= Score equation for a phase-averaged linkage likelihood
For a known-phase contribution $L_1(\theta)\propto\theta^{r_1}(1-\theta)^{m_1-r_1}$ and an independent phase-averaged contribution $L_2(\theta)$, an interior maximum satisfies
$$
[r_1-m_1\theta]L_2(\theta)+\theta(1-\theta)L_2'(\theta)=0.
$$
This follows by differentiating $\log L_1+\log L_2$ and multiplying by $\theta(1-\theta)L_2$. The constrained <maximum-likelihood estimate> on $[0,1/2]$ must also be compared with the endpoints. An interior root cannot be asserted without the observed pedigree counts; complete nonrecombinant data, for example, have their maximum at zero.
// Target: biology.bigb
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