbial communities.

The outcomes of ecological invasions may depend on either characteristics of the invading species or attributes of the resident community. Here we use a combination of experiments and theory to show that the interplay between dynamics, interaction strength and diversity determine the invasion outcome in microbial communities. We find that the communities with fluctuating species abundances are more invasible and diverse than stable communities, leading to a positive diversity-invasibility relationship among communities assembled in the same environment.

Local and extensive fluctuations in sparsely interacting ecological communities.

Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where species abundances always reach a fixed point and a phase where they continuously fluctuate have been found. The dynamics when interactions are sparse, with each species interacting with only a few others, has remained largely unexplored.

Generalized Lotka-Volterra Equations with Random, Nonreciprocal Interactions: The Typical Number of Equilibria.

We compute the typical number of equilibria of the generalized Lotka-Volterra equations describing species-rich ecosystems with random, nonreciprocal interactions using the replicated Kac-Rice method. We characterize the multiple-equilibria phase by determining the average abundance and similarity between equilibria as a function of their diversity (i.e.

Aging by Near-Extinctions in Many-Variable Interacting Populations.

Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding, accompanied by a slowdown of the dynamics (aging). Here, we investigate the connection between near-extinction and aging by introducing an exactly solvable many-variable model, where the time derivative of each population size vanishes at both zero and some finite maximal size. We show that aging emerges generically when random interactions are taken between populations.

Emergent phases of ecological diversity and dynamics mapped in microcosms.

From tropical forests to gut microbiomes, ecological communities host notably high numbers of coexisting species. Beyond high biodiversity, communities exhibit a range of complex dynamics that are difficult to explain under a unified framework. Using bacterial microcosms, we performed a direct test of theory predicting that simple community-level features dictate emergent behaviors of communities.

Local and collective transitions in sparsely-interacting ecological communities.

Interactions in natural communities can be highly heterogeneous, with any given species interacting appreciably with only some of the others, a situation commonly represented by sparse interaction networks. We study the consequences of sparse competitive interactions, in a theoretical model of a community assembled from a species pool. We find that communities can be in a number of different regimes, depending on the interaction strength.

Extinctions of coupled populations, and rare event dynamics under non-Gaussian noise.

The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate in time. We report on two findings.

Dynamical persistence in high-diversity resource-consumer communities.

We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. These fluctuations appear, robustly and predictably, in certain regimes of parameter space. Their origin is closely tied to the ratio of realized species diversity to the number of resources.

Complex interactions can create persistent fluctuations in high-diversity ecosystems.

When can ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where many species populations fluctuate without going to extinction? We show that high-diversity spatially heterogeneous systems can exhibit chaotic dynamics which persist for extremely long times. We develop a theoretical framework, based on dynamical mean-field theory, to quantify the conditions under which these fluctuating states exist, and predict their properties. We uncover parallels with the persistence of externally-perturbed ecosystems, such as the role of perturbation strength, synchrony and correlation time.

Statistical physics of community ecology: a cavity solution to MacArthur's consumer resource model.

A central question in ecology is to understand the ecological processes that shape community structure. Niche-based theories have emphasized the important role played by competition for maintaining species diversity. Many of these insights have been derived using MacArthur's consumer resource model (MCRM) or its generalizations.

Generic assembly patterns in complex ecological communities.

The study of ecological communities often involves detailed simulations of complex networks. However, our empirical knowledge of these networks is typically incomplete and the space of simulation models and parameters is vast, leaving room for uncertainty in theoretical predictions. Here we show that a large fraction of this space of possibilities exhibits generic behaviors that are robust to modeling choices.

Ecological communities with Lotka-Volterra dynamics.

Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations.

Topological Constraints in Directed Polymer Melts.

Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model.

Coalescence Model for Crumpled Globules Formed in Polymer Collapse.

The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived "crumpled globule." The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with large simulations. To unravel this puzzle, we study a coarse-grained model of in-falling spherical blobs that coalesce upon contact.

Frequency-dependent fluctuation-dissipation relations in granular gases.

The Green-Kubo relation for two models of granular gases is discussed. In the Maxwell model in any dimension, the effective temperature obtained from the Green-Kubo relation is shown to be frequency independent and equal to the average kinetic energy, known as the granular temperature. In the second model analyzed, a mean-field granular gas, the collision rate of a particle is taken to be proportional to its velocity.

Fluctuation-dissipation relations in driven dissipative systems.

Exact theoretical results for the violation of time-dependent fluctuation-dissipation relations in driven dissipative systems are presented. The ratio of the correlation to delayed response in the stochastic model introduced in [Phys. Rev.