This is a set of notes and summaries to accompany the
text of Mendel's paper. The notes are arranged
according to the section of the paper to which
they're most relevant.
This page may also serves as a table of contents for the
original text, and annotated English translation,
of Mendel's paper, although a
separate Table of Contents for Mendel's
Paper exists as well. Note that the
sections of the paper
are numbered for convenience only; Mendel did not include
numbers with his section headings in the manuscript of 1865. (My
apologies to lynx users who have their links numbered.)
About Mendel's paper and the English translation at MendelWeb
- Mendel's paper began as two lectures, delivered in German on
February 8 and March 8, 1865, to the
Naturforschedenden Vereins (the Natural History Society) of Brünn
(now Brno, in the Czech Republic). The Society had been in
existence only since 1861, and Mendel had been among its founding members.
According to a letter he wrote to Carl von Nägeli, a
Professor of Botany at the University in Munich, in 1867, one of the
the lectures was to inspire botanists and other experimenters to
replicate or try to verify his results. In this he was disappointed;
"as far as I know,"
he wrote, "no one undertook to repeat the experiments." (Mendel , p. 4).
- Mendel turned these lectures into a (long) paper, written in
published in the 1866 issue of the Verhandlungen des naturforschenden
Vereins, the Proceedings of the Natural History
Society in Brünn. 115 copies of the journal are known to have
been distributed (Olby, p. 103), and one
even found its way into the library of Charles Darwin. We know that
Darwin did not read Mendel's paper (the pages were uncut at the time
of Darwin's death), though he apparently did read
other articles in that issue of the Verhandlungen. Like
Darwin, most of the journal's recipients seem to have been
uninfluenced by Mendel's
- The version of Mendel's original paper at MendelWeb is based on
the text reprinted in the Journal of Heredity (vol. 42,
#1, 1951) and corrected by Blumberg using the copy of Mendel's
manuscript reproduced in Gedda
- An English translation of Mendel's paper was commissioned by the
Royal Horticultural Society of Great Britain, and was
published in its Journal in 1901,
as "Experiments in Plant Hybridization". The translator
was Mr. C. T. Druery (Bateson
- William Bateson reprinted the Druery translation with small
modifications in his book Mendel's Principles of Heredity: A
Defence (1902). This text has been widely reprinted, and has
often been called the "Bateson translation" (e.g. in
Peters ), even though
the version is mostly the work of Druery.
- Although a more contemporary English translation has appeared
(see Stern & Sherwood ), the
translation at MendelWeb is based on the Druery-Bateson version,
with slight stylistic and structural modifications by Blumberg,
based on the copy of Mendel's manuscript mentioned above.
Although this translation may strike readers of German as painfully
inaccurate in places, its significance in the history
of genetics is beyond dispute; when English and American biologists
and students of biology read
Mendel in the first decades of the 20th century, they most often read
the Druery-Bateson translation. I address, and explain the importance
of, some of the translations (and mistranslations) in these Notes, and
in the MendelWeb Glossary.
Mendel writes that his experiments have been motivated by the
observation that, in many cases, the
results of hybridization
have been predictable. He mentions Joseph Gottlieb
Kölreuter (1733-1806), Carl Friedrich von Gärtner
Max Ernst Wichura (1817-1866), and others, as
examples of botanists who have carefully investigated the hybrids of
various species. He notes, however, that no law that would allow one
to predict the form of the hybrids
from the forms of the parents has yet been formulated. This is not
surprising, he says, since the experiments necessary to arrive at such
a law or formulation are difficult, both because they require a great
amount of time to carry out, and
because they must be carefully designed in order
to be successful. In conclusion, Mendel writes that he
will now report the results of the carefully
designed experiments he
has carried out over the past eight years.
- By 1865, the genre of the scientific paper, whether in botany or
in the physical sciences, was well-established (see e.g. Bazerman ). Thus in Mendel's paper it
is not surprising to find, in a brief introduction, a statement about
the motivation for the experiments described in the paper, a summary
of previous work and a claim that the previous work is lacking in
- Mendel makes clear that he is interested in finding a law or
law-like relation that governs the production of hybrid forms, and
that the kind of law he desires will be quantitative as well as
qualitative; he wants to be able to predict not just the kinds of
hybrids that will appear, but their "statistical relations" as
- It's difficult to know exactly what Mendel means by the
experiments", but his training and interest in experimental physics
seems to have led him to the view that the proper way to arrive at a
law governing hybrids was to investigate the behavior of specific
traits, or characters, of those
hybrids (rather than considering the form of the plant as a whole). It
was this decision to look at single characters of plant hybrids
that distinguished Mendel's experiments from those of his
- Mendel's emphasis on the need to perform the experiments over long
periods is, in part, a criticism of work of C. F. von Gärtner.
Gärtner's 1849 book, Versuche und Beobachtungen über die
Bastarderzeungung im Pflanzenreich (Experiments and
Observations concerning the Production of Hybrids in the Vegetable
Kingdom), cited by Mendel, related
a number of
experiments on a variety of plants including
In many cases, however, Gärtner failed to investigate the
individual characteristics of the hybrids into the second and third
generations. In a letter to Carl Nägeli, dated December 31, 1866, Mendel
went further and complained that Gärtner had failed to
give a "detailed description of his experiments," such as would have
allowed them to be carefully replicated. (Mendel )
- By beginning the list of predecessors with Kölreuter and
Gärtner, Mendel reveals what a short and inglorious history the
study of hybrids had prior to the middle of the 19th century. While
hybridization techniques had been used since ancient times to create
new and useful forms of plants and animals, the value of hybridization
studies in the investigation of inheritance was doubted by those
interested in such questions. Although Kölreuter had published
Vorlaufige Nachricht von einigen das Geschlecht der Pflanzen
betreffenden Versuchen und Beobachtungen (1761-1766), a work
that showed the possibility of crossing plants artificially and of
investigating the laws that governed their appearances, his work was
not widely appreciated. Of Kölreuter's work and the neglect of
hybridization studies, Gärtner
wrote , in 1849,
"Hybridization in its scientific significance was so little thought
of, and at the most regarded merely as a proof of the sexuality of
plants, that the many important suggestions and actual data which this
diligent and exact observer recorded in various treatises have found
but little acceptance in plant physiological papers up to the most
recent time." (quoted in Roberts
 p. 78)
- Although it is unclear how we should understand Mendel's use of
the term evolution in this
section, by 1865 the investigation of hybrids was thought by most
naturalists to bear more on questions involving species evolution
than on questions of inheritance. As pointed out by Orel and Hartl  (p. 446), this
was not the
case when Mendel began his experiments in the 1850s, before the
publication of Darwin's Origin
 Selection of the
 Auswahl der Versuchspflanzen.
