Grandsons' atDNA Inheritance: A Case Study

If you are familiar at all with genetic genealogy, you know that children inherit 50% of their autosomal DNA (atDNA) from their mother and 50% from their father. You also may know that while children inherit about 25% of their atDNA from each grandparent, these amounts may vary.

I recently had the opportunity to compare the amount of atDNA shared by two of my grandsons with each of their four grandparents and with one great-grandparent -- father of their maternal grandmother:

	P-GF	P-GM	M-GF	M-GM	M-GGF
G-son A	1852.9 cM	1731.5 cM	1882.2 cM	1719.8 cM	727.2 cM
	25.8%	24.1%	26.2%	23.9%	10.1%
G-son B	2025.7 cM	1558 cM	1584.9 cM	2017.4 cM	885.4 cM
	28.2%	21.7%	22.1%	28.1%	12.3%

As you can see above, the percentage actually shared by each grandson with each grandparent varied from 21.7% to 28.2%. No big surprises there. We have long been told that after the first generation the amount of atDNA inherited is somewhat random and varies from one grandparent/grandchild pairing to another.

Note also that the amount inherited by both grandsons decreased by more that 50% between the amount they inherited from their maternal grandmother (M-GM) and her father (M-GGF). In this case the decrease seemed to be in proportion to the amount they had inherited from their maternal grandmother but I don't think we can come to any solid conclusions from this very small sample.

One thing did jump out at me that I had never though about before. As I mentioned above, it is well known that all children receive 50% of their atDNA from each parent. However, it had never occurred to me that all grandchildren inherit 50% of their atDNA from each pair of grandparents. While the amount inherited from each of the four grandparents may vary considerably, the amount inherited by the maternal grandparents combined or from the paternal grandparents combined will add up to 50%. It is a logical conclusion but not one that I had thought about before.  

Now I'm pondering to what extent this principle can be extended. For example, can we calculate how much atDNA my grandsons may have inherited from the mother of their maternal grandmother (M-MG). Can we conclude that each of the grandsons inherited 25% combined from the parents of their maternal grandmother? That would be useful, if true, because we only have DNA test results from one of the great-grandparents.

I'm still pondering how far, if at all, this bonded inheritance can be extended. Do any of you have data and/or thoughts?