The Full Breadth of Mendel’s Genetics

Gregor Mendel’s “Experiments on Plant Hybrids” (1865/1866), published 150 years ago, is without doubt one of the most brilliant works in biology. Curiously, Mendel’s later studies on Hieracium (hawkweed) are usually seen as a frustrating failure, because it is assumed that they were intended to confirm the segregation ratios he found in Pisum. Had this been his intention, such a confirmation would have failed, since, unknown to Mendel, Hieracium species mostly reproduce by means of clonal seeds (apomixis). Here we show that this assumption arises from a misunderstanding that could be explained by a missing page in Mendel’s first letter to Carl Nägeli. Mendel’s writings clearly indicate his interest in “constant hybrids,” hybrids which do not segregate, and which were “essentially different” from “variable hybrids” such as in Pisum. After the Pisum studies, Mendel worked mainly on Hieracium for 7 years where he found constant hybrids and some great surprises. He also continued to explore variable hybrids; both variable and constant hybrids were of interest to Mendel with respect to inheritance and to species evolution. Mendel considered that their similarities and differences might provide deep insights and that their differing behaviors were “individual manifestations of a higher more fundamental law.”

The publication of Mendel's letters to Carl Nägeli by Correns in 1905 was a service to genetics which seems not to have been fully appreciated by most of those who have since written accounts of Mendel's life and work (Mann Lesley 1927).
"T HESE [seedlings] have rooted well, and should flower next year. Whether they will retain the characteristics of the hybrid, or whether they will show variations, will be determined by next year's observations" (our emphasis). These lines about the progeny of his first artificial hawkweed (Hieracium) hybrid were written by Gregor Mendel on November 6, 1867, in a letter to Carl Nägeli, professor of botany at Munich (Letter III, Stern andSherwood 1966, p. 73). They indicate that from the beginning of his experiments with Hieracium, Mendel expected that constant-hybrid offspring may well occur. Mendel ends the letter with: "I look forward to the coming summer with impatience since the progeny of several fertile hybrids will bloom for the first time. They should be very numerous and I only hope that they repay the yearning [Sehnsucht!] with which I await them with much information concerning their life histories." (quoted in Mann Lesley 1927). These are not the words of a frustrated man.
Gregor Mendel's fame is based on his Pisum (pea) crossing experiments that were published 150 years ago. His only subsequent publication on plants is a preliminary communication on artificial Hieracium hybrids (Mendel 1870). The usual supposition about Mendel's Hieracium experiments, which were carried out over 7 years, is that they were intended to verify the results he obtained with his Pisum experiments (Nogler 2006;Bicknell et al. 2016). Hawkweeds are related to dandelions and, like them, often reproduce by a peculiar and rare breeding system called apomixis. The seeds of apomictic plants are produced clonally and are thus genetically identical to the mother plant. This is achieved by the avoidance of meiosis and the parthenogenetic development of the egg cell. In apomictic hawkweeds, most seeds produced are apomictic, but some may develop after cross-fertilization (for more information on apomixis see Supplemental Material, Section 1, File S1). Hawkweeds are hermaphrodites and produce haploid pollen, so they can act as pollen donors in crosses. Thus the prevalence of apomixis in Hieracium would have made it impossible for Mendel to replicate his Pisum findings in this genus. Apomixis was unknown in Mendel's time; indeed it was many years after his death that the Danish botanist Carl Hansen Ostenfeld (1904) discovered apomixis in Hieracium. The usual interpretation of Mendel's Hieracium experiments then is that his work on this genus was a frustrating failure; we suggest this misinterprets Mendel's purpose.
In "Experiments on Plant Hybrids" Mendel (1866) gives an exemplary description of the formation of hybrids and the diversity among their offspring. Most of the work concerns Pisum, but he confirmed his findings in the genus Phaseolus (common bean). When self-fertilized, F 1 hybrids within these species produce variable progeny. Toward the end of this article, Mendel contrasts his results with the case where "We encounter an essential difference in those hybrids that remain constant in their progeny and propagate like pure strains." (Mendel 1866;Stern and Sherwood 1966, p. 41. Mendel used "reinen Arten", so "pure species" would be a better translation than "pure strains"). When self-fertilized, F 1 hybrids of these other species breed true: their progeny do not vary. Mendel designated these two distinct classes as variable hybrids (Stern and Sherwood 1966, p. 42) and constant hybrids (Stern and Sherwood 1966, p. 41), respectively 1 .
Historians of science (e.g., Olby 1979Olby , 1985Olby , 1997Callender 1988;Müller-Wille and Orel 2007) have argued that Mendel's main motivation for the Hieracium (and Pisum) experiments was his interest in hybridization and speciation rather than the inheritance of traits, and they proposed that Mendel stands in the tradition of earlier plant hybridizers like Joseph Gottlieb Kölreuter (1733-1806) and Carl Friedrich Gärtner (1772Gärtner ( -1850. Recently this "Mendel as a nongeneticist" view has received considerable attention in popular science books (e.g., Endersby 2007;Numbers and Kampourakis 2015) and education journals (e.g., Peterson and Kampourakis 2015). Although we agree with these historians of science that Mendel selected Hieracium to study constant hybrids, we do not think that speciation by hybridization was his only or main motivation. Mendel was also interested in reproductive cells and segregation vs. nonsegregation in the successive generations of progeny from a hybrid (i.e., inheritance). Mendel had multiple reasons for selecting Hieracium as an object for experimental crossing and the importance of these reasons may have shifted over the years of his study. The opportunity to come into contact with Carl Nägeli, the person most likely to value his Pisum findings, would have been additionally attractive.
In addition to his articles, there is a series of 10 letters that record part of his communication with Nägeli. Mendel's notebooks were destroyed after his death, so we must rely on these few documents to form an understanding of his scientific thoughts and motives. From these documents we know that after Pisum and Phaseolus, Mendel investigated many other species from the genera Aquilegia, Antirrhinum, Calceolaria, Campanula, Cheiranthus, Cirsium, Dianthus, Geum, Hieracium, Ipomoea, Linaria, Lychnis, Matthiola, Mirabilis, Tropaeoleum, Verbascum, Zea, and more were planned (Letter II). By far, the largest number of these experiments was conducted in Hieracium (Cetl 1971). In this article, we argue that a (mis)reading of Mendel's first letter to Nägeli has led to the incorrect idea that Mendel's Hieracium experiments were intended to verify his Pisum findings.

