Mather's Book
- To: pumpkins@mallorn.com
- Subject: Mather's Book
- From: H* E* P*
- Date: Tue, 06 Apr 1999 23:16:41 -0700
Dear Pumpkins List
(I am also sending this to my family so they can see what I am doing.)
A book which I have mentioned to Nic is Kenneth Mather's 1938, 1951,
The measurement of Linkage in Heredity. New York: John Wiley and Sons.
It is a tiny 4 x 6.5 inches, 149 pages, book. I have had it for 40 years
and and have not read very much of it because some of it is heavy on
formulas which I did not need prior to AG genetics.
It may have some value to those hoping to find heavy pumpkins genes
linked to visible traits. I will try to get some of it digested into my
pk.htm site this month.
I can easily discuss the table I used the most here. However, Big AGs
are more complex than this simple case.
The question is: How many plants must I grow to get one plant which
has the desired qualities. The book gives numbers for .9, .95, .98, etc.
Here I will give the numbers only for 0.9 (90%).
Expected Number of plants which must be grown to have
Fraction 90% probability of getting one of the desired plants
1/2 3.3 (grow 4 plants)
1/4 8.0 (grow 8 plants)
1/8 17.2 (grow 18 plants)
1/16 35.7 (grow 36 plants)
1/32 72.5 (grow 73 plants)
1/64 146.2 (grow 147 plants)
Some people on this list have said, "Not all the seeds from a cross are
equal in genetic capacity."
Sadly, we have no way to know what ratio of the seeds in a pumpkin
have the capacity to grow Record size pumpkins.
It is Blessed to Give in the AG business:
Let us suppose that your name is Blue and in 1997 you made a cross and
the fruit is known as 888 Blue 1997 and that it had hundreds of seeds
and you gave seeds freely to as many good growers as you could find. You
and your friends grew 64 seeds in 1998 and you have learned the results
of every one of those plants and you have decided 2 of those plants were
wonderful and you are going to do everything possible to get one of
those "Silver Bullets" growing in your garden during 1999.
The Question is: How many seeds do you have to plant to have a 90%
chance of growing one "Silver Bullet". Recall that in 1998, 2 out of 64
were "Silver Bullets". The expected fraction is 2/64 = 1/32. Looking at
the above table you see that you have to plant 73 seeds to have a 90%
chance of planting a Silver Bullet.
If you want a 99% chance of planting a Silver Bullet you should grow
145 plants. I got the 145 came from a part of the table not printed
above. I will try to get the whole table in my site soon.
Here is another example from everyday life. Lots of families would
like to have at least one boy. The expected fraction is 1/2 becaause
about 1/2 of babies are boys. To be 90% sure of a boy plan on having 3.3
kids, to be 95% sure have 4.3 kids, for 99% probability plan on 6.6
childern.
The book has two chapters on linkage in Humans. This comes close to
the situation in AG because in both species matings are somewhat random.
I will try to digest those chapters and get something on my site during
1999. I would do it right away, but it will not be easy to simplify and
the results are for a single gene such as linkage of brown eyes with
brown hair. We do not yet know many genes in AG and trying to link those
to weight (which depends on many genes) is pretty hopeless and
genetically unlikely.
--
Harold Eddleman Ph.D. Microbiologist. i*@disknet.com
Location: Palmyra IN USA; 36 kilometers west of Louisville, Kentucky
http://www.disknet.com/indiana_biolab/pk.htm
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