Ben Hatchwell's lectures Flashcards
W. D. Hamilton’s … … 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 neighbour’s fitness against his own according to the … of relationship appropriate to that situation” - 1964
inclusive fitness, coefficients
The essence of inclusive fitness theory is that individuals can gain fitness in two ways:
- by … themselves (direct fitness)
- by interacting with …. (indirect fitness)
reproducing, relatives (because of shared genetic interest)
Hamilton’s rule: A behaviour will be favoured if … < …
c, br
c =
cost to actor of social behaviour
b =
benefit to recipient of social behaviour
r =
(coefficient of) genetic relatedness between actor and recipient
- not simply shared genetic material, but sharing of genes that are identical by descent (probability of sharing the same allele)
Between parent and offspring r = …
Between siblings r = …
Between uncles and nephews r = …
Between half siblings r = …
Between cousins r = …
0.5, 0.5, 0.25, 0.25, 0.125
Look at slide 11:35 lecture 9
stuff about when c and b are positive/negative
Look at cannibalism slide in phone folder
nice
Tiger salamanders are more likely to develop into cannibalistic morphs if they are in groups containing:
- … conspecifics
- variation in … size
- mostly … individuals - most relevant part to Hamilton’s rule
many (as not even many individuals around to eat and more likely to be related), larval (as females lay many eggs in one go, relatedness is less likely if larvae vary a lot in size as it is likely they have come from different females), unrelated
Game theory: an individual’s behavioural response should depend on the…
behaviour of the individuals around them in the population
An e.g. of game theory is shown in … …: if others are producing sons, it’s better to produce … as this will maximise the number of …-…. If the … … is even, it’s better to produce an even ratio of sons and daughters. This is called an Evolutionary … … (ESS), as it cannot be invaded by a better strategy - Nash equilibrium
sex ratios, daughters, grand-offspring, sex ratio, stable strategy
Hymenoptera females can choose the sex of their offspring as they are …. If they lay a fertilised egg it develops into a …, if they lay an unfertilised egg it will develop into a ….
haplodiploid, female, male
At an even sex ratio sons and daughters give equal … returns. The even sex ration is an ESS. If there is an excess of females in a population then the number of grand-offspring gained per … is greater than the number of grand-offspring gained per …, so a female should over-produce …, driving the population towards…
fitness, son, daughter, sons, a 1:1 sex ratio
- and vice versa
John …-… was a mathematical biologist who was instrumental in introducing the idea of game theory into biology.
Maynard-Smith
The two pairwise contests we will look at are:
- The Hawk-Dove game
- The Hawk-Dove-Bourgeois Game
The Hawk-Dove game imagines that each individual in a population plays one of two strategies. Animals compete for resources in pairs. A Hawk never … and always …, and a dove will …, never … and … if an opponent fights.
share, fights, share, fights, retreats
In this model we must assign fitness payoffs:
v = …
c = …
the value of a resource that is being competed for
the cost of fighting to the loser
We can then put these into a payoff …
matrix
Watch lecture 9 32:00 - 33:55
about hawk-dove matrix
When a hawk comes across a hawk what is the payoff?
(v-c)/2
When a hawk comes across a dove what is the payoff?
v
When a dove comes across a hawk what is the payoff?
0
When a dove comes across a dove what is the payoff?
v/2
Given these payoffs what is the most evolutionary stable strategy? You’d initially assume the hawk strategy as the payoffs look more likely to be high. But it is not that simple. Hawk always wins against Dove, but pays a fighting cost. Dove never fights so doesn’t pay a cost and always shares so it gets some payoff.
If we imagine a population entirely made of doves in which rare mutant hawk strategist arises. Can the hawk invade this population?
The hawk easily invades if v > v/2 (i.e. always)
If we imagine a population made entirely of hawks in which a rare mutant dove strategist arises, can the dove invade?
Dove invades if 0 > (v - c)/2 (i.e. if c > v)
may arise if fighting is very costly
- Hawk can invade a population of Doves if v > v/2
- Dove can invade a population of Hawks if c > v
If 1 and 2 are both true, we get…
invasion from both ends: a mixed ESS, where the payoff of both strategies is equal
(see photo on phone)
If only 1 is true then we get…
a pure ESS of hawks
If only 2 is true then we get…
a pure ESS of doves
Animals don’t necessarily compete for resources as it is not always going to pay off to do so - depends on the strategy that other individuals in the population are adopting, what the costs of competing are, and what the value of the resource that they are competing for is.
Summary innit
John Maynard-Smith also considered another “game”, which he called the Hawk-Dove-Bourgeois game. In this game the Bourgeois is introduced, who…
plays Hawk when resident and Dove when intruder
The outcome of the Hawk-Dove-Borgeois game is the “… …” convention. Bourgeois always invades …, and can invade … and resists Hawks if …
resident wins, dove, hawk, v < c
This rule of … winning does seem to be the case in natural systems
residents
Speckled Wood butterflies: sit on sun patches on the floor of the wood. Periodically, males that are flying around in the canopy will come down towards a sun patch and, if the patch is already occupied by another speckled wood, they will have a brief … flight and the … will always win that brief encounter. The … will retreat to the canopy.
spiral, resident, intruder
In an experiment, residents were removed from sun patches, allowing … to now settle on this territory. The previous residents were then released back onto the territory, and the … resident always won this time. The convention is that … always win the contest, even if the intruder was a previous resident.
intruders, new, resident
Why is this?
Sun patches are a very low value resource as they are ephemeral, so it is not worth wasting energy resources fighting for it.
read handout for lecture 9
goop
Another “game” is the rock-paper-scissors game, which has a … dynamic consisting of 3 strategies. No single strategy … is possible. The ESS for this game is for…
cyclical, ESS, everyone to play rock, paper and scissors with equal frequency
There are two possible ways in which this ESS can be achieved:
- Everyone has an equal probability of playing each strategy at any one time
- Time lag in payoffs of playing particular strategies (cyclical dynamics, where majority play rock, then scissors, then paper etc.)
An example of a rock-paper-scissors game in nature is in side-blotched lizards. There are 3 male mating strategies:
- Large territory holders: … throat
- …: yellow striped throat
- Defenders: … throat
orange, sneakers, blue
Large territory holders are … and hold a large territory that typically has several … living within it.
Sneaker males mimic … and enter large territories for sneaky matings.
Defenders defend … territories with … … … and, because they are only defending this, they are very good at detecting ….
aggressive, females, females, small, one single female, sneakers
The frequency of each morph of male over a succession of years was recorded by Sinervo and Lively (1996), and they found that the population started from a high frequency of … … in one year, but these individuals are susceptible to … … …, so the following year these were most common. These are susceptible to … … … so the following year there was a higher proportion of these, and the following year after that there were more … etc.. This was followed for two whole cycles, showing the cyclical dynamics of this rock-paper-scissors system.
blue defenders, large territory holders, yellow striped sneakers, defenders