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