Suppose that marker loci on different chromosomes are typed on two putative relatives. At locus i, let pij be the likelihood of the observed pair of phenotypes conditional on the relatives being in condensed identity state Sj . In the absence of inbreeding, only the states S7, S8, and S9 are possible. If we want to estimate the true relationship between the pair, then we can write the likelihood of the observations as L(∆) = 

i

(∆7pi7 + ∆8pi8 + ∆9pi9)

and attempt to estimate the ∆’s [11]. Describe an EM algorithm to find the maximum likelihood estimates. The value of L(∆) can be compared under the maximum likelihood estimates and under choices for the ∆’s characterizing typical relative pairs such as parent–

offspring, siblings, first cousins, and so forth. Discuss the merits and demerits of this strategy. For one objection, see Problem 2 of Chapter 5.