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In this paper, we study bistable pulsating waves for a population model in discrete periodic habitat. After obtaining the existence, uniqueness and global exponential stability of the waves, we give a characterization on the sign of the wave speed; in particular, we find parameter regions for propagation failure and success, respectively. [ABSTRACT FROM AUTHOR]

A non-monotone time-delayed lattice equation in discrete periodic habitat is concerned. As a fundamental step, a principle eigenvalue problem is introduced, which viewed as a function on a parameter is proved to be strictly convex, piecewise monotone and positive. With the help of such properties, the existence of pulsating waves is obtained by first constructing super and sub solutions, then using Schauder's fixed-point theorem and finally appealing limiting arguments. The spreading speed and its variational characterization by principle eigenvalue is established by comparison argument. It turns out that the minimal wave speed of pulsating waves coincides with the spreading speed. [ABSTRACT FROM AUTHOR]

Spreading speed of spatio-temporal nonlinear dynamical system can sometimes be determined either by its corresponding linear system with an explicit speed formula, or by the complicated nonlinear system itself with the existence of a pushed wavefront. In this paper, the spreading speed (the minimal speed of wavefronts) for a Lotka-Volterra competition model in spatially periodic habitats is investigated. We establish new results on the linear and nonlinear selections in terms of the spatio-periodic coefficient functions. In the case of nonlinear selection, lower and upper bound estimates of the minimal speed are provided. [ABSTRACT FROM AUTHOR]

Starting from an age-structured diffusive population growth law for single species in a discrete and periodic habitat, we formulate a stage structured population model with spatially periodic dispersal, mortality and recruitment. With a KPP type setting, after establishing the fundamental solution of a discretized heat equation with spatially periodic dispersal, we apply some recently developed dynamical system theories to obtain the existence of the spreading speed and its coincidence with the minimal speed of pulsating waves, as well as the variational characterization of the speed, by which we further analyze how the habitat periodicity influences the speed. In particular, there is a unique optimal dispersal strategy to maximize the speed. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to the study of pulsating fronts and pulsating front-like entire solutions for a reaction–advection–diffusion model of two competing species in a periodic habitat. Under certain assumptions, the competition system admits a leftward and a rightward pulsating fronts in the bistable case. In this work we construct some other types of entire solutions by interacting the leftward and rightward pulsating fronts. Some of these entire solutions behave as the two pulsating fronts approaching each other from both sides of the x -axis, which turn out to be unique and Liapunov stable 2-dimensional manifolds of solutions, furthermore, the leftward and rightward pulsating fronts are on the boundary of these 2-dimensional manifolds. The others behave as the two pulsating fronts propagating from one side of the x -axis, the faster one then invades the slower one as t → + ∞. These kinds of pulsating front-like entire solutions then provide some new spreading ways other than pulsating fronts for two strongly competing species interacting in a heterogeneous habitat. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global dynamics and spreading speeds of a partially degenerate non-local dispersal system with monostable nonlinearity in periodic habitats. We first obtain the existence of the principal eigenvalue for a periodic eigenvalue problem with partially degenerate non-local dispersal. Then we study the coexistence and extinction dynamics. Finally, the existence and characterization of spreading speeds are considered. In particular, we show that the spreading speed is linearly determinate. Overall, we extend the existing results on global dynamics and spreading speeds for the degenerate reaction–diffusion system to the degenerate non-local dispersal case. The extension is non-trivial and meaningful. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trivial steady state for the periodic initial value problem. Then we establish the existence of the rightward spreading speed and its coincidence with the minimal wave speed for spatially periodic rightward traveling waves. We also obtain a set of sufficient conditions for the rightward spreading speed to be linearly determinate. Finally, we apply the obtained results to a prototypical reaction-diffusion model. [ABSTRACT FROM AUTHOR]

We investigate a partially degenerate reaction–diffusion system in a periodic habitat and prove the existence and stability of pulsating waves. More specifically, we show that if the wave speed is greater than the spreading speed, then there exists a pulsating wave connecting the stable positive periodic steady state to the unstable trivial one. Further, this pulsating wave attracts exponentially in time all solutions with initial functions in its bounded neighborhood with respect to a weighted maximum norm. [ABSTRACT FROM AUTHOR]

The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a system is first introduced via the natural features of spreading speeds. The existence and lower bounds of spreading speed intervals are then established. When the periodic dependence of the habitat is only on the time variable, the existence of a single spreading speed is proved. It also shows that, under certain conditions, the spreading speed interval in any direction is a singleton, and, moreover, the linear determinacy holds. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. In an abstract setting, we establish the existence of traveling waves for discrete time and continuous-time monotone semiflows in homogeneous and periodic habitats. The results are then extended to monotone semiflows with weak compactness. We also apply the theory to four classes of evolution systems. [ABSTRACT FROM AUTHOR]

In ephemeral habitats, the same genotypes cope with unpredictable environmental conditions, favouring the evolution of developmental plasticity and alternative life-history strategies ( ALHS). We tested the existence of intrapopulation ALHS in an annual killifish, Nothobranchius furzeri, inhabiting temporary pools. The pools are either primary (persisting throughout the whole rainy season) or secondary (refilled after desiccation of the initial pool), representing alternative niches. The unpredictable conditions led to the evolution of reproductive bet-hedging with asynchronous embryonic development. We used a common garden experiment to test whether the duration of embryonic period is associated with post-embryonic life-history traits. Fish with rapid embryonic development (secondary pool strategy, high risk of desiccation) produced phenotypes with more rapid life-history traits than fish with slow embryonic development (primary pool strategy). The fast fish were smaller at hatching but had larger yolk sac reserves. Their post-hatching growth was more rapid, and they matured earlier. Further, fast fish grew to a smaller body size and died earlier than slow fish. No differences in fecundity, propensity to mate or physiological ageing were found, demonstrating a combination of plastic responses and constraints. Such developmentally related within-population plasticity in life history is exceptional among vertebrates. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to the study of the spreading speeds of a partially degenerate reaction–diffusion system with monostable nonlinearity in a periodic habitat. We first obtain sufficient conditions for the existence of principal eigenvalues in the case where solution maps of the associated linear systems lack compactness, and prove a threshold type result on the global dynamics for the periodic initial value problem. Then we establish the existence and computational formulae of spreading speeds for the general initial value problem. It turns out that the spreading speed is linearly determinate. [Copyright &y& Elsevier]

Abstract: The current paper is devoted to the study of spatial spreading dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In particular, the existence and characterization of spreading speeds is considered. First, a principal eigenvalue theory for nonlocal dispersal operators with space periodic dependence is developed, which plays an important role in the study of spreading speeds of nonlocal periodic monostable equations and is also of independent interest. In terms of the principal eigenvalue theory it is then shown that the monostable equation with nonlocal dispersal has a spreading speed in every direction in the following cases: the nonlocal dispersal is nearly local; the periodic habitat is nearly globally homogeneous or it is nearly homogeneous in a region where it is most conducive to population growth in the zero-limit population. Moreover, a variational principle for the spreading speeds is established. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the development of the theory of spreading speeds and traveling waves for abstract monostable evolution systems with spatial structure. Under appropriate assumptions, we show that the spreading speeds coincide with the minimal wave speeds for monotone traveling waves in the positive and negative directions. Then we use this theory to study the spatial dynamics of a parabolic equation in a periodic cylinder with the Dirichlet boundary condition, a reaction–diffusion model with a quiescent stage, a porous medium equation in a tube, and a lattice system in a periodic habitat. [Copyright &y& Elsevier]