Mendel describes the requirements that experimental plants
must meet in order for the experiments to succeed: 1) They must
possess characteristics that can be observed in every generation
-- flower color
is a good trait to study only if every plant in every generation bears
flowers; 2) The characteristics must allow for precise,
"objective" measurement --
using the term "long" to describe the stem of a plant is a good measure
only if there is no disagreement about whether a particular stem is
long or short; 3) The plants must allow for controlled breeding,
so that for
any given hybrid one can be certain about the origin of both the
pollen and egg that produced it; and 4) The plants must have constant
meaning that the hybrids must all be as fertile as the parental
Mendel then explains that he has selected
Pisum, a genus of Leguminosae that meets all of
the experimental requirements. Furthermore, they can be dependably
crossed artificially; Mendel
briefly describes the technique for doing such a cross, which involves
removing the pollen-carrying stamens and then dusting the stigma with
pollen from another flower.
that he obtained a number of varieties of Pisum and that all
produced constant forms in a two-year trial. Like many plants,
the flowers of the
pea possess both male and female reproductive organs; therefore, if
left to themselves, they will self-fertilize. The specific advantage
with Pisum is that, during this self-fertlization, the
of the flower covers the reproductive organs, so there is no
possibility of pollen coming from other flowers (unless the keel is
damaged or malformed). Mendel writes that he selected 22 of the 34
varieties of peas he first obtained, and that most of these
seemed to be
of the species Pisum sativum (what we call garden
This section of the paper ends with a short discussion of the question
of how to distinguish
from varieties in
plants, and Mendel concludes that the distinction seems in many cases
arbitrary. But he also writes that the distinction is not important for
the purposes of his experiments.
- Mendel's attention to detail in this section is striking, and his
choice of what to explain, and what to leave unexplained, is
characteristic of his choices throughout the paper. He tells us, for
example, the exact number of varieties he procured from the
seedsman, and exactly how to perform an artificial fertilization. At
the same time, he does not explain why he chose only 22 of the
varieties with which to experiment. We can only assume that these
were the seeds that "worked".
- Questions concerning whether or not Mendel should be considered a
"Darwinian" find their origin in this section, and particularly in
Mendel's apparently Darwinian claim about the plastic boundaries
between species and varieties. One difficulty in answering such
questions is that in Mendel's time, and for quite some time
afterwards, the classification of species was a different matter
for botanists than for animal biologists. The definitions of species
proposed by evolutionists frequently involved references to bisexual
reproduction, and these were difficult to apply to plants like peas
(much less to organisms like moss).
Thus, Mendel's implied comment, that two plants
can be considered the same species if experts think they are,
represents a view that necessarily dominated plant biology for a
long time. For an excellent
historical review of how different generations have
addressed the question of whether Mendel was a Darwinian, and whether
Mendel's results were compatible with evolutionary theory,
see Sapp .
- Mendel's final comment on the arbitrary nature of the
species/varieties distinction, seems to echo his earlier comment on
the failure of previous hybrid studies to arrive at a law for the
production of hybrids. Mendel thought about scientific
knowledge more like a physicist than a natural historian, in that
necessary and sufficient conditions in his definitions, and laws to
describe the production of hybrids.
- Often the style of a scientific paper is meant to convey the
uncertainty and open-endedness of experimentation, even as it's clear
that by the time the article is written, the experiments described in
the article are over and the results are known.
Mendel's paper tells the story of a series of
experiments, and narrates them as if they are being carried out while
the paper is being written; yet, we know that this really isn't (and
case. Similarly, Mendel first describes the requirements that his
experimental plants must meet, and then reveals that he has
found a species that meets exactly
those requirements. The narrative creation of suspense and the
fabrication of experimental time, combined
with a feigned ignorance of the experimental outcomes, is part of a
rhetorical strategy common in experimental science papers.
 Division and Arrangement of the
 Eintheilung und Ordnung der
Mendel states that the goal of the
experiments is to observe how the
of parental (true-breeding) plants combine, when they are
crossed artificially to produce hybrids;
and how these characters are then
transmitted to the offspring of those hybrids. He wants to find a
law that describes (and thus can be used to predict) the forms of
those offspring. Mendel
lists more than a dozen observable characters (or traits) of the pea,
and then describes the seven he will follow in the experiments. Each of
the characters exhibit two, and only two, forms, and each form is
easily distinguishable from the other; for example,
the distinction between the
"long" stem (6 or 7 feet tall) and the "short" stem (approximately a
foot tall) is not a subtle one.
The experiments begin with Mendel's crossing plants exhibiting one of
the forms of each character, with plants exhibiting the other form.
This is carried out by artificial fertilization, meaning that pollen
from one plant is brushed onto the
stigma (and thus eventually
united with the
eggs) of the other. In order to assess whether his results were biased
by which plant was the pollen (or egg) donor, Mendel
did "reciprocal crosses", using the same varieties sometimes as pollen
donors and sometimes as egg donors (called here "seed bearers").
Mendel reports choosing only the most
"vigorous" of the plants for further experiments, and describes the
use and importance of controls,
which were experiments he carried out
in a greenhouse.
He concludes with a discussion of the minimal risk
of false impregnation (meaning a fertlization in which the pollen
donor is not clearly known) in
- For the purposes of the experiments described by Mendel,
the growing season of the pea plant can be considered to have
three stages (combined in the
peas (as seeds) are planted in the
Spring. Then, in the early summer, flowering plants appear, and all the
characters associated with the plant and the flowers are considered of
the same generation as the peas that produced them. Fertilization
takes place in the flowers. Finally, in the early Fall,
pods appear where the summer
flowers were, and inside the pods are peas. The pods are of the same
generation as the peas and the plants that bore them; the
peas inside the pods are of the next generation -- the peas that
appear in the Fall are the offspring of the peas planted in the
- When the flowers appear in the summer, one option with
Pisum is to do nothing, to let the plant self-fertilize. The
pollen from the stamens falls onto the pistil (all inside the
protective covering of the keel),
and soon the pods begin to grow.
