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Game-Theoretical Models in Biology 2nd edition [Kõva köide]

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(Virginia Commonwealth University, USA), (City, University of London, UK)
  • Formaat: Hardback, 622 pages, kõrgus x laius: 234x156 mm, kaal: 453 g, 21 Tables, black and white; 103 Line drawings, black and white; 103 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Mathematical Biology Series
  • Ilmumisaeg: 03-Aug-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367456680
  • ISBN-13: 9780367456689
Teised raamatud teemal:
Game-Theoretical Models in Biology 2nd editionSuurem pilt
  • Formaat: Hardback, 622 pages, kõrgus x laius: 234x156 mm, kaal: 453 g, 21 Tables, black and white; 103 Line drawings, black and white; 103 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Mathematical Biology Series
  • Ilmumisaeg: 03-Aug-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367456680
  • ISBN-13: 9780367456689
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367456689.html
Märksõnad:
Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology, Second Edition presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well.

The book describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoners dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use Python to solve various games.

Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behaviour, and the existence of adornments (for example, the peacocks tail), have been explained using ideas underpinned by game theoretical modelling. Suitable for readers studying and working at the interface of mathematics and the life sciences, this book shows how evolutionary game theory is used in the modelling of these diverse biological phenomena.

In this thoroughly revised new edition, the authors have added three new chapters on the evolution of structured populations, biological signalling games, and a topical new chapter on evolutionary models of cancer. There are also new sections on games with time constraints that convert simple games to potentially complex nonlinear ones; new models on extortion strategies for the Iterated Prisoners Dilemma and on social dilemmas; and on evolutionary models of vaccination, a timely section given the current Covid pandemic.

Features











Presents a wide range of biological applications of game theory. Suitable for researchers and professionals in mathematical biology and the life sciences, and as a text for postgraduate courses in mathematical biology. Provides numerous examples, exercises, and Python code.

Arvustused

"It is hard to imagine that the book by Broom & Rychtar is already a decade old, it stills feels fresh! However, in a second edition, the authors have now successfully addressed several novel topics that have developed rapidly in these past 10 years, such as the evolution of cancer or vaccination games. On top of the excellent structure of the original edition of this book, including great exercises, the authors have now included python code and pointers to relevant packages. This is an excellent way to make a new generation of game theorists familiar with the field and at the same time allow them a much more interactive experience!

The new edition of this wonderful book proves that evolutionary game theory is alive and kicking!" Arne Traulsen, Director, Max Planck Institute for Evolutionary Biology, Germany

"The second edition of Game-Theoretical Models in Biology shows the tremendous development and applications that this theory has undergone since its inception fifty years ago. That fact that this theory is still undergoing development and finding new applications is evidenced by the fact that the authors have included completely new chapters reflecting, for example, recent applications in the study of cancer evolution or evolution on graphs in the second edition. The book is suitable both for students of mathematical disciplines, to whom it will show the strong application of mathematics in biology, and for students of biological disciplines, who want to gain a solid theoretical basis for the description of eco-evolutionary laws. It is the most comprehensive treatise on the applications of evolutionary game theory in evolutionary and population biology. " Vlastimil Kivan, University of South Bohemia, Czech Republic

"If you want a solid foundation in the topic of game theory in biology, then work your way through this book. It is an authoritative account of the basics, introduces many important biological applications, and has a plethora of insights. Really excellent." John McNamara, Emeritus Professor at University of Bristol, United Kingdom "In this update of their 2013 book, Broom and Rychtar continue to provide a valuable resource to any researcher interested in evolutionary games. Readers of the original book will especially appreciate the new chapters/sections on recent developments and applications in the field as well as the expanded bibliography. The book will also serve as an excellent self-contained text, with an extensive set of exercises in each chapter, for students at a graduate or senior undergraduate level studying game-theoretic applications to biology" Ross Cressman, Wilfrid Laurier University, Canada

