Mathematical Biology Group
  1. FourC Modelling Project
Mathematical Biology

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 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.

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:

The following North American organisations are partners in the project:

An article highlighting some of our work, New study suggests cancer can be treated as a game between the treating physician and cancer cells is published on the CORDIS website.

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 core group members at the 2017 workshop in London:

The core group members at the 2017 workshop in London.

Workshop photos


The following publications are associated with the project:

1. Amend,S.R., Gatenby,R.A., Pienta,K.J., Brown,J.S. (2018) Cancer foraging ecology:  diet choice, patch use, and habitat selection of cancer cells.  Current Pathobiology Reports 6:209-218.

2. Bauer,J., Broom,M., Alonso, E. (2019) The Stabilisation of Equilibria in Evolutionary Game Dynamics through Mutation: Mutation Limits in Evolutionary Games. Proceedings of the Royal Society of London A 475

3. Bayer, P; Broom,M; Brown,JS; Dubbeldam, JLA, Mon Pere,N. A Markov chain model of cancer treatment. In preparation.

4. 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.

5. Bishop,D.T., Broom,M. & Southwell, R. Chris Cannings: A Life in Games. Accepted by Dynamic Games and its Applications.

6. 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

7. 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

8. Broom,M., Erovenko,I.V., Rowell,J.T., Rychtar (2020) Models and measures of animal aggregation and dispersal. Journal of Theoretical Biology 484

9. Broom,M., Erovenko,I.V., Rychtar,J. Modelling evolution in structured populations involving multiplayer interactions. Submitted.

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

11. Broom,M, Krivan,V. Two-strategy games with time constraints on regular graphs. Submitted.

12. Broom,M., Pattni,K., Rychtar (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.

13. 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

14. 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

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

16. 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.

17. 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.

18. Cannings,C., Broom,M. Game theoretical modelling of a dynamically evolving network II: target sequences of score 1. Accepted by the Journal of Dynamics and Games.

18. Cavallo,G., Di Mauro,F., Pasteris,P., Sapino,M.L., Candan,K.S. (2019) Crowd Sourced Semantic Enrichment (CroSSE) for knowledge driven querying of digital resources. J. Intell. Inf. Syst. 53(3): 453-480

20. Chen,X., Candan,K.S., Sapino,M.L. (2018) IMS-DTM: Incremental Multi-Scale Dynamic Topic Models. AAAI 2018: 5078-5085

21. 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

22. Cressman, R., Apaloo, J. (2018). Evolutionary game theory. Pages 461-510 in Tamer Basar, Georges Zaccour, eds. Handbook of Dynamic Game Theory. Springer.

23. 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.

24. Cressman, R., Koller, M., Garay, B., Garay, J. 2019 Evolutionary substitution and replacement in N-species Lotka-Volterra systems.

25. 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.

26. Cressman, R., Krivan, V. Reducing courtship time promotes marital bliss: The Battle of the Sexes game with costs measured as time lost. Submitted.

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

28. Cunningham J.J., Thuijsman F., Peeters R., Viossat Y., Brown J.S., Gatenby R.A.,  Staňková  K. , Optimal Control to Reach Evo-Evolutionary Stability in Metastatic Castrate Resistant Prostate Cancer. Submitted.

29. Erovemko, I.E., Bauer,J., Broom,M., Pattni,K., Rychtar,J. (2019) The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population. Proceedings of the Royal Society of London A 475

30. Falter, F., Linders, L., Ludwig, D., Raff, T., Salam, J., Sapino, M.L., Hamede, R., Ujvari, B., Thuijsman, F., Stankova,K. Future of Tasmanian Devil: Predictions based on agent-based modelling of transmissible cancer. In preparation.

31. 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.

32. Garay,J; Cressman,R; Xu,F; Broom,M; Csiszár,V, Móri,TF. When optimal foragers meet in a game theoretical conflict: A model of kleptoparasitism. Submitted.