Mendel carried out his "artificial" fertlizations by opening the keel,
and bringing the pollen from one plant to the stigma of
- Mendel's use of controls is
quite extraordinary here, as there seems to have been no precedent for
this technique in the botanical (or biological) literature. The value
of this parallel set of experiments is clear, particularly in Mendel's
use of the indoor results to dismiss certain outdoor results
(e.g. those he
attributes to beetles); it's worth emphasizing that with
controls are used not simply to support or corroborate good results,
but to provide reasons to discount the significance of
poor or unexpected results as well.
- As remarked in earlier sections, it is interesting to note the
things that Mendel explains in great detail, and those things he never
explains. For example, while he gives a number of gardening details
that might be thought unnecessary in a scientific paper, and he is
very frank about his simply discarding
plants he considers poor or unreliable
data. Yet, he does not explain how or why he chose exactly the
seven characters he did -- his list includes fifteen
 The Forms of the Hybrids
 Die Gestalt der Hybriden.
Mendel says that previous experiments with flowering plants
when plants with different character forms are
hybrids do not appear to be a balanced
blend of the parental forms.
Indeed, sometimes the hybrids exhibit one parental
form to the exclusion of the other and this, he says, is what happens
with the pea hybrids. That is, when artificial fertilization is
carried out on parental (true-breeding) plants differing in the form
of a particular character (e.g. pea color), the form of that character
in the offspring is either that of the pollen parent, or the egg
parent, but not both and not a blend of the two.
For each of the seven characters, Mendel identifies the parental form
that appears in the hybrid (e.g. round peas, long stems, green pods),
and calls that form dominant. The
parental form that does not appear in the hybrids (e.g. angular peas,
short stems, yellow pods), he calls the recessive.
Mendel also notes that these results do not depend on which parent
donated the pollen and which the egg, and cites Gärtner to
support the view that, when faced with a hybrid form, it is not
possible to tell from which parent a particular character form has
Mendel concludes by mentioning certain dominant forms which, in the
hybrids, are not identical with that form in the parents. He also
notes that some of the hybrid characters can be observed immediately
following the artificial cross of the parents; this is so because the
peas which grow in the pods, which grew from the fertilized
seed-bearing flower, are the offspring of that flower.
- The idea that offspring are simply a "blend" of their parents was
a widely held view in Mendel's time; today,
when someone speaks of
being "2/3 Russian", or having some "Irish blood", they are using
metaphors that derive from, or are only strictly compatible with, a
theory of blending inheritance. Thus it is
important to see that Mendel questions this view immediately, noting
that his experiments show that perfect blending is not common and
complete dominance of one form is not uncommon.
- The notion that the pollen parent exerts no more (and no less)
influence in the determination of the form of the hybrid is emphasized
by Mendel. The theory of "equal contribution" that such an idea supports
was not common either in 19th century studies of inheritance
or of evolution.
- Mendel's concluding comments describe examples of "hybrid vigor"
cases in which the form of the hybrid is an extreme example of one of
the parental forms. Mendel downplays the significance of hybrid vigor here
(and throughout the paper), because he wants to stress that the
hybrids usually look exactly like the dominant parental form; still,
the finding was well known to botanists and animal breeders alike, and
it too seems at odds with a simple notion of blending
- Obviously, every pea plant exhibits all seven characters in every
generation; yet, Mendel
presents his results as if he is looking at only one character on each
plant. Whether or not this was the case we don't know, though the
number of plants necessary for such an approach seems
implausibly large. Still, Mendel's presentation draws attention
to his method of examining the behavior of
particular characters, or parts, of plants, rather than the plants
considered primarily as whole organisms.
 The First Generation From the Hybrids
 Die erste Generation der
Mendel reports here the results of his letting the hybrids fertilize
themselves, and his observations concerning the forms of their offspring.
He notes first that the offspring
of the hybrids exhibit both dominant and recessive forms,
that these appear to be in a ratio of 3:1, and that no forms other
than the 2 parental forms appeared in this generation.
Mendel presents data from experiments involving each of the seven
characters, and argues that the ratio of
dominant to recessive forms
is approximately 3:1. This is an
average taken from hundreds of plants
and thousands of peas, and he notes that in individual pods, or on single
plants, the ratio of dominant to recessive can be far from 3:1.
Mendel insists that large numbers of experimental plants are necessary
to avoid being misled by "fluctuations", and he also
discusses the need to take
care in properly classifying each pea, and in diagnosing plants that
are sickly or damaged.
The end of this section points to the conclusion that the dominant
form of each character can be of two different sorts: 1) a parental
dominant from which only dominant offspring will come; and 2) a hybrid
dominant, which will produce both dominant and recessive forms when
self-fertilized. Since the appearance
of the two dominant forms is the same, one can only discover whether
the dominant is parental or hybrid by looking at its progeny or
- Recalling his comments in the previous section, Mendel emphasizes
that even in the generation born from the hybrids, blended or
transitional forms do not appear.
- Although Mendel did not use this notation, it is common for
textbook accounts of Mendel's work to refer
to the first generation from the hybrids as the F(1), or "first filial
generation". The generation born of the F(1) is then called the
- The modern distinction between
of an organism, and genotype, the genetic composition or
make-up of the
organism, has its origin in this section of Mendel's paper. In finding
that a dominant form may indicate either a "pure" genetic make-up, or
a "hybrid" make-up (and that there is no way to tell without growing
the plants for another generation), Mendel's work gave rise both to
investigations of visible patterns of character inheritance, and
to attempts to find the material, inside the organism, that is
responsible for these patterns.
- Mendel's report of the reappearance of the recessive forms
in the first
generation from the hybrids would seem to be the first inspiration for
the use of "information"
metaphors to describe the workings of inheritance. Since the hybrids
produce both dominant and recessive offspring, though they appear only
dominant, it is perhaps natural to think of the recessive form as
being somehow "encoded" inside the hybrid plant.
- Mendel's is a statistical argument, since he doesn't report
observing an exact ratio of 3:1 in any particular plant or pod.
Mendel does not here address the
issue of exactly how many plants must be grown in order for the
observed ratios to be considered accurate or "real". In Mendel's view,
which resembled that of 19th century physicist versed in statistics,
the number of plants can be too small, so that the "fluctuations"
too much influence on the observations and thus disguise
the underlying ("real") ratios.