Carl Nägeli
Carl Nägeli was one of the most important botanists of the 19th century (Junker 2011). His research interests were on natural hybrids, an area where he was recognized as the leading researcher; and Hieracium, where again he was the leading authority. Nägeli was the person who could best see the relevance of Mendel's pea results and Mendel also wanted his advice as a Hieracium expert (Section 2, File S1).

Mendel's letters to Nägeli
Carl Correns (1900), one of the three "rediscoverers" of Mendel's work, clearly acknowledged Mendel's contribution. Correns was a student of Nägeli's and (after Nägeli's death) was married to his niece. From Mendel's Hieracium note and from conversations with Nägeli in the past, Correns knew that Mendel and Nägeli had collaborated closely, so he asked the Nägeli family whether they had any letters from Mendel. Correns published the 10 letters that were discovered (Correns 1905), labeling them with the Roman numerals I to X (Table  S1). In 1925, Correns wrote in a letter to Herbert Fuller Roberts that these "first came to light through an accident in 1904" (Roberts 1929, p. 338). Fragments of some of Nägeli's letters to Mendel were found in the monastery in Brno (German: Brünn) and were published by Iltis (1924). The records of their correspondence are thus incomplete. Correns also published some of the keyword summaries that Nägeli had made of his letters to Mendel. The only in-depth analysis of this scientific correspondence we are aware of is Hoppe (1971), in which she discusses it especially in relation to Nägeli's work, but not in relation to Mendel's Hieracium results.
Mendel's Hieracium work has been misunderstood as a frustrating failure to replicate his Pisum work The traditional interpretation of Mendel's motivation for studying Hieracium is expressed by Hartl and Orel (1992): Mendel's "studies of Hieracium and other species were undertaken to verify, with other plants, the result obtained with Pisum," and "the experiments with Hieracium, as recounted in the letters to Nägeli, were one long chronicle of failure and frustration." In 2006 the journal GENETICS marked the 140-year jubilee of Mendel's Pisum article. Crow and Dove (in Nogler 2006) commented negatively about Mendel's Hieracium work: "Here, on this anniversary, instead of extolling his success, we present a scholarly account [Nogler 2006] of Mendel's frustrating attempts to repeat his findings in another species, which, unbeknownst to him, reproduced apomictically." Nogler (2006) starts with: "Mendel hoped that the highly polymorphic genus Hieracium would be particularly promising for verifying the laws of inheritance that he had discovered while working on Pisum." According to Mawer (2006, p. 167), Mendel's Hieracium article is "of no more than curiosity value." Modern articles on the genetics of apomixis often refer to Mendel's frustrating experiences with Hieracium e.g., Koltunow et al. (2011): "Apomixis in hawkweed: Mendel's experimental nemesis." At the Mendel Museum at the Monastery in Brno, Mendel's Pisum experiments, meteorological studies, and beekeeping activities can be seen, but not his Hieracium work, perhaps due to their associated negativity.
It has been argued that Nägeli was instrumental in Mendel's selection of Hieracium (as discussed in Nogler 2006), but from Letter I it is clear that Mendel had already made crosses in Hieracium, Geum, and Cirsium in the summer of 1866, so the parental species must have been collected at least one season earlier. Mendel had thus embarked on his Hieracium experiments by 1865 at the latest. Therefore Nägeli cannot have pushed Mendel to work on Hieracium as is sometimes suggested (Iltis 1924;Mayr 1982); his choice of Hieracium predates his communication with Nägeli and Nägeli's expertise with Hieracium was a likely motivation for Mendel initiating this correspondence.

