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Conflict, Competition, Cooperation and Complexity: Using Evolutionary Game Theory to model realistic populations

Periodic Reporting for period 2 - FourCmodelling (Conflict, Competition, Cooperation and Complexity: Using Evolutionary Game Theory to model realistic populations)

Reporting period: 2018-01-01 to 2019-12-31

"Real animals and human populations are complex, involving structural relationships depending upon space and time and varied interactions between potentially many individuals. Human societies feature family units, communities, companies and nations. Some animal also have complex societies, such as primate groups and social insect colonies. Single organisms themselves can be thought of as complex ecosystems, host to many interacting life forms.

Models of populations are necessarily idealised, and most involve either simple pairwise interactions or ""well-mixed"" structureless populations, or both. In this project we are developing game-theoretical models, both general and focused on specific real population scenarios, which incorporate population structure and within population interactions which are both complex in character. We focus on the themes of Conflict, Competition, Cooperation and Complexity inherent in the majority of real populations.

There are four complementary sub-projects within the overall project. The first focuses on developing a general theory of modelling multiplayer evolutionary games in structured populations, and feeds into each of the other three sub-projects. The second considers complex foraging games, in particular games under time constraints and involving sequential decisions relating to patch choice. The third involves modelling human social behaviours, a particular example being epidemic cascades on social networks. The final sub-project models cancer as a complex adaptive system, where a population of tumour, normal and immune cells evolve within a human ecosystem.

The four sub-projects have been developed in parallel fostered by frequent research visits and interactions, each involving a team comprising of EU and North American researchers, and feed into each other through regular interactions and meetings. The aim is to develop a rich, varied but consistent theory with wide applicability."
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.
The project has developed a number of novel research methodologies, in particular on the consideration of complex population/ relationship structures including neighbourhood characterizations and evolutionary dynamics, on modelling tumours as heterogeneous populations and on the modelling of interactions within populations with time delays. These key developments, and related work, have been the subject of talks at a series of conferences and workshops (over 150 events) and have been disseminated in various other ways, including on our website, social media and training events.

Immediate scientific impact has come from work including two extensive handbook chapters on game theoretical modelling and the work on the influence of social networks. Later impact will come from a variety of areas, including work on novel evolutionary dynamics and on time-delay models including with regard to complex foraging and food-stealing. Work packages 1 and 2 have developed a significant interaction with a number of joint papers, and this has led to unification of two different modelling methodologies, involving time constraints and spatial factors.

Potential socio-economic and scientific impact may arise out of the each of the themes, but especially from the theme on the evolutionary modelling of cancer; for example initial results on therapy resistance are potentially important. This work provides evidence for the need of a paradigm shift in treatment of metastatic cancers, following game-theoretic ideas developed within this project and the success of game-theory based clinical trials. The current standard of care in metastatic cancers should be replaced by so-called evolutionary therapies, which are aligned with Stackelberg evolutionary strategy of a physician in his/her game against cancer cells.

An important outcome of the project has been the development within work package 3 of a number of software modules which are now available to the general public as an open source system, with open source licenses at to be maintained by EmitLab (headed by KSC and MLS) beyond the project’s lifetime of four years. In addition to the proposed feature bases analysis of multivariate time series, the team has also defined tensor-decomposition algorithms able to capture salient aspects of dynamically evolving complex systems, such as pandemics.
A model of blood vessels and growth of different types of cancer cells in their vicinity.