Frequency Dependent Selection (Game Theory)

Question 1

why is fitness not a fixed value for a certain genotype?

Answer 1

• genotypes can respond differently in different environments
• genotypes can have a greater fitness dependent on their frequency

Question 2

when does frequency dependent selection occur?

Answer 2

when genotypes have a smaller of greater fitness dependent on their frequency within the population

Question 3

what is positive frequency dependent selection? and give an example

Answer 3

when common genotypes are selected for- when venomous snakes are common the predator population has been trained to not eat them so there fitness increases

Question 4

what is negative frequency dependent selection? give an example

Answer 4

when low frequency phenotypes are selected for- this occurs with species that mimic venomous species such as the mimicry butterfly that looks like heliconius - when the mimicry is rare the predators have mostly been exposed to venomous so are tricked but when mimicry are common the predators haven’t met poisonous

Question 5

what occurs when positive frequency dependent selection is occurring on two morphs?

Answer 5

both morphs increase in fitness as they increase in frequency - this can be seen in the Mullerian Mimicry of two species of butterflies which are both poisonous and therefore the more one is present the scared predators are, so high amounts of both are good

Question 6

what occurs when positive frequency dependent selection is occurring on two morphs?

Answer 6

both morphs increase in fitness as they increase in frequency - this can be seen in the Mullerian Mimicry of two species of butterflies which are both poisonous and therefore the more one is present the scared predators are, so high amounts of both are good - H. erato and H. melpomene show spectacular parallel geographic variation.

Question 7

what is the evolutionary equilibrium when 2 morphs are ensuring positive frequency dependent selection?

Answer 7

the point of neutrality is when both morphs have the same fitness and in theory this should be evolutionary equilibrium but it is unstable. as soon as it is perturbed by e.g genetic drift then the majority one goes into fixation

Question 8

what is the point of neutrality like in negative frequency dependent selection based populations witth two morphs

Answer 8

very stable- if one because less common and more fit, it will be selected for more, increasing number in population and brought back to equilibrium

Question 9

what does negative frequency dependent selection maintain?

Answer 9

genetic polymorphism

Question 10

what is an example of negative frequency dependent selection?

Answer 10

sex ratio (proportion of males to females):

• fitness= the proportion that a genotype contributes to the next generation relative to the other genotype
• populations typically have a 1:1 ratio
• when there are less males to females, the proportion of males that are contributing to offspring is higher than the proportion of females which is contributing to offspring so they have a great fitness. ( to produce a zygote you need a male and a female)

Question 11

what does the maintenance of the sex ratio cause in terms of allelic selection?

Answer 11

alleles which cause their bearers to invest equally in sons and daughters will not be replaced by alleles that bias the sex ratio - grandparent examples

Question 12

what is sex ratio an example of?

Answer 12

evolutionary stable strategy

Question 13

what does the maintenance of the sex ratio cause in terms of allelic selection?

Answer 13

alleles which cause their bearers to invest equally in sons and daughters will not be replaced by alleles that bias the sex ratio - the number of offspring per male is greater that the number of offspring per female

Question 14

what is sex ratio an example of? and why?

Answer 14

evolutionary stable strategy because it can’t be invaded by another mutated ratio

Question 15

what is the definition of an evolutionarily Stable Strategy?

Answer 15

if all the members of a population adopt it, then no alternative mutant strategy can invade under the influence of natural selection.

Question 16

who first postulate the concept of an ESS and why?

Answer 16

john maynard smith- wondered why animals performed postured fake fights rather than actually fighting

Question 17

what are the two players in a simple evolutionary game theory?

Answer 17

hawk and dove. hawk always fights until it wins or until it is s onerously injured that it cannot continue

dove only threatens and runs away if opponents shows any sign of real aggression- never gets injured but wastes time

Question 18

how does evolutionary game theory work?

Answer 18

when two strategy meets there are pay off associated with victory or injury- these payoffs are related to fitness and determine the success of the player in contributing to th next generation of the game. you then obtain average payoffs for each type of confrontation- you then find an uninvadable strategy for a population

Question 19

what if both strategies can invade each other?

