Lecture 9: Mathematical Insights

Question 1

inclusive fitness theory: WHO AND WHAT

Answer 1

Bill Hamilton 1964

–> every time individuals interact

Question 2

Hamilton’s Rule =

Answer 2

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

Question 3

R really means =

Answer 3

likeliness to share allele

- parent –> Child = 0.5,, relatedness by decent

Question 4

Cannibalism in Tiger Salamanders:

TS are more likely to develop into cannibals if they are in groups containing:

Answer 4

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

Question 5

Game theory originally developed by

Answer 5

John von Neumann in 1940’s

Question 6

in biology what is game theory used for:

Answer 6

to investigate optimal sex ratios and group formation & animal behaviour

Question 7

an equal sex ratio is an

Answer 7

Evolutionary stable strategy (ESS), cannot be invaded by a better strategy
-“nash equilibrium”

Question 8

how does an equal sex ratio arise:

Answer 8

females biased pop benefit to have sons (sons can mate with more than 1 female) , male biased pop benefit to have daughters

Question 9

example of genetically determined sex ratio’s being altered

Answer 9

Seychelles warblers (WZ in F, they're the heterozygous sex) 
-adjust sex ratio of their brood i response to territory quality

Question 10

Hymenoptera and sex ratio:

Answer 10

HAPLODIPLOIDY;
males haploid, females diploid.
-female can decide whether to release sperm & egg / just egg

Question 11

The Hawk-Dove Game:

Answer 11

• 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

Question 12

Hawk vs dove

Answer 12

hawk wins, dove loses everything

Question 13

hawk vs hawk

Answer 13

wins half the time but pays cost of fight

Question 14

dove vs dove

Answer 14

share

Question 15

‘playing the field’ =

Answer 15

mother choosing sex of offspring, contestants all playing eachother

Question 16

competition between paired opponent =

Answer 16

pairwise contests

Question 17

dove common and hawk rare, can hawk invade?

Answer 17

if v >v/2 (v=value of resource) SO ALWAYS

Question 18

hawk common and dove rare –> can dove invade?

Answer 18

only if cost > v

Question 19

Hawk-Dove-Bourgeois Game

Answer 19

Hawk = never shares, always fights 
Dove = will share, never fights, retreats if opponent fights 
Bourgeois = Plays Hawk when resident and Dove when intruder

Question 20

H-D-B Game outcome

Answer 20

Bourgeois always invades Dove

Bourgeois can invade Hawk and resists hawks if v

Question 21

Bourgeois butterflies, speckled wood butterfly

Answer 21

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

Question 22

Rock-paper-scissors game, is a single strategy ESS possible?

Answer 22

NO, rock beats scissors, scissors beats rock etc

Question 23

two possible outcomes of rock paper scissors game =

Answer 23

1/3 of each strategy, cyclical dynamics

Question 24

male lizards play rock paper scissors: 3 strategies

Answer 24

1) large territory holders (orange throat)
2) sneakers (yellow stiped throat)
3) Defenders (blue throat)

Question 25

male lizards play rock paper scissors: large territory holders

Answer 25

orange

-aggressive, hold a large territory with several females

Question 26

male lizards play rock paper scissors: sneakers

Answer 26

mimic females and enter large territories for snaky matings

-yellow striped throat

Question 27

male lizards play rock paper scissors: defenders

Answer 27

-blue throat

defend small territory with one female, can detect sneakers

Question 28

both hawk and dove strategies in population = ___ ESS

Answer 28

mixed, when c>v

Question 29

just hawk in population as dove cannot invade = ___ ESS

Answer 29

pure ESS when c