RESOURCES, TERRITORIES & MIGRATION
• Competing for resources
o ESS theory:
Evolutionary game theory is the application of game theory to interaction-dependent
strategy evolution in populations
Why do we need game theory?
because the costs and benefits of actions often depend on the behaviour of other
individuals in the population
Key components of a game-theoretic model:
- Players: the participants of the game (two-player or multiple-players)
- Payoffs: the costs and benefits of actions
- Actions (or decisions): the option the animal can choose
- Decision mechanism: single or repeated; simultaneous or sequential
Given these components, game theoreticians are seeking the solution:
the evolutionarily stable strategy (ESS) – set of behaviours adopted by all players that
cannot be invaded by any alternative strategy that is initially rare
Hawk-Dove game
Two animals meet, and each want to access a resource with value V
The animals can either
- play Hawk, and attack the opponent and may gain the full resource (V)
attack, however, has a cost of injury C
- play Dove, and don’t fight over the
resource
Best strategy is frequency dependent
- only Dove in the population play Hawk
- only Hawk in the population play Dove
Hawk-Dove game
- probability, p, that an individual plays Hawk in the contest
The ESS depends on the values of V and C:
- p* = V / C when V<C
- p* = 1 when V≥C
, The Hawk-Dove game: examples
o Ideal free distribution
Ideal free distribution (Fretwell 1972)
- every individual is free to choose where to go
- no limit to the number of competitors
Predicted pattern
- the first arrivals go to the rich habitat
- by resource depletion, the more competitors lower the rewards per
individual
- so at point a the poor habitat will be equally attractive
- thereafter, the two habitats should both be filled so that the rewards
per individual are the same in each
Experimental tests of ideal free distribution model
(a) Sticklebacks (Milinski 1979)
- at time x, end B of the tank had twice the amount of food as end A
- at time y the profitabilities were reversed
Dotted lines indicate the number of fish predicted at end A, and the points and dark line
are the observed numbers (mean of several experiments)
(b) Ducks (Harper 1982)
• Competing for resources
o ESS theory:
Evolutionary game theory is the application of game theory to interaction-dependent
strategy evolution in populations
Why do we need game theory?
because the costs and benefits of actions often depend on the behaviour of other
individuals in the population
Key components of a game-theoretic model:
- Players: the participants of the game (two-player or multiple-players)
- Payoffs: the costs and benefits of actions
- Actions (or decisions): the option the animal can choose
- Decision mechanism: single or repeated; simultaneous or sequential
Given these components, game theoreticians are seeking the solution:
the evolutionarily stable strategy (ESS) – set of behaviours adopted by all players that
cannot be invaded by any alternative strategy that is initially rare
Hawk-Dove game
Two animals meet, and each want to access a resource with value V
The animals can either
- play Hawk, and attack the opponent and may gain the full resource (V)
attack, however, has a cost of injury C
- play Dove, and don’t fight over the
resource
Best strategy is frequency dependent
- only Dove in the population play Hawk
- only Hawk in the population play Dove
Hawk-Dove game
- probability, p, that an individual plays Hawk in the contest
The ESS depends on the values of V and C:
- p* = V / C when V<C
- p* = 1 when V≥C
, The Hawk-Dove game: examples
o Ideal free distribution
Ideal free distribution (Fretwell 1972)
- every individual is free to choose where to go
- no limit to the number of competitors
Predicted pattern
- the first arrivals go to the rich habitat
- by resource depletion, the more competitors lower the rewards per
individual
- so at point a the poor habitat will be equally attractive
- thereafter, the two habitats should both be filled so that the rewards
per individual are the same in each
Experimental tests of ideal free distribution model
(a) Sticklebacks (Milinski 1979)
- at time x, end B of the tank had twice the amount of food as end A
- at time y the profitabilities were reversed
Dotted lines indicate the number of fish predicted at end A, and the points and dark line
are the observed numbers (mean of several experiments)
(b) Ducks (Harper 1982)