Contradiction in Mendel's first letter to Nägeli
Mendel's first letter to Nägeli, written on New Year's Eve 1866, was a covering letter for the reprint of his Pisum article. In the letter (Letter I) Mendel clarified his Pisum studies, mentioned his future research plans, and asked if he could rely on Nägeli for the determination of difficult Hieracium and Cirsium (thistle) species, on which Nägeli was an expert. To understand why it is widely believed that Mendel chose Hieracium to test the Pisum findings, paragraphs four and five are crucial, so these are copied below with the paragraph numbers added in parentheses: (4) In order to determine the agreement, if any, with Pisum, a study of those forms which occur in the first generation 2 should be sufficient. If, for two differentiating characters, the same ratios and developmental series which exist in Pisum can be found, the whole matter would be decided. Isolation during the flowering period should not present many difficulties in most cases, since we are dealing only with few plants; those plants whose flowers are being fertilized and a few hybrids which have been selected for seed production. Those hybrids which are collected in the wild can be used as secondary evidence only, as long as their origin is not unequivocally known.
(5) Hieracium, Cirsium, and Geum I have selected for further experiments. In the first two, manipulation in artificial pollination is very difficult and unreliable because of the small size and peculiar structure of the flowers . . . (Stern and Sherwood 1966, p. 57-58).
From this it has been concluded that Mendel chose the genera Hieracium, Cirsium, and Geum to test the Pisum findings. William Bateson (1909, p. 246) wrote: "This genus [Hieracium] being one of the most strikingly polymorphic, he chose it after his discovery regarding the inheritance of peas, as the subject of further [our emphasis] research. We may surmise that he expected to find in it illustrations of the new principles." Bateson's use of the word "further" suggests that he came to this conclusion based on the two paragraphs mentioned above 3 . This interpretation has become the common belief of geneticists. For example, Iltis (1924, translation of Iltis 1966 wrote: "For Mendel the behavior of the hawkweeds remained an enigma, and his experiments upon these composites shattered the hopes he had entertained of finding confirmation of the principles of inheritance worked out by him in the case of Pisum, and thus establishing these principles as universally valid general laws. . . . He had certainly been lucky in his original choice of Pisum as the object of his experiments. But fate played him an ill turn when he went on to hybridize the hawkweeds; and when, with peasant doggedness, urged on by Nägeli, he persevered so long in his researches upon this unsuitable genus." (pp. 174-175). Ernst Mayr (1982, p. 723) stated: "Instead, he [Nägeli] encouraged Mendel to test his theory of inheritance in the hawkweeds (Hieracium), a genus in which, as we now know, parthenogenesis [apomixis] is common, leading to results that are incompatible with Mendel's theory. In short, as one historian has put it, 'Mendel's connection with Nägeli was totally disastrous.' " Was it ill fate, as Iltis suggested? One of the very few who has interpreted this differently is the historian L.A. Callender (1988), who wrote: "Mendel, on the other hand, and before he was certain that he had obtained a single Hieracium hybrid surmised exactly the opposite [of Bateson's proposal that Mendel expected to verify his Pisum results]" and cites a later paragraph from Letter I: "The plant Geum urbanum + rivale deserves special attention. This plant, according to Gärtner (1849), belongs to the few so far 4 known hybrids which produce nonvariable progeny as long as they remain selfpollinated." And subsequently: "The surmise that some species of Hieracium, if hybridized, would behave in a fashion similar to Geum, is perhaps not without foundation. It is, for instance, very striking that the bifurcation of the stem, which must be considered an intermediate 5 trait among the Piloselloids, may appear as a perfectly constant character, as I was able to observe last summer on seedlings of H. stoloniflorum W. K. 6 " This suggests that Mendel expected that Hieracium species could be constant hybrids (see also Orel 1998). Why would Mendel select a genus in which he expected to find constant hybrids, to validate the segregation of variable hybrids? This would be irrational. The eminent Mendel-expert Franz Weiling (1970) expressed it very carefully: "From Mendel's first letter to Nägeli one gets the impression that he, with his crosses in Hieracium, Cirsium as well as Geum-species, wanted to test the generalities which he had found in Pisum" ["Aus dem 1. Brief Mendels an Nägeli (31. Dezember 1866) gewinnt man den Eindruck, daß er mit seinen Kreuzungen bei Hieracium-, Cirsium-, sowie Geum-Arten die bei Pisum gewonnenen Gesetzmäßigkeiten prüfen wollte." (p. 99)]. The wording "one gets the impression" suggests Weiling was aware of the contradiction in the letter. As far as we know, this major contradiction has never been discussed. Here we suggest that the present paragraphs four and five in Mendel's first letter were originally not linked, but were separated by one or more lost pages. The two paragraphs are not logically connected and we propose that Mendel did not select these species to test the Pisum findings.
Could a missing page explain the contradictions in Mendel's first letter?
Because of the contradiction in Letter I, we wondered whether a part of the letter could be missing. Witte (1971), who had photocopies of all the handwritings, compared the original text with the transcript of Correns and found only a few small typographical errors. Therefore an error in the transcription can be ruled out.
We have examined a facsimile of Letter I (December 31, 1866) published by Jelinek (1965) because, despite our efforts, the original could not be traced. In Figure 1 it can be seen that paragraph four ends at the bottom of page two and paragraph five begins at the top of page three. Since the page break does not result in a broken sentence, a missing sheet would go unnoticed, especially in a transcript, where the relationships between paragraphs and pages are different from the original handwriting. In the facsimile, parts of the words written on page two can be seen mirror-wise on page one and vice versa; the same for pages three and four ( Figure S4). This means that the sheets of paper are written on both sides and that one or more sheets could be missing (i.e., two or an even number of pages). We examined copies of Mendel's handwritten pages to see whether there were any structural clues that would enable us to discount the possibility that one or more pages is missing. From a statistical consideration of the location of page and paragraph breaks in Mendel's letters, we concluded that paragraphs usually end in the middle of pages, so the location of a paragraph end at the bottom of a page is consistent with this being deliberate. The paragraph need not have ended there: alignment of the text using the ink marks that can be seen through the paper from one side to the other shows that there was adequate room to continue writing on this piece of paper (Section 3, File S1 and Figure S4). If paragraph five begins at the top of the page, as it does according to Correns' transcript, then a missing page is required to end with a paragraph break. The analysis which leads us to conclude that this is not improbable is set out in Section 3, File S1.

