The project has resulted in 78 publications, covering our four core scientific themes, together with integrated work. In work package 1 we have built upon the evolutionary framework introduced by Broom and Rychtar to complete its core components and to extend it to more general cases to enable it to be used in realistic populations. In particular this has involved the development of evolutionary dynamics and consideration of core independence properties, the development of approximation methods for large complex structures and applications of the models to real scenarios. In work package 2 we have developed a comprehensive theory of complex foraging games involving time constraints. Classic matrix games make two important assumptions: (1) all interactions take the same amount of time, and (2) all individuals pair instantaneously. These assumptions simplify analysis because pair distribution is then described by the Hardy-Weinberg proportions. The novelty of this work package was to explore what happens when either of the two assumptions does not hold. In work package 3, we concentrated our efforts on two main aspects: the study of influence in social networks and the study of the dynamics of the propagation of infectious diseases. We defined new metrics to compare multivariate time series, and new clustering and visualization techniques, and we developed the EpiDMS software which enables domain experts to navigate in the space of multivariate simulations, representing the simulated space of possible evolutions of an infectious disease. Work package 4 focused on building evolutionary game theory tools to define, understand, and model cancer, viewing the cancer cells as the unit of selection so that metastatic cancer is a disease of Darwinian evolution. This advanced and synthesized the emerging field of the game theory of cancer to include neighbourhood effects on the evolution of therapy resistance and spatial variation within the tumour, modelling dynamic, multiple and adaptive therapies and model validation using real data.
The four main research work packages for FourCModelling have developed separate methodology to tackle their own scientific challenges. Yet there is common ground between the different research streams, and one of the main aims of the project was to develop some unified methodology in terms of both population structure and mechanisms (we have produced ten cross work package publications). This is the start of a longer integration process, and further work will be developed following the project. In particular we have submitted a significant new research grant bid with which to continue our exciting research project.
These works were developed from a series of secondments that happened in 2016-2019, and which have now been completed. We have held five workshops associated with the project; the first two in 2016 in Plon, Germany and in Prague, the third in 2017 in London, the fourth in 2018 in Torino and the final one in 2019 in Maastricht. Each workshop consisted of a mixture of talks, training and research discussion sessions both within and across the four core themes.
