Mark Broom (Head of the Department of Mathematics)

Department of Mathematics
City, University of London
Northampton Square
London EC1V 0HB

mark.broom at

Teaching for 2022-23

I will be teaching the following lecture course this year:

Optimization and Decision Making EPM945


My main research interest is the application of game theory to the mathematical modelling of biology, especially using the concept of the Evolutionarily Stable Strategy (ESS). My work has generally been theoretical, considering both purely mathematical work on the theory of games in an evolutionary context and more specific problems when a particular animal behaviour or trait is concerned. I have published and continue to publish work in the three main areas listed below.

Mathematical models of evolution
This area involves the development of the general mathematical theory of evolution, rather than any specific application. Early work considered Patterns of Evolutionarily Stable Strategies; a theoretical investigation into the coexistence of different ESSs in the important game class matrix games. A key theme has been multi-player game theory. Most evolutionary game theory concerns two-player games only; this work includes an extension of the theory to many players. A second important theme has been the modelling of evolution on graphs, where populations can possess a complex non-homogeneous structure. These two area have been brought together in a new framework for more evolution on structured populations, which I have developed with Jan Rychtar from the University of North Carolina at Greensboro, which is a central area of my current research.

Models of parasitism
I have modelled two major types of parasitic behaviour on birds. The first of these involves the modelling of kleptoparasitism, where animals acquire food by stealing from others. This work began with the development of a general modelling framework for kleptoparasitism and considers the circumstances under which it is best to steal food (or not) for different scenarios and varying biological and mathematical assumptions. The second area is the modelling of brood parasitism. Raising young can be costly, and some birds lay their eggs in the nests of other birds to avoid this cost. Various models of both conspecific and interspecific parasitism are considered. I am continuing to work on kleptoparasitism in particular.

Evolutionary responses to predators and group living
A key priority for many animals is the avoidance of predators. Many such prey animals choose to live in groups, and these two features are often strongly related. I have considered two major types of interactions between prey and predators, the first of these being antipredator vigilance in animal groups. This an extension of a well-established theory involving trade-offs in time spent watching for predators and foraging, into dynamic changes in group structure and in spatial and positioning factors. The second is the co-evolution of defence and signalling. Many animals possess high levels of toxins to make them unpalatable to potential predators. Such defences are invisible, so they are often also brightly coloured to signal these defences, and success depends upon a sufficient number of conspecifics with these traits for predators to learn to avoid them.

Research Projects

I would be interested in supervising research students in any of the general areas described above. For more details on my research, look at some of the publications from the list below.


Broom,M. & Rychtar,J. (2013). Game-Theoretical Models in Biology. Chapman and Hall.

The second edition of this book will appear in August 2022.