Mendel's Research Interests Were Broad
Mendel's hypothesis about the germ cells of constant vs. variable hybrids In the concluding remarks of the Pisum article, Mendel stressed the importance of the "essential difference" between variable and constant hybrids; between hybrids like those of pea, which produced variable offspring; and hybrids that produced constant offspring. He also mentioned that "For the history of the evolution of plants this circumstance is of special importance, since constant hybrids acquire the status of new species" (Mendel's emphasis, Stern and Sherwood 1966, p. 41). By "new species" Mendel meant being true breeding and having morphological distinctness. Clearly speciation was one of the interests that Mendel had in constant hybrids.
Mendel was interested in the mechanisms of inheritance and the composition of reproductive cells. So far, this aspect of Mendel's work has not received much attention. According to the report of Mendel's second lecture on March 8, 1865 in the Brünn newspaper Neuigkeiten, "he spoke about cell formation, fertilization and seed production in general and in the case of hybrids in particular . . ." (Olby 1985). In his Pisum article, Mendel developed a hypothesis about the segregation of antagonistic elements among reproductive cells and their reassortment among progeny, based on the different types of progenies of variable and constant hybrids ( Figure 2). This was .20 years before meiosis was discovered and understood by the contributions of van Beneden, Hertwig, Weismann, and others (Mayr 1982).
Mendel (1866) proposed that in variable hybrids that were derived from parents that differed, both the antagonistic elements were temporarily accommodated during the vegetative stage, and separated during the formation of the reproductive cells (egg cells and pollen). In contrast, in constant hybrids, Mendel proposed a permanent mediation. "This attempt to relate the important difference in the development of hybrids as to permanent or temporary association of differing cell elements can, of course, be of value only as a hypothesis which, for lack of well-substantiated data, still leaves some latitude." (Stern and Sherwood 1966, p. 43).  Mendel's interpretation (boxed) of the behavior of determining elements is compared to our current understanding. "Sexual Cross" refers to the specific case of a cross between two homozygotes followed by self-fertilization, and should be compared to "Variable Hybrids" which is classically described in his 1866 article. Mendel's interpretation of "Constant Hybrids" should be compared to "Apomixis." Note that Aa has a different meaning in our current understanding from that in Mendel's scheme; Mendel did not know about meiosis and the distinction between diploid and haploid. Numbers indicate: (1) The union of germinal cells from the female and male (egg and pollen).
(2) The primordial cell (zygote): differences between antagonistic elements are mediated (in the mediating cell).
(3) Vegetative period, the balance/mediation established in the primordial cell continues. (4) In variable hybrids, at the formation of the reproductive cells (gametes) the antagonistic elements are separated and represent "all constant forms which result from the combination of the characters united in fertilization." The "arrangement between the conflicting elements is only temporary," that is, no germinal cells carry the union of conflicting factors. (5) In constant hybrids, at the formation of the reproductive cells (gametes) the antagonistic elements are not separated. The essential difference in the development of constant hybrids is that the union of the factors is permanent. (6) In constant hybrids, the union of germinal cells of identical constitution is proposed (i.e., no parthenogenesis). (7) For comparison, the genetic transmission of apomixis is shown: the unreduced egg cell develops into an embryo by parthenogenesis. Note that in the case of apomixis a breeding system is inherited, which will fix the segregating genetic background of both parents; producing many different apomictic lineages. For simplicity only diploids are shown, but apomixis is often associated with polyploidy. Because apomicts have a simplex dominant genotype (Aaaa) this convenience is used. The type of apomixis shown here is typical for the subgenus Archieracium, which Mendel also used in crosses.
Constant hybrids, such as Hieracium, could provide such well-substantiated data; so, after having studied the variable Pisum hybrids, it was logical that Mendel would have gone on to study constant hybrids, as presaged by his comments in the Pisum article. Moreover, Mendel may not have been satisfied with Gärtner as an "eminent observer" as he wrote in the Pisum article, since in Letter I (Stern and Sherwood 1966, p. 57) to Nägeli he criticized Gärtner's observations with respect to variable hybrids ("it is very regrettable that this worthy man did not publish a detailed description of his individual experiments"). Taken together, these considerations would have provided the impetus for Mendel to investigate constant hybrids himself.

Mendel's interest in Hieracium, Cirsium, and Geum
As he neared the completion of his Pisum experiments, Mendel had started looking for species for new crossing experiments. In 1864 he had made crosses between Verbascum and Campanula species and some of his artificial hybrids were shown at the June 14, 1865 meeting of the Natural Science Society (Naturforschender Verein) of Brünn. The Verbascum hybrids, however, were completely sterile (Letter III, Stern and Sherwood 1966, p. 77). The timing shows that Mendel's interest in variable hybrids continued while he was also studying constant hybrids.
Why did Mendel select Hieracium, Geum, and Cirsium? Mendel mentioned in Letter I that the artificial hybrid Gärtner had made between Geum urbanum and Geum rivale was one of the few hybrids known so far that produced constant progeny plants. Both parental species showed discrete alternative states of traits, which had been a methodological requirement for Mendel's study of variable hybrids. Moreover, the taxon G. intermedium was found in nature, which could be the constant hybrid between G. urbanum and G. rivale. The last page of Mendel's personal copy of Gärtner's (1849) Versuche und Beobachtungen über die Bastarderzeugung im Pflanzenreich (Experiments and Observations on Hybridization in the Plant Kingdom) contains many notes on Geum, Figure 3 Variation in inflorescence color and size in Hieracium hybrids. Ostenfeld (1910) illustrated 23 H. auricula 3 aurantiacum hybrids that he obtained. Mendel obtained 84 flowering hybrids from the same cross. The parental species are shown at the top; H. auricula left, with a yellow small inflorescence; and H. aurantiacum right, with a larger orange inflorescence. Next to the inflorescence a single floret is shown. The original image is from the Biodiversity Heritage Library. Digitized by the Mertz Library, New York Botanical Garden (http://www.biodiversitylibrary.org). and two interesting designations of multigene genotypes of G. intermedium: ABcDEe and ABcdEe (Olby 1985). In these, the heterozygote Ee would be constant and would not segregate.
Mendel was an active member of the Natural Science Society where he gave the two 1865 lectures about his Pisum experiments. In 1869, he was elected as vice president of the society and in June of that year he gave a lecture about his Hieracium hybridization experiments. Both Hieracium and Cirsium were genera in which intermediate and transitional forms between species were common (Nägeli 1866). Nägeli speculated that these might be constant hybrids or products of transmutation. Natural hybrids of Hieracium and Cirsium had already been discussed at several meetings of the society (see Section 4, File S1; Weiling 1969;Orel 1996). In general, the society was more interested in interspecific hybridization ("Bastarde"), than in intraspecific hybridization ("Hybriden"). Although Mendel saw only a graduated difference between varieties and species, he used "Hybriden" in the title of his Pisum article and "Bastarde" in the title of his Hieracium article; showing that he was well aware of the difference. His interest in species vs. varieties may have been influenced by the publication of  Origin of Species [Mendel had a copy of the second edition of the German translation of the Origin of Species (1863), see Fairbanks and Rytting 2001]. Mendel's selection of Hieracium, Geum, and Cirsium for study is therefore something to be expected in the intellectual atmosphere of Brünn at that time.

