Combinatorics 7: Exceptions

This is the last in a series of 7 posts on sharing combinatorics:

Part 1: Combinatorial Principles for DNA Sharing

Part 2: Non-transitivity

Part 3: A Genetic Pigeonhole Principle

Part 4: Transitivity Principles

Part 5: X-Chromosome Transitivity Principles

Part 6: Mutual Sharing Principle

Part 7: Exceptions

 

If 23andMe reports something that seems to violate one of our genetic combinatorial principles, the anomaly is presumably due to one of the following:

(1) [the only true exception] unusual situations where two matches on different strands butt up against one another by coincidence, making what are really two separate matches look like one long match;

(2) genotyping errors;

(3) uncertain boundaries on short, close-to-the-threshold matches;

(4) microdeletions (or other, rarer phenomena such as chimeras);

(5) 23andMe's practice of reporting regions as half-identical even though they have a small number of isolated non-matching SNPs;

or (6) on the X chromosome, 23andMe's varying minimum threshold size for reporting matches, which depends on the genders of the individuals whose genomes are being compared.