1. Broom,M., Cannings,C. & Vickers,G.T. (1993) On the number of local maxima of a constrained quadratic form. Proceedings of the Royal Society of London A 443 573-584.
2. Broom,M., Cannings,C. & Vickers,G.T. (1994) Sequential methods for generating patterns of ESS's. Journal of Mathematical Biology 32 597-615.
3. Broom,M., Cannings,C. & Vickers,G.T. (1996) Patterns of ESS's. Adding pairs to an ESS. Mathematical Biosciences 136 21-34.
4. Broom,M., Cannings,C. & Vickers,G.T. (1996) Choosing a Nest Site: Contests and Catalysts. American Naturalist 147 1108-1114.
5. Broom,M., Cannings,C. & Vickers,G.T. (1996) Some examples of multi-player game dynamics. Proceedings of the European Mathematical Genetics Meeting, Padova University Press 105-114.
6. Broom,M., Cannings,C. & Vickers,G.T. (1997) Multi-player matrix games. Bulletin of Mathematical Biology 59 931-952.
7. Broom,M. Cannings,C. & Vickers,G.T. (1997) A sequential-arrivals model of territory acquisition. Journal of Theoretical Biology 189 257-272.
8. Broom,M. & Ruxton,G.D. (1998) Evolutionarily Stable Stealing: Game Theory applied to Kleptoparasitism. Behavioral Ecology 9 397-403.
9. Broom,M. & Ruxton,G.D. (1998) Modelling responses in vigilance rates to arrivals to and departures from a group of foragers. IMA Journal of Mathematics Applied in Medicine and Biology 15 387-400.
10. Broom,M. & Ruxton,G.D. (1999) A game theoretic model of kleptoparasitism. Proceedings of BioMedSim 99 27-31.
11. Ruxton,G.D. & Broom,M. (1999) Evolution of kleptoparasitism as a war of attrition. Journal of Evolutionary Biology 12 755-759.
12. Proctor,C.J. & Broom,M. (2000) A spatial model of antipredator vigilance. IMA Journal of Mathematics Applied in Medicine and Biology 17 75-93.
13. Broom,M., Cannings,C. & Vickers,G.T. (2000) Evolution in Knockout Contests: the Fixed Strategy Case. Bulletin of Mathematical Biology 62 451-466.
14. Broom,M. (2000) Patterns of ESSs: the Maximal Pattern Conjecture revisited. Journal of Mathematical Biology 40 406-412.
15. Broom,M. (2000) Bounds on the number of ESSs of a matrix game. Mathematical Biosciences 167 163-175.
16. Broom,M., Cannings,C., & Vickers,G.T. (2000) Evolution in Knockout Contests: the Variable Strategy Case. Selection 1 5-21.
17. Broom,M., Cannings,C. & Vickers,G.T. (2000) A sequential-arrivals model of territory acquisition II. Journal of Theoretical Biology 207 389-403.
18. Ruxton,G.D., Broom,M. & Colegrave,N. (2001) Are unusually coloured eggs a signal to potential conspecific brood parasites? American Naturalist 157 451-458.
19. Broom,M. & Ruxton,G.D. (2001) A model of dominance and resource division amongst a group of animals of differing quality. Population Ecology 43 213-220.
20. Proctor,C.J., Broom,M. & Ruxton,G.D. (2001) Modelling antipredator vigilance and flight response in group foragers when warning signals are ambiguous. Journal of Theoretical Biology 211 409-417.
21. Broom,M. & Ruxton,G.D. (2002) A Game Theoretic Approach to Conspecific Brood Parasitism. Behavioral Ecology 13 321-327.
22. Broom,M. (2002) Using game theory to model the evolution of information: an illustrative game. Entropy 4 35-46.
23. Ward,A.J.W.,Hoare,D.J.,Couzin,I.D.,Broom,M. & Krause,J. (2002) The effects of parasitism and body length on positioning within wild fish shoals Journal of Animal Ecology 71 10-14.
24. Broom,M. (2002) A unified model of dominance hierarchy formation and maintenance. Journal of Theoretical Biology 219 63-72.
25. Broom,M. & Cannings,C. (2002) Modelling dominance hierarchy formation as a multi-player game. Journal of Theoretical Biology 219 397-413.