Two phases of Mendel's Hieracium research
Mendel's letters to Nägeli give a unique insight into his character, showing the evolution of his views, his openness and honesty, and his admission that some of his earlier expectations were incorrect. In some places the letters are witty and self-deprecating. Also striking, and contrary to what is often claimed, the correspondence between Mendel and Nägeli is friendly: Nägeli was not arrogant or controlling toward Mendel (Schwartz, 2008, and see salutations and signings Table S1). Although Mendel wrote about experiments with other species, in these letters the Hieracium experiments were by far the most important. Geum and Cirsium did not produce constant hybrids and soon Mendel concentrated on Hieracium. Mendel's letters and his provisional Hieracium communication makes it possible to reconstruct his Hieracium crossing experiments (see Table S2 for a timeline, and Table  S3 in relation to Mendel's interspecific crosses). A large part of the correspondence is about the identification of Hieracium species and the exchanges of plant material, which, although they were important at the time, obscure the purpose of the investigation.
Based on the content of the correspondence, two research phases can be distinguished (see Section 5, File S1); in the first phase Mendel, with great effort, managed to produce some hybrids which indeed propagated constantly. The preliminary communication on Hieracium hybrids of June 9, 1869 can be seen to conclude this phase. In the second phase, Mendel tried to find a solution to the fact that, contrary to his expectation, he found multiple types of constant hybrid. Nogler (2006) gives a good biological description and analysis of Mendel's Hieracium experiments, although it is chronologically incorrect. He wrote that Mendel was first surprised by the many different F 1 hybrids and then by the fact that these hybrids were true breeding. This chronology reinforced the image of a frustrated Mendel. In reality, Mendel initially obtained very few hybrids. It must have been an exciting vindication that the first hybrid was true breeding, fulfilling his Sehnsucht. Only later, to his surprise, he found that there were many different but constant F 1 hybrids. In total, Mendel obtained hybrids in 21 interspecific combinations. Table S3 lists the most important interspecific hybrids and the variability of their offspring.
Mendel's most successful cross was that between H. auricula 3 aurantiacum from which he obtained 84 fertile hybrids (40 years later Ostenfeld repeated this cross, Figure  3). Remarkably, some of Mendel's hybrids still exist as dried specimens in the Herbarium of the Museum of Grenoble (Mendel's first constant hybrid, Figure 4; several H. auricula 3 aurantiacum hybrids, Figure 5). The hybrids that Mendel sent to Nägeli were grown in the experimental garden of the University of Munich. Nägeli's student and later colleague, Albert Peter, edited a collection of exsiccatae "Hieracia Naegeliana" (1885), consisting of 300 herbarium sheets of Hieracium subgenus Pilosella plants, which included 16 of Mendel's hybrids and 12 parental forms. Weiling (1969) located the "Hieracia Naegeliana" in 23 other herbaria in 11 countries throughout Europe, although these are often incomplete.
In the first phase of Mendel's Hieracium experiments, he demonstrated the constancy of the hybrid in subsequent generations. He could have hoped to use this, for example, to study dominance relationships among determinants for the differentiating characters. However, the observation of more than one type of constant hybrid was unexpected because the parents were also true breeding and only one F 1 hybrid type was anticipated. The second phase of the Hieracium experiments was therefore to determine what caused the multiplicity of F 1 types. Mendel knew from his Pisum methodology that he should collect very many F 1 hybrids to "determine the number of different forms in which the hybrid progeny appear . . . and ascertain their numerical interrelationships" (Stern and Sherwood 1966, p. 2). He was well aware of the amount of work this would require and in trying to improve the efficiency of the microscopic Hieracium crosses he nearly ruined his eyesight permanently. In his final letter to Nägeli, reflecting his realization that he did not have sufficient time to complete the necessary experiments, he wrote: "I am really unhappy about having to neglect my plants and my bees so completely. Since I have a little spare time at present, and since I do not know whether I shall have any next spring, I am sending you today some material from my last experiments in 1870 and 1871." (Letter X, Stern and Sherwood 1966, p. 97). All he could do was pass on his experimental material to someone who may have the opportunity to continue the work. If he was frustrated, it was not because his experiments had failed, but because they showed what needed to be done next and his duties as abbot prevented him from continuing this work.

