nraoaoc@nmtsun.nmt.edu (Daniel Briggs) (04/09/90)
I am a astro-physicist and my knowlege of genetics is strictly at the high
school level. Perhaps some of you could straighten me out on a question
I have been wondering about.
Simply put, "Why do children often take after a single parent?"
Here are some simple arguments why I think that *all* kids should look like
a pretty even mix of traits from both parents. I expect that some or all of
the gross overgeneralizations I am about to make are wrong. Can you help
me figure out which ones?
The 0th order model I am working from is this: Assume that every
observable trait either is ascribable to one parent or another, or is
determined by some more subtle mixture of genes and can't be ascribed
to either. Assume also that domnant and recessive traits are
distributed more or less evenly between both parents. That is, Mom
has black hair and blue eyes, and Dad has red hair and brown eyes, to
take a crude example. Assume that a human being is determined by a
large number of *observable* traits. [er, I think these were called
phenotypes, to throw around jargon that I only dimly remember.]
Unless there is some genetic mechansim acting to the contrary, it sure
seems to me that we should all look like an even mix of our parents.
Imagine throwing a 4-sided coin. One side says "Dad", one side says
"Mom", and two sides say "mixture". If we throw this coin 1000 times,
then we expect to get 250 Moms, 250 Dads, and 500 mixtures. (This
choice of coin is vaguely motivated by an inheritance diagram for a
simply dominant gene.) If we throw out the mixtures as being
undecidable, then we can form a percentage of observable traits that
come from a given parent. In the expected case, we have an individual
who is half Mom and half Dad. Based on this model, I calculated
(one-sided) probabilities of seeing an individual with less than p% of
genes from a given parent.
N traits = 100 N traits = 1000
p prob p prob
.5 .5282 .5 .5090
.45 .2421 .45 .01278
.40 .0841 .40 4.02e-6
.35 .0177 .35 9.42e-11
.30 .0025 .30 1.53e-18
.25 .0002 .25 1.472-29
That is, if there are 100 potentially observable traits, there is a
.0002 probability that I will come out *looking* 25% like Mom and 75%
like Dad. There is the same probability that I will come out looking
like 25% Dad and 75% Mom, since I used a one-sided distribution.
(BTW, the funny values at .5 simply reflect that this is a discrete
problem. The value *at* .5 actually contributes a substantial
fraction of the total probability. I had to decide whether to include
it or not. Neither choice will make it come out to .5. It vanishes
in the limit of N going to infinity, though.)
I'm not claiming that this model is correct, but just wanted to make
the point that statistical factors will cause the distribution to peak
sharply about the mean as total number of traits rises.
Now observationally, this is bunk. I look like my mother, (allowing
for the obvious gender based differences ;-) My sister looks like my
father. I've no good way of quantifying this, but wouldn't be
surprised to find that I'm in the 70% - 30% ballpark myself. That is,
I am much further from the mean value than my crude model can allow,
since I don't think that my family is all that atypical.
So crew, your job is to tell me (or speculate) which one of the
assumptions that I made was the most stupid. Here are a few possible
ideas to get you started.
1) There really *is* some genetic mechanism whereby a large percentage
of dominant traits comes from one parent.
2) Sex linked effects are dominant. There is some mechanism
functioning that makes one look like the cross gender parent. (I had
been assuming that one pair out of 23 wouldn't make that much
fractional difference.)
3) The number of potentially observable traits is actually fairly
small. Or more precisely, the number of such traits that people
notice when comparing people is fairly small. If we can beat the
number of important traits down to less than 50 or so, then maybe
statistical effects *do* dominate.
4) Environmental effects are being confused with genetic traits. My
Mom likes broccoli. She trains me to like the stuff, too. We say,
"how coincidental, we both like broccoli -- must be the same taste
buds." I point out though, that my sister was raised in much the same
environment as I, yet our tastes in food closely parallel those of our
respective parents.
5) A combination of 4) and 5) conspiring to produce selection effects.
That is, once the basic similarities had been noted, possibly from
only a few basic traits, then we tended to remember cases that
reinforced this idea, and not remember those cases that disagree with
it.
There may well be some good explanation in the form of basic Mendelian
genetics, but after examining a few diagrams, I kept coming back to
the conclusion that all such things are inherently symmetric. If you
can observe a given trait, (and average over a statistical universe of
such traits), then there was an equal chance it came from Mom or Dad.
I know that some traits are intimately linked with each other, but I
thought these were small scale phenonema. I seem to need large scale
correlation over many traits (and many chromosomes) in order to get the
effect that I think I observe.
All thoughts via E-mail or posts are welcome. Note the .sig if you
use mail, though.
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Dan Briggs / NRAO / P.O. Box O / Socorro, NM / 87801 (U.S. Snail)davison@uhnix2.uh.edu (Daniel B. Davison) (04/11/90)
The poster asked, essentially, why siblings are not "even" mixtures of their parent's traits. The simple-to-say but complex-to-explain answer is that genes which determine complicated phenotypes have what is called "variable penetrance". The degree to which a phenotype is expressed is the result of many, many genes interacting, even eye color or voice pitch (although these two have almost complete penetrance). So, simply, the genetic background of your cells is not the simple union of parentral traits (blue eyes or brown eyes) but the intersection of them (brown eyes + variable activity in pigment-producing cells + variable activity in pigment transport and deposition in the iris). [I hope I haven't reversed the intersection and union concepts, but you get the drift, I hope]. Real human genetics folks who occasionally read this news group like Ted or Henry may be able to add more definitive information to this, but "penetrance" is the key concept. dan -- dr. dan davison/dept. of biochemical and biophysical sciences/univ. of Houston/4800 Calhoun/Houston,TX 77054-5500/davison@uh.edu/DAVISON@UHOU Disclaimer: As always, I speak only for myself, and, usually, only to myself.