26. Ruxton,G.D. & Broom,M. (2002) Intraspecific brood parasitism can increase the number of eggs an individual lays in its own nest. Proceedings of the Royal Society of London B 269 1989-1992.
27. Ward,A.J.W., Botham,M.S., Hoare,D.J., James,R., Broom,M., Godin,J.G.J. & Krause,J. (2002) Association patterns and shoal fidelity in the three-spined stickleback. Proceedings of the Royal Society of London B 269 2451-2455.
28. Proctor,C.J., Broom,M. & Ruxton,G.D. (2003) A communication-based spatial model of antipredator vigilance. Journal of Theoretical Biology 220 123-137.
29. Broom,M & Ruxton,G.D. (2003) Evolutionarily stable kleptoparasitism: consequences of different prey types. Behavioral Ecology 14 23-33.
30. Broom,M. (2003) The use of multiplayer game theory in the modeling of biological populations. Comments on Theoretical Biology 8 103-123.
31. Broom,M., Tang,Q. & Waxman,D. (2003) Mathematical Analysis of a Model describing Evolution of an Asexual Population in a Changing Environment. Mathematical Biosciences 186 93-108.
32. Broom,M., Borries,C. & Koenig,A. (2004) Infanticide and infant defense by males- modeling the conditions in primate multi-male groups. Journal of Theoretical Biology 231 261-270.
33. Luther,R.M. & Broom,M. (2004) Rapid convergence to an equilibrium state in kleptoparasitic populations. Journal of Mathematical Biology 48 325-339.
34. Broom,M. & Ruxton,G.D. (2004) A framework for modelling and analysing conspecific brood parasitism. Journal of Mathematical Biology 48 529-544.
35. Broom,M., Luther,R.M. & Ruxton,G.D. (2004) Resistance is useless? - extensions to the game theory of kleptoparasitism. Bulletin of Mathematical Biology 66 1645-1658.
36. Broom,M. & Ruxton,G.D. (2005) You can run or you can hide: optimal strategies for cryptic prey against pursuit predators. Behavioral Ecology 16 534-540.
37. Broom,M. (2005) Evolutionary games with variable payoffs. Comptes Rendus Biologies 328 403-412.
38. Broom,M., Speed,M.P. & Ruxton,G.D. (2005) Evolutionarily stable investment in secondary defences. Functional Ecology 19 836-843.
39. Ruxton,G.D., Fraser, C. & Broom,M. (2005) An evolutionarily stable joining policy for group foragers. Behavioral Ecology 16 856-864.
40. Yates,G.E. & Broom,M. (2005) A stochastic model of the distribution of unequal competitors between resource patches. Journal of Theoretical Biology 237 227-237.
41. Speed,M.P., Ruxton,G.D. & Broom,M. (2006) Automimicry and the evolution of discrete prey defences. Biological Journal of the Linnean Society 87 393-402.
42. Proctor,C.J., Broom,M. & Ruxton,G.D. (2006) Antipredator vigilance in birds: modelling the `edge' effect. Mathematical Biosciences 199 79-96.
43. Broom,M., Speed,M.P. & Ruxton,G.D. (2006) Evolutionarily stable defence and signalling of that defence. Journal of Theoretical Biology 242 32-43.
44. Jackson,A.L.,Beauchamp,G.,Broom,M. & Ruxton,G.D. (2006) Evolution of anti-predator traits in response to a flexible targeting strategy by predators. Proceedings of the Royal Society of London B 273 1055-1062.
45. Fraser,C.P.,Ruxton,G.D. & Broom,M. (2006) Public information and patch estimation for group foragers: a re-evaluation of patch quitting strategies in a patchy environment. Oikos 112 311-321.
46. Broom,M. & Rychtar,J. (2007) The evolution of a kleptoparasitic system under adaptive dynamics. Journal of Mathematical Biology 54 151-177.
47. Ellis,J.,Broom,M. & Jones,S. (2007) Protein-RNA interactions: Structural analysis and functional classes of Protein-RNA binding sites. Proteins: structure, function and bioinformatics 66 903-911.
