Mark Lewis

Mark Lewis
Kennedy Chair in Mathematical Biology
Mathematics and Statistics

D.Phil. in Mathematics (Mathematical Biology), University of Oxford

Office: DTB-A533

I work on mathematical problems in spatial ecology. My research is interdisciplinary and involves a variety of approaches, ranging from analysis of nonlinear mathematical models to field work.

My philosophy is to immerse myself and my research group in significant new ecological problems where the mathematics has yet to be developed. Many of these problems involve the environmental impacts of anthropogenic disturbance.

Some of the Lewis Research Group are in the lab in Biology and others work in Mathematics and Statistics at the University of Victoria. I also continue supervise students and postdocs who were part of my former lab at the University of Alberta.


    Current Projects

    Animal movement modelling

    Projects include development and analysis of continuous- and discrete-time movement models, memory and animal movement and learning and animal movement. Models and methods include cognitive maps, step-selection functions, partial differential equations, data cloning and Bayesian learning models. The models have been applied to datasets on grizzly bears, wolves, caribou, polar bears, Amazonian birds and pandas to try to understand the complex spatial movement behaviours and their implications.

    Ecological dynamics in aquatic systems

    I study and model the spatio-temporal changes in aquatic systems. Populations range from coral reefs to polar bears and also include nuisance populations such as cyanobacteria as well as delicacies such as spot prawns. All of these models are impacted by human activities, which then modify the spatio-temporal population dynamics. Some questions I am working on include: what are the long-term dynamics of polar bears under changing ice conditions? How can we understand major shifts in coral reef compositions and could these ever be reversed? How can we best manage the spot prawn fishery? and How do human activities affect into cyanobacteria bloom frequency and intensity in recreational lakes? Models often take the form of dynamical systems in discrete or continuous time. A substantial amount of the research involves confronting the models with ecological data to see how the models can inform our understanding of the biological processes.

    Population spread and invasive species

    I am active in modelling and analyzing population spread dynamics. Areas I focus on include analysis of spread with long-distance dispersal and of spread in the context of ecological interactions between species (eg, competitors, predator-prey and so on). I am working on developing mathematical theory for these systems in the context of travelling waves and spreading speed theory. I also collaborate with colleagues on applying methods in machine learning to make predictions of where and when populations will spread. I am making applications of the theory to different areas. These include mountain pine beetle spread dynamics in western Canada (in collaboration wih TRIA-FOR), responses of population distributions to climate change, genetic diversity of spreading populations and zebra mussel spread and control.

    Wildlife disease modelling

    This subject is at the intersection of classical disease modelling and ecological dynamics. Those are both fascinating areas, so their intersection has a lot to offer! I am working on understanding the dynamics of sea lice infections on networks of salmon farms as well as evolutionary aspects of resistance to pesticide treatment for the sea lice. More generally I am interested in the spatio-temporal dynamics of macroparasites and how to model them. From an applied side, I am involved in modelling the spatio-temporal dynamics of the spread of chronic wasting disease in deer. With the recent COVID outbreak I have put some of my modelling skills to use on trying to predict COVID dynamics as well as the impact of human behaviour on the dynamics. In this context I am Codirector of OMNI/REUNIS, a national network taking a One Health approach to modelling emerging diseases in Canada.

    Selected Publications

    • Hamelin, F., Mammeri, Y., Aigu, Y., Strelkov, S.E., Lewis, M.A. (2022) Host diversification may split epidemic spread into two successive fronts advancing at different speeds. Bulletin of Mathematical Biology 84:68
    • Xu, J., Merrill, E., Lewis, M.A. (2022) Spreading speed of chronic wasting disease across deer groups with overlapping home ranges. Journal of Theoretical Biology 547: 111135
    • Thompson, P.R., Derocher, A.E., Edwards, M.A., Lewis, M.A. (2021) Detecting seasonal episodic-like spatio-temporal memory patterns using animal movement modelling. Methods of Ecology and Evolution (epub)
    • Ramazi, P., Haratian, A., Meghdadi, M., Mari Oriyad, A., Lewis, M.A., Maleki, Z., Vega, R., Wang, H., Wishart, D., Greiner, R. (2021) Accurate long-range forecasting of COVID-19 mortality in the USA Scientific Reports 11:13822
    • Lewis, M.A., Fagan, W., Auger-Me;the;, M., Frair, J., Fryxell, J., Gros, C., Gurarie, E., Healy, S., Merkle, J. (2021) Learning and animal movement. In press at Frontiers in Ecology and Evolution DOI: 10.22541/au.159285496.64901842
    • Ramazi, P., Kunegel-Lion, M., Greiner, R., Lewis, M.A. (2021) Exploiting the Full Potential of Bayesian Networks in Predictive Ecology. Methods in Ecology and Evolution, 12(1): 135-149.
    • Peacock, S.J., Krkosek, M., Lewis, M.A., Molnar, P.K. (2020) A unifying framework for the transient parasite dynamics of migratory hosts. Proceedings of the National Academy of Sciences, 117(20): 10897-10903.
    • Heggerud, C.M., Wang, H., Lewis, M.A. (2020) Transient dynamics of a stoichiometric cyanobacteria model via multiple-scale analysis. SIAM Journal on Applied Math, 80(3): 1223-1246.
    • Marculis, N.G., Lewis, M.A. (2020) Inside dynamics of integrodifference equations with mutations. Bulletin of Mathematical Biology, 82: 7.
    • Peacock, S.J., Krkosek, M. Bateman, A.W., Lewis, M.A. (2020) Estimation of spatiotemporal transmission dynamics and analysis of management scenarios for sea lice of farmed and wild salmon. Canadian Journal of Fisheries and Aquatic Science, 77(1): 55-68.