Stochastic three species systems

Sridhara, Rajeshwari; Watson, Ray

doi:10.1007/bf00164165

Cited by 5 publications

(2 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alternative approaches to coexistence that make allowance for the risk of extinction close to the boundary would obviously be desirable, but unfortunately those currently available, such as the region of ultimate confinement (Goh 1980:85 ff. ) and stochastic models (e.g., Hitchcock 1986, Sridhara andWatson 1990), are not tractable for large ecological communities.…”

Section: Jansen's Condition For Permanence: Interpretation and Limitamentioning

confidence: 99%

Self‐Assembling Food Webs: A Global Viewpoint of Coexistence of Species in Lotka‐Volterra Communities

Law¹,

Blackford²

1992

Ecology

View full text Add to dashboard Cite

It has been suggested that the structure of ecological communities is constrained by dynamical instability of certain configurations of interacting species. Analysis of this has most often been based on asymptotic (local) stability analysis of equilibria at which all species are present, on the grounds that a configuration with an unstable equilibrium is less likely to occur in the real world than one with an asymptotically stable equilibrium. Since species may also coexist on limit cycles or chaotic orbits, we argue that a global condition that species should increase when rare could be more appropriate. Conditions for such "permanence" exist and their use makes it possible to focus on fundamental qualitative questions of coexistence of species, even though the quantitative properties of their dynamics may be very complex. We describe a straightforward and general method for distinguishing between permanent and nonpermanent Lotka—Volterra food webs; this method is due to Jansen (1987). A numerical analysis of four—species food webs with different degrees of omnivory shows that many that would be rejected as unstable in a local analysis are at the same time permanent in the global analysis. Using permanence methods, food webs of high connectance are shown to rebuild themselves more readily than those of low connectance, and therefore to recover more readily from disturbance than those of low connectance. The significance of this result for the relationship between complexity and stability of communities is discussed, together with the merits and drawbacks of permanence for studying the coexistence of species in communities.

show abstract

Section: Jansen's Condition For Permanence: Interpretation and Limitamentioning

confidence: 99%

Self‐Assembling Food Webs: A Global Viewpoint of Coexistence of Species in Lotka‐Volterra Communities

Law¹,

Blackford²

1992

Ecology

View full text Add to dashboard Cite

show abstract

“…Thus assuming the process to be in quasi-equilibrium, the means (Nf~), variances and covariances (Nho) of X can be obtained approximately, in terms of the system parameters 0 = (e~, fit, 20, #0) by setting the left hand side of (2) equal to zero (see Sridhara and Watson 1990). If the process ~ is observable, then the means, variances and covariances can be estimated by observing the population sizes at a number of separate time points.…”

Section: Introductionmentioning

confidence: 99%

Inference on system parameters in a model for interacting species

Sridhara

1990

J. Math. Biol.

View full text Add to dashboard Cite

show abstract

Analysis of a stochastic tri-trophic food-chain model with harvesting

2016

View full text Add to dashboard Cite

We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic levels; however, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for existence of optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model.

show abstract

Stochastic three species systems

Cited by 5 publications

References 37 publications

Self‐Assembling Food Webs: A Global Viewpoint of Coexistence of Species in Lotka‐Volterra Communities

Self‐Assembling Food Webs: A Global Viewpoint of Coexistence of Species in Lotka‐Volterra Communities

Inference on system parameters in a model for interacting species

Analysis of a stochastic tri-trophic food-chain model with harvesting

Contact Info

Product

Resources

About