48. Broom,M.,Ruxton,G.D. & Speed,M.P. (2007) Evolutionarily Stable Investment in Anti-predatory Defences and Aposematic Signalling. In: Mathematical Modeling of Biological Systems, Volume II. A. Deutsch, R. Bravo de la Parra, R. de Boer, O. Diekmann, P. Jagers, E. Kisdi, M. Kretzschmar, P. Lansky and H. Metz (eds). Birkhauser, Boston, 37-48.
49. Luther,R.M., Broom,M. & Ruxton,G.D. (2007) Is food worth fighting for? ESS's in mixed populations of kleptoparasites and foragers. Bulletin of Mathematical Biology 69 1121-1146.
50. Broom,M.,Nouvellet,P.,Bacon,J.P. & Waxman,D. (2007) Parameter-free testing of the shape of a probability distribution. Biosystems 90 509-515.
51. Yates,G.E. & Broom,M. (2007) A stochastic model of kleptoparasitism. Journal of Theoretical Biology 248 480-489.
52. Ruxton,G.D., Speed, M.P. & Broom,M. (2007) The importance of initial protection of conspicuous mutants for the coevolution of defense and aposematic signaling of the defense: A modeling study. Evolution 61 2165-2174.
53. Langridge,K.V., Broom,M. & Osorio, D. (2007) Selective signalling by cuttlefish to predators. Current Biology 17 R1044-R1045.
54. Broom,M., Ruxton,G.D. & Kilner,R.M. (2008) Host life history strategies and the evolution of chick-killing by brood parasitic offspring. Behavioral Ecology 19 22-34.
55. Broom,M. & Rychtar,J. (2008) An analysis of the fixation probability of a mutant on special classes of non-directed graphs. Proc. Roy. Soc. London A 464 2609-2627.
56. Broom,M., Rychtar,J. & Sykes,C. (2008) The Evolution of Kleptoparasitism under Adaptive Dynamics Without Restriction. Journal of Interdisciplinary Mathematics 11 479-494.
57. Broom,M., Luther,R.M., Ruxton,G.D. & Rychtar,J. (2008) A game-theoretic model of kleptoparasitic behavior in polymorphic populations. Journal of Theoretical Biology 255 81-91.
58. Harrison,M.D. & Broom, M. (2009) A game-theoretic model of interspecific brood parasitism with sequential decisions. Journal of Theoretical Biology 256 504-517.
59. Broom,M. Rychtar,J. & Stadler,B. (2009) Evolutionary Dynamics on Small-Order Graphs. Journal of Interdisciplinary Mathematics 12 129-140.
60. Broom,M., Luther,R.M. & Rychtar,J. (2009) A Hawk-Dove game in kleptoparasitic populations. Journal of Combinatorics, Information and System Science 4 449-462.
61. Broom,M. & Rychtar,J. (2009) A game theoretical model of kleptoparasitism with incomplete information. Journal of Mathematical Biology 59 631-649.
62. Broom,M., Koenig,A. & Borries,C. (2009) Variation in dominance hierarchies among group-living animals: modeling stability and the likelihood of coalitions. Behavioral Ecology 20 844-855.
63. Kiss, I. Z., Broom, M., and Rafols, I. (2009) Can epidemic models describe the diffusion of research topics across disciplines? In Birger Larsen and Jacqueline Leta (Eds.) Proceedings of the 12th International Conference of the International Society for Scientometrics and Informetrics, Rio de Janeiro.
64. Ruxton,G.D., Speed,M.P. & Broom,M. (2009) Identifying the ecological conditions that select for intermediate levels of aposematic signalling. Evolutionary Ecology 23 491-501.
65. Broom,M. (2009) Balancing risks and rewards: the logic of violence. Frontiers in Neuroscience Vol.3.
66. Kiss, I.Z., Broom, M., Craze, P. & Rafols, I. (2010) Can epidemic models describe the diffusion of topics across disciplines?. Journal of Informetrics 4 74-82.
67. Broom,M., Crowe.M, Fitzgerald.M & Rychtar,J. (2010) The stochastic modelling of kleptoparasitism using a Markov process. Journal of Theoretical Biology 264 266-272.
68. Broom,M., Hadjichrysanthou,C. & Rychtar,J. (2010) Evolutionary games on graphs and the speed of the evolutionary process. Proceedings of the Royal Society A 466 1327-1346.
