Evolutionary Game Theory
1. The definition of ESS, basic assumptions, and definitions The problems of optimization for frequency dependent selection. The definition of strategy and the evolutionary stable strategy (ESS). Introduction of the classical Hawk-Dove game. Pure and mixed strategies, polimorph populations. The Bishop-Cannings theorem.
2. Games with more ESSs, games without ESS. The Hawk-Dove-Retailator model. Which ESS will become realized. The Rock-Scissors-Paper game, where ESS might be absent. Finding of ESS in a general symmetric matrix game.
3. The dynamical view: replicator dynamics The continuous and discrete replicator dynamics for pure strategies. Fixed points and their stability. Some simple mathematical examples. Replicator dynamics in the case of mixed strategies. Mathematical connections between the fixed points of replicator dynamics and the ESS.
4. Biological examples for the Hawk-Dove and the Rock.Scissors-Paper games. The behaviour of Uta stansburiana males and the Rock-Scissors-Paper game. The reproductive strategies of Uta stansburiana females and the Hawk-Dove game. Experiments on the E. coli tribes. The role of weak mixing on maintaining coexistence of tribes being in cyclical competition hyerarchy.
5. Frequency dependent selection in finite populations. The definition of ESS in finite populations. The Hawk-Dove game in finite populations. Mixed strategies and the polimorph population in finite populations. The definition of stochastic ESS. The stochastic replicator dynamics in finite populations.
6. Playing in the field The definition of ESSin the playing in the field situation. Seed-germination strategies and the frequency of sexes. When the 1:1 ratio can modify?
7. Asymmetrical matrix games Asymmetry in ownership. The description of the problem by bimatrix games. The Selten theorem. Biological examples. The role of estimation in solving conflicts. Biological examples for estimation. The sequential estimation game.
8. Web defense behaviour of the Agelenopsis aperta. More asymmetries in the conflict, observations and experiments. The analysis of the web defense behaviour by a simple game theoretical model.
9. Arms race. The masic model of arms race. Information transfer in the erms race model. The generalized arms race model. Asymmetrical arms race. Biological examples.
10. Communication among animals Why communication is honest? Fisher's theory, Zahavi's handicap principle. Experiments to verify the handicap principle. The Sir Philip Sydney game and the conditions for the honest signalling. Classification of biological signals. Definitions, and biological examples.
11. Adaptive dynamics, and some applications. The basic assumptions of adaptive dynamis. Convergence stability and ESS. Branching points in the evolution. Speciation in an adaptiv dynamical model.
12. Evolutionary games in spatially explicit models. General assumptions is spatial games. The Hawk-Dove game in grids. Comparison of classical and the spatially explicit models. The spatial Hawk-Dove-Retailator model. The sensitivity of the model to the update rules. Cost-free honest signalling in a spatial model.
13. Cooperation and reciprocal altruism. The problems of origin and evolutionary stability of cooperation and reciprocal altruism. Game theoretical models: prisoners' dilemma and the snowdrift games. Opportunities to solve the dilemma: the iterated prisoner's dilemma game, spatially explicit models. Biological examples.
14. Genetical constraints, phenotipical evolution. The problem of fitness maximization in diploid sexual populations. When evolutionary game theory applicable at one locus two alleles heritability system? When phenotypic evolution is in concordance with the genetical constraints: the streetcar theory.
Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K. and Walter, P.: Molecular Biology of the Cell, Taylor & Francis, 2014, ISBN 9780815344322