Concluding Remarks
In this article we have argued that Mendel's Hieracium experiments, and the reasons underlying them, have been misunderstood for more than a century. We propose that this misunderstanding rests on the obscurity of the originals of his written letters and that a missing page (or pages) in his first letter to Nägeli would explain the common misreading of that letter. There is no proof that a page is missing; this could become a certainty only if it were found, which seems highly unlikely. Notwithstanding, the traditional view of Mendel's Hieracium experiments is not the only one possible. The interpretation we set out here is consistent with the whole of Mendel's known writings and does not involve the contradiction necessary for the traditional view. We therefore consider our interpretation the more likely. A missing page is not a necessary requirement for our interpretation, but its suggested location would help to explain the prolonged misinterpretation.
Although Mendel's letters to Nägeli mainly concern the Hieracium crosses, as would be expected because of their collaboration, the letters also contain important information about his variable hybrids and this has been neglected, perhaps because of the negative view of his Hieracium work. In July 1870 (Letter VIII), Mendel wrote: "Of the experiments of previous years, those dealing with Matthiola annua and  -Touv. MHNGr. 191437163, 191437164, 191437165, and 191437173). glabra, Zea, and Mirabilis were concluded last year. Their hybrids behave exactly like those of Pisum. Darwin's statements concerning hybrids of the genera mentioned in The Variation of Animals and Plants Under Domestication, based on reports of others, need to be corrected in many respects." (Stern and Sherwood 1966, p. 93). This clearly shows that Mendel had found additional support for his understanding of inheritance in variable hybrids. In the same letter and in the next (Letter IX, September 27, 1870), Mendel also described repeated experiments to test whether a single pollen grain is sufficient to fertilize a single egg cell and an experiment with two pollen grains, each from a different flower color genotype, to investigate if an egg cell could be fertilized by two pollen grains simultaneously. These experiments are a rigorous test of the basic principles of his theory of inheritance in Pisum. Contrary to the historians' view, there can be no doubt that Mendel was above all a geneticist.
"My time is yet to come" are the famous prophetic words attributed to Mendel by his friend Gustav von Niessl. It is not widely known that Mendel said these words in the garden among his Hieracium and Cirsium plants. ("aber ich hörte im Garten, an den Beeten seiner Hieracien und Cirsien von ihm die prophetischen Worte: 'Meine Zeit wird noch kommen,' " Von Niessl 1905, p. 8). A more appropriate location is hard to imagine. Mendel's interest in hybrids (both inter-and intraspecific) was broadly based and encompassed the mechanism of their formation, inheritance in general, as well as the consequences of hybridization for evolution. He clearly recognized two contrasting types of hybrid (constant and variable) and he chose to study both. In one of his last letters to Nägeli, he commented: "Evidently we are here dealing only with individual phenomena, which are the manifestation of a higher, more fundamental, law" (Stern and Sherwood 1966, p. 90). With hindsight we see this to be entirely correct. Mendel's observations in Hieracium demonstrated the pollen transmission of apomixis that can now be understood in terms of the Mendelian genetics of the process of inheritance itself.

Acknowledgments
The idea for this article sprouted from the "Research in Plant Genetics" Conference on September 7-10, 2015, organized by the Mendel Museum of the Masaryk University at Brno, Czech Republic. We thank Bengt Olle Bengtsson, Julie Hofer, and John Parker for critically reading and commenting on draft versions of the manuscript. We are grateful to Brigitte Hoppe for discussions and help with the transcription of Nägeli's first letter. Welcome and insightful comments of the reviewers helped to improve the manuscript. We thank Thomas Notthoff of the Archives of the Max Planck Society in Berlin for proving us with a photocopy of the handwriting of Mendel's letter II. We thank the following organizations for permission to reproduce images they own: The Muséum d'Histoire Naturelle de Grenoble, Catherine Gauthier, and Matthieu Lefebvre for pictures of herbarium specimens of Mendel's Hieracium hybrids which are part of the Casimir     (1905), Kříženeck (1965), Stubbe (1965), Stern and Sherwood (1966) and Orel (1996) The variability / uniformity of the F1 and later generations, based on Correns (1905). Note that the distinct types of hybrid in the first generation had uniform offspring so they are not 'variable hybrids', but distinct lineages of 'constant hybrids'.

Supplemental Files 1
Supplemental file S1 Apomixis in Hieracium 2 3 Hawkweeds (genus Hieracium) belong to the family Compositae (or Asteraceae), named after the flower 4 head, which is an inflorescence composed of many small flowers (florets) on a basis (capitulum). In 1904 5 Carl Hansen Ostenfeld discovered apomixis in the genus Hieracium and in most of the Hieracium species 6 that Mendel had used in his crosses (Ostenfeld 1904). Apomixis is reproduction through clonal seeds as 7 a consequence of two developmental processes: 1. Avoidance of meiosis (apomeiosis) and 2. 8 Parthenogenesis (the development of the egg cell into an embryo without fertilization). Ostenfeld was 9 the first to suggest that the enigmatic results of Mendel's Hieracium crossing experiments might be 10 related to the occurrence of apomixis in this genus (Nogler 2006). Apomixis is rare and estimated to be 11 the mode of reproduction in about 1 in 1,000 angiosperm species (Mogie 1992). 12

