In my first paper (“Calculating Autosomal DNA Match Coverage: A generalized additive recursive method”), I gave the pseudo-code for a generalized additive recursive algorithm to accurately calculate the lower bound of the range of DNA coverage for a target person.  In that paper, Appendix 4 (“Calculating the Shared DNA Component: Dealing with Ranges”) provided an extended set of scenarios showing how the coverage of a person for whom none of their children tested can only accurately be reported as a range, with a lower bound and an upper bound. Like the cone of uncertainty in a hurricane forecast, there is no one single value that can be considered to be the coverage estimate when no children of the target person have tested.

Dr. David Stumpf made the first implementation of the algorithm in his Graphs for Genealogists (GFG) software. Jonny Perl then created the DNA Painter “Coverage Estimator” tool, which implemented the method of Paul Woodbury as used by Leah Perle Larkin, a method that propagates the average (instead of the lower bound) up the generations from the test takers to the target ancestor. So, the DNA Painter implementation and both the algorithm in my prior paper and in GFG will give different single numbers, neither of which fully represents the range that is the reality of the coverage for the referenced ancestor in no-child-tested scenarios.

In this paper, I extend the algorithm to accurately calculate both the lower and the upper bounds of the range. I also explore the behavior of the ranges and their average and of the propagated average (as used in DNA Painter). I then provide an intuitive understanding of DNA coverage ranges to understand who the best target tester is to improve the overall coverage of the target ancestor.

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