Spatial Patterns: Biology and Chemistry

Naturally-Occurring Spatial Patterns in Biology and Chemistry

Degree type


Closing date

25 September 2023



Citizenship requirement

Domestic / International

About the research project

In some biological systems, and in some chemical reactions, spatial patterns can arise spontaneously in the system.  The populations of animals, or the prevalence of a disease, or the concentrations of certain chemicals, can self-organize into patterns in which regions of high concentration alternate with regions of low concentration.  The possibility of these patterns forming spontaneously in a biological or chemical system was first recognized by the famous British Mathematician Alan Turing, and the process is now known as the Turing Instability (see [1]).

Here at the University of Tasmania, we have been studying the effect these spatial patterns can have upon the spread of disease in Tasmanian wildlife.  In [2], we formulated a model for the spread of Ross-River virus, and very recently, we are studying similar mathematical models of mite infestation of Wombats, which result in the spread of  sarcoptic mange throughout those populations [3].

This project would ideally consider a combination of applications in biology and chemistry, because of the very close mathematical similarity involved in these two areas.  One aim is to study the effect of spatial pattern formation in the distribution of the bee varroa mite (Varroa destructor) in Australian honey-bee populations, using a mathematical model that is expected to be very close to the sarcoptic mange model already developed in [3].  The intention here would also be to study how targetted treatment regimes may assist in controlling the spread of this devastating introduced pest.  In some chemical reactions, remarkable time-dependent oscillations in the concentrations of various chemical species have been shown to occur, and in these situations, spatial patterns can also arise.  A second aim of this project will be to study spatial (Turing) patterns in either the Bray iodine oscillator reaction or else the Briggs-Rauscher reaction (see [1]), since spatial variations in these famous reactions are not well studied.  Spatial patterns can also occur in combustion reactions such as the Sal'nikov reaction [4], and a further application of the techniques developed here to the spread and control of bushfires in Australian bushland may also be undertaken.  A combination of classical Applied Mathematical techniques (linearization, transform methods) with novel spectral-method computational techniques developed here at the University of Tasmania will be used to gain new understanding of these spatial patterns, and it is anticipated that the results will enhance knowledge of some important environmental processes.


[1]  James D Murray, "Mathematical Biology", Springer-Verlag, Berlin (1989)  767 pages.

[2]  Luke Denholm, Nicholas J Beeton, Lawrence K Forbes, Scott Carver,  "A model for the dynamics of Ross River Virus in the Australian environment",  Letters in Biomathematics  4 (1)  (2017), 187-206

[3]  Ivy J Hindle, Lawrence K Forbes, Scott Carver,  "The effect of spatial dynamics on the behaviour of an environmentally transmitted disease",  Journal of Biological Dynamics 16 (1)  (2022), 144-159

[4]  Rhys A Paul, Lawrence K Forbes,  "Combustion waves in Sal'nikov's reaction scheme in a spherically symmetric gas",  Journal of Engineering Mathematics 101, (2016)  29-45

Primary Supervisor

Meet Prof Andrew Bassom


Applicants will be considered for a Research Training Program (RTP) scholarship or Tasmania Graduate Research Scholarship (TGRS) which, if successful, provides:

  • a living allowance stipend of $31,500 per annum (2023 rate, indexed annually) for 3.5 years
  • a relocation allowance of up to $2,000
  • a tuition fees offset covering the cost of tuition fees for up to four years (domestic applicants only)

If successful, international applicants will receive a University of Tasmania Fees Offset for up to four years.

As part of the application process you may indicate if you do not wish to be considered for scholarship funding.

Other funding opportunities and fees

For further information regarding other scholarships on offer, and the various fees of undertaking a research degree, please visit our Scholarships and fees on research degrees page.


Applicants should review the Higher Degree by Research minimum entry requirements.

Additional eligibility criteria specific to this project/scholarship:

  • Applicants must be able to undertake the project on-campus

Selection Criteria

The project is competitively assessed and awarded.  Selection is based on academic merit and suitability to the project as determined by the College.

Application process

  1. Select your project, and check that you meet the eligibility and selection criteria, including citizenship;
  2. Contact Prof Andrew Bassom to discuss your suitability and the project's requirements; and
  3. In your application:
    • Copy and paste the title of the project from this advertisement into your application. If you don’t correctly do this your application may be rejected.
    • Submit a signed supervisory support form, a CV including contact details of 2 referees and your project research proposal.
  4. Apply prior to 25 September 2023.

Full details of the application process can be found under the 'How to apply' section of the Research Degrees website.

Following the closing date applications will be assessed within the College. Applicants should expect to receive notification of the outcome by email by the advertised outcome date.

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