THE BIRTH OF GENETICS AND
GREGOR MENDEL'S LAW OF SEGREGATION
(Moti Nissani)
Mendel’s Abbey, 2005
Mendel’s Abbey, a side view, 2005
Historical
Background
Science
begins with simple questions. "Why
is the sky blue?" Why do
non-freckled parents have only non-freckled children?" "Why do pea plants only give rise to
peas, not to cows or roses?" Some
scientific discoveries are made, routinely, by all of us. For instance, sometime during your early
childhood you might have looked at a mirror and figured out, all by yourself,
that you were actually facing your own reflection. Similarly, discoveries, even great discoveries made by
professional scientists, do not seem to require much more than a healthy dose
of curiosity, open‑mindedness, and imagination (and a very small dose of
TV, materialism, and propaganda and memorization masquerading as schooling). Antony van
Leeuwenhoek discovered a whole
world in a drop of pound water. With
his improved telescope, Galileo could see Jupiter's moons. Though we admire the technical ingenuity,
courage to challenge dogmas, or curiosity about the world which such
discoveries require, we understand how the likes of Leeuwenhoek and Galileo could
come around to making them. With a bit
more time, brains, and imagination, we too, we feel, could have discovered the
existence of spermatozoa or Jupiter's moons.
It took genius to discover them, but only "ordinary"
genius. There is, however, another kind
of genius which has an almost magical quality to it. We might, or might not, understand such work, but we are
astounded by the psychological process that gave rise to it. How in heaven's name, we wonder, did it
occur to a "magical" genius to carry out his/her work? And how did this person manage to interpret
it in such a radical new way?
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 Austrian-Hungarian 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?
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] is 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:
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?
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.
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Switch II
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On
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Off
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Switch I
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On
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Off
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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?
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Vial 2
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Red
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Green
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Vial 1
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Red
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Green
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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, freckle-lessness
is more or less true‑breeding‑‑without knowing any of the freckle-less
couples you are familiar with, a geneticist can be fairly certain that their
children are freckle-less 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, 2nd edition, pp. 143-155.
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).