Coexistence and extinction for stochastic Kolmogorov systems

@article{Hening2018CoexistenceAE,
  title={Coexistence and extinction for stochastic Kolmogorov systems},
  author={Alexandru Hening and Dang Hai Nguyen},
  journal={The Annals of Applied Probability},
  year={2018}
}
In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and empirical studies have shown that coexistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of $n$ populations that live in a stochastic environment and which can interact nonlinearly (through… Expand
Persistence and extinction for stochastic ecological difference equations with feedbacks
TLDR
This work uses the stochastic analog of average Lyapunov functions to develop sufficient and necessary conditions for all population densities spending little time at low densities and provides quantitative estimates on the fraction of time that the system is near the extinction set, and the probability of asymptotic extinction as a function of the initial state of the system. Expand
Stationary distributions of persistent ecological systems
TLDR
A powerful method for numerically approximating invariant probability measures is developed, which allows us to shed light upon how the various parameters of the ecosystem impact the stationary distribution. Expand
Stochastic functional Kolmogorov equations II: Extinction
Abstract This work, Part II, together with its companion-Part I develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equationsExpand
The competitive exclusion principle in stochastic environments
TLDR
In various settings, in various settings how a variable (stochastic) environment enables a set of competing species limited by a smaller number of resources or other density dependent factors to coexist is shown. Expand
A general theory of coexistence and extinction for stochastic ecological communities.
TLDR
A general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations is analyzed, able to significantly generalize the recent discrete time results to non-compact state spaces, and provide stronger persistence and extinction results. Expand
Persistence and extinction for stochastic ecological models with internal and external variables
TLDR
Stochastic models of evolutionary games, Lotka–Volterra dynamics, trait evolution, and spatially structured disease dynamics are analyzed, demonstrating environmental stochasticity facilitates coexistence of strategies in the hawk–dove game, but inhibits coexistence in the rock–paper–scissors game and a Lotka-volterra predator–prey model. Expand
Analysis of an epidemiological model driven by multiple noises: Ergodicity and convergence rate
TLDR
A mathematical system to investigate the impact of environmental noise on disease transmission dynamics is presented, which incorporates Brownian noise, Markovian switching noise and nonlinear incidence and shows that the long-term dynamics of the stochastic system is determined by a threshold parameter which is closely related to the Stochastic noise. Expand
Coexistence, dispersal and spatial structure in metacommunities: a stochastic model approach
We propose a stochastic model for interacting species in a metacommunity in order to study the factors affecting the intensity of the competition/colonization trade-off as a coexistence mechanism inExpand
A classification of the dynamics of three-dimensional stochastic ecological systems.
TLDR
For a large class of three-species, stochastic differential equation models, this paper proves a variant of Palis' conjecture: the long-term statistical behavior is determined by a finite number of stationary distributions and it is proved that the classification reduces to computing Lyapunov exponents that correspond to the average per-capita growth rate of species when rare. Expand
Stochastic functional Kolmogorov equations, I: Persistence
This work (Part (I)) together with its companion (Part (II) [45]) develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equationsExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 54 REFERENCES
Persistence in fluctuating environments
TLDR
A mathematical theory extending the nonlinear theory of permanence for deterministic systems to stochastic difference and differential equations is developed and it is illustrated that environmental noise enhances or inhibits coexistence in communities with rock-paper-scissor dynamics depending on correlations between interspecific demographic rates. Expand
Stochastic population growth in spatially heterogeneous environments: the density-dependent case
TLDR
It is proved that persistence is robust to small, possibly density dependent, perturbations of the growth rates, dispersal matrix and covariance matrix of the environmental noise and the stochastic growth rate depends continuously on the coefficients. Expand
Persistence of structured populations in random environments.
TLDR
This work provides a general theory for persistence for density-dependent matrix models in random environments and shows that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space. Expand
Competitive or weak cooperative stochastic Lotka–Volterra systems conditioned on non-extinction
TLDR
This work studies the existence and uniqueness of a quasi-stationary distribution, that is convergence to equilibrium conditioned on non-extinction, and generalizes in two-dimensions spectral tools developed for one-dimensional generalized Feller diffusion processes. Expand
Coexistence in locally regulated competing populations and survival of branching annihilating random walk
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analyticExpand
Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments
TLDR
It is shown that adding environmental stochasticity results in an ESS that, when compared to the ESS for the corresponding model without stochasticsity, spends less time in patches with larger carrying capacities and possibly makes use of sink patches, thereby practicing a spatial form of bet hedging. Expand
Quasi-stationary distributions and diffusion models in population dynamics
In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have anExpand
Persistence in Stochastic Lotka–Volterra Food Chains with Intraspecific Competition
TLDR
It is shown that one can classify, based on the invasion rates of the predators, which species go extinct and which converge to their unique invariant probability measure, and provides persistence/extinction criteria for food chains of length 4. Expand
Variable effort harvesting models in random environments: generalization to density-dependent noise intensities.
  • C. Braumann
  • Mathematics, Medicine
  • Mathematical biosciences
  • 2002
TLDR
This paper generalizes the previous results to density-dependent positive noise intensities of very general form so that they also become independent from the way environmental fluctuations affect population growth rates. Expand
Invasibility and stochastic boundedness in monotonic competition models
We give necessary and sufficient conditions for stochastically bounded coexistence in a class of models for two species competing in a randomly varying environment. Coexistence is implied by mutualExpand
...
1
2
3
4
5
...