Notes

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 goals of 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 [1950], p. 4).
• Mendel turned these lectures into a (long) paper, written in German and 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 paper.
• 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 [1956].
• 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 [1919], v.).
• 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 [1959]), even though the version is mostly the work of Druery.
• Although a more contemporary English translation has appeared (see Stern & Sherwood [1966]), 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.

[1] Introductory Remarks
[1] Einleitende Bemerkullgen

Summary: 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 (1772-1850), 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.

Notes:

1. By 1865, the genre of the scientific paper, whether in botany or in the physical sciences, was well-established (see e.g. Bazerman [1988]). 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 certain respects.
2. 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 well.
3. It's difficult to know exactly what Mendel means by the phrase "detailed 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 predecessors.
4. 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 Pisum sativum. 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 [1950])
5. 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 [1965] p. 78)
6. 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 [1994] (p. 446), this was not the case when Mendel began his experiments in the 1850s, before the publication of Darwin's Origin of Species.

Summary: 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 fertility, meaning that the hybrids must all be as fertile as the parental forms.

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.

Mendel reports 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 keel 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 peas).

This section of the paper ends with a short discussion of the question of how to distinguish species 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.

Notes:

1. 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".
2. 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 [1990].
3. 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 he wanted necessary and sufficient conditions in his definitions, and laws to describe the production of hybrids.
4. 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 wasn't) the 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.

Summary: Mendel states that the goal of the experiments is to observe how the characters 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 Pisum.

Notes:

1. 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 drawing from Thomé [1886]). First, 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 Spring.
2. 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 another.
3. 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 Mendel 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.
4. 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 possibilities.

Summary: Mendel says that previous experiments with flowering plants revealed that, when plants with different character forms are crossed, the 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 come.

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.

Notes:

1. 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.
2. 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.
3. Mendel's concluding comments describe examples of "hybrid vigor" (or "heterosis"), 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 inheritance.
4. 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.

Summary: 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 offspring.

Notes:

1. 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.
2. 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 F(2).
3. The modern distinction between phenotype, the appearance 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.
4. 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.
5. 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.

Summary: 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 forms.

Notes:

1. 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 ratio.
2. 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.
3. 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.
4. 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.
5. 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 [1908]), which in turn was the foundation for the Hardy-Weinberg Law in population genetics.

Summary: 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.

Notes:

1. There is a transition in this section of the paper, from an almost naive presentation of experimental results to a noticeably theoretical approach. 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 be correct.
2. 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.
3. 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.
4. 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 [1995], p. 60).

Summary: 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 characters.

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:

• 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 peas.
• Some of the plants grown from the wrinkled yellow peas produce both yellow and green wrinkled peas, while others produce only yellow wrinkled peas.
• 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 green peas.

1. 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.
2. 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.
3. Those offspring that are double-hybrid, AaBb, of which there appear 138.

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 involving n 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 multiple-character experiments.

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.

Notes:

1. 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.
2. 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) comment that 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.
3. 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.
4. 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 crosses.
5. 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.

Summary: 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). Since hybrids 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 self-fertilize 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:

• 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 original hybrids.

• 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 dominant character forms will "cover up" the forms carried by the pollen. Therefore, in the next generation one should find four kinds of offspring: yellow round (abAB), yellow wrinkled (abAb), green round (abaB) and green wrinkled (abab); 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 offspring.

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 differentiating 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.

Notes:

1. 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 equal proportion. 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.
2. 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.
3. 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 [1936]) and continues to provoke comment (e.g. Corcos and Monaghan [1986]). The data presented in this section -- the numbers conforming to 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 [1966], p. 173). Yet it remains unclear what important conclusions one can draw from a statistical observation of this kind.
4. 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, ending with 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.

Summary: 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 not.

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 Pisum-like characters (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.

Notes:

1. 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. Peters [1959]).
2. 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.

3. 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 character.
4. 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.

Summary: 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 characters 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 species. 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.

Notes:

1. 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 species.
2. 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 describe the 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.
3. 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.
4. 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.