69. Broom,M., Higginson,A.D. & Ruxton,G.D. (2010) Optimal investment across different aspects of anti-predator defences. Journal of Theoretical Biology 263 579-586.
70. Broom,M., Hadjichrysanthou,C., Rychtar,J. and Stadler,B. (2010) Two results on evolutionary processes on general non-directed graphs. Proceedings of the Royal Society A 466 2795-2798.
71. Broom,M. & Rychtar,J. (2011) Kleptoparasitic melees - modelling food stealing featuring contests with multiple individuals. Bulletin of Mathematical Biology 73 683-699.
72. Broom,M. & Ruxton,G.D. (2011) Some mistakes go unpunished - the evolution of all or nothing signalling. Evolution 65 2743-2749.
73. Hadjichrysanthou,C., Broom,M. & Rychtar,J. (2011) Evolutionary games on star graphs under various updating rules. Dynamic Games and Applications 1 386-407.
74. Broom,M., Rychtar,J. & Stadler,B. (2011) Evolutionary dynamics on graphs - the effect of graph structure and initial placement on mutant spread. Journal of Statistical Theory and Practice 5 369-381.
75. Broom,M & Voelkl, B. (2012) Two Measures of Effective Population Size for Graphs. Evolution 66 1613-1623.
76. Barker,H.A., Broom,M. & Rychtar,J. (2012) A game theoretical model of kleptoparasitism with strategic arrivals and departures of beetles at dung pats Journal of Theoretical Biology 300 292-298.
77. Broom,M. & Rychtar,J. (2012) A general framework for analysing multiplayer games in networks using territorial interactions as a case study. Journal of Theoretical Biology 302 70-80.
78. Hadjichrysanthou,C. & Broom,M. (2012) When should animals share? Game theory applied to kleptoparasitic populations with food sharing. Behavioral Ecology 23 977-991.
79. Broom,M., Hughes,R.N., Burrows,M. & Ruxton,G.D. (2012) Evolutionarily stable sexual allocation by both stressed and unstressed potentially simultaneous hermaphrodites within the same population. Journal of Theoretical Biology 309 96-102.
80. Hadjichrysanthou,C., Broom,M. & Kiss,I.Z. (2012) Approximating evolutionary dynamics on networks using a neighbourhood configuration model. Journal of Theoretical Biology 312 13-21.
81. Broom,M. & Ruxton,G.D. (2012) Perceptual advertisement by the prey of stalking or ambush predators. Journal of Theoretical Biology 315 9-16.
82. Argasinski,K. & Broom,M. (2013) Ecological theatre and the evolutionary game: how environmental and demographic factors determine payoffs in evolutionary games. Journal of Mathematical Biology.
83. Broom,M. & Ruxton,G.D. (2013) On the evolutionary stability of zero-cost pooled-equilibrium signals. Journal of Theoretical Biology 323 69-75.
84. Broom,M. (2013) Interactions between searching predators and hidden prey in Search Theory: A Game Theoretic Perspective Alpern S., Fokkink R., Gasieniec L., Lindelauf R., Subrahmanian V.S. (eds) Springer.
85. Broom,M. & Cannings,C. (2013) Evolution of a network with strategic link formation governed by individual preferences. Journal of Theoretical Biology 335 160-168.
86. Argasinski,K. & Broom,M. (2013) The nest site lottery: how selectively neutral density dependent growth suppression induces frequency dependent selection. Theoretical Population Biology 90 82-90.
87. Broom,M., Rychtar,J. & Sykes,D.G. (2013) The effect of information on payoffs in kleptoparasitic interactions. Springer Proceedings in Mathematics and Statistics 64 125-134.
88. Broom,M., Ruxton,G.D. & Schaefer,H.M. (2013) Signal verification can promote reliable signalling. Proceedings of the Royal Society B 280 20131560.
89. Bruni,M., Broom,M. & Rychtar,J. (2014) Analysing territorial models on graphs. Involve 7 129-149.