His casually calling the ratio 2.98:1 a ratio
of 3:1, implies a belief that the observed ratio would in fact
approach 3:1 as the number of experimental plants and
peas was increased.
 The Second Generation From the Hybrids
 Die zweite Generation der
Mendel lets the first generation from the hybrids self-fertilize and
observes their offspring; the offspring belong to the
second generation from
the hybrids. Mendel begins by reporting that the recessive forms
bred true; that is, plants that exhibited recessive forms of
particularly characters produced all and only recessive forms of those
characters in the next generation. For example, Mendel found that short
plants in the first generation produced only short plants in the
second, and green peas of the first generation produced only green
peas in the second.
Mendel then reports that 2/3 of the first generation dominants
produced both dominant and recessive forms, while 1/3 produced only
dominant forms. He concludes that 2/3 of the first generation
dominants must be like the hybrid dominants observed in previous
generations, while 1/3 must be like the parental (or true-breeding)
dominant. He presents data from experiments concerning each of the
seven characters, and argues that the average ratio approximates
2:1 (i.e. 2/3 : 1/3).
Putting the results from this and the previous section together, Mendel
concludes that the 3:1 ratio of dominant to recessive forms observed
in the first generation from the hybrids, can now be represented as a
ratio of three kinds of forms:
hybrid dominant, parental dominant, and recessive. He
writes that the ratio of these is 2:1:1, respectively.
Mendel concludes that these ratios show that, for a given
character in a (self-fertilizing) hybrid plant:
1) the hybrids form seeds
having one or the other form of that
character; 2) half of the hybrids produce hybrid offspring;
3) half of the hybrids produce constant (i.e. true-breeding, or
parental) offspring; and 4) half of the hybrids that produce
constant offspring produce dominant forms, and half produce recessive
- Mendel distinguishes in this section between the ratio of
dominant to recessive forms, and the ratio of parental dominant,
hybrid (dominant) and recessive forms. The former refer to the way the
plants and peas appear, while the latter refers to the kinds of
offspring they will produce. Today we would call the former a
phenotypic ratio, and the latter a genotypic
- Although the ratio of dominant to recessive forms could be
assessed by direct observations, in order to discover the
distribution of parental dominants, hybrid dominants and recessives in
a particular generation, Mendel had to observe the plants and peas
in the next generation.
- The final paragraph of the section presents the results that
Mendel feels a good theory must explain. That is, what is required is
a theory that assumes hybrids produce both dominant and
recessive forms of seeds, and explains how, when those
seeds are united in
fertilization, the offspring are 1/2 hybrid dominant, 1/4 parental
dominant, and 1/4 recessive.
- One of Mendel's strategies in writing this paper was to first
present his experimental results, without overtly theoretical
explanation, and then later discuss a theory to explain those
results. Of course, we have no reason to think that Mendel couldn't
or didn't experiment and theorize at the same time, so his
method of separating experiment and theory in the paper
is worth noticing.
- Although the next section makes the point more explicitly,
this section makes it clear that the 3:1 ratio found in the first
generation from the hybrids does not imply that, in the long run,
there will be three times the number of dominant forms as
recessive. A misunderstanding concerning this point led to the famous
paper by the mathematician G.H. Hardy (Hardy ), which in turn was the
foundation for the Hardy-Weinberg Law in population
 The Subsequent Generations From the
 Die weiteren Generationen der
Mendel says that the subsequent generations from the hybrids exhibit
the same inheritance patterns that were found in the first two
generations. That is: parental dominants breed true, producing
only parental dominants; recessives also breed true; and hybrids
produce parental dominants, hybrid dominants, and recessives in a
ratio of 1:2:1.
Mendel remarks that other botanists have noted that hybrids are
"inclined" to revert to parental forms. He explains that this
follows simply from the model he has been describing; namely
that, over time, many more constant (or
parental) forms are produced than hybrid forms. Mendel presents a
mathematical model to show how this comes to be.
Representing the offspring of the hybrids with the series A + 2Aa +
a (to represent the production of parental dominants, hybrid
dominants and recessives in a 1:2:1 ratio),
Mendel constructs a table showing how the
distribution of different forms will evolve. The notation reflects
Mendel's view that, for a given character, the hybrids (Aa) produce
seeds for both forms of that character.
For the purposes of the
demonstration, Mendel makes several simplifying assumptions, including the
assumption that every plant produces only 4 seeds and thus only 4
plants in the next generation.
For example, if we were to begin with 1 parental dominant, 2 hybrids
and 1 recessive in the "1" generation:
1) the parental dominant would produce 4 plants in the
next generation and all would be parental dominants; 2) the recessive
would produce 4 plants and all would be recessive; and 3) each hybrid
would produce 4 plants, 2 of which would be hybrid, 1 of which would
be parental dominant and 1 of which would be recessive. Thus in
generation "2" we will have 6 parental dominants, 4 hybrids and 6
recessives. In his table, Mendel carries out this sort of calculation
for several generations and presents a formula for the number of forms
in the nth generation as well.
- There is a transition in this section of the paper, from an almost
naive presentation of experimental results to a noticeably theoretical
Mendel adopts a notation that reflects his view of the kinds and
proportions of seeds produced by parental and hybrid forms. He then
uses this notation in a mathematical model that generates
predictions about the distribution of those forms in future
generations. In later sections of the paper, when
experimental results are seen to match the predictions of this model,
Mendel will argue that the assumptions of the model must therefore
- From this section, and the section that follows, it is clear that
Mendel wants to stress the 1:2:1 ratio as the pattern of offspring
produced by the hybrids, and therefore as the pattern that any good
theory must account for.
- In the reference to Gärtner and Kölreuter, we see the
sort of descriptions Mendel wishes to replace with laws. Rather than
talk of "inclinations" and "reversions", terms that seem to imply
intention on the part of the plants, Mendel prefers to show that the
observations can be derived from a mathematical (and thus
non-intentional) model, and that
inheritance patterns are the consequence of laws or at least are
the expression of law-like behavior.
- Mathematics allowed Mendel both to formulate models from which
to derive predictions (and other models), and to avoid questions
concerning the physical mechanisms and material basis of heredity.
Though we sometimes think of mathematical arguments as being "deeper"
than those that use only natural language, Mendel's case shows how
mathematics can be used to simply avoid the questions
non-mathematicians find deep.
