May 28, 1953

Dear Luca:

Your letter of the 19th and manuscript arrived 2 days ago. It is unforthnate
that we have to work under such pressure of time; in better circumstances, I am
sure that the tasks would be far more pleasurable.

On the whole, the ms. is in quite good shape, and with the exception of the
biometric problem at issue batween us, I would not be distreased to see it publisked
Just as is. However, I have marked a number of points for your attention, all in
red pencil to make them more conspicuous. Most of these are formalities, or improve-
ments in phraseology, of which your judgment mst be final. In two places, I have
suggested softening a phrase to mitigate possible personal criticisms. The points
to which I ask your ppecial consideration are marked*, but again I will acquiesce
to your considered judgment.

We seem each to have become rigidly convinced on the question raisedon p. 8,
which perhaps means that I am no longer really thinking about it. Perhaps I have not
fully understood your point. I am willing to admitnthat several parameters might
be needed to describe the response of a population, one of these possibly deseribing
the distribution of potential resistance among the cells, about another parameter,
their mean response (or probability of forming a resistant colony). Such parameters
may have values corresponding to what you call interasal inhomogeneity. But if the
parameters are the same from culture to culture, i.e., if these gan be regarded as
unbiassed samples from the same universe, I contend that these samples will have to
show a Podssonian distribution. Of course, if the cultures are not unbiassed samples,
i.e., if for any underlying reason af environment or heredity, the individual variates
(cells) are correlated within cultures with respect to any parameter (mean or sikxpwmrs
moment), then e.g. a negative binomial might ensue. But this is not, as I would call
it. internal heterogeneity, but a modification of Hinshelwood's proposals of uncon-
trolled or even accidental variation in the state (i.e. the parameters) of one culture
as against another.

I have best been able to convince myself of the conclusion by taking the extreme
cases. Consider two "species" of bacteria, of which one has a probability = 6 of
becoming resistant, while the second has a probability =1. Then of course, so long
as the second species is rare, regplicate cultures among which the proportion of
the two species is subject pnly to random or sampling error, will give a Po&sson
distribution. To postulate a non-random variation ia the propéftion of species
is to bring in some specific factor, different from tube to tube, responsible for the
difference (e.g. common heredity). The same consideration should apply to a system
of mimerous species, each with a charecteristic probability of survival.

In fact, the problem seems quite analogous to Fisher's treatment of "the relation
between the number of species and the number of individuals in a random sample of
an animal population" (J. Animal Ecol. 12:42, 1943 or paper 43 in the collection
"Contributions to Mathematival Statistics" "In strictly parallel samples, i.e. equivalent
sampling processes applied to homogeneous material, the numbers catight of each indi-
vidual species will be distributed in a Po&sson series, and it easily follows that
the same is true of the aggregate number of all species...."

I am not sure of the Greenwood-Yule paper to which you refer. Professor Crow
Sgowed me the J. Roy. Stat. Soc. 83, 1920, concerning the distribution of accidents
among workmen. It readily follows that an appropriate spread of accident-liability
among different individuals tested over a period of time long enough to permit
cumulation will lead to a negative-binomial distribktion of accidsnts among individuals
He does not treat directly the problem of the distribition of accidents among
factories (of uniform size) which would be more relewant to the present problem.
I can imagine that there would be a distortion of the Poisson distribution even
here, if the observations were continued long enough to include repeated injuries
by one person, but this is only because the repeated occurrences are correlated
with each other. In our present problem, if there i even a transient persistence
of characteristic response through one or more cellg divisions (as might be expected
of cell size) adeviation from the Poisson would be expected, but IT assume that even
this vestige of heritability is dehied. This is pmax a point, however, that L&D did
not adejuately consider, as they distinguished only the extremes of full heritability
versus entire wandemaese non-correlation of relatives, and Hinshelwood would likely
be in favor of an intermediate. or better _/Yudkin

Perhaps this is what you had in mind.

The results with B are interesting indeed. I had thought we had tested B,(auxatrophs x
Hfr) with negative results, but I rather suspect that several cultures are masquerading
under the nams B, and this may account for differences. Id the fact of crossability
itself, in your gaterial, confirmed? I did not fully understand your marginal note.

I hope you will not hold me to my (not entirely serious) proposal of a book, but
if I could manage to as little work on it as for the preparation of this paper I would
be glad to help. The thought of more literary work just now is rather terrifying!
But perhaps time will help relieve this.

June-October are tye least pleasant months of the yearp but by all means start
preliminary enquiries. I can almost certaihly raise the funds for a supplementary salary
($250-300/mo.) but will know more surely in a couple of months. There are some other
vexatious problema of lab. space, but we will surely find some way of accomodating both
of you, regardless of contingencies, On the whole, 1 would think WHO would be both more
likely to support a short-term fellowship, and also would be useful in disposing of
fuss with passpert—visa problem. Make sure that an extra salary here would be unobjec~
tlonable both to WHO and to the US consular authorities.

As you have probably guessed, I have temporarily turned over most of the Hfr work
to Nelson, while I finished some Salmonella problems. I am nearly readg to go back to
cytology of Hfr X F-,(which had given some promising results),and am sure that we will
not get so far as to preclude a very active collaboration on it if you can get here next
year, a possibility to which I look forward with anticipated pleasure. His most recent
experiments, by the wag, show that St (and therefore certainly F+) Het Mal- Lac- X Y10
or XY10 S* give akmetxix diploids, about 90% Male Lac+/-, and 10% Mal-/. Lac+/-, There
is therefore certainly mqmmtx an elimination of the contribution of the F+ parent in
10% of the diploids, in confirmation of previous data. We are currently trying to clean
up with some real data the suppositions on the role of F polarity gn eliminatiog, as the
basis off the effects on segregation (ef. p.727 paragraph 2 of our Genetics paper), since
we know have Het M- F- stocks (by passage through motility agar. On this point, a single
experiment in Novick's chemostat seems to show that prolonged cultivation at great dilution
is sufficient to yield F-, as may possibly explain the motility agar effect, but this
result needs to be substantiated ).

Have you received the filter as yet? Thank you for the ca. 200 reprints of the JGM
papet, received during several days this week. I am not sure how freely to distribute these,
Probably, I will get most of the US-originating requests. I do not wish to ask for any
part of your supply, but it will help me to judge how well the "market" can be saturated
if I know how many you have purchased, and how many will be left after you complete a
routine mailing(unless you advise me to the contrary, I assuge that you will be distribu-
ting yourself to a general list which would probably be congruent with my own.)
I regret that there was only one copy of the ms. with your letter. If you can
send an-a— a second (perhaps with those changes to which you would accede) it
would be appreciated, but not indispensable. I will try to refrain from perpetuating
the discussion.

Iwill return the tear-sheets of your paper for the Biochemical Congress in Paris
in the near future. Could you get for me the full name, publisher, and price
so that I can get our library to buy the volume? [Please do not consider assuming
this burdeh yourself! ]

Unfortunately, I have to think of two other mss. along with this cne, so my
mind is not so clear on other issues that may have accwmlated. I assume that you
will be increasingly busy (if not frantic!) with the forthcoming meetings. I will
wait for your acknowledgment éf this hefore trying to collect our past correspondence
and resume in a more coherent way.

Only one person seems to be going to Europe this summer from this department,
one of my students (Miss Helen Byers). I intend to ask her to bring back the
printed materials from the Congress for me, if possible. If there is any comparable
favor I can ask of her, please let me know— but she will probably be flying, and
may be tight for baggage weight.

Yours sincerely,

‘

Seghad Lederberg
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