90. Teichmann,J., Broom, M. & Alonso, E. (2014) The application of temporal difference learning in optimal diet models. Journal of Theoretical Biology 340 11-16.
91. Teichmann,J., Broom,M. & Alonso, E. (2014) The evolutionary dynamics of aposematism: a numerical analysis of co-evolution in finite populations. Mathematical Modelling of Natural Phenomena 9 148-164.
92. Broom,M., Rychtar,J. & Sykes,D.G. (2014) Kleptoparasitic interactions under asymmetric resource valuation. Mathematical Modelling of Natural Phenomena 9 138-147.
93. Broom,M. & Rychtar,J. (2014) Asymmetric games in monomorphic and polymorphic populations. Dynamic Games and Applications 4 391-406.
94. Broom,M. & Cannings,C. (2015) Graphic deviation. Discrete Mathematics 338 701-711.
95. Broom,M, Johanis,M. & Rychtar,J. (2015) The effect of fight cost structure on fighting behaviour. Journal of Mathematical Biology 71 979-996.
96. Kura,K, Broom,M. & Kandler,A. (2015) Modelling dominance hierarchies under winner and loser effects. Bulletin of Mathematical Biology 77 927-952.
97. Broom,M, Lafaye,C., Pattni,K. & Rychtar,J. (2015) A study of the dynamics of multi-player games on small networks using territorial interactions. Journal of Mathematical Biology 71 1551-1574.
98. Teichmann, J., Alonso, E. & Broom, M. (2015) A reward-driven model of Darwinian fitness, Proceedings of the 7th International Joint Conference on Computational Intelligence (IJCCI 2015) - Volume 1: ECTA, pp. 174-179, Lisbon, Portugal, Scitepress.
99. Pattni,K., Broom,M., Rychtar,J. & Silvers,A.J. (2015) Evolutionary graph theory revisited: when is an evolutionary process equivalent to the Moran process?. Proceedings of the Royal Society A 471 2015.0334.
100. Broom,M. & Rychtar,J. (2016) A model of food stealing with asymmetric information. Ecological Complexity 26 137-142.
101. Broom,M., Rychtar, J. & Spears-Gill,T. (2016) The game-theoretical model of using insecticide-treated bed-nets to fight malaria. Applied Mathematics 7 852-860.
102. Raza,M.S. & Broom,M. (2016) Survival analysis modelling with hidden censoring. Journal of Statistical Theory and Practice 10 1-14.
103. Li,A., Broom,M., Du.J. & Wang,L. (2016) Evolutionary dynamics of general group interactions in structured populations. Physical Review E 93 022407.
104. Broom,M. & Rychtar,J. (2016) Nonlinear and Mulitplayer Evolutionary Games in Advances in Dynamic and Evolutionary Games, Thuijsman,F., Wagener,F. (eds) Birkhauser.
105. Kura,K., Broom,M. & Kandler,A. (2016) A game-theoretical winner and loser model of dominance hierarchy formation. Bulletin of Mathematical Biology 78 1259-90.
106. Broom,M. & Rychtar,J. (2016) Ideal cost-free distributions in structured populations for general payoff functions. Dynamic Games and Applications doi:10.1007/s13235-016-0204-4.
107. Broom,M. & Rychtar,J. (2017) Evolutionary games with sequential decisions and dollar auctions. Dynamic Games and Applications doi: 10.1007/s13235-016-0212-4.
108. Chawsheen,T. & Broom,M. (2017) Seasonal Time-Series Modelling and Forecasting Monthly Mean Temperature for Decision Making in the Kurdistan Region of Iraq. Journal of Statistical Theory and Practice 11 604-633.
109. Argasinski,K. & Broom,M. (2017) Evolutionary stability under limited population growth. Eco-evolutionary feedbacks and replicator dynamics. Ecological Complexity doi:10.1016/j.ecocom.2017.04.002.
110. 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.
111. Broom,M. & Cannings,C. (2017) Game theoretical modelling of a dynamically evolving network I: general target sequences. Journal of Dynamics and Games

