Related papers: Stability of difference equations with interspecif…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…
Understanding the stability of complex communities is a central focus in ecology, many important theoretical advancements have been made to identify drivers of ecological stability. However, previous results often rely on the…
Microbial communities routinely have several possible species compositions or community states observed for the same environmental parameters. Changes in these parameters can trigger abrupt and persistent transitions (regime shifts) between…
In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many…
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…
The dynamics of a two-species community of $N$ competing individuals is considered, with an emphasis on the role of environmental variations that affect coherently the fitness of entire populations. The chance of fixation of a mutant…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a…
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…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, and others). The formulation…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
For a large family of nonautonomous scalar-delayed differential equations used in population dynamics, some criteria for permanence are given, as well as explicit upper and lower bounds for the asymptotic behavior of solutions. The method…
The Lotka-Volterra system is a set of ordinary differential equations describing growth of interacting ecological species. This model has gained renewed interest in the context of random interaction networks. One of the debated questions is…
The current paper is concerned with the asymptotic dynamics of two species competition systems with/without chemotaxis in heterogeneous media. In the previous work \cite{ITBWS17a}, we find conditions on the parameters in such systems for…
We present properties of Lotka-Volterra equations describing ecological competition among a large number of competing species. First we extend to the case of a non-homogeneous niche space stability conditions for solutions representing…