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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…

Cooperation and competition between pathogens can alter the amount of individuals affected by a co-infection. Nonetheless, the evolution of the pathogens' behavior has been overlooked. Here, we consider a co-evolutionary model where the…

Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and…

In tropical regions, fires propagate readily in grasslands but typically consume only edges of forest patches. Thus forest patches grow due to tree propagation and shrink by fires in surrounding grasslands. The interplay between these…

Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the…

This chapter aims to inform a practitioner about current methods for predicting potential distributions of invasive species. It mostly addresses single species models, covering the conceptual bases, touching on mechanistic models, and then…

Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of…

Locust infestation of some regions in the world, including Africa, Asia and Middle East has become a concerning issue that can affect the health and the lives of millions of people. In this respect, there have been attempts to resolve or…

Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…

We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…

The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…

Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits…

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…

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…

Concerns about biodiversity and the long-term stability of forest ecosystems have lead to changing attitudes with respect to plantations. These artificial communities are ubiquitous, yet provide reduced habitat value in comparison to their…

The dynamics of infection spread in populations has received popular attention since the outbreak of Covid-19 and many statistical models have been developed. One of the interesting areas of research is short-time dynamics in confined,…

When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic…

To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect…

Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…