Concerning the role of mathematics in biology, a role pioneered by
Mendel and others, the biologist Jean-Pierre Changeux has said:
"Mathematics plays a definite predictive role for the biologist, but a
limited one. It doesn't give us direct access to structure.
... Mendel showed that the hereditary transmission of color in pea
blossoms follows a behavior expressed by an extremely simple
mathematical equation. These laws make it possible to infer the
existence of stable, hereditarily transmissible determinants, but they
certainly didn't predict that chromosomes, much less DNA, are the
material supports of heredity." (Changeux and Connes , p. 60).
 The Offspring of Hybrids in Which Several Differentiating Characters are Associated
 Die Nachkommen der Hybriden, in
welchen mehrere differirende Merkmale verbunden sind.
The experiments Mendel presents prior to this section
record and analyze the behavior of the forms of single
characters. In this section, Mendel says he will see whether the
law he found to govern the transmission of single characters "applies"
when more than one character is observed during crossing and over
several generations. He continues to use the notation introduced in
the previous section; for a given character, he uses a single capital
letter to represent the parental dominant, a single small letter to
represent the recessive, and the capital-small combination to
represent the hybrid.
The first experiment involves a cross between plants grown
from round and yellow peas, and those grown from wrinkled and green
peas. Mendel says he used a large number of plants for the cross, and
that the (hybrid) peas resulting from this cross were all round and
yellow; i.e. the hybrids exhibited the dominant form of each of the two
Mendel then lets these hybrids self-fertilize and observes the forms of
the peas in the first generation from the hybrids. He finds that four
different kinds of peas result, with the greatest number being of the
round and yellow (i.e. double-dominant) form, and the smallest
number being wrinkled and green (i.e. double-recessive). In order to
figure out what the distribution of parental dominant, hybrid and
recessive forms is in this generation, he lets
the plants grown from these peas self-fertilize, and observes the
forms in the next generation. He finds:
Mendel divides these offspring, the second generation from the
hybrids, into nine different categories,
each with a different symbolic representation (because Mendel
is studying two
characteristics of peas, each of which can be represented as
parental dominant, hybrid, or
recessive forms, there are 3^2 or 9 possible representations).
Mendel then reduces the nine groups to three:
- The plants from the green and wrinkled peas produce only green
and wrinkled peas; i.e. they breed true
- Some of the plants grown from the round green peas produce both green
round, and green wrinkled peas, while others produce only green round
- Some of the plants grown from the wrinkled yellow peas produce
both yellow and green wrinkled peas, while others produce only yellow
- Some of the plants grown from the round and yellow peas produce
only round and yellow peas, others produce yellow and green round
peas, others produce round yellow and wrinkled yellow peas, an yet
others produce round yellow and green peas and wrinkled yellow and
Mendel notes that the ratio between these three groups of offspring
(33:65:138) seems close to 1:2:4, and this, he says, is the
parental dominants, hybrids and recessives was in the first generation
from the hybrids. Thus, Mendel
represents the first generation from the hybrids,
in the two-character cross,
by the series:
AB + Ab + aB + ab + 2ABb + 2aBb + 2AaB + 2Aab + 4AaBb.
He notes that this expression is just the combination
(i.e. product) of the two single-character
expressions for the first generation from the hybrids
: A + 2Aa + a and B + 2Bb + b.
- Those offspring that have parental, true
breeding forms of both characters: AB, Ab, aB and ab. Each, he says,
is represented about 33 times; they all
will breed true in subsequent generations.
- Those offspring that have one parental form and one
hybrid form: ABb, aBb, AaB, and Aab. Each appears approximately 65
times, he says, and they will vary only in the
hybrid form in subsequent generations.
- Those offspring that are double-hybrid, AaBb, of which there
Mendel goes on to report the results of an experiment involving three
characters (the third being the color of the seed coat). As in the
previous experiment, he finds that the
combination series that represents the
first generation from the hybrids is just the product of the
single-character expressions: A + 2Aa + a, B + 2Bb + b, and
C + 2Cc + c.
Mendel concludes from these results that, in a multiple-character
cross, the behavior of each character is independent of the others. In
other words, the "law" that applied to "each pair of
differentiating characters" continues to apply when several characters
are studied at once.
The independence of different characters gives rise to several
calculations of the number of forms possible in multiple-character
crosses. If one is concerned only with the constant or parental (i.e.
dominant and recessive) forms of each character, then in a cross
characters, in which both forms of each character are represented in
the parental generation, there will be 2^n possible forms produced in
the first generation from the hybrids. If we are concerned with three
forms per character (parental dominant, hybrid and recessive) then
there will be 3^n forms in that generation; therefore,
3^n will also be the
number of terms in the combination series for that cross.
Mendel notes that all of
the forms predicted by these calculations appeared in his
Following a paragraph about the investigation of the character of
flowering time in
the hybrids, Mendel repeats the conclusion that the
characters behave independently in multiple-character crosses. The
section ends with Mendel's strong claim
that the predictable
behavior of the characters he has observed in these experiments
must be similar to the behavior of all the characters of the plant.
- Mendel's euphoric use of numbers in this section may be
a bit overwhelming, but his basic results are the same as in previous
sections: the ratio 1:2:1, which describes the offspring of the
hybrids, is the "law" which allows one to predict the form of the
offspring from the form of the parents. This is so, this section
shows, no matter how many characters are observed.
- Mendel's choice of which characters to study here is revealing,
because while the two-character offspring can be observed in the same
growing season as the fertilization that produces them (the flower is
fertilized in the summer and the peas appear in the early Fall), the
third character cannot be assessed until the following year.
Corcos and Monaghan (p. 115)
Mendel could have made his experiment easier by picking three
characters observable at the same time (e.g. stem length, pod shape
and pod color); but perhaps Mendel deliberately tried to choose
characters that seemed immediately observable, even though
they were not.
- Although this is the first section in which multi-character
crosses are described, we know that all of Mendel's crosses
involved more than one character! Mendel was obviously observing
several characters on every plant throughout his experiments,
and it is only in the
presentation of his results that he "pretends" to start with
observations concerning one character, then two, then three and so
on. The purpose of this pretense is a rhetorical one and, from his
letters and his autobiography, we know that Mendel
recognized that a good scientific investigation involved careful
experimental and communicative techniques.
- Hybrid flowering time was not one of the characters listed by
Mendel in the third section of the paper,
and the paragraph about flowering time may seem a bit out of place.
