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The impact of forest roads on the rate of biological invasion

  • Full or part time
  • Application Deadline
    Wednesday, February 06, 2019
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

Roads can play an important role in the spread of invasive plant species by serving as corridors for movement as well as providing prime habitat for establishment (see reference [1]). The aim of the proposed project is to develop a mathematical and computational model of biological invasion to predict how invasive plants will be spreading when the landscape conditions in the forest are changed by building a road.
Biological invasion will be modelled by an integro-difference equation (IDE) (refs.[2] &[4]) and the dispersal kernel in the IDE will simulate long distance dispersal which is the primary dispersal type for many invasive plants (e.g. ref.[3]). The model is stage-structured where the reproduction and dispersal stage are considered independently at each discrete time step. At the beginning of the project a simple `no road’ problem will be investigated by the PhD student to let them gain the experience with the model. The IDE will be solved numerically in a two-dimensional domain with relevant initial and boundary conditions to find the density of the invasive species in the domain and evaluate the rate of spread. At the next stage of the project a road will be introduced into the model as a strip of the finite width splitting the domain into two parts. The definition of the dispersal kernel in the IDE will be changed: long distance dispersal will be used to simulate the propagule movement outside the road while short distance dispersal will be employed to simulate the movement along the road. The rate of spread will be computed and compared to the `no road’ case. The model will then be made more realistic by (a) considering spatially dependent reproduction coefficient in the IDE and (b) considering more challenging road geometry, i.e. road bends. At the final stage of the project the rate of spread of a selected invasive plant will be evaluated from data available in the literature (e.g. ref.[3]). The model parameters will then be determined to simulate the spatio-temporal dynamics of the invasive plant and conclude about the rate of spread when a new landscape feature (a road) is introduced.

Biological invasion is identified as one of the most serious environmental problems currently facing society. Any action to prevent or mitigate the consequences of biological invasion in the forest is important as the environment and economics suffer from huge losses related to spread of invasive species into native forest areas (ref.[5]). Hence, this project is related to major theme B in the Forest Edge programme as it aims to answer the question `Can we design interventions to enhance forest resilience?’ by investigating the conditions under which building forest roads can prevent propagation of invasive plant species rather than facilitate it. A dominant cross-link for this project is link II (Complexity) as the mathematical and computational model developed in the project enhances our understanding of ecosystem processes by predicting the ecosystem behaviour, (in particular, spatio-temporal patterns of the invasive species) under various ecological conditions.

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics, Applied Mathematics, Theoretical Physics or related subject. Solid knowledge of at least one programming language is required (MATLAB, FORTRAN, C/C++ or similar) and good programming skills are essential. A relevant experience in one or more of the following will be an advantage: numerical methods, the probability theory, ordinary and partial differential equations, stochastic processes.

Further information about the Forest Edge Doctoral Scholarships programme is available at

Funding Notes

Full payment of tuition fees at Research Councils UK fee level for year of entry (£4,270 in 2018/19), to be paid by the University;
An annual maintenance grant at current UK Research Councils rates (national minimum doctoral stipend for 2018/19 is £14,764), to be paid in monthly instalments to the Leverhulme Trust Doctoral Scholar by the University.
All studentships will come with a minimum of £3,000 Research Training Support Grant. This can be increased up to a maximum of £12,000. Supervisors should indicate from where any further costs necessary for the project will be sourced.


[1] D. A. Mortensen, E. S. J. Rauschert, A. N. Nord, and B. P. Jones. Forest Roads Facilitate the Spread of Invasive Plants. Invasive Plant Science and Management 2009, 2:191–199
[2] L.A.D.Rodrigues, D.C.Mistro, E.R.Cara, N.B.Petrovskaya, and S.V.Petrovskii. Patchy Invasion of Stage-Structured Alien Species with Short-Distance and Long-Distance Dispersal. Bulletin of Mathematical Biology 2015, 77:1583-1619
[3] L. Straigytė, G. Cekstere, M. Laivins, V. Marozas. The spread, intensity and invasiveness of the Acer negundo in Riga and Kaunas. Dendrobiology 2015, 74:157–168
[4] M.A. Lewis, S.V. Petrovskii, and J. Potts. The Mathematics Behind Biological Invasions. 2016, Springer, Berlin
[5] T.P. Holmes, J.E. Aukema, B. Von Holle, A. Liebhold, and E.Sills. Economic Impacts of Invasive Species in Forests. Annals of the New York Academy of Sciences 2009, 1162: 18–38

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