THE
BIRTH OF GENETICS AND
GREGOR MENDEL'S LAW OF SEGREGATION
Mendel’s
Abbey, 2005
Mendel’s Abbey, a side view, 2005
Historical
Background
One such
magical genius was Gregor
Mendel, perhaps one of the greatest scientists of the nineteenth
century. His experiments
not only revolutionized
biology, but left historians of science wondering: What mental processes led to their conception?
How did Mendel have the intellectual courage
to traverse new territories for so many years, totally alone?
What made it possible for him to come up
with his beautiful deductions and with a radically new theory of
heredity? How did he
come to see, for the first time
in the history of biology, that simple numerical ratios provided an
important
key to unlocking one of nature secrets?
Mendel
lived in central Europe, in a
region which now belongs to the Czech Republic but that, during his
lifetime,
belonged to the AustrianHungarian Empire.
He spent most of his adult life as a monk (and later, abbot) in
an Augustinian
monastery. As a farmer's
son in class‑conscious
Europe, the monastic life, in his words, spared him the "perpetual
anxiety
about a means of livelihood." It
also
gave him free time to tinker with peas, tornadoes, hawkweed, bees, and
other curiosities of nature.
He
carried out his experiments with the
common edible pea in his small garden plot in the monastery.
These experiments were begun in 1856 and
completed some eight years later.
In
1865, he described his experiments in two lectures he gave at a
regional
scientific conference. In
the first
lecture he described his observations and experimental results.
In the second, which was given one month
later, he boldly explained them.
The forty
or so scientists which made up
his audience listened to him politely enough, but no one asked a
single
question. Most likely,
they didn't
understand what he was talking about.
Later, he also carried a correspondence with one of the most
eminent
biologists of the time, who also failed to appreciate Mendel's work. In 1886, Mendel’s results
were published in
an obscure scientific journal. He
might
as well dropped a leaded spoon into the ocean; the paper was ignored
by the
scientific community. At
times, he must
entertained doubt about his work, but not always: "My time will come," he reportedly told a friend.
His
time came, though later than he
might have expected. His
emergence from
obscurity began in 1900‑‑sixteen years after his death.
In the West his work was generally accepted
by the scientific community by the 1920s.
Conceptually,
Mendel's experiments were
not all that difficult. His
scientific
contemporaries lacked, for one thing, open‑mindedness.
Moreover, they might have been unable to
accept, deep down, the proposition that an obscure monk, a farmer's
son, and a
person who was discouraged from completing his university education
because he
"lacked insight," could have something important to say.
At any rate, in your case all this is not a
problem. You probably
accept history's
judgment that he was an insightful person and that geniuses can spring
from
impoverished, plebian backgrounds.
What
you do have in common with Mendel's scientific contemporaries is, most
likely,
ignorance of elementary statistics.
The
next section will give you the necessary background information. To get the most out of it,
try to actually
answer each question as you go along.
Probability: Random Events
Q1. Let us first examine the results of single random events. Suppose you toss a coin
once. What are the
chances of getting heads
(H)? ____ Tails (T)? ____
Q2. What are the chances that your next child will be a boy?
____ A girl? ____
Q3. Now toss a coin 10 times and record the number of heads (Hs)
and
tails (Ts) in the space below. (Make
sure
that the process is indeed random.
Flip the coin a few times in your hand before each toss;
examine it only
after it lands on the floor).
H
___
T ___
For the
class as a whole, the results
were: H ___ T ___
Q4. Most likely, some of your classmates' observations are not
in
line with the expected 50/50 distribution?
Why?
Q5. Are class totals more or less in line with the expected
distribution? Why?
Mark
Twain (citing Benjamin Disraeli)‑‑a
contemporary of Gregor Mendel‑‑observed that there are "lies,
damn lies, and statistics." In
a
sense, he was right. If
you tossed a
coin just once, and got H, then you didn't get the 1 in 2 distribution
statistical
theory seems to demand, but a 1 in 1 distribution. Similarly, although each participant flipped a coin 10
times, the
data of some diverged considerably from the expected 1 in 2
distribution. Assuming a
minimum of 10 students in your
class, however, data for the entire class almost certainly approached
the
theoretical expectation of equal odds.
These commonsense observations suggest two generalizations:
‑‑Actual
distributions of
random events rarely match theoretical expectations. A coin that has been randomly tossed 400 times will almost
never
yield 200 Ts and 200 Hs. As
a rule,
something like 195 Ts and 205 Hs is all we can expect.
‑‑The
larger the number of
trials, the closer the fit between observed and theoretical values. Thus, if you toss a coin
just once, theory
demands a 1 in 2 chance of H or T, in real life you would always
observe just
one event. In 30 trials,
you very well
might get a 20/10 distribution.
But in
3000 trials, you will almost never get a 2000/1000 distribution.
Until
artificial offspring sex selection
becomes a reality, the distribution of boys and girls obeys similar
rules. The coin flipper
in this case is nature. To
put it in a somewhat simplified form, as
far as a child's sex is concerned, a woman's anatomy plays a fairly
passive
role. Semen contains two
populations of
sperm in roughly equal numbers.
One
type, when united with a woman's egg, gives rise to a girl (G).
The other, when united with the same egg,
gives rise to a boy (B). For
any given
conception, chance determines which type of sperm will fertilize the
egg.
Q6. What are a couple's chances of having a girl?
Q7. Assuming that either type of sperm is as likely as the other
to
fertilize an egg (reality is a bit more complicated), what is the
expected
distribution of boys and girls in a small village of 100 souls?
___
In a city of two million?
___
Probability: Two Independent Events
Imagine
that you simultaneously tossed a
nickel and a dime. Each
coin alone, we
know already, has an equal chance of yielding H or T, but what can we
expect
when the 2 are flipped at the same time?
Obviously, the nickel can be H or T, and so can the dime. Our problem is putting the
two together to
determine the types of events and their respective probabilities.
Let
us
then construct a table, and carry out an experiment.
Please divide into pairs, and construct the
following table (a penny or a quarter will be just as good).
Simultaneously, one person should toss a
nickel and the other person should toss a quarter. For each toss of the two coins, 4 outcomes are possible. Please record each outcome
with one vertical
line in the table below, and then summarize the total of 10
simultaneous tossed
for your pair. Next,
summarize the
totals for your entire row. We
shall
then summarize, on board, the results for the entire class.
Q8. Our prediction: ??? Our
actual
results for the class as a whole?


