Mark Broom
Centre for
Mathematical Science
City
University
Northampton Square
London EC1V 0HB
mark.broom at city.ac.uk
Teaching for 2010-11
I will be teaching on four lecture courses this year:
Algebra MA1605
Managing Risk and Uncertainty EPM944
Optimization and Decision Making EPM945
Evolutionary Game Theory MAM604
Research
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 significant branch of this work on
multi-player games involves modelling dominance hierarchy formation and maintenance. I have also been involved
in the development of other aspects of mathematical evolutionary theory. The most important recent work in this
area involves the modelling of evolution on graphs, where populations can possess a complex non-homogeneous
structure; I have a PhD student Christoforos Hadjichrysanthou working in this area. Two new areas of research
are patch models of evolution with Jan Rychtar from the University of North Carolina and the integration of
evolutionary games and life history theory with Marie Curie Fellow Krzysztof Argasinski (based at the University
of Sussex).
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. Work on kleptoparasitism together with Jan Rychtar from the University
of North Carolina is continuing.
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. A new project, continuing a long-standing
collaboration with Graeme Ruxton from the University of Glasgow, considers how honest signals to
predators can evolve in a more general context.
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.
Publications
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. & Rychtar,J. Kleptoparasitic melees - modelling food stealing featuring contests with multiple individuals. Accepted by the Bulletin of Mathematical Biology.
71. Broom,M., Hadjichrysanthou,C. & Rychtar,J. Two results on evolutionary processes on general non-directed graphs. Accepted by Proceedings of the Royal Society A.