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We investigate the Generalized Lotka-Volterra (GLV) equations, a central model in theoretical ecology, where species interactions are assumed to be fixed over time and heterogeneous (quenched noise). Recent studies have suggested that the…
Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological…
Despite the knowledge that social, economical, and ecological networks are often of a small-world nature with inter-nodal distance growing even slower than logarithmically with system size, we often assume theoretical systems to be outside…
Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the…
In this paper, we study in detail the structure of the global attractor for the Lotka--Volterra system with a Volterra--Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in [19] and prove that its…
In this monograph, we introduce a new model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility. The interactions among these populations are described not in terms of…
Quantifying population dynamics is a fundamental challenge in ecology and evolutionary biology, particularly for species that are cryptic, microscopic, or extinct. Traditional approaches rely on continuous representations of population…
This paper is divided into two parts. The first part is devoted to the study of a class of Approximate Message Passing (AMP) algorithms which are widely used in the fields of statistical physics, machine learning, or communication theory.…
The generalized Lotka-Volterra (gLV) equations, a classic model from theoretical ecology, describe the population dynamics of a set of interacting species. As the number of species in these systems grow in number, their dynamics become…
We develop a landscape-flux framework to investigate observed frequency distributions of vegetation and the stability of these ecological systems under fluctuations. The frequency distributions can characterize the population-potential…
Group formation and coordination are fundamental characteristics of living systems, essential for performing tasks and ensuring survival. Interactions between individuals play a key role in group formation, and the impact of resource…
Dynamic processes of interacting units on a network are out of equilibrium in general. In the case of a directed tree, the dynamic cavity method provides an efficient tool that characterises the dynamic trajectory of the process for the…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
A fundamental problem in community ecology is to understand how ecological processes such as selection, drift, and immigration give rise to observed patterns in species composition and diversity. Here, we present a simple, analytically…
Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime…
We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed, or equivalently the valid equilibria of multispecies Lotka-Volterra equations with self-regulation in the special…
We analyse the equilibrium behaviour and non-equilibrium dynamics of sparse Boolean networks with self-interactions that evolve according to synchronous Glauber dynamics. Equilibrium analysis is achieved via a novel application of the…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…