Preface xix
Authors xxiii
1 Introduction
1(12)
1.1 The history of evolutionary games
1(6)
1.1.1 Early game playing and strategic decisions
2(2)
1.1.2 The birth of modern game theory
4(1)
1.1.3 The beginnings of evolutionary games
5(2)
1.2 The key mathematical developments
7(3)
1.2.1 Static games
8(1)
1.2.2 Dynamic games
9(1)
1.3 The range of applications
10(2)
1.4 Reading this book
12(1)
2 What is a game?
13(16)
2.1 Key game elements
14(9)
2.1.1 Players
14(1)
2.1.2 Strategies
15(1)
2.1.2.1 Pure strategies
15(1)
2.1.2.2 Mixed strategies
16(1)
2.1.2.3 Pure or mixed strategies?
17(1)
2.1.3 Payoffs
18(1)
2.1.3.1 Representation of payoffs by matrices
19(1)
2.1.3.2 Contests between mixed strategists
20(1)
2.1.3.3 Generic payoffs
21(2)
2.1.4 Games in normal form
23(1)
2.2 Games in biological settings
23(3)
2.2.1 Representing the population
24(2)
2.2.2 Payoffs in matrix games
26(1)
2.3 Further reading
26(1)
2.4 Exercises
27(2)
3 Two approaches to game analysis
29(20)
3.1 The dynamical approach
29(5)
3.1.1 Replicator dynamics
29(1)
3.1.1.1 Discrete replicator dynamics
29(1)
3.1.1.2 Continuous replicator dynamics
30(1)
3.1.2 Adaptive dynamics
31(1)
3.1.3 Other dynamics
32(1)
3.1.4 Timescales in evolution
33(1)
3.2 The static approach -- ESS
34(8)
3.2.1 Nash equilibria
35(2)
3.2.2 Evolutionarily Stable Strategies
37(1)
3.2.2.1 ESSs for matrix games
38(1)
3.2.3 Polymorphic versus monomorphic populations
39(2)
3.2.4 Stability of Nash equilibria and of ESSs
41(1)
3.3 Dynamics versus statics
42(3)
3.3.1 ESS and replicator dynamics in matrix games
43(1)
3.3.2 Replicator dynamics and finite populations
44(1)
3.4 Python code
45(1)
3.5 Further reading
46(1)
3.6 Exercises
47(2)
4 Some classical games
49(24)
4.1 The Hawk-Dove game
49(4)
4.1.1 The underlying conflict situation
49(1)
4.1.2 The mathematical model
50(1)
4.1.3 Mathematical analysis
50(1)
4.1.4 An adjusted Hawk-Dove game
51(1)
4.1.5 Replicator dynamics in the Hawk-Dove game
51(1)
4.1.6 Polymorphic mixture versus mixed strategy
51(2)
4.2 The Prisoner's Dilemma
53(5)
4.2.1 The underlying conflict situation
54(1)
4.2.2 The mathematical model
54(1)
4.2.3 Mathematical analysis
55(1)
4.2.4 Interpretation of the results
55(1)
4.2.5 The IPD, computer tournaments and Tit for Tat
56(2)
4.3 The war of attrition
58(5)
4.3.1 The underlying conflict situation
58(1)
4.3.2 The mathematical model
59(1)
4.3.3 Mathematical analysis
59(2)
4.3.4 Some remarks on the above analysis and results
61(1)
4.3.5 A war of attrition game with limited contest duration
61(1)
4.3.6 A war of attrition with finite strategies
62(1)
4.3.7 The asymmetric war of attrition
63(1)
4.4 The sex ratio game
63(2)
4.4.1 The underlying conflict situation
64(1)
4.4.2 The mathematical model
64(1)
4.4.3 Mathematical analysis
65(1)
4.5 Python code
65(4)
4.6 Further reading
69(1)
4.7 Exercises
70(3)
5 The underlying biology
73(24)
5.1 Darwin and natural selection
73(2)
5.2 Genetics
75(6)
5.2.1 Hardy-Weinberg equilibrium
77(2)
5.2.2 Genotypes with different fitnesses
79(2)
5.3 Games involving genetics
81(3)
5.3.1 Genetic version of the Hawk-Dove game
82(1)
5.3.2 A rationale for symmetric games
