9: maths in behaviour

Question 1

what theory did W.D.Hamilton come up with, when and what was said about how social behaviour evolves?

Answer 1

inclusive fitness theory
1964
evolves so the individual values his neighbours fitness against his own

Question 2

what are each of the component parts of hamilton’s rule and when is the behaviour favoured?

Answer 2

c= cost to actor of social behaviour + fitness is reduced
b= benefit to recipient + fitness increased
r= genetic relatedness between actor and recipient
c < br

Question 3

in terms of r, genetic relatedness, it is looking at how many what are shared?

Answer 3

alleles

Question 4

what is r for:

a) siblings/offspring
b) aunts and uncles
c) cousins

Answer 4

a) 0.5
b) 0.25
c) 0.125

Question 5

what is c and b for each situation?

a) give food to recipient
b) steal food from recipient
c) swim past recipient

Answer 5

a) c: + b: -
b) c: - b: -
c) c: 0 b: 0

Question 6

when is giving food to a recipient only favoured by NS?

Answer 6

if received by kin so r is +ve

Question 7

when is stealing food from a recipient only favoured by NS?

Answer 7

if actor steals from non kin r=0

Question 8

if food is given to a recipient (1 loss and 3 gain) what is the behaviour favoured by and is hamilton’s rule satisfied if r=0.5?

Answer 8

high relatedness

1 < 3r so the rule is satisfied as 1 < 1.5

Question 9

if a recipient is cannibalised (-1 gain food and -10 die) what is the behaviour favoured by and is hamilton’s rule satisfied?

Answer 9

low relatedness
-1 < -10r
not satisfied as -1 < -5

Question 10

how can cannibalism be considered a social action?

Answer 10

directed to members of the same species in the environment

Question 11

in tiger salamanders when are groups more likely to develop into cannibals?

Answer 11

• many conspecifics
• variation in larval size
• mostly unrelated individuals

Question 12

when was game theory first developed and what did John Maynard smith do in 1970s to do with it?

Answer 12

1940s

applied it to animal behaviour

Question 13

in terms of sex ratios within game theory in general what is it better to produce?

Answer 13

an even sex ratio of daughters and sons

Question 14

if more sons are being produced what is it better to produce?

Answer 14

more daughters so more grand offspring

Question 15

what is an evolutionarily stable strategy, ESS?

Answer 15

• even sex ratio
• cant be invaded by another strategy
• nash equilibrium: beneficial to also produce even sex ratio if others are doing so

Question 16

in terms of number of mates and offspring how does an even sex ratio population compare to a female biased population?

Answer 16

• even: 1 mate and n offspring

- female biased: 2 mates and 2n offspring

Question 17

what do many animals such as humans have to as a proximate cause to determine sex and give an even sex ratio?

Answer 17

genetic mechanism such as XY chromosome

Question 18

how do seychelle warblers determine the sex of their brood?

Answer 18

chromosomal determination and females adjust the ratio based on territory quality

Question 19

how can hymenoptera females decide the sex of her offspring?

Answer 19

choosing whether to release sperm from storage organ after egg is laid to fertilise it or not

Question 20

what is the honeybee conflict between mother queen and daughter workers over sex ratio?

Answer 20

workers cause female biased sex allocation ratio by killing male larvae and queen resists by laying fewer female eggs

Question 21

in a male biased population if the daughter is producing more offspring than the son what should be done?

Answer 21

overproduce daughters to drive sex ratio back to even 1:1

Question 22

at an even sex ratio what do sons and daughters give?

Answer 22

equal fitness returns

Question 23

what did John Maynard Smith notice some contests take place between?

Answer 23

paired opponents such as if both competing for a resource

Question 24

what are the 2 pairwise contests John Maynard smith looked at?

Answer 24

• hawk dove game

- hawk dove bourgeois game

Question 25

in the hawk dove game what is the behaviour like for the hawk and dove?

Answer 25

hawk: never shares, always fights
dove: shares, retreats in fight

Question 26

in the hawk dove game what are the pay-offs in the matrix?

Answer 26

value of resource =v

cost of fighting to loser = c

Question 27

what is the pay off matrix in the hawk dove game when each is the focal individual:

a) hawk
b) dove

Answer 27

a) vs hawk= (v-c)/2
vs dove = v
b) vs hawk = 0
vs dove = v/2

Question 28

what are the costs like in the hawk dove game

Answer 28

• hawk always wins but pays fighting cost

- dove never fights so no cost but shares so some pay off

Question 29

what happens if the dove is common and the hawk is rare?

Answer 29

• hawk invades if v > v/2

- hawk has higher payoff than dove

Question 30

what happens if the hawk is common and the dove is rare?

Answer 30

• dove invades if 0 > (v-c)/2

- invades if c > v

Question 31

in the hawk dove game what is the case if both the dove and hawk can invade and what is the case if only one of these are true?

Answer 31

• mixed ESS where both strategies are present and proportions depend on values of c and v
• pure ESS of hawks

Question 32

in the hawk dove game what are each of these alternate roles?

a) retaliator
b) prober retaliator
c) bully

Answer 32

a) plays dove first then fights back
b) occasionally fights but will back down
c) always fights but will back down

Question 33

what is the behaviour of the bourgeois?

Answer 33

will play as hawk when resident and dove when intruder

Question 34

with bourgeois what does it do to hawk and dove populations in the resident wins scenario?

Answer 34

• dove always worse off as v>0

- can invade and be resistant to hawk if v < c

Question 35

what is the bourgeois example for speckled wood butterfly? (3)

Answer 35

• play hawk when resident and dove if intruder
• if resident of one patch moved to another both residents will play hawk in escalated contest
• resident male will always win an encounter for sun patch over a non resident

Question 36

when looking at rock paper scissors game no single strategy ESS is possible so what are the 2 possible outcomes?

Answer 36

• 1/3 of each strategy

- cyclical dynamics

Question 37

what is cyclical dynamics?

Answer 37

one strategy invades another and is then invaded by a third which in turn is invaded by the first

Question 38

list the 3 male mating strategies/morphs described by John maynard smith for side blotched lizards as a rock paper scissors game example

Answer 38

• large territory holders: orange throat
• sneakers: yellow striped throat
• defenders: blue throat

Question 39

what are features of the orange throat large territory holding lizards? (4)

Answer 39

• aggressive
• dominant
• attack other coloured males but not orange as much
• hold large territory with many females

Question 40

what are features of the yellow striped throat sneaker lizards? (5)

Answer 40

• mimic females
• enter large territories to sneak mating
• dishonest signal
• can fool oranges
• hunted by blue males

Question 41

what are features of the blue throat defender lizards? (3)

Answer 41

• defend small territory with 1 female
• can detect sneakers and hunt them
• oranges defeat them in attack

Question 42

what sort of dynamic is the side blotched lizard example and what happens each year?

Answer 42

cyclical

proportion of each morph changes and one dominates each year