Related papers: Persistence versus extinction under a climate chan…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…
We study the change in the speed of pushed and bistable fronts of the reaction diffusion equation in the presence of a small cut-off. We give explicit formulas for the shift in the speed for arbitrary reaction terms f(u). The dependence of…
We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The…
In this paper we consider a free boundary problem which models the spreading of an invasive species whose spreading is enhanced by the changing climate. We assume that the climate is shifting with speed c and obtain a complete…
Recent studies of biological, chemical, and physical pattern-forming systems have started to go beyond the classic `near onset' and `far from equilibrium' theories for homogeneous systems to include the effects of spatial heterogeneities.…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
The magnitude and variability of Earth's biodiversity have puzzled scientists ever since paleontologic fossil databases became available. We identify and study a model of interdependent species where both endogenous and exogenous impacts…
We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
In this paper we consider the diffusive competition model consisting of an invasive species with density $u$ and a native species with density $v$, in a radially symmetric setting with free boundary. We assume that $v$ undergoes diffusion…
This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
We investigate the phenomenology emerging from a 2-species dynamics under the scenario of a quasi-neutral competition within a metapopulation framework. We employ stochastic and deterministic approaches, namely spatially-constrained…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
The temperature in the transient climate response is lower than the equilibrium temperature for the same amount of forcing. The degree of disequilibrium is not constant in time and depends on various climate parameters. We derive intuition…