Towards a reaction-diffusion framework for population spread in dendritic habitats
Daniel Bearup (University of Leicester)
Thursday 29th January 14:00-15:00
Maths 311B
Abstract
The reaction-diffusion framework is often used to describe the spread of a reproducing species within a space; for example, a population of animals within a landscape. The use of this framework assumes that the underlying space is fundamentally isotropic, i.e.
- any variation in the space that influences the species is random;
- it is possible to move between two points via any other point.
Dendritic (or tree-like) spaces, such as river networks, do not have these characteristics. Instead growth rate and maximum population size depend on location within the space, due to systematic variation in habitat availability. Furthermore, movement paths between similar locations can vary substantially depending on where they fall in the overall structure.
In this talk, I will outline a modelling framework for the dynamics of populations in a landscape with regular dendritic structure. I will describe how population spread differs from that seen within a typical isotropic landscape. Finally, I will discuss how a generalised reaction-diffusion framework could be developed to describe population dynamics in habitats with these features.
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