Perhaps Mendel wished to acknowledge his recognition of character
forms that were intermediate in hybrids (flowering time is such a
character), or perhaps he was addressing a question raised during his
presentation at the Brünn Society. Whatever the case,
this paragraph does seem a strange insertion, followed as it is
by a return to the previous discussion of multi-character
- Although it is easy today to dismiss Mendel's claim about similar
relations holding for all characters, it is worth trying to figure out
how Mendel could have held this view. Perhaps he thought that, just as
the complex results of multiple-character crosses could be "reduced"
to single-character expression, so the behavior of more
complex characters (flowering time perhaps?) could be reduced to
simple expressions for factors governing those characters.
 The Reproductive Cells of the Hybrids
 Die Befruchtungs-Zellen der
Mendel begins by presenting conclusions he has reached concerning the
kinds and proportions of pollen and egg cells produced by both
hybrid and constant (i.e. parental) plants. Since constant forms breed
true, Mendel writes, they must produce only one sort of pollen and egg
(i.e. that which is capable of producing the constant offspring).
produce constant as well as hybrid offspring, they must
produce more than one sort of pollen and egg; but, given
that the constant
forms they produce are indistinguishable from
the constant forms
produced by parentals, the hybrids must produce the same sorts of
pollen and eggs as the parents, but in some combination.
Mendel says that
these conclusions are sufficient to account for the patterns of
inheritance he has observed, provided one also assumes that hybrids
produce the different kinds of pollen and eggs
in approximately equal numbers.
Mendel then describes an experiment designed to test these conclusions
(which are the foundations of his theory concerning the reproductive
cells of the hybrids). He begins with parental, round and yellow peas,
and green and wrinkled peas. He plants them, allowing some to
while performing artificial
fertilization on others. Consequently he
has, in the next generation, both hybrids and parental forms. He
performs a series of crosses and observes whether the pattern of forms
that appears in the offspring
is consistent with his theory of pollen and egg production.
In first experiment, Mendel performs the following crosses:
Mendel goes on to describe a similar experiment, in which long-stemmed
violet-red flowering plants are crossed with short-stemmed white
flowering plants, and the idea is again to observe whether the results
are consistent with Mendel's view of how parental and hybrid plants
produce pollen and eggs.
- 1. The pollen from plants grown from parental yellow and round
peas is united with
the eggs of the hybrids (which are
plants grown from peas which also appear
yellow and round). Under
Mendel's assumptions, the parentals make only one sort of pollen, and
the hybrids make four sorts of eggs: those which carry the yellow
round form, those which carry the yellow wrinkled form,
those which carry the green round form, and
those which carry the green wrinkled form.
Also according to Mendel's assumptions, the hybrids will make
these sorts of eggs in roughly equal numbers.
Of course the peas produced from this cross will all appear
round and yellow, since round and yellow are the dominant forms and
will therefore "cover" any of the recessive forms. But some of these
yellow round offspring will be parental dominants (AB) while
others will be hybrids (e.g. AaBb). Because the pollen
carried a double-dominant form,
Mendel cannot observe anything about the sorts of eggs produced
by the hybrid unless he plants these round yellow peas, lets them
self-fertilize and examines their offspring. Only then can he
determine, in retrospect, the sorts of eggs made by the
- 2. The pollen from plants grown from green and wrinkled peas
(one not need to say "parental" here, since that is the only
sort of green and wrinkled peas that exist) is crossed
with the eggs of the hybrids. On Mendel's
assumptions, the green wrinkled pea plants produce only
one sort of pollen
(represented as ab), while the hybrids produce four
sorts of eggs, in approximately equal numbers (represented as
AB, Ab, aB and ab).
Because all the pollen carry recessive forms, any eggs carrying
character forms will "cover up" the forms carried by the pollen.
Therefore, in the next generation one should find four kinds of
round (abAB), yellow wrinkled (abAb), green round
(abaB) and green
these should appear in roughly equal proportion. This is
exactly what Mendel reports finding.
- 3. The eggs from plants grown from parental yellow round peas
are crossed with the pollen from the hybrids. On Mendel's assumptions,
the eggs will be of only one sort (AB), while the hybrids
will produce four kinds of pollen, in equal proportion. Although the
offspring here will all look yellow and round, Mendel will be able to
discover the kinds of pollen produced by the hybrids by allowing these
yellow round offspring to produce plants, self-fertilize, and produce
another generation of peas.
- 4. The eggs from plants grown from green wrinkled peas are crossed
with pollen from the hybrids. On Mendel's assumptions, the eggs will
all be of one sort (ab), while the hybrids will produce four
kinds of pollen (AB, Ab, aB and
ab). Since the eggs carry recessive forms, the kinds of
pollen produced by the hybrids will be evident in the offspring.
Mendel's theory predicts four kinds of offspring (yellow
round (ABab), yellow wrinkled (Abab),
green round (aBab) and green
wrinkled (abab)), in equal proportion, and
these are the kinds (and proportions) Mendel reports finding in the
Before giving the results of either experiment, Mendel points out
that one should not expect
perfect agreement between the predicted ratios and the
actual ratios. Still, in the offspring he finds that the actual
ratios are quite close to those predicted (e.g. 20:23:25:22 as an
instance of the predicted ratio 1:1:1:1), and the experiments, he
says, successfully confirm his initial assumptions about the
production of pollen and eggs. Specifically, they
confirm the view that if a plant is hybrid for a given
character it must produce pollen and eggs for both forms of that
character, and in equal proportion.
Mendel elaborates on the meaning of these assumptions, by looking at
the model for the first generation from the hybrids, the offspring
represented by the series: A+2Aa+a. He notes that
in this expression, there are four individuals distributed into three
different classes (1 parental dominant, 2 hybrids, and 1 recessive).
The four individuals are produced, he writes, by
only two sorts of reproductive cells, A and a, which
are produced in equal proportion by the hybrid.
Using this model, Mendel shows how
the pollen cells of the
hybrid (A and a), when united randomly
with egg cells of the hybrid (A and a), produce
both parental and hybrid forms in a proportion of 1:2:1. He
emphasizes that this shows how hybrids
come to produce not only constant
forms but hybrids as well; and thus the process of self-fertilization
in the hybrid can be considered a "repeated hybridization" in addition
to a generation of parental forms.
