A wonderful new tool was released last month at DNA Painter, called “What Are the Odds?”. It expands on the already wonderful “Shared cM” tool. The “Shared cM” tool takes in a DNA match size and returns the possible relationships between two individuals, with their corresponding probabilities. The “What Are the Odds?” tool combines multiple probabilities from the “Shared cM” tool. This is very useful in situations where a person of unknown parentage matches a number of people who are also known relatives of each other. Leah Larkin has a great description of the tool here: Science the Heck Out of Your DNA — Part 7.
The way it works is to start with a target person. For example, the target can be an adoptee. Then you need a group of people who match the target and who are known relatives of each other. Start building a tree with an ancestor or ancestral couple of the matches who are known relatives of each other. (It may be wise to choose an ancestral couple further back in time to be able to chart all the possible relationships.) From that couple, build the tree down to each match. For each match, add the match size with the target person. Define any half-sibling relationships. Then add the target to the tree in a reasonably exhaustive way, setting up a number of possibilities.
It may be helpful to enter the closest match in the “Shared cM” tool to see the set of possible relationships. Make sure those relationships are in the tree. Remember that relationships like first cousin, once removed imply two possibilities, that the target is one generation lower than or one generation higher than the match. (It feels a bit like the knight in chess.) Relationships that are not listed there will end of with a probability of zero, so aren’t needed, but it’s more important to have extra possibilities rather than miss some. Remember to consider half-relationships.
The “What Are the Odds?” tool takes in the match information and calculates relative probabilities. Ironically I was just considering how to do this last month, when this tool came out, for a proof argument I was writing for my ProGen class. I didn’t add an overall theory to my paper, because I was debating whether each result should get the same weight. But this month as I am revising my paper, Voila! I came across this tool. The assumption this tool uses is that each match is weighted equally. The probabilities are scaled so the least likely nonzero probability is given a weight of 1. The tool also suggests that when the most likely case is at least 20 times the next most likely case, that “suggest significant statistical support.”
Be aware that the “What Are the Odds?” tool right now has more accuracy than that “Shared cM” tool. It accepts decimal inputs for match size, whereas the older tool truncates the input at the decimal point. It also seems to store some more digits of accuracy for each of the relationship probabilities than are shown. Don’t be thrown off if you see this. Just use the “What Are the Odds?” numbers if you want more accuracy.