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Mutations : Random or not really so random afterall

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  • Mutations : Random or not really so random afterall

    I posted the same question on the DF27 forum but then the topic is more general so I might as well reach out to a broader audience. I often see these claims like that mutations are really random: That is, any mutation is as likely as any other mutation after taking the mutation rate into account. This puzzles me a and keeps me awake! I will try to explain below:

    Starting with DF27+, if I take all 1240 haplotypes from the YSTR charts, and count all the mutations, there is something I can't put together. DYS19=15 occurs in 13% of all cases, DYS392=14 occurs in 5% of all cases. There are 194 haplotypes for the first 11 markers with one 1-step mutation from the modal ("13 24 14 11-11 14 12 12 11 13 13")
    Still, there is NONE with DYS392=14 (== "13 24 14 11-11 14 12 12 11 13 14") and only 3 with DYS19=15 (== "13 24 15 11-11 14 12 12 11 13 13"). Statistically that doesn't make sense, does it?

    Now to be fair, in my modal example I used DYS439=11, but in reality the modal value is 12. Still, looking at the DF27+ DYS439==11 population only = 291 persons, 45 = 15% have DYS19=15 and 11 = 4% have DYS392=14, so the statistics are more or less the same wether I use all of the DF27+ population, or only those that have DYS439=11 as a starting point. If I rerun the same excercise with one 1-step mutations forcing DYS439=11, there are 86 that are 1 step away over the first 10 markers (+DYS439=11, fixed). And again, this should give 13 and 3-4 people on average with the named extra mutation, but there are only 3 and none, resp.

    Maybe I am simply asking after a fact that is long known, any links to this are appreciated. Maybe this is a genetic drift of some sort? (i.e. some mutations are found more in some branches then others, others here being modal). Any feedback appreciated.

  • #2
    I can add some maths as well. If the mutation rate of marker #i is mi, and G is number of generations, M is sum of mutation rates for all considered markers, then:
    1. chance that modal remains modal after G generations = exp(-M*G)
    2. change for only one 1-step mutation of ANY marker after G generations = M*G*exp(-M*G)
    3. chance for only one 1-step mutation of just marker #i after G generations = mi*G*exp(-M*G)
    4. chance for a 1-step mutation of marker #i irrespective of any other marker after G generations = mi*G*exp(-mi*G)


    Now M*G is of the order 1-2 ca and hence mi*G is much smaller, maybe like 0.1-0.2 (or much less for some markers that don't mutate that often). The chance of a mutation of marker #i among all one 1-step mutations is simply mi/M. This has to be compared to ~mi*G from above: if MG==1 then the two are equal, if MG>>1 then the chance of one 1-step mutation of marker #i among all one 1-step mutations is much less (by factor M*G) then the same mutation of marker #i irrespective of any other mutation. My take is M*G is around 1-2, certainly not 10. This follows simply from observing :
    1. chance that modal has not changed : exp(-M*G)
    2. chance of one 1-step mutation : M*G*exp(-M*G)

    comparing the population sizes gives a reasonable estimate for M*G, which I take around 1-2. I can check again and get more accurate numbers.

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