Finally, Mendel uses this model to predict the forms that appear in the
first generation from the hybrids when more than one character is
considered. He derives the
two-character series arrived at in the
eighth section of the paper, and writes that the
three-character series from that section can be derived as well.
Mendel concludes by stating that the law which governs the production
of hybrids, which he identified in the early sections of the paper, is
explained by this theory of pollen and egg production.
Specifically, the ratios and patterns he observes in single and
multi-character crosses follow directly from the principle
that if a plant is
hybrid for a given character, it will produce pollen and eggs for both
forms of that character, and in equal proportion.
- Mendel's theory of how reproductive cells are produced in hybrids
is often called the "law of random segregation". It states that a
hybrid produces both "dominant" and "recessive" reproductive cells, in
The second "law" attributed to Mendel, that of "independent
assortment", is also evident in this section of the paper, in the
discussion of the production of pollen
and eggs in plants hybrid for more than one character. Here, the law
implies that the distribution of "dominant" and "recessive" forms of
one character, in the reproductive cells, is
independent of the
distribution of forms of the other characters.
- It is interesting to note that in earlier sections, when Mendel
presented experimental data followed by model ratios, he gave no
disclaimer concerning how well one should expect the data to "fit"
those ratios. In this section, he presents the models first, and warns
the reader that the fit of the data to those models will not be
perfect. Such a disclaimer is rather peculiar, since it's not clear
who he worries will think there should
be perfect agreement between the model
and the data; and because, in the experiments reported in this
section, the data is remarkably close to the
predicted ratios, and closer than the experiments reported in any
other section of the paper.
- Similarly, this section is perhaps most famous because of
controversies about whether Mendel's data was "too good" (i.e.
whether Mendel did not report his data honestly). This issue was first
raised by the statistician and biometrician R. A. Fisher (see
Fisher ) and continues to
provoke comment (e.g. Corcos and Monaghan
). The data presented in this section -- the numbers
the predicted ratios of 1:1:1:1 -- is probably the clearest example in
the paper of
data that "fits more closely than can be expected from accidents of
sampling" (Wright , p.
173). Yet it remains unclear what important conclusions one can
draw from a statistical observation of this kind.
- For more than thirty years, one of the most common
sources for an English version of Mendel's paper has been
Classic Papers in
Genetics, edited by James A. Peters. The book contains the
so-called "Bateson" translation, but omits the 10th and 11th sections,
the conclusion to this (the ninth) section. This is unfortunate, but
understandable; in the sections that follow, Mendel presents no new
data to support his theories,
and no new principles concerning hybrids.
 Experiments with Hybrids of Other
Species of Plants
 Versuch über die Hybriden
In this section, Mendel discusses
several experiments meant to determine whether the laws and
explanations he has found for the development of character forms
Pisum are valid
for other kinds of plants.
He first describes an experiment in which he observed three characters
(pod color, pod shape, and stem length), each with two forms,
in a cross between two
varieties of bean plant
(Phaseolus). He reports
that the ratios he found were the same as with peas, and further that
the number of constant forms that appeared in the first generation
from the hybrids was consistent with the model developed for
Pisum; 2^3, or 8 constant forms appeared in the first
generation from the hybrids.
Mendel then describes an experiment involving a cross between
one variety of bean plant from the first investigation and a the
variety Phaseolus multiflorus. He reports that while some
characters behaved as in Pisum, the character of flower color
did not. Furthermore, the
fertility of the hybrids from
this cross was reduced. Mendel writes that he continued this
experiment for several generations, despite the fertility problems,
and concludes that while characters of the plant and pods conform to
the Pisum findings, the "color characters" apparently do
But Mendel speculates that the color patterns
he observes might be explained
by considering flower color in Phaseolus multiflorus
to be the product not of
a single character, but of a
combination of several characters. He then
presents a model that shows how a cross between a plant with flower
color represented by parental dominant forms of two
(A(1) and A(2)), and a
plant with flower color represented by a single character (in its
recessive form), a, can give rise to nine different forms in
the first generation from the hybrids. The demonstration is meant to
show how a combination of several characters that behave as in
Pisum could produce a range of forms and proportions,
like that observed in the Phaseolus flower-color results.
Mendel notes that such a demonstration is based on a hypothesis that
requires stronger experimental support.
Mendel then addresses the argument that the stability characterizing
the behavior of plants (and specifically the coloring of
ornamental plants) in the wild is lost when
these plants are cultivated. He writes that no one
seriously doubts that the
laws that apply to plants grown in the wild must also apply to
cultivated plants. Mendel agrees that
cultivation favors the development of new species, but he writes that
this does not
mean that the ability inherent in the plant is somehow altered;
rather, the gardener (and/or the garden) simply
makes the most of the variability of the plants.
Mendel writes that the uncertainties
associated with the great variability of cultivated plants might well
be due to many of these plants actually being hybrids, i.e. plants
that have been produced by accidental fertilizations between
different plants in the garden.
Evidence for this is provided by finding that ornamental
plants, when self-fertilized
under carefully controlled conditions, sometimes
give rise to a variety of forms themselves.
Thus the plants we may identify or treat as separate species or
varieties may in fact only be different hybrid forms of a smaller
number of species and varieties.
Mendel concludes that whoever studies the behavior of ornamental
plants over generations will be convinced that their behavior is
predictable and follows laws of development (presumably similar to
those found for Pisum). He notes that such laws may be
discovered by considering flower color as the product or combination
of several independent characters for color.
- Although the title of this section leads the reader to expect a
presentation of experimental results, Mendel's approach is quite
different here than in previous "experimental" sections. He
presents virtually no
data, and his descriptions of the experiments contain a noticeable
lack of detail. It is perhaps understandable that this section has
puzzled some readers, and has been considered irrelevant to Mendel's
contribution to modern genetics by others (e.g.
- Mendel's purpose in this section seems not so much to relate the
results of experiments with other species as to give an argument for
the plausibility of the claim that the laws governing
Pisum have general application. The
argument has three basic components:
- In experiments with other species, some
characters clearly behave like those of Pisum.
- If some traits are viewed as products of several (rather than just
one) Pisum-like characters, then a broad range of forms are
possible. Indeed, if the number of characters be selected properly,
just about any range of forms is possible.
- Extensive variability, as is seen in some
ornamental plants, is not an expression of lawlessness, but rather
of character complexity.
