### Using mathematics and history to predict the future of semi-arid vegetation

Van Leeuwenhoek Lecture on BioScience.

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**Speaker:**

Jonathan Sherratt is professor of Mathematics at Heriot-Watt University, School of Mathematical and Computer Sciience, since 1998. He was an undergraduate at Cambridge, went to the University of Washington and obtained his PhD at the University of Oxford (1991). From 1991-1997 he has been a lecturer at Warwick.

His research concerns the application of mathematics to problens in ecology, cell biology and medicine. The objective in this research is to use mathematics to obtain a better understanding of complex behaviour in biology. Often this involves developing new mathematics in order to study the mathematical models. Specific topics on which his research is focused include spatiotemporal dynamics of cyclic populations, vegetation patterns in semi-arid environments, and long-range cell interactions in developmental biology and tumour growth.

*Vegetation in semi-arid regions has complicated dynamics, with a tendency to self-organise into spatiotemporal patterns. Given the lack of laboratory replicates, and the practical difficulties associated with fieldwork, mathematical modelling plays a key role in understanding these dynamics. In this lecture, I will discuss the ability of simple mathematical models of semi-arid vegetation to provide important and often surprising insights into spatial patterning. I will emphasise the coexistence of multiple pattern wavelengths, which means that wavelength prediction requires the solution of a pattern selection problem. For example, the degradation of uniform vegetation and the colonization of bareground lead to different patterns. This "history-dependence"means that prediction of future vegetation levels requires detailed information on past levels. Focussing on the specific case of the Sahel region of Africa, I will show how this can be obtained by combining modelling with data on climate history. Using prediction of future rainfall levels from global climate models, I will go on to discuss the prediction of future vegetation levels in the Sahel, up to the end of the 21st century - an issue with major ecological and socioeconomic importance.*

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