Statistical evaluation of the Luria - Delbruck thought experiment

  mean  (xi) / c
  variance 2 [ - xi]2 / c
 
But in 1943, alternative MOSSOM formula for variance simplifies calculation by mechanical calculating machine.

Both Thought Experiments involve 10 observed
Tonr cells our of 64 total cells

Suppose
probability of induction (a = 10 random events / 64 cells = 15%
    observed = 3, 1, 5, & 1 = 10 Tonr colonies      
       mean
= (3 + 1 + 5 + 1) / 4 = 2.5 Tonr  per culture

       variance = [(2.5 - 3)2 + (2.5 - 1)2 + (2.5 - 5)2 + (2.5 - 1)2] / 4 = 2.75
                                                        or ( 9 + 1 + 25 + 1) / 4  -  2.52  = 2.75

        Induction Hypothesis predicts a Poisson Distribution for rare, random events: variance = mean


Suppose
mutation rate (a) = 2 events / 60 cell divisions = 0.033 mutations / cell / generation
        observed = 2, 0, 8, & 0 = 10 Tonr colonies
        mean  = (2 + 0 + 8 + 0) / 4 = 2.5 Tonr as before
        earlier Tonr mutations leave more offspring (as in Culture 3)
       variance [(2.5 - 2)2 + (2.5 - 0)2 + (2.5 - 8)2 + (2.5 - 0)2] / 4 = 10.75
                                                               or (4 + 0 + 64 + 0) / 4  2.52 = 10.75
       after 5 generations, when the number of Tonr cells has doubled in each culture:
        variance' [(5.0 - 4)2 + (5.0 - 0)2 + (5.0 - 16)2 + (5.0 - 0)2] / 4 = 48.00

        Mutation Hypothesis predicts variance >> mean, as g increases


All text material ©2017 by Steven M. Carr