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  1. Mathematics, Computer Science and Engineering
  2. Mathematics
  3. Mathematical Biology
  4. FourC Modelling Project
About City

Conflict, Competition, Cooperation and Complexity: Using Evolutionary Game Theory to Model Realistic Populations

Project Summary

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 shall develop 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 will focus on the themes of Conflict, Competition, Cooperation and Complexity inherent in the majority of real populations.

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

The four sub-projects will be developed in parallel fostered by frequent research visits and interactions, each involving a team comprising of EU and North American researchers, and will feed into each other through regular interactions and meetings. The aim is to develop a rich, varied but consistent theory with wide applicability.

Project Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 690817, as part of the Research and Innovation Staff Exchange (RISE) programme. The Project Coordinator gave a talk to the new group of project coordinators for successful  proposals at the RISE coordinators' workshop in Brussels held on January 18-19 2018.

Project Consortium Members and Partners

The following EU universities are members of the project consortium:

Biology Center, Ceske Budejovice webpage

City, University of London webpage

Eotvos Lorand University webpage

Maastricht University webpage

University of Szeged webpage

University of Torino webpage

The following North American organisations are partners in the project:

Arizona State University webpage webpage

Moffitt Cancer Center webpage

University of Illinois at Chicago webpage

University of North Carolina at Greensboro webpage

Wilfird Laurier University webpage

Here is a photo of most of the core group members at the 2017 workshop in London. Here are more photos of the 2017 and 2018 events. An article highlighting some of our work is published on the CORDIS website at https://cordis.europa.eu/news/rcn/130027_en.html?WT.mc_id=exp

Project Workshops

There have been an annual series of workshops associated with the project. The project was launched at a workshop in Plon, Germany, January 13-15, 2016 at the Max Planck Institute for Evolutionary Biology. The first annual workshop then took place in Prague from June 28-July 1 2016 at Vila Lanna. A short report on these events together with programmes for both can be found

. The second annual workshop took place at City, University of London from July 3-7, 2017. A short report on this event together with the programme can be found here. The third annual workshop took place at the University of Torino
from July 16-19, 2018. A short report on this event together with the programme can be found here. The fourth and final workshop took place at Kasteel Vaalsbroek near
Maastricht from July 7-11, 2019. A short report on this event together with the programme can be found here.


The following publications are associated with the project:

1. Bayer,P., Brown,J.S., Stankova,K. (2018) A two-phenotype model of immune evasion by cancer cells. Journal of Theoretical Biology 455 191-204.

2. Broom,M., Cannings,C. (2017). Game theoretical modelling of a dynamically evolving network I: general target sequences. Journal of Dynamics and Games 4 285 – 318 doi:10.3934/jdg.2017016

3. Broom,M., Cressman,R., Krivan,V. (2019) Revisiting the “fallacy of averages” in ecology: Expected gain per unit time equals expected gain divided by expected time doi.org/10.1016/j.jtbi.2019.109993

4. Broom, M., Krivan, V. (2018). Biology and evolutionary games. Pages 1039-1077 in Tamer Basar, Georges Zaccour, eds. Handbook of Dynamic Game Theory. Springer.

5. Broom,M., Pattni,K.,  Rychtar,J (2018) Generalised social dilemmas: the evolution of cooperation in populations with variable group size. Bulletin of Mathematical Biology. doi:10.1007/s11538-018-00545-1.

6. Broom,M., Rychtar,J. (2016). Evolutionary games with sequential decisions and dollar auctions. Dynamic Games and its applications.doi:10.1007/s13235-016-0212-4

7. Broom,M., Rychtar,J. (2016) Ideal cost-free distributions in structured populations for general payoff  functions. Dynamic Games and its applications. doi:10.1007/s13235-016-0204-4

8. Brown,J.S. (2016) Why Darwin would have loved evolutionary game theory. Proceedings of the Royal Society B 283: 20160847

9. Brown,J.S., Cunningham,J.J, Gatenby,R.A. (2016). Aggregation Eects and Population-based dynamics as a source of therapy resistance in cancer. Accepted by Transactions of Biomedical Engineering.