Answer 19

then there can be a mix of strategies

Question 20

construct a table of payoffs for a hawk and dove strategy. when injury = -20, victory= +10 and time wasting= -3. determine what the ESS is

Answer 20

find it is mixed so you must find the optimum frequency of each if you assign the ESS frequency of HAWK as X and and the ESS frequency of dove to be Y then:

• hawk receives a payoff of -5 at X and +10 at Y = -5x+10Y
• dove receives payoff of 0 at X and +2 at Y so = 2y
• +5X+10Y=2Y
• 5x=8y
• swap it round so 8/13 hawks and 5/13 doves

Question 21

what does evolutionary game theory evaluate the importance of?

Answer 21

resource value and cost of injury

Question 22

are there examples of animals adjusting their strategy when resource value and the cost of injury vary?

Answer 22

• red spotted newt: larger females show high fecundity so males will wrestle with each other for longer when the females are bigger (bigger payoff for winning) - they show more hawkish behaviour if resource value is higher
• atlantic salmon- once they enter the freshwater to breed they won’t return so there is a low cost of injury so they fight more- more hawkish behaviour when cost of injury is low
• the same can be seen in fig wasps who once mate, don’t continue living

Question 23

when does hawkish behaviour general increase in animals?

Answer 23

when cost of injury is low or payoff of winning is high

Question 24

give an example of a mixed hawk and dove strategy in nature

Answer 24

Red Deer stags compete for the attention of hinds (females) and defend the hinds that they have successfully attracted. The dominant stag may be approached by rival males who wish to claim the hinds that the dominant male has attracted. A small, young male may only posture and “roar” before running away due to a lack of confidence in his ability to successfully fight the dominant male. These males show a dove strategy. However, stronger males will embark on a fight with the dominant stag in order to gain access to the herds of females that he is guarding. These stags show a hawk strategy.

Question 25

what is the bourgeois strategy?

Answer 25

when an individual owns a resource it will fight like a hawk to defend it but when an individual doesnt own it, it will act as dove - this shows a respect for ownership - ownership conventions

Question 26

what does ownership convention mean?

Answer 26

there is respect for owners of a resource - show dovish behaviour

Question 27

what explanation can you give for the bourgeois strategy?

Answer 27

perhaps when individuals own a resource they have already fight for it so are likely to be very strong and not a good idea to fight
- also when the payoff of winning is low- perhaps the probability of finding the resource elsewhere is high

Question 28

give an example of the bourgeois strategy in nature

Answer 28

speckled wood butterflies. These butterflies protect areas of sunlight when they are searching for mates. When an intruder approaches the owner and intruder participate in a spiral flight in which the owner of the light patch always wins. The fact that these sunlight patches are transient means that the reward of obtaining one is fairly low and therefore the initiation of a fight by an intruder would not be worth the potential cost of injury.

Question 29

how do you construct a bourgeois pay for table?

Answer 29

payoff to hawk when meets a B = 0.5 x HH and 0.5HD
payoff to dove when meets a B = 0.5 X HD and 0.5DD
payoff to b when meets a H = 0.5 x HH + 0.5DH
payoff to b when meets dove= 0.5HD + 0.5 DD
payoff to b when meets b= 0.5+x HD + 0.5 x DH

Question 30

give an example of ownership conventions in nature

Answer 30

lion prides- other males respect the male lion of a pride

Question 31

what is evolutionary game theory used to do?

Answer 31

ESS models can’t tell us what strategies will evolve just what strategy will be stable given a define set of alternatives. can obtain an insight into the likely evolution of animal interactions - can be used to see if a mutation bringing about large beetles will invade small beetles etc- can see whether a mutation will become fixed

Question 32

what a beetle example of evolutionary game theory?

Answer 32

small beetles wt, large beetles mutates, large beetles out compete small beetles for food but maintaining a large body size is costly on metabolism and need more food source so work out the pay offs

Question 33

explain in what situation a bourgeois strategy will invade?

Answer 33

is the ESS when C>V, in an environment where there are no so called desperados. These are individuals who are doomed to not reproduce unless they fight. When this is not the cause: non-owners can hope that ther situation will improve. This may be the case if the chances of finding a vacant resource is high or in the case of a juvenile who hopes to gain more experience and therefore increase his resource holding potential. Therefore, the B will be the ESS when the resource in question forms only a small part of lifetime fitness.

Question 34

give an example of a reason why owners may fight for longer for a territory?

Answer 34

• tarantula- correlation between how long one has owned a breeding area and how hard it will defend it