Department of Mathematics
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    1. FourC Modelling Project
Department of Mathematics

Mathematical Biology

The Mathematical Biology group applies mathematical methods to increase our understanding of the biological world, and the central focus is on the mathematical modelling of evolution.

Group members

  • Dr Andrea Baronchelli (Lecturer in Mathematics)
  • Professor Mark Broom (Professor of Mathematics, Head of Group)
  • Dr Christoforos Hadjichrysanthou (Visiting Fellow and former PhD student)
  • Dr Anne Kandler (former Lecturer in Mathematics, 2012-2016)
  • Laura Alessandretti (PhD student, 2015-)
  • Johann Bauer (PhD student, 2017-)
  • Abeer Ebahrawy (PhD student, 2016-)
  • Fabiano Ribeiro (Visiting Researcher 2017-18)

Recently completed PhD students:

The group hosts regular short term research visitors, most recently Roberta Amato (University of Barcelona) and Pedro Schimit (Universidade Nove de Julho, Brazil).

There are three main areas of research: evolutionary game theory, cultural evolution, network science.

Evolutionary game theory

Since its inception in the 1960s, evolutionary game theory has become increasingly influential in the modelling of biology. Important biological phenomena, such as the fact that the sex ratio of so many species is close to one half, the evolution of cooperative behaviour and the existence of costly ornaments like the peacock's tail, have been explained with ideas underpinned by game theoretical modelling.

Our work involves the development of the general mathematical theory of evolution, including an extension of the standard two player models to the multiplayer case, the integration of evolutionary games and life history theory, as well as the consideration of evolutionary games on networks.

We also model specific biological behaviour. In particular we consider parasitic behaviour such as food stealing (kleptoparasitism) and brood parasitism, where birds lay eggs in the nests of others. We also investigate biological signalling, where animals signal invisible properties in order to attract mates or ward off predators.

Human behaviour, collective dynamics and network science

Human cognition is the product of the interaction of tens of billions of neurons, societies are constituted by millions of individuals, and ecosystems consist of many interacting species. However, understanding the system-scale emerging properties of such complex systems starting from the knowledge of their constituents is unfeasible. A powerful framework to overcome this problem is provided by network science. Thanks to the network approach, where the units of the system are described as nodes and their interaction patterns as links, network science has provided in the last 15 years a unifying framework to study different systems under the same conceptual lens, with important practical consequences.

Research in the Mathematical Biology group includes fundamental investigations on the behaviour of dynamical processes on complex networks (e.g., random walks, reaction-diffusion processes, etc.), and more interdisciplinary research efforts. Among the latter, issues in language dynamics (consensus problems, emergence of conventions, etc.), evolution (biological conditions for language diversity, evolution in a changing environment, etc.), social sciences (the study of information and opinion spreading in online and offline social networks), and cognitive science (emergence of shared categorisation systems).

Modelling cultural evolution

Cultural evolution is characterised as a Darwinian selection process and often expresses itself in usage or occurrence frequencies of different cultural traits that change over time and space. (An example of such a process is the changing number of fluent Gaelic speakers in Scotland over the last centuries).

The aim of our research is to understand the underlying evolutionary principles of observed episodes of cultural change in human populations. We do so by linking observable empirical patterns of cultural change to mathematical models. These models are able to provide an explanation of cultural and demographic processes that could or, even more importantly, could not have produced the observed patterns. Our modelling frameworks include n-population reaction-diffusion systems, Markov processes and their diffusion approximation, simulations as well as Bayesian computation.

This research programme is highly interdisciplinary and the group successfully collaborates with biologists, linguists, archaeologist and anthropologists on a diverse range of questions concerning cultural evolution (e.g. dynamic of languages shift, diffusion of innovations, evolution of social learning strategies, statistical inference methods of cultural transmission processes).

If you are interested in finding out more about research in Mathematical Biology at City, University of London, please contact Professor Mark Broom.

Publications

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