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DNA STUDY

The Calculator shows the most likely number of mutations for any given set of markers, generation gap and average mutation rate. The formula uses a standard probability mechanism, which looks more complicated than it actually is :

Where :

P = the mutation rate (eg quoted as 0.0033 and not a percentage at 0.33)

T= the total number of markers tested multiplied by the number of generations x the number of people in the comparison

t = the number of markers that have mutated

! = factorial, for example 6! is the as 6x5x4x3x2x1

To work out the probability of 2 mutations in 44 markers over 7 generations, between 2 people using a mutation rate of 0.33%:

P = 0.0033

T = 44 x 7 x 2 = 616

t = 2

Plugging the numbers in to the equation :

= (1-0.0033)^(616-2) x 0.0033^2 x (616!/614!)/2!

= 0.131394 x 0.00001089 x (616x615)/(2x1)

= 0.271 or 27.1%

Note that if you try to calculate 616!, your calculator or computer will find this number to big to handle. We used a short cut above used to calculate 616!/614!, which is the same as 616x615. To calculate 64!/60!, this is the same as 64 x 63 x 62 x 61. Don’t bother with long hand however, just use the Calculator. Below is an example of 2 people being compared over 4 generations, comparing 63 markers and using a mutation rate of 0.0041, or 0.41%. (a screen shot is below). There are 504 opportunities to see a single mutation and the most likely outcome is to see 2 mutations, at a 27% chance.