graph the CSS

graph the CSS - ai =. ares =. astar =. R =. Wi =. Cd =....

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ai = . ares = . astar = . R = . Wi = . Cd = . Noffspring = . Variables are defined as in class, except that Noffspring is the number of offspring produced by each females. As you will see, this is a constant, and drops out of the solution. This is Fisher's sex allocation problem. We what to show that the solution ares=1/2 is a CSS. Wi = Noffspring R H 1 - ai L Cd + R H ai L Cs H 1 - ares Cd H ares Cs Noffspring H 1 - ai L R Cd + ai H 1 - ares L R ares Cd Firstder = D @ Wi, ai D Noffspring - R Cd + H 1 - ares L R ares Cd Now we want to determine the effect of ares on the firstderivative in order to evaluate convergence stability. Note that the first derivative is equal to zero at ares = 1/2. Also note that the slope is negative at that point. Hence, the solution ares=1/2 is con- vergence stable. That means that if the population is away from ares=1/2, mutants that are closer to 1/2 will be favored by selection, and the population will converge on the equilibrium of one half.
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Noffspring = 5; R = 1; Cd = 1 ê 10; Firstder
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graph the CSS - ai =. ares =. astar =. R =. Wi =. Cd =....

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