10. Brown,J.S., Stankova,K., (2017) Game theory as a conceptual framework for managing insect pests. Current Opinion in Insect Science 21 26-32 doi:10.1016/j.cois.2017.05.007.

11. Chowell,G., Mizumoto,K. Banda,J.M., Poccia,S., Perrings,C. (2019) Assessing the potential impact of vector-borne disease transmission following heavy rainfall events: a mathematical framework doi.org/10.1098/rstb.2018.0272.

12. Cressman, R., Apaloo, J. (in press). Evolutionary game theory. Pages xxxx in Tamer Basar, Georges Zaccour, eds. Handbook of Dynamic Game Theory. Springer.

13. Cressman,R., Halloway,A., McNickle,G.G., Apaloo,J., Brown,J.S., Vincent, T.L. (2017). Unlimited Niche Packing in a Lotka-Volterra Competition Game. Theoretical Population Biology, 116 1-17.

14. Cressman,R., Krivan,V. (2019) Bimatrix games that include interaction times alter the evolutionary outcome: The Owner–Intruder game. Journal of Theoretical Biology 460:262-273.

15. Cunningham,J.J., Brown,J.S., Gatenby,R.A., Stankova,K. (2018) Optimal Control to Develop Therapeutic Strategies for Metastatic Castrate Resistant Prostate Cancer. Journal of Theoretical Biology 459 67-78.

16. Garay,J., Cressman, R., Mori,T.F., Varga, T. (2018) The ESS and replicator equation in matrix games under time constraints. Journal of Mathematical Biology doi 10.1007/s00285-018-1207-0.

17. Garay, J., Csiszar, V., Mori, T.F. (2017). Evolutionary stability for matrix games under time constraints. Journal of Theoretical Biology 415 1-12.

18. Garay,J., Csiszar, V., Mori T.F. (2017).. Survival Phenotype, Selfish Individual versus Darwinian Phenotype. Journal of Theoretical Biology 430 86–91.

19. Garg,Y., Poccia,S. (2017). On the Effectiveness of Distance Measures for Similarity Search in Multi-Variate Sensory Data. ICMR’17: 489-493.

20. Gatenby,R.A., Zhang,J., Brown,J.S. (2019) First Strike–Second Strike Strategies in Metastatic Cancer: Lessons from the Evolutionary Dynamics of Extinction doi: 10.1158/0008-5472.CAN-19-0807

21. Guo, R. Shakarian, P. (2016) A Comparison of Methods for Cascade Prediction, 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining. ASONAM-2016

22. Hadjichrysanthou,C., Broom,M., Rychtar,J. (2017). Models of kleptoparasitism on networks: the effect of population structure on food stealing behaviour. Journal of Mathematical Biology doi:10.1007/s00285-017-1177-7.

23. Kim, J.H., Li, M.L., Candan, K.S., Sapino, M.L. (2017) Personalized PageRank in Uncertain Graphs with Mutually Exclusive Edges. International ACM SIGIR Conference on Research and Development in Information Retrieval, Tokyo,
Japan August 7-11, 2017.

24. Krivan, V. (2017) Kdyz se matematika potka s biologii: Matematicka ekologie (When mathematics meets biology: Mathematical ecology). PMFA 62:185-201.

25. Krivan,V, Cressman,R (2017). Interaction times change evolutionary outcomes: Two-player matrxi games. Journal of Theoretical Biology 416 199-207.

26. Krivan, V., Galanthay, T.E., Cressman, R. (2018). Beyond replicator dynamics: From frequency to density dependent models of evolutionary games. Journal of Theoretical Biology 455 232-248.

27. Kumar, N., Guo, R., Aleali, A. Shakarian, P. (2016) An Empirical Evaluation of Social Influence Metrics, ASONAM Workshop on Social Influence-2016.

