Related papers: Dispersal-enhanced resilience in two-patch metapop…
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though…
In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…
Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables…
The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half, or none of the offspring disperse. The spatial scale (number of patches)…
Dispersal networks critically shape the fate of ecological communities, yet the mechanisms linking connectivity and persistence remain poorly understood. We show that an interplay between asymmetric dispersal and asynchronous dynamics…
The metapopulation theory explores the population persistence in fragmented habitats by considering a balance between the extinction of local populations and recolonization of empty sites. In general, the extinction and colonization rates…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
A population balance model coupled with large eddy simulations (LES) is adapted and applied to study the evolution of oil droplets in a turbulent jet including the effects of droplet breakup. A key unknown in simulating secondary breakup in…
We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end…
We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…
Synchronous oscillations of spatially disjunct populations are widely observed in ecology. Even in the absence of spatially synchronized exogenous forces, metapopulations may synchronize via dispersal. For many species, most dispersal is…
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
Population survival depends on a large set of factors that includes environment structure. Due to landscape heterogeneity, species can occupy particular regions that provide the ideal scenario for development, working as a refuge from…
Models of ordering dynamics allow to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to…
We consider individuals of two species distributed over m patches, each with a hosting capacity $d_i N$ , where $d_i \in (0, 1]$. We assume that all the patches are linked by the dispersal of individuals. This work examines how the…
The persistence of populations depends on the minimum habitat area required for survival, known as the critical patch size. While most studies assume purely diffusive movement, additional movement components can significantly alter habitat…