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Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
We propose a model for the dynamics of frequencies of a costly defense trait. More precisely, we consider Lotka-Volterra-type models involving a prey (or host) population consisting of two types and a predator (or parasite) population,…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
This paper is concerned with a nonlocal diffusion Lotka-Volterra type competition model that consisting of a native species and an invasive species in a one-dimensional habitat with free boundaries. We prove the well-posedness of the system…
We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…
In this study, we investigate the dynamics of a spatial and non spatial prey-predator interaction model that includes the following: (i) fear effect incorporated in prey birth rate; (ii) group defence of prey against predators; and (iii)…
Coexistence of competing species is, due to unavoidable fluctuations, always transient. In this Letter, we investigate the ultimate survival probabilities characterizing different species in cyclic competition. We show that they often obey…
The transition between strong and weak Allee effects in prey provides a simple regime shift in ecology. A deteriorating environment changes weak Allee effects into strong ones. In this paper, we study the interplay between the functional…
We study the influence of spatially varying reaction rates on a spatial stochastic two-species Lotka-Volterra lattice model for predator-prey interactions using two-dimensional Monte Carlo simulations. The effects of this quenched…
We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but…
Recurrence plots and their associated quantifiers provide a robust framework for detecting and characterising complex patterns in non-linear time-series. In this paper, we employ recurrence quantification analysis to investigate the…
We investigate cyclic dominance models and their extensions to both network systems and reaction-diffusion frameworks. Using linear stability analysis, we establish the relationship between the stability of synchronized states in network…
This work deals with the influence of the neighborhood in simple rock-paper-scissors models of biodiversity. We consider the case of three distinct species which evolve under the standard rules of mobility, reproduction and competition. 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…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…
A central goal in ecology is to understand how biodiversity is maintained. Previous theoretical works have employed the rock-paper-scissors (RPS) game as a toy model, demonstrating that population mobility is crucial in determining the…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of…
We develop a theory of generalist predation showing how alternative prey species are affected by changes in both mean abundance and variability (coefficient of variation) of their predator's primary prey. The theory is motivated by the…