9: maths in behaviour Flashcards
what theory did W.D.Hamilton come up with, when and what was said about how social behaviour evolves?
inclusive fitness theory
1964
evolves so the individual values his neighbours fitness against his own
what are each of the component parts of hamilton’s rule and when is the behaviour favoured?
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
in terms of r, genetic relatedness, it is looking at how many what are shared?
alleles
what is r for:
a) siblings/offspring
b) aunts and uncles
c) cousins
a) 0.5
b) 0.25
c) 0.125
what is c and b for each situation?
a) give food to recipient
b) steal food from recipient
c) swim past recipient
a) c: + b: -
b) c: - b: -
c) c: 0 b: 0
when is giving food to a recipient only favoured by NS?
if received by kin so r is +ve
when is stealing food from a recipient only favoured by NS?
if actor steals from non kin r=0
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?
high relatedness
1 < 3r so the rule is satisfied as 1 < 1.5
if a recipient is cannibalised (-1 gain food and -10 die) what is the behaviour favoured by and is hamilton’s rule satisfied?
low relatedness
-1 < -10r
not satisfied as -1 < -5
how can cannibalism be considered a social action?
directed to members of the same species in the environment
in tiger salamanders when are groups more likely to develop into cannibals?
- many conspecifics
- variation in larval size
- mostly unrelated individuals
when was game theory first developed and what did John Maynard smith do in 1970s to do with it?
1940s
applied it to animal behaviour
in terms of sex ratios within game theory in general what is it better to produce?
an even sex ratio of daughters and sons
if more sons are being produced what is it better to produce?
more daughters so more grand offspring
what is an evolutionarily stable strategy, ESS?
- even sex ratio
- cant be invaded by another strategy
- nash equilibrium: beneficial to also produce even sex ratio if others are doing so
in terms of number of mates and offspring how does an even sex ratio population compare to a female biased population?
- even: 1 mate and n offspring
- female biased: 2 mates and 2n offspring
what do many animals such as humans have to as a proximate cause to determine sex and give an even sex ratio?
genetic mechanism such as XY chromosome
how do seychelle warblers determine the sex of their brood?
chromosomal determination and females adjust the ratio based on territory quality
how can hymenoptera females decide the sex of her offspring?
choosing whether to release sperm from storage organ after egg is laid to fertilise it or not
what is the honeybee conflict between mother queen and daughter workers over sex ratio?
workers cause female biased sex allocation ratio by killing male larvae and queen resists by laying fewer female eggs
in a male biased population if the daughter is producing more offspring than the son what should be done?
overproduce daughters to drive sex ratio back to even 1:1
at an even sex ratio what do sons and daughters give?
equal fitness returns
what did John Maynard Smith notice some contests take place between?
paired opponents such as if both competing for a resource
what are the 2 pairwise contests John Maynard smith looked at?
- hawk dove game
- hawk dove bourgeois game
in the hawk dove game what is the behaviour like for the hawk and dove?
hawk: never shares, always fights
dove: shares, retreats in fight
in the hawk dove game what are the pay-offs in the matrix?
value of resource =v
cost of fighting to loser = c
what is the pay off matrix in the hawk dove game when each is the focal individual:
a) hawk
b) dove
a) vs hawk= (v-c)/2
vs dove = v
b) vs hawk = 0
vs dove = v/2
what are the costs like in the hawk dove game
- hawk always wins but pays fighting cost
- dove never fights so no cost but shares so some pay off
what happens if the dove is common and the hawk is rare?
- hawk invades if v > v/2
- hawk has higher payoff than dove
what happens if the hawk is common and the dove is rare?
- dove invades if 0 > (v-c)/2
- invades if c > v
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?
- mixed ESS where both strategies are present and proportions depend on values of c and v
- pure ESS of hawks
in the hawk dove game what are each of these alternate roles?
a) retaliator
b) prober retaliator
c) bully
a) plays dove first then fights back
b) occasionally fights but will back down
c) always fights but will back down
what is the behaviour of the bourgeois?
will play as hawk when resident and dove when intruder
with bourgeois what does it do to hawk and dove populations in the resident wins scenario?
- dove always worse off as v>0
- can invade and be resistant to hawk if v < c
what is the bourgeois example for speckled wood butterfly? (3)
- 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
when looking at rock paper scissors game no single strategy ESS is possible so what are the 2 possible outcomes?
- 1/3 of each strategy
- cyclical dynamics
what is cyclical dynamics?
one strategy invades another and is then invaded by a third which in turn is invaded by the first
list the 3 male mating strategies/morphs described by John maynard smith for side blotched lizards as a rock paper scissors game example
- large territory holders: orange throat
- sneakers: yellow striped throat
- defenders: blue throat
what are features of the orange throat large territory holding lizards? (4)
- aggressive
- dominant
- attack other coloured males but not orange as much
- hold large territory with many females
what are features of the yellow striped throat sneaker lizards? (5)
- mimic females
- enter large territories to sneak mating
- dishonest signal
- can fool oranges
- hunted by blue males
what are features of the blue throat defender lizards? (3)
- defend small territory with 1 female
- can detect sneakers and hunt them
- oranges defeat them in attack
what sort of dynamic is the side blotched lizard example and what happens each year?
cyclical
proportion of each morph changes and one dominates each year
