Transient Propagation of the Invasion Front in the Homogeneous Landscape and in the Presence of a Road.

Understanding the propagation of invasive plants at the beginning of invasive spread is important as it can help practitioners eradicate harmful species more efficiently. In our work the propagation regime of the invasive plant species is studied at the short-time scale before a travelling wave is established and advances into space at a constant speed. The integro-difference framework has been employed to deal with a stage-structured population, and a short-distance dispersal mode has been considered in the homogeneous environment and when a road presents in the landscape. It is explained in the paper how nonlinear spatio-temporal dynamics arise in a transient regime where the propagation speed depends on the detection threshold population density. Furthermore, we investigate the question of whether the transient dynamics become different when the homogeneous landscape is transformed into the heterogeneous one. It is shown in the paper how invasion slows down in a transient regime in the presence of a road.

Propagation of invasive plant species in the presence of a road.

Invasive plant species pose a significant threat to biodiversity and the economy, yet their management is often resource-intensive and expensive, and further research is required to make control measures more efficient. 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. We have developed a novel mathematical model to analyse the impact of roads on the propagation of invasive plants. The integro-difference equation model is formulated for stage-structured population and incorporates a road sub-domain in the spatial domain. The results of our study reveal, 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 barriers to invasion, lead to a formation of a beachhead in front of the road, or act as corridors allowing the invasive species to invade the domain in front of the road. Analytical and computational findings on how roads can impact the spread of invasive species show that a small change in conditions of the environment 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 spread.