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
