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Mendelian Genetics
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In the middle 1800’s Gregor Mendel, an Austrian monk, did famous
experiments that allowed him to understand quite a bit about how heredity
works. Of course he knew nothing of the existence of DNA or anything about
chemistry, actually, but from his work he was able to make out some
mathematical patterns that then allowed him to make good inferences about
how the system works. We will look at two principles he discovered and then
tie them to what we know of DNA structure and function.
Mendel studied peas because he could grow them under controlled conditions
in the abbey’s garden, control their pairings (by hand pollination), and get more
than one generation per year – something not possible with most animals.
Among the characteristics he studied we will examine two: shape and color.
Mendel saw that there were two shapes to the peas when they were dried:
smooth (left) and wrinkled (right).
When Mendel sorted his dried peas
after crossing them he always found
the two shapes (which we call
phenotypes) in approximately the
ratio 75% round and 25% wrinkled
(3:1) after the second crossing.
Make sure you realize that this
observation is not based on four
peas, but on many thousands of
peas. Statistically the ratio
consistently holds, and the bigger
the sample the closer to a perfect
3:1 ratio it gets.
Mendel reasoned that any consistent
ratio of phenotypes indicates that
1) whatever causes heredity comes in
unit “packages”, and
2) these packages are of two types.
He reasoned further that one version
of each type came from each parent,
creating what we see as a blend of
parental characteristics in the
offspring. He was the first to see that
it wasn’t a blend in the way it had
always been considered – like making
orange paint by mixing red and yellow.
Rather it was more like making orange
color on a page by mixing red dots
and yellow dots of small size. (Mixing
pixels on a screen, as was done to
make the shading on the images on
this page is a better example.)
The fact that the ratio is not 50:50 (or 1:1)
suggested to Mendel that one trait was
dominant and the other recessive. That is, if
the code for one trait (in this case smooth
shape) is present in either of the parental
genes in the package then the peas are
smooth, regardless of the other parent’s gene.
To illustrate this he assigned a letter to both
possible versions of the code: R from a parent
(capital to indicate dominance) coded for a
round pea and r (lower case for recessive) for a
wrinkled one.
Each parent contributes one letter to the code.
There are exactly four possible combinations:
RR, Rr, rR, and rr. Let’s go a little deeper.
Assume that the first letter is the code supplied
by the father and the second by the mother.
“RR” means that both parents contributed the
code for round peas. Rr means that the father
contributed code for round peas and the
mother for wrinkled ones. Work out the other
two if the system is not crystal clear to you.
Now, which code pairs make round peas and
which make wrinkled ones?
Remember that as long as there is
one R in the code the pea will grow
round. Only one combination (rr)
can make a wrinkled pea.all the
other three make round peas. That
is what causes the 3:1 ratio of
shapes.
The visible traits of an organism
(including this one for peas -- round
or wrinkled) is called the phenotype.
The code that grows the traits is
called the genotype.
A contingency table is a good way to illustrate this. The cells of the table
effectively list all the possible combinations.
Dad’s version
R
The gene from Dad can be either the
dominant or the recessive version, and the
same is true for the one from Mom. Notice
that we are not talking about any particular
genes in one offspring; we are talking about
all possible versions in all possible
offspring.
R
r
R from both
parents
r
R
r
r
Mom’s version
R
There are exactly four possibilities in the
offspring as shown. We’ll see them one at
a time.
Dad’s version
R
r from Dad
and R from
Mom.
R
r
r
R
r
Mom’s version
R
R from Dad
and r from
Mom.
r
R
r
R
RR
rR
Rr
rr
r
R
r
Mom’s version
R
r
Dad’s version
r from both
parents
So the possible phenotypes are:
And they occur in a 3:1 ratio
Mendel dubbed this system of coding for
characters in two alternate states the
principle of segregation. The code for
round, in other words was a separate thing
for the code for wrinkled – the codes were
segregated.
Mendel, of course, knew nothing of DNA – even its
existence. We now know the architecture of the
principle of segregation. When the homologous
chromatids in the two gametes come together
during meiosis the one from Dad has a version of a
large number of genes on it. The one from Mom
has versions of exactly the same genes, but
different versions. This explains the part of
Mendel’s first principle that says the traits come in
two mutually exclusive versions.
In characters like pea color and shape, one version
will be preferentially expressed over the other in the
phenotype – it will be dominant. This was the part
of the principle that explained the ratios. If both
versions of the gene were the dominant version (a)
then the dominant version will appear in the
phenotype.