82(1)
5.3.3 Restricted repertoire and the streetcar theory
83(1)
5.4 Fitness, strategies and players
84(2)
5.4.1 Fitness 1
84(1)
5.4.2 Fitness 2
84(1)
5.4.3 Fitness 3
85(1)
5.4.4 Fitness 4
85(1)
5.4.5 Fitness 5
85(1)
5.4.6 Further considerations
86(1)
5.5 Selfish genes: How can non-beneficial genes propagate?
86(4)
5.5.1 Genetic hitchhiking
87(1)
5.5.2 Selfish genes
88(1)
5.5.3 Memes and cultural evolution
89(1)
5.5.4 Selection at the level of the cell
90(1)
5.6 The role of simple mathematical models
90(1)
5.7 Python code
91(2)
5.8 Further reading
93(1)
5.9 Exercises
94(3)
6 Matrix games
97(30)
6.1 Properties of ESSs
97(6)
6.1.1 An equivalent definition of an ESS
97(1)
6.1.2 A uniform invasion barrier
98(2)
6.1.3 Local superiority of an ESS
100(1)
6.1.4 ESS supports and the Bishop-Cannings theorem
101(2)
6.2 ESSs in a 2 × 2 matrix game
103(2)
6.3 Haigh's procedure to locate all ESSs
105(2)
6.4 ESSs in a 3 × 3 matrix game
107(3)
6.4.1 Pure strategies
107(1)
6.4.2 A mixture of two strategies
108(1)
6.4.3 Internal ESSs
108(1)
6.4.4 No ESS
109(1)
6.5 Patterns of ESSs
110(5)
6.5.1 Attainable patterns
111(1)
6.5.2 Exclusion results
112(1)
6.5.3 Construction methods
113(1)
6.5.4 How many ESSs can there be?
114(1)
6.6 Extensions to the Hawk-Dove game
115(3)
6.6.1 The extended Hawk-Dove game with generic payoffs
116(1)
6.6.2 ESSs on restricted strategy sets
117(1)
6.6.3 Sequential introduction of strategies
117(1)
6.7 Python code
118(5)
6.8 Further reading
123(1)
6.9 Exercises
124(3)
7 Nonlinear games
127(24)
7.1 Overview and general theory
127(3)
7.2 Linearity in the focal player strategy and playing the field
130(4)
7.2.1 A generalisation of results for linear games
130(2)
7.2.2 Playing the field
132(1)
7.2.2.1 Parker's matching principle
133(1)
7.3 Nonlinearity due to non-constant interaction rates
134(3)
7.3.1 Nonlinearity in pairwise games
135(2)
7.3.2 Other games with nonlinear interaction rates
137(1)
7.4 Nonlinearity due to games with time constraints
137(5)
7.4.1 The model
138(4)
7.5 Nonlinearity in the strategy of the focal player
142(2)
7.5.1 A sperm allocation game
143(1)
7.5.2 A tree height competition game
143(1)
7.6 Linear versus nonlinear theory
144(1)
7.7 Python code
145(2)
7.8 Further reading
147(1)
7.9 Exercises
148(3)
8 Asymmetric games
151(20)
8.1 Selten's theorem for games with two roles
152(3)
8.2 Bimatrix games
155(4)
8.2.1 Dynamics in bimatrix games
156(3)
8.3 Uncorrelated asymmetry--The Owner-Intruder game
159(2)
8.4 Correlated asymmetry
161(6)
8.4.1 Asymmetry in the probability of victory
161(1)
8.4.2 A game of brood care and desertion
162(1)
8.4.2.1 Linear version
162(2)
8.4.2.2 Nonlinear version
164(1)
8.4.3 Asymmetries in rewards and costs: the asymmetric war of attrition
165(2)
8.5 Python code
167(1)
8.6 Further reading
168(1)
8.7 Exercises
169(2)
9 Multi-player games
171(24)
9.1 Multi-player matrix games
172(10)
9.1.1 Two-strategy games
174(1)
9.1.2 ESSs for multi-player games
175(2)
9.1.3 Patterns of ESSs
177(1)
9.1.4 More on two-strategy, m-player matrix games
177(3)
9.1.5 Dynamics of multi-player matrix games
180(2)
