# Evolution

### Lecture 1. 11-12 Complexity Lecture Room

#### Introduction. Evidence for evolution. Fitness. Competition

### Lectures 2 & 3. 2-4 Room B1.01

#### Continuation of Competition and introduction to Genes and Genetics. Followed by computer practicals.

#### Computer Practicals using MATLAB

**Task 1**) Investigate the competition between two predator 'species' in the simple deterministic Lokta-Volterra model. Determine the long-term dynamics and the selection pressure on the two predator parameters.Extension a) Consider the dynamics when there is a trade-off between the two parameters. Investigate the ESS.

**Task 2**) Investigate the evolutionary dynamics in a simulation of the Lotka-Volterra model.

**Extension a**) You may wish to allow evolution of multiple parameters simulaneously.

**Extension b**) You may wish to consider predator and prey parameters to be linked, how does this interaction change the dynamics.

**Task 3**) For the Gene Dynamics model consider the dynamics of Haemophilia * W*=(0.1, 1, 1); Sickle-Cell Anaemia

**=(0.5 , 1.2, 1); and a Fatal dominant Mutation**

*W**W*=(0.5, 0.5, 1).

### Lecture 4. 11-12 Complexity Lecture Room

#### Game Theory. Two player games and dynamics.

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### Lectures 5 & 6. 2-4 Complexity Lecture Room

#### Sex and Speciation. Sexual selection. Males as parasites. Why sexual reproduction? How do new species arise?

#### Computer Practicals using MATLAB

**Task 4**) For the Pure Games model consider the dynamics of the Prisoner's Dilemma * W*=(1 0 ; A B) [where 1<A<2 and 0<B<1]; the Hawk-Dove model

*=(1 0; A B) [where A>1 and B<0]; the Self-Help Matrix*

**W***=(1 0; A B) [where 0<A<B]; and the Volunteer's dilemma*

**W***=(0 0; 1 A) [where A<-1].*

**W****Task 5)** For the Mixed Games model where individuals can play a mixture of strategies investigate the pair-wise invasibility plots for the models above; it may be easier to start with the Hawk-Dove model.

**Task 6**) For the simulation of the Mixed Games model, investigate the evolutionary dynamics of multiple 2-player games.

**Extension a**) You may wish to investigate the alternative piece of code that means each individual plays with just one other random individual before breeding. How does this change the behaviour and why.

**Task 7**) Using the simulation of Sexual Selection for a costly trait, explore the relationship between the ESS, the sampling of males (by females) and the cost of the trait.

**Extension a**) You may wish to investigate why the population is often driven extinct, and what can prevent this.

**Extenstion b**) You could think about adapting this model to capture the more complex senario where individuals have 'vigour' and females can either select for costly or uncostly traits.