Lecture 9 - Mathmatical and theoretical insights into animal behaviour

Question 1

what do you need to make predictions?

Answer 1

theory

Question 2

what is the inclusive fitness theory?

Answer 2

“The social behaviour of a species evolves in such a way that in each distinct behaviour-evoking situation the individual will seem to value his neighbours’ fitness against his own according to the coefficients of relationship appropriate to that situation.”

• underpins everything we do in animal behaviour

Question 3

who came up with the inclusive fitness theory?

Answer 3

w.d hamilton

Question 4

what is direct fitness?

Answer 4

increasing the reproductive success of the individual

Question 5

what is indirect fitness?

Answer 5

increasing the fitness of relatives

Question 6

what is hamiltons rule

Answer 6

behaviour is favoured if rb >c

Question 7

what do c, b and r stand for in hamiltons rule

Answer 7

c-‘cost’ to actor of social behaviour
b-‘benefit’ to recipient of social behaviour
r -genetic relatedness between actor and recipient

Question 8

would c and b be positive or negative when an individual gives food to a recipient

Answer 8

c is positive- as cost has increased

b is positive - positive because they benefit

Question 9

would c and b be positive or negative when an individual steals food from a recipient

Answer 9

c is negative - no cost because they gain food

b is negative - negative because they die

Question 10

what would the values of c and b be if they swim past a recipient

Answer 10

c is zero

b is zero

Question 11

describe an example of hamiltons rule for ‘helping’

Answer 11

Give food to recipient -
Actor recipient
1 (lose food) 3 (gain food) c is positive b is positive
1<3r

Question 12

would the behaviour of ‘helping’ be favoured by relatedness?

Answer 12

yes this behaviour is favoured by high relatedness.

e.g. if r = 0.5 (siblings or parent-offspring) then Hamilton’s rule is satisfied because 1 < 1.5

Question 13

what effect does the behaviour ‘cannibalism’ have on relatedness

Answer 13

Cannibalise recipient
actor recipient
-1 (gain food) -10 (die) c is negative b is negative
Hamilton’s Rule: -1 < -10rThis behaviour is favoured by low relatedness.
e.g. if r = 0.5 (siblings) then Hamilton’s rule is not satisfied because -1 > -5

Question 14

when are tiger salamanders more likely to develop into cannibals?

Answer 14

are more likely to develop into cannibals if they are in groups containing:

(1) many conspecifics
(2) variation in larval size
(3) mostly unrelated individuals

Question 15

what is the essence of game theory?

Answer 15

• normally when an individual makes a decision it is solely about their own behaviour
• the essence of game theory is that ‘your behavioural response should depend on what others in the population are doing’

Question 16

describe game theory in terms of sex ratios

Answer 16

If others are producing sons, it’s better to produce daughters as this will maximise number of grand-offspring.
If the sex ratio is even (1F:1M) it’s better to produce an even ratio of sons and daughters.
= Evolutionarily Stable Strategy (ESS)

Question 17

example of species that can choose which sex to produce?

Answer 17

• haplodiploidy in insects - fertilised eggs produce females and unfertilised produces males
• some reptiles produce different sexes depending on the temperature their eggs are incubated at

Question 18

has the ESS phenomena been seen in humans before?

Answer 18

after the world war the population was female biased - there was recorded a surge in baby boys then born

Question 19

what are the fitness values of the sexes at an even sex ratio?

Answer 19

At an even sex ratio sons and daughters give equal fitness returns. The even sex ratio is an:
Evolutionarily Stable Strategy (ESS)

Question 20

what effect does a female bias have?

Answer 20

then there is more females for the males to mate with so the sons can produce more offspring and is more valuable o the parent because they are passing on more of their genes and increasing fitness - therefore parents will want to produce more males and eventually the sex ratio will balance out - opposite for an excess of sons

Question 21

what theories did john maynard-smith introduce?

Answer 21

• game theory and pairwise interactions

Question 22

2 examples of pairwise contests

Answer 22

The Hawk-Dove Game

The Hawk-Dove-Bourgeois Game

Question 23

describe the hawk and dove in pairwise interactions

Answer 23

Hawk- Never shares, always fights

Dove - Will share, never fights, retreats if opponent fights

Question 24

what do you have to do modle the hawk dove theory

Answer 24

have to assign fitness pay off to each strategy
value of resource = v
cost of fighting to loser = c

Question 25

what is the pay off equation for a hawk v hawk

Answer 25

(v-c)/2

Question 26

what is the pay off equation for when a dove is a focal individual and its opponent is a hawk

Answer 26

0

Question 27

what is the pay off equation for when a hawk is a focal individual and a dove is the opponent

Answer 27

v

Question 28

what is the pay off equation for dove v dove

Answer 28

v/2

Question 29

which strategy is most successful between the hawk and the dove?

Answer 29

(ESS)- cannot be invaded by another strategy

• Hawk always wins against Dove, but Hawk pays a fighting cost
• Dove never fights so doesn’t pay a cost and always shares so gets some pay-off

Question 30

what happens when one of the strategies is rare?

Answer 30

• hawk can always invade if dove are common and hawk rare - v>v/2
• dove can invade is c>v i.e cost of fighting to loser is bigger than the resource value

Question 31

what does the hawk dove strategy help us to understand

Answer 31

why animals dont always fight for resources - it depends on the strategy of others

Question 32

when would you get a mixed ESS?

Answer 32

when a hawk can invade (v>v/2) and when a dove can invade (c>v) - if only one is true we get either a pure ESS of hawks or doves

Question 33

what is the hawk-dove bourgeois game?

Answer 33

Hawk- Never shares, always fights
Dove- Will share, never fights, retreats if opponent fights
Bourgeois- Plays Hawk when resident and Dove when intruder
- biologically sensible behaviour

Question 34

what is the outcome of the hawk-dove-bourgeois game?

Answer 34

• Bourgeois always invades Dove

- Bourgeois can invade Hawk and resists Hawks if v < c

Question 35

describe the bourgeois butterflies

Answer 35

• speckled wood butterflies territory are sun spots
• in a battle for territory the resident always wins
• when residents are removed and intruders take their sports once the old residents are re introduced the intruders continue to occupy the territory
• results show residents always win the contest because the territory is ephemeral (as soon as the sun moves the sun patch does)
• no point using allot of energy to win a patch that will soon be gone

Question 36

what is the ESS out come of rock paper scissors?

Answer 36

no single strategy ESS is possible

• two possible outcomes:
  1) 1/3 of each strategy
  2) cyclical dynamics

Question 37

describe rock paper scissors in side blotched lizards

Answer 37

Three male mating strategies

1. Large territory holders - aggressive, several females: orange throat
2. Sneakers- mimic females, enter large territories to sneak matings: yellow striped throat
3. Defenders- small territory with one female, can detect sneakers : blue throat
   - each year would have a different dominant strategy that isnt effective against one of the other types so the new strategy takes over = cyclic