Related papers: The multi-patch logistic equation with asymmetric …
We consider population dynamics on a network of patches, each of which has a the same local dynamics, with different population scales (carrying capacities). It is reasonable to assume that if the patches are coupled by very fast migration…
In a recent paper published in Ecosphere, their authors suggest that extending the logistic growth model in its usual r - K parametrization to a multi-patch environment results in undesirable properties, that were referred to as the…
In this paper we consider a simple two-patch model in which a population affected by a disease can freely move. We assume that the capacity of the interconnected paths is limited, and thereby influencing the migration rates. Possible…
The possible dynamics of an ecosystem with three interconnected patches among which one population can migrate are investigated, paying attention to the consequences that possible disruption in the communicating paths can cause.
Many populations in nature are fragmented: they consist of local populations occupying separate patches. A local population is prone to extinction due to the shot noise of birth and death processes. A migrating population from another patch…
We introduce a meta-population version of models of asymmetric exclusion models, consisting of a spatial arrangement of patches. Patches are of a specific size, indicating the maximal number of particles they can hold. We use an expansion…
This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic solutions are obtained. In particular,…
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage, and are interested in the regime in which the…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying…
Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
Species growing in environments that change in time and space will vary in their abundance across locations, even in the absence of persistent location preferences. Here we quantify this non-equilibrium effect by studying a minimal model of…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics include the Allee effect. We show that mixing between patches dramatically influences the…
In the problem of online load balancing on uniformly related machines with bounded migration, jobs arrive online one after another and have to be immediately placed on one of a given set of machines without knowledge about jobs that may…
While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…
We propose a method for obtaining joint probabilistic projections of migration rates for all countries, broken down by age and sex. Joint trajectories for all countries are constrained to satisfy the requirement of zero global net…
Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to…
In this paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the…