3 Evolutionary Game Theory with notes .pdf
Transcript
3 Evolutionary Game Theory 23 Friday, 13 October 2023 3 Evolu(ona… 14:34 Evolutionary stable strategies derived fr rom game theory John maynard smith -the father of game theory in biology Talks about migrating geese and traits that are dictated by The decisions these geese make e.g where...
3 Evolutionary Game Theory 23 Friday, 13 October 2023 3 Evolu(ona… 14:34 Evolutionary stable strategies derived fr rom game theory John maynard smith -the father of game theory in biology Talks about migrating geese and traits that are dictated by The decisions these geese make e.g where they fly in pack enviromennt Biology game theory - organisms aren't trying to do a specific plan being selected based on what plan they follow. No teleology, no preconceived outcome Evolutionary stable strategy ( important ) strategy so that if all mem population adopt it, then no mutant could invade, by natural select Frequency dependence is central to these ideas that fitne their environment. is dictated by the others in their or path but are mbers of tion ess pay offs rely on own Frequency dependence is central to these ideas that fitne phenotype and other phenotype frequency in the environ others in a population Means they go around doing what's best for their own interes Things that seem no selfish may actually be selfish ess pay offs rely on own nment e.g. mimicry resembling sts Hawk dove game Hawkish ( aggressive ) versus dovish ( peaceful ) individuals Strategy within a species not different species Pay off matrix Values are called expectations = average outcome of battle Pay off matrix Values are called expectations = average outcome of battle These are average value pay offs e.g. doves half resources for d Top left - hawk meeting hawk = 0.5( V-C). Half the time individual gets resource and half times they pay Expectation is half time get V and half time get -C Dove can't be an ESS, as in population of all dove, when a haw doves. Because expectation of Hawk v dove is bigger than expectatio Hawk can be an ESS if hawk versus hawk expectation is above But if cost is bigger than value you get mixture of strategies. dove v dove the cost. wk comes, it does better than all on of Hawk v hawk e 0 e.g. value is bigger than cost But if cost is bigger than value you get mixture of strategies. You want each strategy to have equal fitness to keep To work out hawk fitness and dove you do this calculatio To work out their abundance P=probability of playing as a hawk or dove When value increases hawk favoured When cost increases dove favoured This has to be true to be stable because if decrease in the population. these mixed strategies on f not one will increase and one will decrease in the population. Types of reproductive strategies 1. Alternative strategies - P a p r v 2. Mixed strategies - Some times play 1 strategies sometimes play ano 3. Conditional strategies - Individuals don’t have a choice and forced into do circumstances - Best of a bad job - Phenotypic placisticy - Common Phenotypic plasticity is defined as the property of organisms to produce distinct phenotypes in response to environmental variation. other oing what they're doing due to Alternative reproductive strategy example Different colours go with different behaviours of lizard as shown o on side We see there is some heritability, some genetic polymorphism for See yellow fathers give yellow sons etc, we see it’s a genetic polym Far left shows amount of lizard morph in populati Far right diagram shows the fitness of different lizards When orange are common they hold big territory an mate without being seen As yellows accumulate, oranges hold smaller territor behaviour of yellows. Then blue takes over, and it be territory and then should be yellow again. It cycles of ratios of lizards in population this trait. morphism ion s against each other nd yellows can come sneak in and ry's which are resistant to sneaky ecomes correct to hold bigger This is a diagram showing the cycling what morph of lizard is co ommon in population Conditional strategy example - cooperative breeders In winter the birds go arouind together and autumn form The birds are susceptible to nest destruction and predatio Birds can go on and build their own nest ( but now in spring characteristics ) and raise own chicks ( costly ) Or can join in another nest - normally a close relative, help all energy costs m pairs and nests on g its not such good nesting raise offspring. Don’t have to do More surviving relatives by doing this. You can model success You can model success Breeding is generally best strategy than helping, but isn't consis When predation occurs, benefit of breeding reduces. Period of time about April where breeding is really goo should go help relatives Seen in birds, that those nests destroyed in April they closer to may birds re nest less and less Following strategy to get best they can, and this is forc circumstances , which makes it conditional strategy. Lrs = number of chicks raisedn Individuals that never have own chick is 0.2, which sh stent od, but after ( closer to may ) keep re-nesting, but as you get ced onto them by predation hows its not great to do It, but it is Individuals that never have own chick is 0.2, which sh best of a bad job. hows its not great to do It, but it is Every genetic contribution from male and female is equal to pro More females than males in an example here 2:1, each ma Reproductive success of males is higher than females. Prod will spread in population oduce offspring. ale will mate with 2 females. ducing sons is now favourable and More females than males in an example here 2:1, each ma Reproductive success of males is higher than females. Prod will spread in population Example in colours if you have 2 males and 1 female. T male produces 2 kids ) compared to Having two females and a male you only produce 4 kid Which is worse Sex ratio is an evolutionary stable state Evidence for this? ale will mate with 2 females. ducing sons is now favourable and These three produce 5 kids (.1 ds. Example of Sex ratio under selection Atlantic silverside Big variation of temperature of where they live up Atlantic c Party genetic partly environment sex determination Brought fish in different locations along Atlantic coast. South - sensitive to temperature Brought to North where sex ratio was genetically determine Reared young in lab and found in south carolina fish, and all 50:50 sex ratio - genetically determined 50:50 ratio as the te affect coast, ed. l cases really moved towards emperature and place has no The rules diploid species Nucleus has to be in control of sex determination Costs and benefits of sexes are equal Sex ratio evolution Parasitoid wasps Can control sex ratio by decided to birth diploid females or ha aploid males. Sex ratio evolution Parasitoid wasps Can control sex ratio by decided to birth diploid females or ha Wasps take into account local competition on hosts. Normally lay lots of female eggs as few males fertilise lots of e When lots of females laying eggs on host, they change sex rat competitions for daughters. Becomes more worthwhile to lay Female offspring stay at home to help parents Strong suggestion that vertebrates can control sex ratio Cooperative breeder Female offspring help parents to raise kids In high quality territories (non salty middle of island ) - helper Low quality territories (salty coastal areas - helpers decrease aploid males. eggs tio, where there will be males y more male eggs Live on island where there are differences in terrory quality, Good quality territory on inside and bad on outside of island rs increase success success by eating food sources In high quality territories (non salty middle of island ) - helper Low quality territories (salty coastal areas - helpers decrease In different quality territory; In high quality sex ratio bias to make female eggs ( to help t In low quality sex ratio bias to make more males ( so that h Prisoners dilemma rs increase success success by eating food sources this ) herlpers don’t stay and reduce help ) Prisoners dilemma pay off matrix for cooperating and defecting If you play once - you should always defect If its iterated the best thing to do is tit for tat strategy pay outs If its iterated the best thing to do is tit for tat strategy Example of vampire bats They need to feed on a nightly basis, as they have high metabo But they can beg for blood meals from others to stay alive for o Note that when you are really hungry or starved a little bit of b olism, or starve to death one night blood gives you large weight gain. But they can beg for blood meals from others to stay alive for o Note that when you are really hungry or starved a little bit of b Also kin selection pay a roll - you are far more likely to help som but However, the most likely factor to weather you will receive Is actually if you have had received blood from a bat before Kin selection doesn’t play that strong of a role in if one night blood gives you large weight gain. meone related to you, due to kin selection e food, e f you get blood or not
