Mathematical modelling of invasive spread in the heterogeneous landscape

Deeley, Bradly Frederick (2024). Mathematical modelling of invasive spread in the heterogeneous landscape. University of Birmingham. Ph.D.

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Abstract

Invasive plant species pose a significant threat to biodiversity and the economy, and their management is often resource-intensive and expensive. Evidence suggests that roads can have an important effect on the spread of invasive plant species, although little is known about the underlying mechanisms at play. Further research and the application of mathematical models is required to make control measures more efficient.

In this thesis, we develop a novel mathematical model to analyse the impact of roads on the propagation of invasive plants in both the one-dimensional and two-dimensional spatial domains. An integro-difference equation model is formulated for stage-structured population and incorporates a road sub-domain in the spatial domain. We show that, depending on the definition of the growth function in the model, there are three distinct types of behaviour in front of the road. Roads can act as: (1) a barrier to invasion; (2) a temporary obstacle, leading to the formation of a beachhead; (3) as a corridor for invasion. Small changes in conditions favouring the invasive species can change the case for the road, allowing the invasive species to invade the domain in front of the road where it previously could not. We investigate the propagation regime of the invasive plant species studied at the short-time scale before a travelling wave is established and advances into space at a constant speed. Using this approach, we demonstrate how nonlinear spatio-temporal dynamics arise in a transient regime where the propagation speed depends on the detection threshold population density.

In the two-dimensional spatial domain, a long-distance dispersal kernel is incorporated along the road sub-domain. We show how long-distance dispersal along the road can lead to increased invasion in the domain.

Finally, additional landscape heterogeneities around the edge of the road, the edge effect, are investigated. Leading to an increase or decrease in the population density of the species in the spatial domain around the road.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):