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Table of contents
Definitions
I Well mixed
1 Adaptation
1.1 Stochastic evolutionary models
1.1.1 Moran model
Genetic drift
Constant selection
1.1.2 Wright-Fisher model
1.1.3 Galton-Watson model
1.2 Time-scales
1.2.1 Fixation times
Fixation time in presence of selection
Fixation time in presence of genetic drift
1.2.2 Comparisons
A first comparison: selection vs drift
A second comparison: mutation vs selection
1.3 Speed of adaptation
The Gaussian shape of the travelling wave
1.3.1 Successional mutations
1.3.2 Clonal interference
1.3.3 Concurrent mutations
More involved calculations
1.3.4 Infinite population size
2 Population Temperature
2.1 Population as a thermal system
2.1.1 Detailed Balance
2.1.2 Glasses
Real glasses
Correlation
Trap model and ergodicity breaking
Canyon model
2.1.3 Coarse grained population dynamics
2.2 Population glass
2.2.1 Boolean satisfiability
Physical interpretation
2.2.2 M population, 1/M temperature
Correlations and the glass-phase transition
2.2.3 Test of detailed balance
Crooks relation
A test of the Crooks relation
2.3 Phenomenology of population thermodynamics
2.3.1 Kovacs effect
Memory effects
2.3.2 Parallel tempering
2.3.3 Rejuvenation in fluctuating environment
3 Coupled models
3.1 Fitness REM
3.1.1 REM
3.1.2 A single model
3.2 Interacting models
3.2.1 Two systems
A time-scale separation mechanism
Limited jumps
3.2.2 More systems
II Space and Mutation
4 Space as a limiting resource
4.1 Constant population size in space
The wandering island of individuals
4.2 Freely growing population
4.2.1 Drift in space
Linear front
Circular front
4.2.2 Deterministic growth
Linear growth
Circular growth
5 The selective effects of mutation
5.1 Mutational Eden Model
5.1.1 Active and inactive phases
5.1.2 Front properties
5.2 Selective advantage of stability in well-mixed
5.3 Selective advantage of stability in space
5.3.1 Speed of growth
Saturation effects
5.3.2 Mutation rate evolution
Conclusions
A Computations of the entropy
