Positions of Yield Maxima

The position of the yield curve maximum, x, is obtained by setting the right-hand side of equation (19) equal to zero for solving x. Thus, x is given by the solution of 

For the doubly biphasic case LQk.LQm), rrii and ki are zero for all i 3. Under these conditions, equation (20) can be written explicitly in the form 

The straightforward radical solution of such a cubic quickly mires us in algebraic quicksand, and so we proceed by dealing first with the simpler nonlinear cases in which equation (22) can be reduced to linear or quadratic forms. 

For linear killing and quadratic mutation, we can put k2 and rrii equal to zero so that equation (22) reduces to 

for systems in which survival is exponential and mutation induction purely quadratic, the initial slope of the yield curve must be zero (because mi = 0), and the maximum yield occurs at twice the LD37. If these stringent conditions are not met, then macromolecular theories based on square-law frequency curves over limited dose ranges must be viewed with considerable skepticism. 

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