Efficient computation of lod scores: genotype elimination, genotype redefinition, and hybrid maximum likelihood algorithms.

Calculation of multilocus lod scores presents challenging problems in numerical analysis, combinatories, programming, and genetics. It is possible to accelerate these computations by exploiting the simple pedigree structure of a CEPH-type pedigree consisting of a nuclear family plus all four grandparents. Lathrop et al. (1986) have done this by introducing likelihood factorization and transformation rules and Lander & Green (1987) by the method of 'hidden Markov chains'. The present paper explores an alternative approach based on genotype redefinition in the grandparents and systematic phase elimination in all pedigree members. All three approaches accelerate the computation of a single likelihood. Equally relevant to multilocus mapping are search strategies for finding the maximum likelihood estimates of recombination fractions. Hybrid algorithms that start with the EM algorithm and switch midway to quasi-Newton algorithms show promise. These issues are investigated in the context of a simulated 10 locus example. This same example allows us to illustrate a simple strategy for determining locus order.