Competing for Resources Flashcards
Competition and Evolutionarily Stable Strategies
- When individuals compete, the best way for an individual to behave will depend on what its competitors are doing
- Payoffs for a given strategy are ‘frequency-dependent’
-Evolutionarily stable strategy (ESS): a strategy that, if all members of a population adopt, cannot be beaten by a different strategy
What is an evolutionarily stable strategy (ESS)?
- A strategy that, if all members of a population adopt, cannot be beat by a different strategy
- E.g. in a concert: sitting is not an ESS (because in a crowd of sitters, a stander can do better
- Standing is an ESS (once everyone stands, it doesn’t benefit anyone to sit)
- An ESS is not always what is best for everyone – it is what becomes fixed
The hawk-dove game
- Dove: never fights
- Hawk: always fights, can injure their opponents, sometimes get injured
- Winner gets 50 (V=50), Loser gets 0, Cost of injury is 100 (C=100)
- Assume: When a hawk meets a hawk, it wins half the time and gets inured half the time
- Hawks always beat doves
- Doves retreat when they meet a hawk
- When doves meet, they share the resources
Is either ‘hawk’ or ‘dove’ (or both) an ESS?
- Dove is not an ESS: dove-dove payoff is 25, and any mutant hawk in the population would spread (because hawk-dove = 50)
- Hawk is not an ESS: hawk-hawk is -25, and any mutant dove would do better because it retreats and gets 0, which is more than -25
- Each strategy does best when it’s relatively rare
What is frequency-dependent selection
Selection in favor of one strategy over the other depending on its frequency (rarity or commonness in the population)
Explain frequency-dependent selection for the hawk-dove game
- The equilibrium point exists for a population that is part dove and part hawk
- Where the average payoff for each strategy is equal, given the likelihood of encountering hawks and doves
- If the population strays from the equilibrium, one strategy will start to do better, increase in frequency and then suffer reduces success as a result –> back to equilibrium
What is the equilibrium point between? (hawk-dove game)
- h = proportion of hawks in the population, so the proportion of doves is 1-h
- Any payoff for a hawk is the payoff for each contest type x its probability
- h average = -25h + go(1-h)
- Payoff for dove: d average = 0h + 25(1-h)
- Solving for h in this equation yields h=1/2
- So this population will be stable (at its ESS) when it is half hawks and half doves
Can a population be half hawks and half doves?
1) This could be a polymorphic population, where half the individuals
play hawk all the time and half the individuals play dove all the time
2) The individuals themselves could adopt mixed strategies: a given
individual could be a hawk half the time, and a dove half the time
Other Considerations re: Hawk-Dove Games
-In the scenario we discussed, average pay-off per contest is 12.5, but if everyone was a dove, the payoff would be 25.
* ESS isn’t necessarily highest benefit, but the highest benefit strategy could be
“invaded” by a hawk
-We assumed V < C (benefits from winning < costs of injury)
* Often the case in nature
* But not always! When a resource is extremely valuable, competition should be fierce (willing to risk high C)
-Hawk-Dove games are overly simplistic
* There are often more than 2 strategies, strategies can vary within an individual, encounters don’t necessarily occur at random
The ideal free distribution
- Assume two habitats: one rich and one poor in resources
- Assume no territoriality and no fighting – each individual can exploit the habitat where it would achieve the highest pay-off/consume resources at a higher rate
- As more competitors occupy the resource-rich habitat, the resource will get depleted
- At a certain point, new arrivals will do better in the poorer-quality habitat
- Then, the two habitats should be filled such that the probability for an individual is the same in each one
Sticklebacks and the ideal free distribution
- Milinski put six sticklebacks in a tank
- Dropped prey items in: at one and, prey dropped in at twice the rate of the other end
- Where should the fish go? How many should go to each end?
- Fish distributed themselves according to the predictions from the Ideal Free Distribution
- Under any other distribution (say 3 on each side), one fish would profit from moving to the other side
Competition by resource defense: the despotic distribution
- Imagine the same habitats as before, but this time, assume territoriality/defense
- The first individuals to settle on the landscape establish territories and defend their resources
- Later arrivals must occupy the poor quality habitat even though they will do less well
- When the poor habitat fills up too, the latest arrivals may be excluded entirely
Which form of resource defense should an animal adopt?
- Some animals compete for resources by exploiting them more efficiently (e.g. the ideal free distribution)
- Some defend resources using territoriality and defense (e.g. the Despotic Distribution)
- The type of resource defense an animal should adopt depends on the resources ‘economic defendability’
-Defending a resource has costs and benefits
-Animals should be territorial whenever the benefits of territoriality are greater than its costs
Shared resource defense
-Pied wagtails patrol on a stretch of riverbank and eat insects that wash up on the shore
- Territory owners patrol and revisit each part of their territory every ~40 mins
- Some territory owners allow a second bird to be on their territory
- Each bird visits the stretch of territory approx every ~20 mins
- Cost: lower feeding rate for the territory owner
-Benefit: satellite bird helps chase away intruders, saving the territory owner defense time
- On days when a lot of insects wash ashore, the cost of sharing is low, favoring territory sharing
Strategies and morphologies in pied wagtails
- Pied wagtails can switch between ‘territory owner’ and ‘territory sharer’
- The tactic they employ shifts with environment
- However, in many cases, strategies are fixed within an individual (and don’t change with age)
- Genetic makeup -> morphology -> behavioral strategy