13
The genus Hieracium is divided into three subgenera of which the two largest, Pilosella and Archieracium 14 (now Hieracium sensu stricto), have an original Eurasian distribution and were both studied by Mendel. It 15 is now known that in both Pilosella and Archieracium, diploids are sexual and polyploids are sexual or 16 apomictic. The mechanism of apomeiosis in the subgenera is different: apospory in Pilosella and 17 diplospory in Archieracium (for details see Hand et al. 2015). As a consequence, Pilosella species are 18 facultative apomicts, with a small percentage of residual sexual reproduction, whereas Archieracium 19 species are virtually obligate apomictic. This largely explains why Mendel was much more successful in 20 making interspecific hybrids in Pilosella than in Archieracium, viz. 19 species combinations in Pilosella 21 versus only two in Archieracium (Correns 1905). 22 Species of the Pilosella subgenus differ in their degree of apomixis; some are completely sexual, e.g. H. 24 auricula, some are partially apomictic, e.g. H. praealtum, and some are fully apomictic, e.g. H. 25 aurantiacum. Initially Mendel used a partially apomictic seed (female) parent, which explained why only 26 one or a few hybrids were produced in a background of apomicts. When two hybrids from the same 27 cross differed, Mendel initially attributed this to contamination with outcross pollen (see Letter VIII). 28 Later, Mendel used fully sexual H. auricula as seed parent in conjunction with a male we now know to be 29 apomictic, which explains why he obtained many more hybrids, in which variation was much more 30 obvious and could no longer be explained by contamination; in Letter VIII Mendel records this change in 31 his opinion. 32 33 Not knowing of the existence of apomixis, Mendel assumed that Hieracium species were true breeding 34 due to self-fertilization. To prevent presumed selfing he had to emasculate the tiny florets in the 35 inflorescence. Since Mendel found maternal offspring even after emasculation, he assumed that 36 emasculation had been unsuccessful and concluded that selfing had occurred before emasculation (at 37 least two days before the florets opened). The immature florets were very sensitive to mechanical 38 damage so the success rate of crossing was low. Mendel complained about exhaustion of his eyes due to 39 the intense light needed for these manipulations and he suffered from a serious eye ailment for six 40 months (Letter VIII). In retrospect all this effort was not necessary, since apomictic offspring do not result 41 from selfing and sexual Hieracia are self-incompatible (due to a sporophytic self incompatibility system; 42 Gadella 1987). Ironically, in his first letter, Nägeli advised Mendel to use pollen-sterile plants. Mendel 43 was aware of the fact that such pollen sterile plants occurred in Hieracium; in the Hieracium paper he 44 writes: "It not rarely happens that in fully fertile species in the wild state the formation of the pollen fails, 45 and in many anthers not a single good grain is developed" (Mendel 1869 occurrence of parthenogenesis in seed plants had been passionately discussed a decade before Mendel's 51 Hieracium publication; in which Nägeli had taken a prominent part and had stressed that 52 parthenogenetic offspring would be highly uniform (Fürnrohr, 1856). One of the reprints that Nägeli sent 53 to Mendel even mentioned the word "parthenogenesis". Moreover, parthenogenesis was known to 54 occur in bees, and being an ardent bee keeper Mendel must have known this. However, in the second 55 half of the 1850's after thorough evaluation, many cases of supposed parthenogenesis were shown to be 56 caused by pollen contamination and therefore rejected. In 1869, when Mendel gave his lecture, the 57 occurrence of parthenogenesis was widely accepted only in the Australian dioecious species 58 Coelebogyne ilicifolia (Alchornia ilicifolia). At Kew Gardens three female specimens of this plant produced 59 exclusively female offspring (Smith 1839/1841). Parthenogenesis in a dioecious stonewort Chara crinita 60 was also widely accepted and in 1876 Kerner reported on a supposed case of parthenogenesis in 61 dioecious Antennaria alpina. All these dioecious cases (separate male and female plants) were supported 62 by reproduction in geographic regions where no male individuals were found, which raised questions 63 about their mode of reproduction. Parthenogenesis in a hermaphroditic pollen producing seed plant like 64 Hieracium was not obvious. Nogler (2006) noticed that Correns, De Vries and Bateson did not foresee 65 parthenogenesis in Hieracium either and the same can be said about Sutton (1903). It was only in 1904, 66 when Ostenfeld showed that seed development still occurred after removal of both anthers and styles, 67 that parthenogenesis became obvious. 68 69 Christoff (1942) repeated Mendel's H. auricula x aurantiacum crosses and concluded that high levels of 70 heterozygosity were masked by apomictic reproduction. Heterozygosity becomes apparent when the 71 apomict is used as a pollen donor in crosses with sexual plants, resulting in segregation of traits like 72 inflorescence color, but also segregation for the apomictic mode of reproduction. Therefore some (but 73 not all) of the F1 hybrids reproduce by apomixis and become "constant hybrids", as Mendel had found. 74 Christoff also concluded that apomixis was controlled by a dominant gene. In other Hieracium species, 75 separate loci for apomeiosis, parthenogenesis and autonomous endosperm development have been 76 identified (Catanach et al. 2006;Koltunow et al. 2011;Ogawa et al. 2013)

Carl Nägeli, the person who could best see the relevance of Mendel's pea and hawkweed results 107
Carl Nägeli 1 became professor in botany in Zürich in 1850 and later in Munich in 1857. His PhD thesis 108 (Nägeli, 1841) concerned the systematics of the genus Cirsium. Subsequently he published a paper on 109 the species and natural hybrids of Hieracium, subgenus Pilosella (Nägeli, 1845). were specifically about the genus Hieracium (Nägeli 1866 a,b,c,d,e). 117 118 Although Nägeli's review was presented more than six months after Mendel's two Pisum lectures, the 119 timing was such that it was published too soon to include reference to Mendel's work. All of Nägeli's 120 1866 (and earlier) papers were available to Mendel in summer of that year and it is likely that he read 121 them before he sent his first letter to Nägeli (Weiling 1969). 122 123 Even before the publication of Darwin's 'Origin of Species' in 1859, Nägeli had accepted that species 124 were not constant but could evolve (Junker 2011). The genus Hieracium seemed to be particularly 125 suitable for empirical studies on the process of speciation. This highly polymorphic genus consisted of 126 many different forms with clear species ("Hauptarten") connected by a continuum of intermediate forms 127 ("Mittel-or Zwischenformen"). Nägeli, "in the spirit of the Darwinian teaching, defended the view that 128 these forms are to be regarded as [arising] from the transmutation of lost or still existing species" 129 (Mendel 1870, Stern andSherwood, 1966, p. 51). In other words, in Hieracium, the 'missing links' 130 between the species were still present. In contrast to other Hieracium experts, Nägeli did not deny 131 hybridization, especially in the early steps of speciation. After his early studies of the subgenus Pilosella 132 (between 1841 and 1846), Nägeli returned to studying this subgenus in 1864 when, with the publication 133 of Darwin's work, speciation became topical. 134

