Lecture 9: Mathematical Insights Flashcards
inclusive fitness theory: WHO AND WHAT
Bill Hamilton 1964
–> every time individuals interact
Hamilton’s Rule =
behaviour favoured if c < br
- c = cost to actor
- b = benefit to recipient of social behaviour
- r = genetic relatedness between actor & recipient
- –> considered for when favoured by high/low relatedness
R really means =
likeliness to share allele
- parent –> Child = 0.5,, relatedness by decent
Cannibalism in Tiger Salamanders:
TS are more likely to develop into cannibals if they are in groups containing:
2 morphs cannibal&herbivore
- TS are more likely to develop into cannibals if they are in groups containing:
1) many conspecifics (same species)
2) variation in larval size
3) mostly unrelated individuals
Game theory originally developed by
John von Neumann in 1940’s
in biology what is game theory used for:
to investigate optimal sex ratios and group formation & animal behaviour
an equal sex ratio is an
Evolutionary stable strategy (ESS), cannot be invaded by a better strategy
-“nash equilibrium”
how does an equal sex ratio arise:
females biased pop benefit to have sons (sons can mate with more than 1 female) , male biased pop benefit to have daughters
example of genetically determined sex ratio’s being altered
Seychelles warblers (WZ in F, they're the heterozygous sex) -adjust sex ratio of their brood i response to territory quality
Hymenoptera and sex ratio:
HAPLODIPLOIDY;
males haploid, females diploid.
-female can decide whether to release sperm & egg / just egg
The Hawk-Dove Game:
- John Maynard-Smith
- Competition between to individuals, which is best? Hawk = fight if opponent fights, dove = share resource if opponent doesnt fight and retreat if they do
Hawk vs dove
hawk wins, dove loses everything
hawk vs hawk
wins half the time but pays cost of fight
dove vs dove
share
‘playing the field’ =
mother choosing sex of offspring, contestants all playing eachother
competition between paired opponent =
pairwise contests
dove common and hawk rare, can hawk invade?
if v >v/2 (v=value of resource) SO ALWAYS
hawk common and dove rare –> can dove invade?
only if cost > v
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
H-D-B Game outcome
Bourgeois always invades Dove
Bourgeois can invade Hawk and resists hawks if v
Bourgeois butterflies, speckled wood butterfly
can play both hawk and dove
- play hawk when resident/owner of sun patch
- if you remove owner, place new owner in sun patch, returning previous owner won’t stay
Rock-paper-scissors game, is a single strategy ESS possible?
NO, rock beats scissors, scissors beats rock etc
two possible outcomes of rock paper scissors game =
1/3 of each strategy, cyclical dynamics
male lizards play rock paper scissors: 3 strategies
1) large territory holders (orange throat)
2) sneakers (yellow stiped throat)
3) Defenders (blue throat)
male lizards play rock paper scissors: large territory holders
orange
-aggressive, hold a large territory with several females
male lizards play rock paper scissors: sneakers
mimic females and enter large territories for snaky matings
-yellow striped throat
male lizards play rock paper scissors: defenders
-blue throat
defend small territory with one female, can detect sneakers
both hawk and dove strategies in population = ___ ESS
mixed, when c>v
just hawk in population as dove cannot invade = ___ ESS
pure ESS when c