28. Li, A., Broom, M., Du, J. & Wang, L. (2016) Evolutionary dynamics of general group interactions in structured populations. Phys. Rev. E 93, 022407. 582-585

29. Li,X., Candan, K.S., Sapino, M.L. (2017) nTD:Noise-Profile Adaptive Tensor Decomposition. WWW 2017: 243-252.

30. Liu,S., Poccia, S.R., Candan,K.S., Sapino M.L (2016) epiDMS: Data Management and Analytics for Decision-Making From Epidemic Spread Simulation Ensembles. Journal of Infectious Diseases 214 S427-S432. doi: 10.1093/infdis/jiw305.

31. Liu, S., Poccia, S.R., Candan, K.S., Sapino, M.L., Wang, X. (2018) Robust Multi-Variate Temporal Features of Multi-Variate Time Series ACM Transactions on Multimedia Computing, Communications and Applications 14/1 1-24.

32. Muros,F.J., Maestre, J.M. You, L. Stankova,K. (2017) Model Predictive Control for Optimal Treatment in a Spatial Cancer Game. In the Proceedings of the 56th IEEE Conference on Decision and Control, Melbourne, Australia, December

33. Overton,C.E., Broom,M., Hadjichrsanthou,C.  Sharkey,K.J. (2019) Methods for approximating stochastic evolutionary dynamics on graphs. Journal of Theoretical Biology 468 45–59.

34. Pattni,K., Broom,M. & Rychtar,J. (2017) Evolutionary dynamics and the evolution of multiplayer cooperation in a subdivided population. Journal of Theoretical Biology 429 105-115.

35. Pattni,K., Broom,M. & Rychtar,J (2018) Evolving multiplayer networks: modelling the evolution of cooperation in a mobile population. Discrete and Continuous Dynamical Systems B 23 1975-2004.

36. Poccia, S.R., Sapino M.L., Liu, S., Chen, X., Garg, Y., Huang, S., Kim,J.H., Li, X., Nagarkar, P. Candan, K.S. (2017) SIMDMS: Data Management and Analysis to Support Decision Making through Large Simulation Ensembles. EDBT 2017:

37. Revilla, T. A., Krivan, V. (2016) Pollinator foraging exibility and the coexistence of competing plants. Plus One 11: e0160076. 10.1371/journal. pone.0160076

38. Revilla, T., Krivan, V.  (2018) . Competition, trait-mediated facilitation, and the structure of plant-pollinator communities. Journal of Theoretical Biology 440 42-57.

39. Schimit,P.H.T, Pattni,K.  Broom,M. (2019) Dynamics of multi-player games on complex networks using territorial interactions. Physical Review E, 99(3). doi:10.1103/physreve.99.032306.

40. Spencer,R., Broom,M. (2018) A game-theoretical model of kleptoparasitic behaviour in an urban gull (Laridae) population. Behavioral Ecology 29 60-78 doi.org/10.1093/beheco/arx125

41. Stankova, K., Brown, J.S., Dalton, W.S., Gatenby, R.A.(2018) Optimizing Cancer Treatment Using Game Theory: A Review. JAMA Oncology DOI: 10.1001/jamaoncol.2018.3395

42. You,L., Brown, J.S., Thuijsman,F., Cunningham,J.J., Gatenby,R.A., Zhang,J. Stankova,K. (2017) Spatial vs. non-spatial eco-evolutionary dynamics in a tumor growth model. Journal of Theoretical Biology 435 78-97 doi:10.1016/j.jtbi.2017.08.022.

43. You, L. von Knobloch,M., Lopez,T., Peschen,V.,Radcliffe,R.,Koshy Sam,P., Thuijsman,F., Stankova,K., Brown,J.S. (2019) . Including Blood Vasculature into a Game-Theoretic Model of Cancer Dynamics. Games 10(1), 13

44. Zhang,J., Cunningham,J.J., Brown,J.S., Gatenby,R.A. (2017) Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer.  Nature Communications 8:1816.  DOI: 10.1038/s41467-017-01968-5

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