Lecture 9 - Mathmatical and theoretical insights into animal behaviour Flashcards
what do you need to make predictions?
theory
what is the inclusive fitness theory?
“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
who came up with the inclusive fitness theory?
w.d hamilton
what is direct fitness?
increasing the reproductive success of the individual
what is indirect fitness?
increasing the fitness of relatives
what is hamiltons rule
behaviour is favoured if rb >c
what do c, b and r stand for in hamiltons rule
c-‘cost’ to actor of social behaviour
b-‘benefit’ to recipient of social behaviour
r -genetic relatedness between actor and recipient
would c and b be positive or negative when an individual gives food to a recipient
c is positive- as cost has increased
b is positive - positive because they benefit
would c and b be positive or negative when an individual steals food from a recipient
c is negative - no cost because they gain food
b is negative - negative because they die
what would the values of c and b be if they swim past a recipient
c is zero
b is zero
describe an example of hamiltons rule for ‘helping’
Give food to recipient -
Actor recipient
1 (lose food) 3 (gain food) c is positive b is positive
1<3r
would the behaviour of ‘helping’ be favoured by relatedness?
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
what effect does the behaviour ‘cannibalism’ have on relatedness
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
when are tiger salamanders more likely to develop into cannibals?
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
what is the essence of game theory?
- 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’
describe game theory in terms of sex ratios
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)
example of species that can choose which sex to produce?
- 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
has the ESS phenomena been seen in humans before?
after the world war the population was female biased - there was recorded a surge in baby boys then born
what are the fitness values of the sexes at an even sex ratio?
At an even sex ratio sons and daughters give equal fitness returns. The even sex ratio is an:
Evolutionarily Stable Strategy (ESS)
what effect does a female bias have?
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
what theories did john maynard-smith introduce?
- game theory and pairwise interactions
2 examples of pairwise contests
The Hawk-Dove Game
The Hawk-Dove-Bourgeois Game
describe the hawk and dove in pairwise interactions
Hawk- Never shares, always fights
Dove - Will share, never fights, retreats if opponent fights
what do you have to do modle the hawk dove theory
have to assign fitness pay off to each strategy
value of resource = v
cost of fighting to loser = c
what is the pay off equation for a hawk v hawk
(v-c)/2
what is the pay off equation for when a dove is a focal individual and its opponent is a hawk
0
what is the pay off equation for when a hawk is a focal individual and a dove is the opponent
v
what is the pay off equation for dove v dove
v/2
which strategy is most successful between the hawk and the dove?
(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
what happens when one of the strategies is rare?
- 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
what does the hawk dove strategy help us to understand
why animals dont always fight for resources - it depends on the strategy of others
when would you get a mixed ESS?
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
what is the hawk-dove bourgeois game?
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
what is the outcome of the hawk-dove-bourgeois game?
- Bourgeois always invades Dove
- Bourgeois can invade Hawk and resists Hawks if v < c
describe the bourgeois butterflies
- 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
what is the ESS out come of rock paper scissors?
no single strategy ESS is possible
- two possible outcomes:
1) 1/3 of each strategy
2) cyclical dynamics
describe rock paper scissors in side blotched lizards
Three male mating strategies
- Large territory holders - aggressive, several females: orange throat
- Sneakers- mimic females, enter large territories to sneak matings: yellow striped throat
- 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
