Permanence of delay competitive systems with weak Allee effects

Egami, Chikahiro

doi:10.1016/j.nonrwa.2010.03.001

Cited by 5 publications

(2 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…y t+1 = y t e r(1−yt)−axt by t 1 + by t (21) where r represent the intrinsic growth rates as well as intra-specific competition coefficient; b represent the product of an individual's searching efficiency and the carrying capacities and a represents the inter-specific competition coefficient. If…”

Section: Two Dimensional Strong Allee Effects Of Symmetric Competitio...mentioning

confidence: 99%

Dynamics of a generalized Ricker–Beverton–Holt competition model subject to Allee effects

Kang

2016

Journal of Difference Equations and Applications

View full text Add to dashboard Cite

In this article, we propose and study a generalized Beverton-Holt competition model subject to Allee effects to obtain insights on how the interplay of Allee effects and contest competition affects the persistence and the extinction of two competing species. By using the theory of monotone dynamics and the properties of critical curves for non-invertible maps, our analysis shows that our model has relatively simple dynamics, i.e., almost every trajectory converges to a locally asymptotically stable equilibrium if the intensity of intra-specific competition intensity exceeds that of inter-specific competition. This equilibrium dynamics is also possible when the intensity of intra-specific competition intensity is less than that of inter-specific competition but under conditions that the maximum intrinsic growth rate of one species is not too large. The coexistence of two competing species occurs only if the system has four interior equilibria. We provide an approximation to the basins of the boundary attractors (i.e., the extinction of one or both species) where our results suggests that contest species are more prone to extinction than scramble ones are at low densities. In addition, in comparison to the dynamics of two species scramble competition models subject to Allee effects, our study suggests that (i) Both contest and scramble competition models can have only three boundary attractors without the coexistence equilibria, or four attractors among which only one is the persistent attractor, whereas scramble competition models may have the extinction of both species as its only attractor under certain conditions, i.e., the essential extinction of two species due to strong Allee effects; (ii) Scramble competition models like Ricker type models can have much more complicated dynamical structure of interior attractors than contest ones like Beverton-Holt type models have; and (iii) Scramble competition models like Ricker type competition models may be more likely to promote the coexistence of two species at low and high densities under certain conditions: At low densities, weak Allee effects decrease the fitness of resident species so that the other species is able to invade at its low densities; While at high densities, scramble competition can bring the current high population density to a lower population density but is above the Allee threshold in the next season, which may rescue a species that has essential extinction caused by strong Allee effects. Our results may have potential to be useful for conservation biology: For example, if one endangered species is facing essential extinction due to strong Allee effects, then we may rescue this species by bringing another competing species subject to scramble competition and Allee effects under certain conditions.

show abstract

Section: Two Dimensional Strong Allee Effects Of Symmetric Competitio...mentioning

confidence: 99%

Dynamics of a generalized Ricker–Beverton–Holt competition model subject to Allee effects

Kang

2016

Journal of Difference Equations and Applications

View full text Add to dashboard Cite

show abstract

“…Weak Allee effects are the cases when there is no such critical threshold but still there is a positive correlation between the per capita growth and population density or size at low population densities/sizes. Excellent reviews on Allee effects and their ecological implications can be found in [7] and some related recent work can be found in [1,3,14,15,25,29,34,35,41,45,50].…”

Section: Introductionmentioning

confidence: 99%

A host–parasitoid system with predation-driven component Allee effects in host population

Kang

Sasmal

Bhowmick

et al. 2014

Journal of Biological Dynamics

View full text Add to dashboard Cite

Allee effects and parasitism are common biological phenomena observed in nature, which are believed to have significant impacts in ecological conservation programmes. In this article, we investigate population dynamics of a discrete-time host-parasitoid system with component Allee effects induced by predation satiation in host to study the synergy effects of Allee effects and parasitism. Our model assumes that parasitism attacks the host after the density dependence of the host. The interactions of component Allee effects and parasitism can lead to extremely rich dynamics that include but are not limited to extinction of both species due to Allee effects at their low population density, multiple attractors, strange interior attractors and even crisis of strange attractor due to high parasitism. We perform local and global analysis to study the number of equilibria and their stability; and study the extinction and permanence of our hostparasitoid system. One of the most interesting results shows that the combination of strong Allee effects and parasitism may promote the coexistence of both host and parasite at their high population density. In addition, component Allee effects may destroy interior equilibrium under different values of parameters' ranges.

show abstract

Scramble competitions can rescue endangered species subject to strong Allee effects

Kang

2013

Mathematical Biosciences

View full text Add to dashboard Cite

Permanence of delay competitive systems with weak Allee effects

Cited by 5 publications

References 18 publications

Dynamics of a generalized Ricker–Beverton–Holt competition model subject to Allee effects

Dynamics of a generalized Ricker–Beverton–Holt competition model subject to Allee effects

A host–parasitoid system with predation-driven component Allee effects in host population

Scramble competitions can rescue endangered species subject to strong Allee effects

Contact Info

Product

Resources

About