L5

Question 1

Inclusive fitness theory: Hamilton’s rule

Answer 1

• Shifted focus away from individual to gene level
  -Individuals can gain fitness by assisting reproduction of close relatives
  -Animals expected to be more helpful to close relatives than non-relatives

Question 2

What is the equation for a favoured behaviour in Hamilton’s rule?

Answer 2

C - cost to actor of social behaviour
B - benefit to recipient of social behaviour
R - genetic relatedness between actor and recipient

sibling relatedness = 0.5

cost < r x b

Question 3

Examples of social actions and their cost and benefits, giving food to recipient

Answer 3

• C is positive as is B

Food is worth more to recipient than actor eg recipient could not find food and was hungry

Cost has to be less than benefit x relatedness for it to occur

Question 4

Cannibalism

Answer 4

• Cost to actor is negative
  -Benefit to recipient is also negative
• Recipient loses out

-For it to occur cost < r x b
- Favours little to no relatedness

Tiger salamanders are more likely to develop into cannibals if they are in groups containing:
- Many conspecifics (other salamanders)
- Variation in larval size
- Mostly unrelated individuals

Question 5

Game theory

Answer 5

• Optimal way to behave can sometimes depend upon other individuals

Eg time trial vs race

If others are producing sons (or daughters), it’s better to produce daughters (or sons) to maximise number of grand-offspring
If the sex ratio is even its better to produce an even ratio of sons and daughters

= evolutionary stable strategy (ESS)

Question 6

Evolutionary stable strategy (ESS)

Answer 6

If others are producing sons (or daughters), it’s better to produce daughters (or sons) to maximize number of grand-offspring
If the sex ratio is even its better to produce an even ratio of sons and daughters

Question 7

Sex ratios P1

Answer 7

• Two daughters each produce 4 offspring
  
  • Each matriarch female ends up with 8 grand offspring
    -If an equal sex ratio then each son will have one mate producing 4 grand offspring
  • 9 grand offspring again

Question 8

Sex ratios P2

Answer 8

If twice as many females, each son mates with two females producing twice as many grand offspring as daughters

If the sex ratio is male biased a female having daughters will have a higher fitness than the male having sons

Selection tends to favour an even sex ratio

Oscillation till equilibrium at an even sex ratio

Sons and daughters are equally as good at passing on genes

Question 9

Animal contests - Pairwise contests examples

Answer 9

-The hawk dove game
-Rock paper scissors game

Question 10

The hawk dove game

Answer 10

Two individuals contest ownership of a resource in pairs

Hawk- dove game

Hawk
* Never shares, always fights
* Big win vs large loss
* High risk

Dove
* Will share, never fights, retreat if opponent fights
* Low risk
* Never get whole resource
* Little gain

Question 11

Payoffs

value of resource = v
Cost of fighting to loser = c

Payoff matrix =

Answer 11

Payoff matrix

- Each dove gets half of resource

- Each hawk vs hawk wins half and loses half (v-c)/2

- Hawk gets entire resource vs dove, but pays a fighting cost against other hawks

- Dove gets nothing against a hawk but doesn’t incur a cost

- Dove shares so gets some pay-off against other doves

Question 12

Invasion of rare strategies

Answer 12

Lone dove strategy
* Doves payoff is nothing

Hawks is costly
- Dove invade when 0 is greater than doves cost
- Dove theory can invade population

Question 13

Hawk will:

Answer 13

• With a hawk population a dove can push population towards dove strategy
  • Doesnt have to be 50/50 for each strategy
  • Both strategies create evolutionary stability
  • We can get a pure ESS of hawks or invasion from both ends producing a mixed ESS

Question 14

Bourgeois

Answer 14

• Individual plays hawk when resident and dove when intruder
  
  • Resident wins (convention)
  • Bourgeois always invades dove
  • Bourgeois can invade hawk and resists hawks if v< c

Question 15

Bourgeois butterflies

Answer 15

Sit on sun spots waiting for females

Unoccupied spot they will take over it

Occupied spots they try and take it over

Resident always wins

Eg once owner is gone a new resident comes and will always win

Question 16

Rock paper scissors game

Answer 16

No single strategy ESS is possible

Proportions = 1

Two possible outcomes

⅓ each strategy
Or cyclical dynamics

Eg all rock ,

All scissors

All paper

Question 17

Rock paper scissors example in nature

Answer 17

Male side blotched lizards have 3 morphs each with a different mating strategy

1. Large territory holders
- Aggressive, hold a large territory with several females (orange throat)

2. Sneakers 
- Mimic females and enter large territories for sneaky matings (yellow striped throat)

3. Defenders
- Defend a small territory with one female, can detect sneakers (blue throat)

No single ESS, cyclical nature