Dime 



H 
T 
Nickel 
H 


T 


How can
we explain what we have just
seen? For any given
throw, the nickel
has a 1 in 2 chance of yielding H.
Assuming that the nickel yielded an H, the dime is equally
likely to
yield H or T. So the
chances of
[nickel: H; dime: H] are
one‑half
of that one‑half, or one‑quarter.
Similarly, there is a one‑quarter chance of [nickel: H, dime
T].
The
nickel also has a one‑half
chance of yielding T, leading again to 2 equally probable events;
[Nickel: T,
dime H]; and [Nickel: T;, dime: T].
Looking then at the simultaneous toss of two coins, we have
four equally
probable events, as we have seen.
Similar
probabilities prevail in a large
population of two‑child families:


Dad 



B 
G 
Mom 
G 


G 


In other
words, in a population of
100,000 such families, one expects some 25,000 with 2 boys, 25,000
with an
older girl and a younger boy, 25,000 with an older boy and a younger
girl, and
25,000 with two girls.
These
examples suggest the following
generalization:
‑‑The
probability that two
independent events will occur together equals the product of their
individual
probabilities. Thus,
when you randomly
toss two coins, the two events are independent: the outcome of one has no bearing on the outcome of the
other. Since the
probability of each is 1/2, their
combined probability is 1/2 X 1/2 or 1/4.
You are
ready now to work out a few more
puzzles.
Q9. In this population of 100, 000, what are the chances of
having a
boy and a girl, irrespective of their order of birth? ___
Q10. What are the chances for two girls? ___
Q11. Let's divide these 100,000 two‑child families into 2
categories. The first
consists of
families with 2 girls. The
second
consists of all other two‑child families. How many families would belong to the first group (the one
with 2
girls)? _____ How
many to the second
(all the other combinations)?
If you
divide the second number by the first, the expected ratio between them
would be ___ to 1.
Q12. Imagine that a philanthropist came up with a $1000 prize to
any
family in your community that meets the following conditions:
it has 2, and only 2, natural born
daughters. Imagine that
all qualified
families applied for the bonus, and that after being checked for
accuracy,
100,000 received the prize. The
philanthropist
now comes up with an even more curious announcement:
He will give a $1,000,000 prize to the first
person who would tell him, and then properly explain his deductions,
the
approximate number of two‑child families in this community who do not
have two girls. How
would you go about
getting this prize?


Dad 



B 
G 
Mom 
G 


G 


Imagine
yourself a banker. To
save money, you devised an ingenious
scheme of monitoring the vigilance of your bank's night watchman. At the opposite ends of the
building, there
are 2 light switches. Every
hour during
his 10‑hour shift, the guard must approach one switch and flip a
coin. If it's Heads, he
is to turn the
switch on, if it's Tails, he is to turn it off. He then must approach the second switch and repeat the same
procedure. If both
switches are on, the
light is on. If either
one is off, or
if both are off, the light is off.
You
have installed a special machine that tells you, for every hour,
whether the
light has been on or off. Four
months
and 1000 hours later, you examine the lighting record to determine
whether the
guard should receive a raise or be fired.
You observe that during that time, the light has been on 570
hours and
off 430 hours.