9.2 The multi-player war of attrition
182(3)
9.2.1 The multi-player war of attrition without strategy adjustments
182(2)
9.2.2 The multi-player war of attrition with strategy adjustments
184(1)
9.2.3 Multi-player war of attrition with several rewards
185(1)
9.3 Structures of dependent pairwise games
185(3)
9.3.1 Knockout contests
186(2)
9.4 Python code
188(3)
9.5 Further reading
191(1)
9.6 Exercises
192(3)
10 Extensive form games and other concepts in game theory
195(20)
10.1 Games in extensive form
195(7)
10.1.1 Key components
196(1)
10.1.1.1 The game tree
196(1)
10.1.1.2 The player partition
196(1)
10.1.1.3 Choices
196(1)
10.1.1.4 Strategy
197(1)
10.1.1.5 The payoff function
197(1)
10.1.2 Backwards induction and sequential equilibria
197(4)
10.1.3 Games in extensive form and games in normal form
201(1)
10.2 Perfect, imperfect and incomplete information
202(4)
10.2.1 Disturbed games
202(2)
10.2.2 Games in extensive form with imperfect information-- The information partition
204(2)
10.3 Repeated games
206(2)
10.4 Python code
208(4)
10.5 Further reading
212(1)
10.6 Exercises
213(2)
11 State-based games
215(18)
11.1 State-based games
216(7)
11.1.1 Optimal foraging
216(2)
11.1.2 The general theory of state-based games
218(1)
11.1.3 A simple foraging game
219(1)
11.1.4 Evolutionary games based upon state
220(3)
11.2 A question of size
223(3)
11.2.1 Setting up the model
224(1)
11.2.2 ESS analysis
224(1)
11.2.3 A numerical example
225(1)
11.3 Life history theory
226(2)
11.4 Python code
228(2)
11.5 Further reading
230(1)
11.6 Exercises
230(3)
12 Games in finite populations and on graphs
233(34)
12.1 Finite populations and stochastic games
233(8)
12.1.1 The Moran process
233(2)
12.1.2 The fixation probability
235(2)
12.1.3 General Birth-Death processes
237(1)
12.1.4 The Moran process and discrete replicator dynamics
238(1)
12.1.5 Fixation and absorption times
239(1)
12.1.5.1 Exact formulae
239(1)
12.1.5.2 The diffusion approximation
240(1)
12.2 Games in finite populations
241(2)
12.3 Evolution on graphs
243(11)
12.3.1 The fixed fitness case
246(1)
12.3.1.1 Regular graphs
247(1)
12.3.1.2 Selection suppressors and amplifiers
248(3)
12.3.2 Dynamics and fitness
251(3)
12.4 Games on graphs
254(6)
12.4.1 Strong selection models
254(2)
12.4.1.1 Theoretical results for strong selection
256(2)
12.4.2 Weak selection models
258(2)
12.4.2.1 The structure coefficient
260(1)
12.5 Python code
260(4)
12.6 Further reading
264(1)
12.7 Exercises
265(2)
13 Evolution in structured populations
267(22)
13.1 Spatial games and cellular automata
267(2)
13.2 Theoretical developments for modelling general structures
269(3)
13.3 Evolution in structured populations with multi-player interactions
272(5)
13.3.1 Basic setup
272(1)
13.3.2 Fitness
273(1)
13.3.3 Multi-player games
274(1)
13.3.4 Evolutionary dynamics
274(1)
13.3.5 The Territorial Raider model
275(2)
13.4 More multi-player games
277(4)
13.4.1 Structure coefficients and multi-player games
277(2)
13.4.2 Games with variable group sizes
279(2)
13.5 Evolving population structures
281(3)
13.5.1 Games with reproducing vertices
281(2)
13.5.2 Link formation models
