September 21, 1953

Dr. P. Armitage

NRO Statistical Research Unit
London School of Hygiene
Keppel Street, Gower St.
London W.C. 1, England

Dear Dr. Armitage:

Iwas most pleased to note your article on the statistical theory of
bacterial mutation in the last Journal of Hygiene. The discussion at this
level should be of considerable value to workers dealing with this problem.
Bub perhaps the most impressive conclusion is how unsatisfactory are the
estimates determined from counts of mitants. I think there is little doubt
that the technique used by Novick and Szilard (as cited by yourself, and

in the Cold Spring Harbor Symposium, 1951) 1s by far the best approach to
the measurement of rates.

In teaching this subject to a class whth very poor mathematical prepara—
ticn, I have found it expedient to focus on the "meam clone size", i.e.,
y/m = my r/aN = d, and to explain the effects of phenotypic delay, dominance,
and assumptions on the mtational model as they influence d. If I interpret
you correctly, we are agreed that the least ambiguous unit for expressing
rates is the probability of mutation per bacterial division. Many bacterialo-
gists with a rudimentary training in the calculus have had great difficulty
with the unit "per bac&érium per division". If we can someday find a system
in which phenotypic delay can be discounted, it would be worthwhile to test
the mitation models by direct estimation of d, e.g. from a Newcombe's type
of experiment.

The enclosed sheetemay be of doubtful interest to you.

From other lines of work it is possible to get some assurances on the
matter of dominance. Almost all of the mitations that have been exploited
for rate measurements are recessive, 6.g., resistance to bacteriophages,
resistance to drugs, requirement for growth factors. However, the "reversions"
to nutrilitseindependence (e.g. histidineless to wild type), and from lactose~
negative to lactose-posétive, are almost certainly dominant. However, too
little is known of phenotypic delay and, correlatively, of thevextent to which
the existing phenotypes of’ the cells are tested (rather than that of their des—
cendants) to draw a full picture of any of these systems.

Tf not too mchopftag dppgadtioapr PAE FoPN¢ehss Fggued tafionl naadpdisdonsad
Rb¢yGG #82 S°BASE-Pavor and will reciprocate with any of our papers on subjects

of mutual interest.