112. 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.

113. Teichmann,J., Alonso,E. & Broom, M. (2017) Reinforcement learning is an effective strategy to create phenotypic variation and a potential mechanism for the initial evolution of learning. Proceedings of the Conference on Artificial Evolution 2017.

114. Teichmann,J., Alonso,E. & Broom, M. (2017) Reinforcement Learning as a model of aposematism. Proceedings of the Conference on Artificial Evolution 2017.

115. Broom,M, Johanis,M. & Rychtar,J. (2018) The effect of fight cost structure on fighting behaviour involving simultaneous decisions and variable investment levels. Journal of Mathematical Biology 76 457-482.

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

117. Broom,M., Collins,D., Vu,T.H. & Thomas,P. (2018) The Four Regions in Settlement Space: A Game-Theoretical Approach to Investment Treaty Arbitration. Part I: Modelling. Law, Probability and Risk 17 55-78.

118. Broom,M., Collins,D., Vu,T.H. & Thomas,P. (2018) The Four Regions in Settlement Space: A Game-Theoretical Approach to Investment Treaty Arbitration. Part II: Cases. Law, Probability and Risk 17 79-98.

119. Broom,M. & Krivan,V. (2018) Biology and Evolutionary Games: in Tamer Basar, Georges Zaccour, eds. Handbook of Dynamic Game Theory. Springer.
120. Argasinski,K. & Broom,M. (2018) Interaction rates, vital rates, background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics. Theory in Biosciences 137 33-50.
121. 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.

122. Broom, M., Pattni, K. & Rychtar, J. (2018) Generalized Social Dilemmas: The Evolution of Cooperation in Populations with Variable Group Size. Bulletin of Mathematical Biology. doi:10.1007/s11538-018-00545-1.

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

124. 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.

125. Wang, L., Ruxton, G.D., Cornell, S.J., Speed, M.P. & Broom, M. (2019) A theory for investment across defences triggered at different stages of a predator-prey encounter. Journal of Theoretical Biology 473 9-19.

126. Broom,M., Cressman,R., & Krivan,V. (2019) Revisiting the `fallacy of averagesí in ecology: Expected gain per unit time equals expected gain divided by expected time. Journal of Theoretical Biology483 article 109993.

127. Erovenko,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 20190399.

128. 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 20190355.

129. Broom,M., Erovenko,I.V., Rowell,J.T. & Rychtar,J. (2020) Models and measures of animal aggregation and dispersal. Journal of Theoretical Biology 494 110002.

130. Cannings,C. & Broom,M. (2020) Game theoretical modelling of a dynamically evolving network II: target sequences of score 1. Journal of Dynamics and Games 7 37-64.

131. Varga,T., Garay,J., Rychtar,J. & Broom,M. (2020) A temporal model of territorial defence with antagonistic interactions. theoretical Population Biology 135 15-35.

132. Bishop,D.T., Broom,M. & Southwell, R. (2020) Chris Cannings: A Life in Games. Dynamic Games and Applications 10 591-617.

133. Garay,J., Cressman,R., Xu,F., Broom,M., Csiszar & V., Mori, T. (2020) When optimal foragers meet in a game theoretical conflict: A model of kleptoparasitism. Journal of Theoretical Biology 502 110306.

134. Broom,M. & Krivan,V. (2020) Two-strategy games with time constraints on regular graphs. Journal of Theoretical Biology 506,110426.

135. Broom,M., Erovenko,I. & Rychtar,J. (2021) Modelling evolution in structured populations involving multiplayer interactions. Dynamic Games and Applications 11 270-293.

136. Sun.S, Broom,M., Johanis,M & Rychtar,J (2021) A mathematical model of kin selection in floral displays. Journal of Theoretical Biology 509,110470.

137. Argasiski,K & Broom,M. (2021) Towards a replicator dynamics model of age structured populations. Journal of Mathematical Biology 82 44.

138. Aizouk,R. & Broom,M. (2022) Modelling conflicting individual preference: target sequences and graph realization. Discrete and Continuous Dynamical Systems Series B, doi: 10.3934/dcdsb.2022001

139. Scaramangas,A. & Broom,M. (2022) Aposematic signalling in prey-predator systems: determining evolutionarily stability when prey populations consist of a single species. Journal of Mathematical Biology 85(2) 13.