283(1)
13.6 Python code
284(1)
13.7 Further reading
285(1)
13.8 Exercises
286(3)
14 Adaptive dynamics
289(18)
14.1 Introduction and philosophy
289(1)
14.2 Fitness functions and the fitness landscape
290(4)
14.2.1 Taylor expansion of s(y, x)
292(1)
14.2.2 Adaptive dynamics for matrix games
293(1)
14.3 Pairwise invasibility and Evolutionarily Singular Strategies
294(5)
14.3.1 Four key properties of Evolutionarily Singular Strategies
294(1)
14.3.1.1 Non-invasible strategies
294(1)
14.3.1.2 When an ess can invade nearby strategies
294(1)
14.3.1.3 Convergence stability
295(1)
14.3.1.4 Protected polymorphism
295(1)
14.3.2 Classification of Evolutionarily Singular Strategies
295(1)
14.3.2.1 Case 5
296(1)
14.3.2.2 Case 7
296(2)
14.3.2.3 Case 3--Branching points
298(1)
14.4 Adaptive dynamics with multiple traits
299(3)
14.5 The assumptions of adaptive dynamics
302(1)
14.6 Python code
303(1)
14.7 Further reading
304(1)
14.8 Exercises
304(3)
15 The evolution of cooperation
307(30)
15.1 Kin selection and inclusive fitness
308(2)
15.2 Greenbeard genes
310(3)
15.3 Direct reciprocity: developments of the Prisoner's Dilemma
313(7)
15.3.1 An error-free environment
313(2)
15.3.2 An error-prone environment
315(1)
15.3.3 ESSs in the IPD game
316(1)
15.3.4 A simple rule for the evolution of cooperation by direct reciprocity
317(1)
15.3.5 Extortion and the Iterated Prisoner's Dilemma
317(3)
15.4 Public Goods games
320(5)
15.4.1 Punishment
321(2)
15.4.2 General social dilemmas
323(2)
15.5 Indirect reciprocity and reputation dynamics
325(3)
15.6 The evolution of cooperation on graphs
328(1)
15.7 Multi-level selection
329(1)
15.8 Python code
330(2)
15.9 Further reading
332(1)
15.10 Exercises
333(4)
16 Group living
337(22)
16.1 The costs and benefits of group living
337(1)
16.2 Dominance hierarchies: formation and maintenance
338(8)
16.2.1 Stability and maintenance of dominance hierarchies
338(3)
16.2.2 Dominance hierarchy formation
341(1)
16.2.2.1 Winner and loser models
342(2)
16.2.3 Swiss tournaments
344(2)
16.3 The enemy without: responses to predators
346(3)
16.3.1 Setting up the game
346(1)
16.3.1.1 Modelling scanning for predators
347(1)
16.3.1.2 Payoffs
347(1)
16.3.2 Analysis of the game
348(1)
16.4 The enemy within: infanticide and other anti-social behaviour
349(3)
16.4.1 Infanticide
349(2)
16.4.2 Other behaviour which negatively affects groups
351(1)
16.5 Python code
352(3)
16.6 Further reading
355(1)
16.7 Exercises
356(3)
17 Mating games
359(22)
17.1 Introduction and overview
359(1)
17.2 Direct conflict
360(5)
17.2.1 Setting up the model
360(1)
17.2.1.1 Analysis of a single contest
361(1)
17.2.1.2 The case of a limited number of contests per season
361(2)
17.2.2 An unlimited number of contests
363(1)
17.2.3 Determining rewards and costs
364(1)
17.3 Indirect conflict and sperm competition
365(5)
17.3.1 Setting up the model
366(1)
17.3.1.1 Modelling sperm production
366(1)
17.3.1.2 Model parameters
366(1)
17.3.1.3 Modelling fertilisation and payoffs
367(1)
17.3.2 The ESS if males have no knowledge
367(1)
17.3.3 The ESS if males have partial knowledge
368(1)
17.3.4 Summary
369(1)