D
D
D
D
X
d
a
D
b
Indeed, if either version is the dominant version
then the dominant phenotype is expressed (b & c).
Only if neither parental gene version is the
dominant version then the recessive version will be
expressed by default (d).
D
d
a
X
D
d
d
d
a
Mendel found a number of other traits in his peas that followed the principle of
segregation. One was color. The peas (when dry) were either a bright green
(as frozen peas are in the store) or greenish yellow. Given the picture below,
which shows the typical ratio of phenotypes, determine which trait is dominant
and which recessive. Then assign a code letter (the first letter of the dominant
color – capital if dominant and lower case if recessive). Then list all the
possible combinations and determine what the phenotype would be for each
genotype.
The possibilities are shown below. Note that in any four randomly selected
peas you wouldn’t be able to tell what the genotypes of three of them are.
(You’d always be able to recognize yy.) This figure just shows what the
possibilities are. In a large population you’d expect equal numbers of all four
genotypes, yielding the Yellow : Green = 3:1 ratio of phenotypes.
yy
yY
Yy
YY
Y
y
Y
YY
yY
y
The contingency table and phenotype possibilities are:
Yy
yy
Mendel also wondered if the traits were connected to each other in some
way. Were green peas more likely to be smooth, or green ones more
likely to be wrinkled?
The solution to this he reached in a similar way: if they are independent
then there should be a specific ratio of the four possible phenotypes
(green/smooth, green/wrinkled/yellow smooth/yellow wrinkled) in the
population after some number of generations. If they are connected then
the ratio should be different from that – still a specific ratio, but a different
one.
What he found was that the ratio of phenotypes was exactly that predicted
by the independent hypothesis.
This is known as Mendel’s principle of independent sorting.
To simplify the calculations Mendel started with peas he knew the genotypes for. His round yellow peas were RRYY (which
he had to work to isolate) and his wrinkled green ones were rryy. He did not have to work at all to isolate these. Because
wrinkled and green are both recessive then any wrinkled green pea must have this phenotype. We could go either way, but
let’s assume that the Dad’s pollen was RRYY and the Mom’s ovum rryy.
In the first generation the offspring will always get a dominant version of both genes from the Dad and recessive versions
from Mom, so the only possible combinations are various shufflings of RrYy: RY, Ry, rY, and ry. Follow this through and
make sure you see it. If these peas are then used as Mom (ovum) and Dad (pollen) then the next generation will have
more genetic complexity and a contingency table is useful.
And the phenotypes are:
RY Ry
rY
ry
The genotypes are:
RY
Ry
rY
ry
RrYy
Rryy
rrYy
rryy
RrYY
RryY
rrYY
rrYy
RRYy
RRyy
rRYy
rRyy
RRYY
RRyY
rRYY
rRyY
Expected ratio:
9 : 3: 3 : 1
Mendelian genetics can only go so far. The traits that Mendel studied
were the easy ones – the ones with complete dominance and perfect
segregation. Many other traits are much messier, for several reasons. I’ll
only mention a couple of very general ones:
Some traits are influenced by more than one gene. Brown and blue eyes
can be explained by Mendel’s simple model, but green ones result from
the activities of other genes – how much brown gets mixed with the blue.
A little and they’re green, more and they’re hazel, more and they’re just
brown.
Similarly, some genes code for more than one character – the characters
are linked, in other words. In some cases this means that a dominant
trait is nowt often expressed because it is linked to another trait that isn’t
so great for the bearer.
Mendelian models of how many genes in a population behave are very useful for things like
predicting how genetic diseases would spread in the population, or how traits of a certain type
would spread through the population under certain conditions.
These population genetic models have been used in the past to study how evolution would
proceed under various environmental scenarios. Indeed, it was the rediscovery of Mendel’s
work in the early 20th century that led to the resurrection of Darwin’s hypothesis of Natural
Selection as the driving mechanism for evolution in the “Modern Synthesis”.
As it turns out, if “evolution” just means spreading some trait through an existing population
(like, “the evolution of drug resistance”, or of “pesticide resistance” then the models work well.
For those of us who think evolution encompasses the origin of new species and of higher taxa,
population genetics turns out not to be so interesting.
All the published examples of “natural selection” (including the one in your book) leading to
evolution are actually not interesting because they don’t explain where the alternative traits
came from in the first place. They only explain (very well) why one is more adaptive in some
conditions and the other in some other conditions, and so why some populations have more
phenotypes of one sort rather than the other. We’re are left to assume that the same thing that
spreads them around differently also created them, which I think is not wise because it doesn’t
fit the model of “critical thinking”.