Related papers: Deterministic extinction by mixing in cyclically c…
In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this…
A number of authors have in recent years proposed that the processes of macroevolution may give rise to self-organized critical phenomena which could have a significant effect on the dynamics of ecosystems. In particular it has been…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
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. This turns out to be closely related to the ratio…
The relationship between the M-species stochastic Lotka-Volterra competition (SLVC) model and the M-allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the…
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
A binary mixture of two-different-sizes proliferating motile disks is studied. As growth is space-limited, we focus on the conditions such that there is coexistence of both large and small disks, or dominance of the larger disks. The study…
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…
We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
The causes of major and rapid transitions observed in biological macroevolution as well as in the evolution of social systems are a subject of much debate. Here we identify the proximate causes of crashes and recoveries that arise…
In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means…
A fundamental problem in evolutionary ecology research is to explain how different species coexist in natural ecosystems. This question is directly related with species trophic competition. However, competition theory, based on the…
Explaining biodiversity in nature is a fundamental problem in ecology. An outstanding challenge is embodied in the so-called Competitive Exclusion Principle: two species competing for one limiting resource cannot coexist at constant…
A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations…
The study of interactions between multiple species in an ecosystem is an active and impactful direction of inquiry. This is true in particular for fragile systems in which even small perturbations of their functional parameters can produce…
We study the extinction of epidemics in a generalized susceptible-infected-susceptible model, where a susceptible individual becomes infected with the rate $\lambda$ when contacting $m$ infective individual(s) simultaneously, and an…
A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We…