17.4 The Battle of the Sexes
370(6)
17.4.1 Analysis as a bimatrix game
370(1)
17.4.2 The coyness game
371(1)
17.4.2.1 The model
371(1)
17.4.2.2 Fitness
372(2)
17.4.2.3 Determining the ESS
374(2)
17.5 Python code
376(1)
17.6 Further Reading
377(1)
17.7 Exercises
378(3)
18 Signalling games
381(22)
18.1 The theory of signalling games
381(1)
18.2 Selecting mates: signalling and the handicap principle
382(8)
18.2.1 Setting up the model
383(1)
18.2.2 Assumptions about the game parameters
384(2)
18.2.3 ESSs
386(1)
18.2.4 A numerical example
386(1)
18.2.5 Properties of the ESS--honest signalling
387(2)
18.2.6 Limited options
389(1)
18.3 Alternative models of costly honest signalling
390(5)
18.3.1 Index signals
390(1)
18.3.2 The Pygmalion game: signalling with both costs and constraints
391(3)
18.3.3 Screening games
394(1)
18.4 Signalling without cost
395(2)
18.5 Pollinator signalling games
397(2)
18.6 Python code
399(1)
18.7 Further Reading
400(1)
18.8 Exercises
401(2)
19 Food competition
403(28)
19.1 Introduction
403(1)
19.2 Ideal Free Distribution for a single species
403(4)
19.2.1 The model
403(4)
19.3 Ideal Free Distribution for multiple species
407(2)
19.3.1 The model
407(1)
19.3.2 Both patches occupied by both species
408(1)
19.3.3 One patch occupied by one species, another by both
408(1)
19.3.4 Species on different patches
409(1)
19.3.5 Species on the same patch
409(1)
19.4 Distributions at and deviations from the Ideal Free Distribution
409(2)
19.5 Compartmental models of kleptoparasitism
411(8)
19.5.1 The model
412(1)
19.5.2 Analysis
413(4)
19.5.3 Extensions of the model
417(2)
19.6 Compartmental models of interference
419(2)
19.7 Producer-scrounger models
421(4)
19.7.1 The Finder-Joiner game--the sequential version with complete information
422(1)
19.7.1.1 The model
422(1)
19.7.1.2 Analysis
422(2)
19.7.1.3 Discussion
424(1)
19.7.2 The Finder-Joiner game--the sequential version with partial information
424(1)
19.8 Python code
425(2)
19.9 Further reading
427(1)
19.10 Exercises
428(3)
20 Predator-prey and host-parasite interactions
431(30)
20.1 Game-theoretical predator-prey models
431(3)
20.1.1 The model
432(1)
20.1.2 Analysis
433(1)
20.1.3 Results
434(1)
20.2 The evolution of defence and signalling
434(6)
20.2.1 The model
435(1)
20.2.1.1 Interaction of prey with a predator
435(1)
20.2.1.2 Payoff to an individual prey
436(1)
20.2.2 Analysis and results
437(1)
20.2.3 An alternative model
437(2)
20.2.4 Cheating
439(1)
20.3 Brood parasitism
440(3)
20.3.1 The model
440(1)
20.3.2 Results
441(2)
20.4 Parasitic wasps and the asymmetric war of attrition
443(5)
20.4.1 The model
444(1)
20.4.2 Analysis--evaluating the payoffs
445(2)
20.4.3 Discussion
447(1)
20.5 Complex parasite lifecycles
448(2)
20.5.1 A model of upwards incorporation
448(2)
20.5.2 Analysis and results
450(1)
20.6 Search games involving predators and prey
450(4)
20.6.1 Search games
451(1)
20.6.2 The model of Gal and Casas
451(1)
20.6.3 The repeated game
452(1)
20.6.4 Capture can occur in transit
453(1)
20.7 Python code
454(3)
20.8 Further reading
457(1)
20.9 Exercises
458(3)
21 Epidemic models
461(24)
21.1 SIS and SIR models
