See 2021 update: Review article prepared for the book Genomic Prediction of Complex Traits, Springer Nature series Methods in Molecular Biology. Genotyping from few cell embryo biopsy is now routine.
This new Nature paper describes a genotyping technique that can be performed using only a small number of human cells. One implication is that we are close to non-destructive sequencing of human zygotes. For example, parents participating in IVF can potentially genotype fertilized eggs before deciding which to implant.
... we describe a low-cost DNA sequencing and haplotyping process, long fragment read (LFR) technology, which is similar to sequencing long single DNA molecules without cloning or separation of metaphase chromosomes. In this study, ten LFR libraries were made using only ~100 picograms of human DNA per sample. Up to 97% of the heterozygous single nucleotide variants were assembled into long haplotype contigs. Removal of false positive single nucleotide variants not phased by multiple LFR haplotypes resulted in a final genome error rate of 1 in 10 megabases. Cost-effective and accurate genome sequencing and haplotyping from 10–20 human cells, as demonstrated here, will enable comprehensive genetic studies and diverse clinical applications.See this earlier post Maxwell's Demon and genetic engineering:
... The amount of variation in intelligence within a particular family is almost as large as in the population as a whole, mainly due to the diploid nature of our genomes (half of the genes come randomly from each parent). Thus, as Fisher noted, superior characteristics do not "breed true" ... It is unlikely for a particular descendant to inherit most of the positive variants from both the mother and the father. If loci with positive effect on intelligence were identified, and selection performed on gametes (or zygotes), one could ensure offspring with many more advantageous alleles than normally obtained by chance. We would obtain the best from the set of possible offspring of a given mother and father. A process of this type can be thought of as a Maxwell's Demon of reproduction -- it suppresses fluctuations of the wrong sign.