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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]

As a generalization of stage-based matrix models, integral projection models (IPMs) have been used to describe the size-based dynamics of wildlife and fisheries populations. Although some matrix models have explicitly included species interactions, few IPMs have expanded beyond single species, which limits their ability to describe the competitive dynamics of co-occuring taxa. We present a coupled system of IPMs where intra- and inter-specific competition may reciprocally affect the life-histories of two species. We investigated the potential role that competition has on two over- lapping fish species in the upper Mississippi River system: the native gizzard shad (Dorosoma cepedianum) and the invasive silver carp (Hypophthalmichthys molitrix). Numerical simulations of this system indicated that the coupled IPMs could exhibit asymptotic behaviors similar to traditional, non-linear competition models. Specifically, by altering the competition coefficients, we demonstrate this model's ability to detect competitive exclusion, species coexistence, and dual extinction outcomes. [ABSTRACT FROM AUTHOR]

A general notion of the Allee effect for higher dimensional triangular maps is proposed. A global dynamics theory is established. The theory is applied to multi-species hierarchical models. Then we provide a detailed study of the global dynamics of three-species Ricker competition models with the Allee effect. Regions of extinction, exclusion and coexistence are identified. [ABSTRACT FROM AUTHOR]

In this paper, we explore the structure of pre-images of invariant sets of a discrete-time two-species competition model with singularity at the origin. We first show that this competition model is persistent with respect to the total population of two species, i.e. all initial conditions in are attracted to a compact set which is bounded away from the origin. Then we study the properties of pre-images of this system and give the explicit structure of all pre-images of invariant sets for this system under certain parameter range. These results are analogous to the one-dimensional discrete system. Our study is the first step to explore the structure of the basins of attractions of interior attractors of a general discrete-time two-species model (e.g. the locally asymptotically stable interior period-2 orbit). Finally, we discuss how our results give useful insights on the future study for coexistence of the species and list some open problems related to our system. [ABSTRACT FROM PUBLISHER]