Why 414 and other question about DNG math

[pd3]

Hi, I was looking at the DNG math and the implementation and can't figure out where the 414 term in this expression https://github.com/ultimatesource/denovogear/blob/develop/src/dnm/makeLookup.cc#L260 comes from? The comment suggest that 414 is the number of all triallelic cases, but I don't think that is true, as there are 552 trio configurations with 3 alleles.

[reedacartwright]

Honestly, I don't know. At this point the DNM code is over ten years old, and the people who developed the model haven't been active with DNG development for years.

[pd3]

Thank you. I am adding more questions in case someone could explain:

• In the supplementary material of your 2011 Nature Genetics paper, page 11, the L(G_1,G_2) calculation sometimes use the factor of 0.002 and sometimes 0.001. I don't immediately see what is the reason for 0.001, apart for being half of 1-0.998=0.002. In other words, what is the rule for where to use 0.002 or 0.001?
  https://static-content.springer.com/esm/art%3A10.1038%2Fng.862/MediaObjects/41588_2011_BFng862_MOESM37_ESM.pdf

• The code uses the prior of 0.998 for drawing hom-ref genotype, which I accept. However, I don't know why the prior of drawing two hom-ref genotypes (mother+father) is in the code 0.998*0.995. Note the "5" instead of "8". I don't think it is a bug, because the factor 0.995 is used further in the code as well for other cases.
  https://github.com/ultimatesource/denovogear/blob/develop/src/dnm/makeLookup.cc#L292

• A comment in the code suggests that the L(G_1,G_2) prior is split equally among all triallelic cases and so the term 0.002**2 is divided by 414. However, I believe there are 552 trio configurations with 3 alleles, so was wondering how was the number 414 derived.
  https://github.com/ultimatesource/denovogear/blob/develop/src/dnm/makeLookup.cc#L260

For male chrX inheritance there are incorrect priors assigned, I believe they are simply bugs in the code. So far I discovered these three:

• The transmission probability P(0/1 + 0 -> 0) should be equal to P(0/1 + 0 -> 1). Both should be 0.5, however the code evaluates one to 0.5 and the other to 1
• The prior probability P(0/0 + 0 -> 0) should be equal to P(0/0 + 1 -> 0), father's genotype should be irrelevant
• Similarly, P(0/1 + 1 -> 1) should be equal to P(0/1 + 0 -> 1)