Derivation of the Incomplete Dominance case of the General Selection Model

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 Given:    genotype:      AA          AB         BB
            phenotype:      W₀       W₁       W₂
                     or           1-s₁       1         1-s2

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  Recall from the numerator of the General Selection Equation that

       q     [(q)(W₂ - W₁) + (p)(W₁ - W₀)] 

 So, to find q at equilibrium () (read as, "q hat") where  q = 0

 set     0   = [(q)(1 - s₂ - 1) + (p)(1 - 1 + s₁)]
        
             = -s₂q + s₁p

             = s₁(1 - q) - s₂q

             = s₁ - s₁q - s₂q

  Then    s₁ = s₁q + s₂q = (q)(s₁ + s₂)

   and    =  (s₁)/(s₁ + s₂)

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Med6390 homework: re-derive the above for "p" at equilibrium 

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Text material © 2004 by Steven M. Carr

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