would contribute to the next phasing step, this ensured that only very high quality results would be carried over. Note that at Step 2, data of surrogate parents entered the processing of a proband as unphased. But every surrogate parent was himself a proband. At Step 3, surrogate parents carried with them the phasing information obtained from Step 2. This in effect utilized surrogate relatives with Erdös distance 2. Probands who were partially phased at Step 2 could now have more of their heterozygous genotypes being phased. Most of the probands who were not phased at all before due to incompatibilities were also phased here. With additional information provided by some of the putative surrogate parents who were now partially phased, a reasonable but ad-hoc, i.e. rule-based instead of model-based, procedure (Supplementary Methods) was used to resolve the incompatibilities. Sometimes, for a proband successfully phased for most of the SNPs, an individual SNP could be declared unphasable because of incompatibilities that resulted from the genotypes of many surrogate parents. Often the cause could be a genotyping error in the proband. Nevertheless, genotype correction was not attempted. Note that probands were processed one at a time, but the updated information for
