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This paper is concerned with the propagation phenomena for a nonlocal dispersal Lotka–Volterra competition model with shifting habitats. It is assumed that the growth rate of each species is nondecreasing along the x-axis, positive near ∞ and nonpositive near - ∞ , and shifting rightward with a speed c > 0 . In the case where both species coexist near ∞ , we established three types of forced waves connecting the origin, respectively to the coexistence state with any forced speed c; to itself with forced speed c > c ∗ (∞) ; and to a semi-trivial steady state with forced speed c > c ¯ (∞) , where c ∗ (∞) and c ¯ (∞) are two positive numbers. In the case where one species is competitively stronger near ∞ , we also obtain the existence and nonexistence of forced waves connecting the origin to the semi-trivial steady state. Our results show the existence of multiple types of forced waves with the same forced speed. The mathematical proofs involve integral equations and Schauder's fixed point theorem, and heavily rely on the construction of various upper-lower solutions, which adds new techniques to deal with the "shifting environments" problem. [ABSTRACT FROM AUTHOR]

We establish conditions to ensure global stability of a competitive periodic system from hypotheses on individual maps. We study planar competitive maps of Kolgomorov type. We show how conditions for global stability for individual maps will remain invariant under composition and hence establish a globally stable cycle. Our main theoretical contribution is to show that stability for monotone non-autonomous periodic maps can be reduced to a problem of global injectivity. We provide analytic conditions that can be checked and illustrate our results with important competition models such as the planar Leslie-Gower and Ricker maps. [ABSTRACT FROM AUTHOR]

We develop a staged-structured population model that describes the competitive dynamics of two functionally similar, congeneric invasive species: zebra mussels and quagga mussels. The model assumes that the population survival rates are functions of temperature and turbidity, and that the two species compete for food. The stability analysis of the model yields conditions on net reproductive rates and intrinsic growth rates that lead to competitive exclusion. The model predicts quagga mussel dominance leading to potential exclusion of zebra mussels at mean water temperatures below $$20\,^\circ \hbox {C}$$ and over a broad range of turbidities, and a much narrower set of conditions that favor zebra mussel dominance and potential exclusion of quagga mussels at temperatures above $$20\,^\circ \hbox {C}$$ and turbidities below 35 NTU. We then construct a two-patch dispersal model to examine how the dispersal rates and the environmental factors affect competitive exclusion and coexistence. [ABSTRACT FROM AUTHOR]

Based on the concept of competition for resources, the distribution of trees upon reforestation in windfall areas is studied. As a theoretical model for competition, a Zipf-Pareto model of ranking the distribution of resources is used. Analysis shows that the processes resulting from competitive interactions between the trees of different species proceed slowly in a windfall area where coniferous species get replaced by deciduous ones. In the territory where deciduous species initially dominated, competitive interactions between trees of different species turn out to be formed almost immediately upon natural reforestation after the windfall. By the time the ratio of species stabilizes and becomes a steady state, the ranks of individual species also stabilize. This result is obtained on the basis of a quantitative assessment of the change in leadership between competing species in time using Spearman's rank correlation coefficient. [ABSTRACT FROM AUTHOR]