461(8)
21.1.1 The SIS epidemic
462(1)
21.1.1.1 The model
462(1)
21.1.1.2 Analysis
463(1)
21.1.1.3 Summary of results
464(1)
21.1.2 The SIR epidemic
465(1)
21.1.2.1 The model
465(1)
21.1.2.2 Analysis and results
466(1)
21.1.2.3 Some other models
466(1)
21.1.3 Epidemics on graphs
467(2)
21.2 The evolution of virulence
469(4)
21.2.1 An SI model for single epidemics with immigration and death
469(1)
21.2.1.1 Model and results
469(1)
21.2.2 An SI model for two epidemics with immigration and death and no superinfection
470(1)
21.2.2.1 Model and results
470(1)
21.2.3 Superinfection
471(1)
21.2.3.1 Model and results
471(2)
21.3 Viruses and the Prisoner's Dilemma
473(1)
21.3.1 The model
473(1)
21.3.2 Results
473(1)
21.3.3 A real example
474(1)
21.4 Vaccination models
474(4)
21.5 Python code
478(3)
21.6 Further reading
481(1)
21.7 Exercises
482(3)
22 Evolutionary cancer modelling
485(14)
22.1 Modelling tumour growth -- an ecological approach to cancer
486(2)
22.2 A spatial model of cancer evolution
488(2)
22.3 Cancer therapy as a game-theoretic scenario
490(2)
22.4 Adaptive therapies
492(2)
22.5 Python code
494(1)
22.6 Further reading
495(1)
22.7 Exercises
496(3)
23 Conclusions
499(14)
23.1 Types of evolutionary games used in biology
499(7)
23.1.1 Classical games, linearity on the left and replicator dynamics
499(2)
23.1.2 Strategies as a continuous trait and nonlinearity on the left
501(1)
23.1.3 Departures from infinite, well-mixed populations of identical individuals
501(2)
23.1.4 More complex interactions and other mathematical complications
503(1)
23.1.5 Some biological issues
504(1)
23.1.6 Models of specific behaviours
505(1)
23.2 What makes a good mathematical model?
506(2)
23.3 Future developments
508(5)
23.3.1 Agent-based modelling
508(1)
23.3.2 Multi-level selection
509(1)
23.3.3 Unifying timescales
509(1)
23.3.4 Games in structured populations
509(1)
23.3.5 Nonlinear games
510(1)
23.3.6 Asymmetries in populations
510(1)
23.3.7 What is a payoff?
510(1)
23.3.8 A more unified approach to model applications
511(1)
23.3.9 A more integrated understanding of the role of natural selection
511(1)
23.3.10 Integrating player and strategy evolution into evolutionary dynamics
511(2)
A Python 513(2)
Bibliography 515(76)
Index 591
Mark Broom is a professor of mathematics at City, University of London. For over 30 years, he has carried out mathematical research in game theory applied to biology. His major research themes include multi-player games, patterns of evolutionarily stable strategies, models of parasitic behavior (especially kleptoparasitism), the evolution of defence and signalling, and evolutionary processes in structured populations. He earned his PhD in mathematics from the University of Sheffield.







Jan Rychtá

is a professor of mathematics at Virginia Commonwealth University. Prior to joining VCU, he was a Professor at UNC Greensboro. He works on game theoretical models and mathematical models of kleptoparasitism. His recent research interests include mathematical biology and game theory. He earned his PhD in mathematics from the University of Alberta.