Related papers: Bifurcations and multistability in empirical mutua…

What determines biodiversity in nature is a prominent issue in ecology, especially in biotic resource systems that are typically devoid of cross-feeding. Here, we show that by incorporating pairwise encounters among consumer individuals…

Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…

Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any…

Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and…

Microbial communities routinely have several alternative stable states observed for the same environmental parameters. Sudden and irreversible transitions between these states make external manipulation of these systems more complicated. To…

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…

Understanding the influence of structure of dispersal network on the species persistence and modeling a much realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the…

This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here we consider species assembly models where the population dynamics is kept far from fixed points through the…

Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…

Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability thus shapes…

Mutualistic networks have been shown to involve complex patterns of interactions among animal and plant species. The architecture of these webs seems to pervade some of their robust and fragile behaviour. Recent work indicates that there is…

We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the…

Mutualistic interactions, where individuals from different species can benefit from each other, are widespread across ecosystems. This study develops a general deterministic model of mutualism involving two populations, assuming that…

Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…

For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…

Current theories about mechanisms promoting species co-existence in diverse communities assume that species only interact ecologically. Species are treated as discrete evolutionary entities, even though abundant empirical evidence indicates…

We consider the local bifurcation and global dynamics of a predator-prey model with cooperative hunting and Allee effect. For the model with weak cooperation, we prove the existence of limit cycle, heteroclinic cycle at a threshold of…

This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…

Microorganisms live in environments that inevitably fluctuate between mild and harsh conditions. As harsh conditions may cause extinctions, the rate at which fluctuations occur can shape microbial communities and their diversity, but we…

This paper studies a two microbial species model in competition for a single resource in the chemostat including general interspecific density-dependent growth rates with distinct removal rates for each species. We give the necessary and…