When sharing of maternal DNA is distinguished from sharing of paternal DNA, we proved in Section 5 that for each type of sib-pair
In this case, the second derivative of the transition matrix at 
is
hence the score statistic for each type of sib-pair is of the form
where 
is the number of sib-pairs (ASP, DSP or USP) sharing DNA IBD on i paternal and j maternal chromosomes, i,j= 0,1. Note that in general the score statistic is no longer independent of the genetic model.