I received my 23 and me results and it says I share 52% DNA with my mom.
Is this possible?
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This could also be explained if the parents share DNA. If you took the same test with your father and it also was > 50%, it could indicate they are distantly related. A single shared chromosome could appear as ~52%. Even if dad only shows 50%, he could have passed the shared DNA but mom did not pass it down, so it would overlap with the DNA mom did not pass down.
The sex chromosomes are likely what make up the discrepancy. I'm guessing you are male.
Females will share exactly 50% of their DNA with each parent, since they inherit 22 autosomes from each parent, and an X-chromosome from each parent.
Males will share slightly more DNA with their mother than their father, since they also inherit 22 autosomes from each parent, but inherit an X-chromosome from their mother, and a Y-chromosome from their father. The X-chromosome contains significantly more DNA than the Y-chromosome. Therefore, as a percentage of DNA inherited, sons get a little more from their mother.
23andMe note in their Average Percent DNA Shared Between Relatives that parent-child relationships will share "50% (but 47.5% for father-son relationships)". Or if you calculate it the other way, 52.5% for mother-son relationships. The sex chromosomes presumably account for this difference. Many "autosomal" tests such as 23andMe also include many markers on the X-chromosome, and sometimes some on the Y-chromosome.
Of course, when DNA testing is performed there may also be some small margin of error, so these numbers may not match absolutely perfectly in each case, but they should always be close.