Switch
II 



On 
Off 
Switch I 
On 


Off 


Q13. What are your theoretical expectations for the number of
hours
the lights should have been on and off?
Why? Should the
guard be promoted
or sacked?
Now let
us carry out this thought
experiment. Imagine that
I gave you 2
vials, each containing one red and one
green toothpick.
Each vial is covered with a lid.
At the bottom of each lid there is a hole through which, at any
given
time, the head of one, and only one, toothpick can pass when the vial
is
shaken. So shaking a
vial leads to the segregation
of the two toothpicks‑‑they separate from each other, one remains
wholly inside, the other is protruding out of the vial.
Imagine
that the class is now divided
into pairs. One member
of each pair is
holding the first vial, the other, holds the second vial.
In each case, by shaking both vials at the
same time, either a red or a green
toothpick pops through the hole:
the two toothpicks segregate from
each other. We expect in this case 4 equally probable 2‑toothpicks
permutations. From this
we can
calculate any given ratio.
If a red toothpick is just as
likely to penetrate the hole
as the green one, what is your
theoretical
expectation for 100 trials for both events?


Vial
2 



Red

Green 
Vial 1 
Red 


Green 


Q14. How many are expected to be either Red/Green or Red/Red? ___
Q15. What is the ratio between them [Red/Green + Red/Red]: [Green/Green]? ___ to 1.
Mendel's
Observations
One
wonders what might have happened had
Mendel given three lectures on the subject of heredity, instead of
two, with
the first paper containing the elementary lesson in statistics you
have just
struggled through. But
let's leave
these idle speculations to historians, and see if we can make heads or
tails of
Mendel's observations.
Mendel’s experimental plot, the way it appeared in 2005 (Mendel’s
statue is in the background, to the left)
In
his
day, gardeners could obtain all kinds of true‑breeding pea varieties
from commercial seed houses. For
example,
one variety was guaranteed to give only tall plants (6 ft or so);
another, only short plants (about 1 ft in height). If you crossed one tall plant to itself or to another tall
plant,
collected the resultant seeds some three months later, planted them,
and
observed the height of this second‑generation of plants, all would be
tall. Similarly, only
short plants
would result from a cross between true‑breeding short peas.
This would continue generation after
generation. One stock
would only give
rise to tall plants; the other only to short plants. (Incidentally, in
humans,
frecklelessness is more or less true‑breeding‑‑without
knowing any of the freckleless couples you are familiar with, a
geneticist can
be fairly certain that their children are freckleless too).
Mendel
then crossed the two varieties.
Q16.
Before we continue, can you
guess the height of the offspring?
The
cross Short X Short, we have seen, yields short plants.
Tall X Tall yields only Tall.
But how tall would the descendants of a Tall
X Short cross be?
The
surprising answer is that, in this
case, all the first generation plants were tall.
Q17.
Mendel then crossed these
new tall plants (the offspring of the
Tall X Short cross) to themselves or to each other. Can you guess the outcome?
The
actual results from this cross
were: 787 plants among
the second
generation ("grandchildren" of the original true‑breeding
tall/true‑breeding short "couple") were tall, and 277 were
short. Note that the short characteristic which disappeared from sight
in the
first generation, reappeared in the second.
This means that although the factor which caused short stature
was
temporarily out of sight, it was still there.
Note also that the ratio between tall and short plants was
787/277, or
2.84 to 1 (approximately 3 to 1).
Mendel
obtained similar results for many
other characteristics, suggesting that a general rule is at work here. For instance, in Mendel's
time one could
order dry pea seeds with either smooth or wrinkled surfaces.
Again, Mendel established that neither type
was true‑breeding. When
plants
arising from smooth seeds were crossed to plants arising from wrinkled
seeds,
all their offspring produced smooth seeds.
In the next generation, 5,474 of the plants produced smooth
seeds and
1,850 wrinkled seeds, yielding a 2.96 to 1 ratio (an almost exact 3 to
1
ratio).
These are
some of the observations Mendel
recounted to his audience on that cold February evening of 1865, in
the little
Moravian (a region of the Czech Republic) town of Brno.
A month later he reappeared before them and
put forward an elegant explanation for his results.
Q18. Imagine you found yourself in Mendel's shoes.
What would you tell your audience?
Mendel
deductions are by no means
confined to peas. Owing
to the close
affinity between them, living creatures often obey the same rules. When crossed to fruit flies
of the same
strain, red‑eyed individuals produce only red‑eyed offspring while
brown‑eyed individuals produce only brown‑eyed offspring.
In one experiment, all the progeny of a
cross between a red‑eyed male and a brown‑eyed female had red
eyes. When these sisters
and brothers
were mated to each other, they produced 308 red‑eyed and 93 brown‑eyed
offspring.
Q19. Please use the
insights
you gained from this exercise to explain these observations.
Bibliography
Campbell
et
al. 2007. Essential Biology, 2^{nd} edition, pp.
143155.
Carlson,
E.
A. The Gene:
A Critical History (1966).
Iltis,
Hugo. Gregor Mendel and
his Work
(1943). Reprinted in: Shapley, H. et al. (eds) A Treasury of Science
(1958)
Mendel,
Gregor. Experiments in
plant‑hybridization. In:
Peters, James A. (ed) Classic
Papers
in Genetics (1959).