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

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

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

36. Gatenby,R.A., Artzy-Randrup,Y., Epstein,T., Reed,D.R., Brown,J.S. (2020) .  Eradicating metastatic cancer and the eco-evolutionary dynamics of Anthropocene extinctions.  Cancer Research, DOI: 10.1158/0008-5472.CAN-19-1941.

37. Gatenby, R.A., Brown,J.S. Integrating evolutionary dynamics into cancer therapy.  Accepted by Nature Review Cancer.

38. 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

39. 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.

40. 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.

41. Halloway A., Staňková  K., Brown J.S., Non-Equilibrial Dynamics in Under-Saturated Communities. Submitted.

42. 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.

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

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

45. 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.

46. Krivan,V., Revilla, T. (2019). Plant coexistence mediated by adaptive foraging preferences of exploiters or mutualists. Journal of Theoretical Biology 480:112-128

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

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

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

50. Li, X., Candan,K.S., Sapino,M.L. (2018) M2TD: Multi-Task Tensor Decomposition for Sparse Ensemble Simulations. ICDE 2018: 1144-1155

51. 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.

52. 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.

53. 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 2017.

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

55. 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.

56. 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.

57. Pienta, K.J., Hammarlund,E.U. , Axelrod,R., Brown,J.S.,Amend,S.R. Poly-Aneuploid cancer cells promote evolvability thereby generating lethality of metastasis.  Accepted by Evolutionary Applications.

58. Pienta, K.J, E.U. Hammarlund, R. Axelrod, S.R. Amend and J.S. Brown. Hyperspeciation of the cancer clade, convergent evolution, and the origins of lethal cancer. Accepted by Molecular Cancer Research.

59. Poccia,S., Liu.,S., Candan,K.S., Sapino.,M.L.  Frequently Recurring Contextually-Distinct Multi-Variate Motif Discovery. In preparation.

60. Poccia,S; Erovenko; I Broom,M, Sapino,ML, Candan, KS. A data driven approach to modelling the evolution of cooperation in a mobile population. In preparation.

61. 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: 582-585

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

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

64. Rossini,R., Poccia,S.R., Candan,K.S., Sapino,M.L. (2019) CA-Smooth: Content Adaptive Smoothing of Time Series Leveraging Locally Salient Temporal Features. MEDES 2019: 36-43

65. Salvioli, M., Dubbeldam J., Staňková, K., Brown , J.S. Game theory of fisheries management. Submitted.

66. Salvioli, M., Dubbeldam J., Brown , J.S.,  Staňková, K. Stackelberg evolutionary games of cancer treatment. Submitted.

67. 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.

68. Schüller, K., Staňková, K., Brown, J.S. Surplus Ovules Permit Female Choice in Oak Trees. Submitted.

69. Spencer,R., Broom,M. (2018) A game-theoretical model of kleptoparasitic behaviour in an urban gull (Laridae) population. Behavioral Ecology 29 60-78

70. Staňková, K., (2019). Resistance Games, Nature Ecology & Evolution 3(3), pp. 336-337. doi: 10.1038/s41559-018-0785-y

71. 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

72. Varga,T., Mori,T.F., Garay,J. (2019)The ESS for evolutionary matrix games under time constraints and its relationship with the asymptotically stable rest point of the replicator dynamics. Journal of Mathematical Biology doi:10.1007/s00285-019-01440-6

73. Varga,T; Rychtar,J; Garay,J and Broom,M .A temporal model of territorial defence with antagonistic interactions. Submitted.

74. West,J, Dinh,M., Brown,J.S.,Zhang,J., Anderson,A., Gatenby,R.A. (2019) Multidrug cancer therapy in metastatic castrate-resistant prostate cancer: An evolution-based strategy.  Clinical Cancer Research DOI: 10.1158/1078-0432.CCR-19-0006.

75. West, J.,You,L., Brown,J.S., Newton,P.K., Anderson,A.R.A. Towards multi-drug adaptive therapy.  Accepted by Cancer Research.

76. 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.

77. You,L., von Konbloch,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;

78. 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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