Available PhD projects

Variation of the global oxygen production by marine phytoplankton in response to global warming

(Supervisor: Prof. Sergei Petrovskii)

Ocean dynamics is known to have a strong effect on the global climate change and on the composition of the atmosphere. It is estimated that about 70% of the atmospheric oxygen is produced in the oceans due to the photosynthetic activity of phytoplankton. The project will build on the recent discovery of a new type of a global ecological catastrophe resulting from the global warming [1,2]. A sustainable oxygen production is only possible in an intermediate range of the production rates, which in their turn depend on the oxygen concentration in water. If, in the course of time, the oxygen production rate becomes too low or too high, the system's dynamics bifurcates and may evolve to the regime with the oxygen depletion and plankton extinction. Obviously, this catastrophic scenario implies a drastic decrease of oxygen concentration in the Earth atmosphere and a vital hazard for most of the life on the Earth. Hence, the depletion of atmospheric is a possible ecological disaster, accompanying the global warming, that has been overlooked.  

The project will extend the above results onto more realistic models of natural system and also link them to some available data. In the real ocean, the rate of oxygen production depends on many factors, including water temperature and its acidity, the latter being directly related to the concentration of carbon dioxide in the atmosphere. The increasing temperature leads to the decreasing oxygen production rate and solubility of oxygen in water. In contrast, the increasing concentration of carbon dioxide in the atmosphere enhances the oxygen production rate, but is accompanied with the increasing acidity of water; the later may be harmful for the growth activity of the phytoplankton’s cells. The global warming is thought to be provoked by the drastic increase of the carbon dioxide concentration in the atmosphere, therefore the both processes -- of the ocean warming and the increase of the CO2 concentration are to be addressed together.   

[1] Sekerci, Y., Petrovskii, S.V. Mathematical modelling of plankton-oxygen dynamics under the climate change. Bull. Math. Biol. 77, 2325 (2015).

[2] Petrovskii, S.V., Sekerci, Y., and Venturino, E. (2017) Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change. J. Theor. Biol. 424, 91-109.


Modelling biological invasions and pattern formation in complex landscapes

(Supervisor: Prof. Sergei Petrovskii)

Understanding of mechanisms of pattern formation in population dynamics is a major problem in contemporary ecology. Often pattern formation can be linked to the spatial spread of invasive species resulting from a biological invasion. Although considerable progress has been made in modelling and understanding of biological invasions over the last two decades, e.g. see [1-4], many questions remain open. One problem of significant theoretical and practical importance is the scenarios of species spread subject to complex geometries of the environment. In this project, this problem will be addressed theoretically by means of mathematical modelling. A particular attention will be paid to different scenarios of species spread, such as through propagation of a continuous population front or through a patchy invasion, with the ultimate goal to provide a better understanding of the relation between these two basic scenarios. The mathematical framework is given by differential equations, both ODEs and PDEs, and the required mathematical tools will include both analytical methods and numerical algorithms for differential equations.

[1] Shigesada, N., Kawasaki, K. (1997) Biological Invasions: Theory and Practice. Oxford University Press, UK.

[2] Petrovskii, S.V., Li, B.-L. (2006) Exactly Solvable Models of Biological Invasion. Chapman & Hall / CRC Press.

[3] Malchow, H., Petrovskii, S.V., Venturino, E. (2008) Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, Simulations. Chapman \& Hall / CRC Press.

[4] Lewis, M.A., Petrovskii, S.V., Potts, J. (2016) The Mathematics Behind Biological Invasions. Interdisciplinary Applied Mathematics, Vol. 44. Springer.


Multiscale mathematical approaches to ecological monitoring

(Supervisor: Prof .Sergei Petrovskii)

Trapping is central to studying the ecology of insects and is often an essential monitoring tool in integrated pest management [1]. Despite this, the interpretation of trap counts is challenging and they tend to be used to make relative population estimates. One reason for this is that the theory of trapping is under-developed and there is no universal mathematical model to aid interpretation. The principal goal of this project is to develop a general theoretical and methodological framework to interpret count data from single and multiple insect trap catches by baited and passive traps in order to derive a reliable and cost-effective estimate of the absolute population density. This will involve a number of mathematical and modelling techniques, cf. [1-4], such as an equation-based diffusion-type models, simulation-based random walk models (either diffusion or Levy-types), as well as application of some relevant statistical tools.

[1] Petrovskii, S.V., Petrovskaya, N., and Bearup, D. (2014) Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks. Physics of Life Reviews 11, 467-525.

[2] Tilles, P.F.C., Petrovskii, S.V., and Natti, P.L. (2017) A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes. Scientific Reports 7, 14364.

[3] Petrovskaya, N., and Petrovskii, S.V. (2017) Catching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization. J. R. Soc. Interface 14, 20160855.

[4] Bearup, D., Benefer, C.M., Petrovskii, S.V., and Blackshaw, R. (2016) Revisiting Brownian motion as a description of animal movement: a comparison to experimental movement data. Methods in Ecology and Evolution 7, 1525-1537.


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