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, JOHN INNES HORTICULTURAL INSTITUTION.

’

31 licstyr nond,
nerton Park,
London, S.W.19,
Ingland.

Sth August, 1947.

vear Lederberg,

Your letter of Isst month arrived just as I
was settine off for 9» Conference of Plant Breeders. I have
also been to snother Conference on “rowth and pifferentiation
since then, as well as having to give 2 preat deal of time to
my crops which are in full flower in July snd ausust. So
please excuse my delay in replyins to vour letter.

You seem to have entcred well and truly into the
mathemetica of crossing-over and its measurement. There was
a great deal done with it some ten or fifteen years ago} and,
while your spproach is a new one in many ways, you might find
the older literature of some interest. JI «am semding a review
of mine under scpurate cover. It will help you to trace any
papers thet you might wish to read.

Ag you will see from this review, I am aware that
not oli cross-overs are recovered as such, and in my original
caleuls ition of map-distances from your data, if I used the
term “cross-over" I implied "recornisable cross-over" The
estimates of map distance must of course be minizal for this
reason. iI did not think that greater accuracy (such as might
be achievea by a priori adjustment for unrecognisable double
cross-over) would, however, be worth while as the basic
agsumption of the calculation was that there was no interference
between the three regions. This is itself, of course, a
questionable assumption which would serve to mininise the
extended value of x (total distance).

Your calculstion adjusts for wmrecognisable double
crossing-over within each region by using the same assumption
of no interference. These adjustments may well be too large,
because, if we are to judge by higher organisms, interference
over short distances is the rule rather than the exception. So,
I wonder whether your more elaborate calculations are made worth
while by such additional accuracy as they might achieve as
compared with ny eimpler. Ones «

\

 
about the results from the 2 and 4 strand caleulstions;

surely these must te identical if you assume that, in the 4 strand
case, the strands crossing-over at any one chinsma are independent
of those crossing-over at any other, i.e. in other words if you
assume the absence of . hat we always called chromatid interference.
i can see no escape from this conclusion mwpelf, so that I would
regard any Uiscrepaney between your © and 4 strand estimates as
suspicious, rather than any egreement as secidentel.

Iwas interestec in your slrebra of 4 strand cross ing-
cvere co tar as IJ am aware it is suite unique, and would be of

3

valuc to anyone doine such anclysea. Can i+ ne mide to take care
of chrometia interference? T empeet it can.

(we further point, on pege 3, line 4, of your letter,
you refer to the enumeration of zypotes. are your individuals
2ygotes? I thought you esswsed (as I certainly have in our
discussions) that weiosis (or its equivalent) followed fusion

so tnat single products, the ccvivaelents of gametes, were
recovered for observation. If so, your “approximation” on page 3

is already contained in the initial ossumptiors.

2
u

ofy YT say
observations you have rade on recombination between Bi, Lac,
V, anu TLe Sueh cota sive s really worth vhile basis for
celculetion.

All good wishes te Urs. Lederberg ond yourself.

Youre cincerely,

K. Lather.

Dr. Je Lederberg,

Osborn Botanical Laboratory,
Yale University,

New Haven,

Connecticut,

U.SeAe