Bionb2210_Assignment9 - BioNB 2210 – Introduction to...

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Unformatted text preview: BioNB 2210 – Introduction to Behavior Fall 2010 Discussion sections Assignment 9 – Modeling behavior – Before completing this week’s assignment, we strongly suggest that you work through the game theory tutorial that Professor Reeve mentioned in lecture, located at the following website: The exercises on the website should provide you with enough background knowledge about modeling to enable you to construct your own game theory models of behavior. You may also find it helpful to review your lecture notes and complete the problem set on game theory (posted on the course website) before attempting this week’s assignment. The goal of this week's assignment is for you to create a game theory model to represent the payoffs for two alternative mating strategies exhibited by a small shorebird known as the ruff (Philomachus pugnax). The strategies are described in the following paper, which is listed on the course website as an optional reading for this week's discussion section: Widemo, F. 1998. Alternative reproductive strategies in the ruff, Philomachus pugnax: a mixed ESS? Animal Behaviour, 56, 329 ­336. During the mating season, males gather on a display ground known as a “lek” and display to females, who choose which males to mate with on the basis of these displays. As described in the paper, male ruffs on leks exhibit one of two genetically ­determined alternative mating strategies. Independent males establish territories on the lek, display to females, and copulate with the females they attract onto their territory. Satellite males are not attractive to females and cannot obtain copulations on their own, but they can choose to “couple” with an independent, territorial male. When an independent has a “coupled” An “Independent” male ruff satellite, more females are attracted to his territory. However, displaying to females a coupled satellite can also steal some percentage of copulations with the females on the territory when the independent male is distracted. Your assignment for this week has three parts: 1) Create a payoff matrix to represent the payoffs to the independent (territorial) and satellite ruff males on a lek. 2) Beneath the payoff matrix, clearly define the meaning of any variables you used. 3) Use your payoff matrix to calculate the evolutionarily stable proportion of independents in this population in terms of the variables you’ve defined. BioNB 2210 – Introduction to Behavior Fall 2010 Discussion sections Helpful Hints: Variables: Before defining your variables, consider how the independent and satellite males interact with one another, and the ways in which they affect one another’s fitness. Aim for a maximum of three variables. Your variables should represent the values that would be most relevant to the interactions between the two types of ruff strategies. For example, in the hawk/dove game the interactions involve fighting over a resource, so the variables are V (value of the resource) and C (cost of injury). Think about what the important variables in the ruff game would be (NOTE: these will NOT be the same variables as in the hawk/dove game, because the nature of these interactions is different). Payoff matrix: When constructing your payoff matrix, think about what the payoffs would be in each type of interaction (Independents with Independents, Independents with Satellites, Satellites with Independents, and Satellites with Satellites). Remember that each element in your matrix represents the payoff to the row strategy playing against the column strategy. The aim of this model is to represent the effect of the ruffs’ coupling behavior, so for now please assume that males of the same type have no effect on one another. So, for example, the payoff for an independent playing against another independent can just be thought of as the payoff to a lone independent (without a coupled satellite). This assignment will be due at the start of section on October 26 ­28, 2010. You can choose to either type up your assignment or write it out neatly by hand. Please include your name and section time on your assignment. ...
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