Mendel argues each of these claims in the course of the section, and
all may be thought necessary for a claim about the generality of the
laws he found in his experiments with peas.
- Corcos and Monaghan have commented
that, in his model for flower color in the second Phaseolus
experiment, there is a discrepancy between the proportion of recessive
flowers predicted by the model (1/15) and that found in the experiment
(1/31). The authors say that Mendel fails to mention this discrepancy
(p. 151). Another interpretation, however, is that
the purpose of the model was not to duplicate
that particular proportion, but simply to
show that ratios (and in fact any ratio) other than 1:2:1 could be
arrived at easily by
assuming flower color to be determined by more than one
- In this section, more than in previous sections,
we learn something of
Mendel's ideas concerning evolution. In Mendel's time
it was common for botanists and biologists to think that
the "conditions of life" could exercise an enormous influence over the
form and development of species over time. (Such a view is sometimes
termed "Lamarckian," because it was part of a theory of evolution
proposed by Jean Baptiste Pierre Antoine de Monet Chevalier de Lamarck
(1744-1829) in 1800.) Mendel probably thought so too, but
in this section he insists that cultivation cannot instill variability
but can only take advantage of it, and
this is consistent with a
non-Lamarckian, Darwinian view.
 Concluding Remarks
Mendel begins his final section with a general summary of results
reported by Kölreuter, in Vorlaufige Nachricht von einigen das
Geschlecht der Pflanzen betreffenden Versuchen und
Beobachtungen (1761-1766), and Gärtner, in the book
mentioned by Mendel in the Introduction, Versuche und
Beobachtungen über die
Bastarderzeungung im Pflanzenreich, concerning the form and
behavior of hybrids. Although the results of these studies vary,
Mendel writes that the
development of hybrids
agrees with the behavior found in
Pisum, except in cases he calls "exceptional".
For future studies of hybrids, Mendel explains the
experimental outcomes that should follow if
the "law valid for Pisum"
is assumed, and stresses the large number of plants that must be grown
in order for these
outcomes to be clearly observed. Because a hybrid produced from
parents differing in several
will itself produce many
different forms, and because hybrids can easily be mistaken for
parental forms if only their appearance is observed, large numbers
of plants must be grown in each generation so that accurate ratios,
and accurate assessments of the "internal nature" of the plants,
can be discerned.
Mendel then considers the case of hybrid forms that breed true
(i.e. that behave like parental or constant forms, producing only one
sort of offspring). Such hybrids were not
observed by Mendel in Pisum, but he does not dispute their
existance or their importance for understanding the development of new
Mendel writes that since the hybrids in Pisum were
shown to make different
kinds of reproductive cells, and that this is
what must go on in all hybrids that behave like Pisum, the
"constant hybrids" must be produced in such a way that they can make
reproductive cells of only one sort. This, he says, must be due to a
fusion of pollen and egg into a single, compound cell, which then
behaves like those associated with parental forms in Pisum.
Mendel characterizes the difference between this sort of fusion, and
what must go on in the production of Pisum hybrids, as a
difference between a "permanent" and a "temporary" union of
pollen and egg in the cells of the hybrid.
Mendel then writes that more experiments are necessary in order to
determine whether his Pisum law is valid and generally
applicable to plants of all sorts. But he implies that if the law is
valid, is must be assumed generally applicable since "the unity in the
developmental plan of organic life is beyond question."
Mendel concludes this section with a long discussion of
investigations, carried out primarily by Gärtner, concerning
the transformation of species
through hybridization; that is, using
cross fertlization and cultivation, over several generations, to
transform one species of plant
into another. Mendel
writes that, if one assumes that hybrids are produced according to the
laws found for Pisum, transformation is simply explained:
if one views two species as just different parental constant
forms, then controlled artificial fertilizations over many years could
effect the transformation. He presents a combination series showing the
distribution of constant and hybrid forms that would
results from such a hypothetical fertilization. Mendel then
describes an experiment he carried
out on two species of Pisum, that showed that while
transformation is certainly possible, it may practically depend on
which species is transformed into which.
Gärtner argued that these (artificial)
transformations proved that species must have naturally fixed limits
beyond which they cannot change. Otherwise, went his argument, the
stability of plant species over time could not be explained. Mendel
concludes the section by noting that, whether or not Gärtner's
argument be accepted, his investigations confirm the views expressed
at the beginning of this section, concerning the ways that hybrids of
cultivated plants can vary.
- Mendel's use of the term species
in this section shows how little
importance he attributed to having a precise definition for that term.
Recalling his remarks in the second section
of the paper,
where he noted that the boundary between species and varieties
was difficult to determine and was
arbitrarily drawn in many cases, it is clear that for the purposes of
his investigations of hybrids he did not
consider the distinction one of great importance. When he uses the
term in this section, he does so merely to note that forms
thought significantly different by botanists were often thought
members of different species. Since the different species discussed
were capable of producing fertile offspring when crossed, we would
today consider them different varieties of a single
- The English word accommodated, as it
appears in this section,
is a rather idiosyncratic translation of the German "vermittelt", but
it nicely describes what Mendel seems to be doing with
the studies by Gärtner and others in this section. He shows,
in every case, how the results of the studies
concerning hybrid forms and the transformation of species can be
accomodated, explained, and furthered by the "laws" found to
development of hybrids in Pisum. It is clear that Mendel
hoped to show not only that his results were consistent with the
hybrid studies of Gärtner and Wichura, but that the
principles he claimed governed the forms of hybrids in peas
could be tested, in various kinds of hybrid studies, on various kinds
of plants. That he hoped to promote such tests we know from his
letters to Carl Nägeli.
- This section, and thus Mendel's paper, ends on an almost hurried,
somewhat ambiguous note. It is not clear whether Mendel is claiming
that Gärtner's experiments confirm Gärtner's view about the
natural fixity of species, or whether his experiments merely confirm
the extensive variability of hybrids described in the opening
paragraphs. Clearly, Mendel was not as interested in taking a position
on the fixity of species question as he was in offering an explanation
for the variability of the hybrids.
- The question of whether Mendel "knew about," or postulated the
existance of, discrete units of inheritance has generated some
controversy among biologists and historians of science.
While it would be silly to say that Mendel "knew about genes", it is
clear from this section that Mendel thought there were heritable
elements that could remain discrete and constant, and were not
altered (or altered completely) in the fertilized egg.
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