135
Nägeli was an expert in the identification of natural Hieracium hybrids. He collected Hieracium seeds and 136 plants from many different taxa and localities and grew these in the common garden at Munich. By 1884 137 he had cultivated almost 4500 Hieracium accessions (Nägeli 1884). Although Nägeli did not carry out 138 artificial hybridizations himself, spontaneous hybrids between different accessions were found in the 139 common garden (Peter 1884). 140 141 A collaboration in the field of Hieracium would give Mendel the opportunity to bring his Pisum work to 142 the attention of Nägeli, who was the best qualified person in the world to appreciate and therefore 143 promote his work. Interestingly, in addition to Mendel's covering letter for the Pisum reprint which he 144 sent to Nägeli, the covering letter for the reprint which he sent to Anton Kerner von Marilaun has 145 survived. The latter was written on New Year's day 1867, one day after the former. Kerner was Professor 146 in Botany in Innsbruck and had studied with Mendel in Vienna. Although a lesser authority than Nägeli,147 Kerner was a distinguished professor who was well known for his research on natural hybrids. Whereas 148 Mendel wrote a long letter to Nägeli of at least 4 pages, his letter to Kerner is only half a page, identical 149 to the first and last formal paragraphs of the letter addressed to Nägeli (Supplemental figure SF1). 150 Mendel did not consider it worthwhile to explain his Pisum work and his future plans to Kerner. Kerner's 151 reprint of Mendel's paper was found later, uncut. 152

153
Translations of Mendel's letters to Nägeli 154 In 1950, at the Golden Jubilee of the rediscovery of Mendel's work, the American Genetics Society 155 published a full English translation of Mendel's letters to Nägeli, together with the 1900 publications of 156 de Vries, Correns and Tschermak. This translation was done by Piternick and Piternick (1950) and was 157 also used in the Mendel Source book of Stern and Sherwood (1966); it can be found at the Electronic 158 Scholarly Publishing website: (http://www.esp.org/foundations/genetics/classical/browse/). In places, 159 the Piternick and Piternick (1950) German to English translation of Mendel's letters tends to be rather 160 negatively biased compared to other translations, but since the Piternick and Piternick translation is the 161 most extensive, we use this translation in our 'Perspective', unless otherwise indicated. 162

164
Missing letters from Mendel to Nägeli 165 We know that at least two of Mendel's letters to Nägeli are lost. In the most obvious case it is clear that 166 Nägeli did not receive Mendel's letter written in the spring of 1873 (Letter M3 of Supplemental Table  167 ST1). In his last letter (X) Mendel wrote that despite his best intentions he could not keep the promises 168 he had made in spring. From this Nägeli deduced that Mendel had sent a letter in spring which he had 169 not received, which he recorded in his notes (Correns 1905).  Mendel. Whereas in previous letters Mendel thanked Nägeli for material within one month, Mendel's 177 letter VII is dated seven months later and does not contain a word of thanks for the material received. 178 Letter M1 would be appropriate for these thanks as well as discussing the Cirsium hybrid No 15. We 179 conclude that a letter by Mendel, written between September 1868 and April 1869, must also be lost. 180 181 There may be a third missing letter (Letter M2, Supplemental Table ST1)  In Letter I Mendel wrote about Gärtner's crosses: "In most cases it can at least be recognized that the 209 possibility of an agreement with Pisum is not excluded", indicating that Mendel thought the Pisum type 210 of inheritance (variable hybrids) was most common. Concerning constant hybrids he wrote: "This plant 211 [the Geum hybrid], according to Gärtner, belongs to the few known hybrids so far, which produce 212 nonvariable progeny as long as they remain self-pollinated", indicating that he thought this type of 213 inheritance was rare. Mendel was right, we now estimate 1 in 1,000 angiosperm species to be apomictic 214 other parent species occurred and he bred offspring to convince himself that they were true breeding. In 221 the summer of 1866, he tried to make the first crosses. Clearly this project had been conceptualised 222 much earlier (Supplemental Table ST2  to be tested further (A, a, AB, Ab, aB, ab). I expect that sooner or later (by inbreeding) they will vary 236 again. For example 'A' contains half 'a' of which it cannot get rid of by inbreeding" (Hoppe 1971). 237 Mendel's Pisum findings however are outside the scope of this paper. Nägeli advised Mendel to continue 238 his attempts to fertilize Hieracium: "It would seem to me especially valuable if you were able to effect 239 hybrid fertilisations in Hieracium, for this will soon be the genus about whose intermediate forms we 240 shall have the most precise knowledge" (Iltis 1966, p. 192). Hieracium hybridizations from the summer of 1866 failed, only "selfed" offspring was produced (Mendel 251 assumed selfing, but now we know that apomixis was the cause). In Cirsium, he also tried mass 252 pollination, without removing the anthers, in the hope of obtaining a few hybrids, since only a few 253 hybrids were required to test the hypothesis of constancy and Mendel expected only one type of 254 constant hybrid per species combination. Mendel was planning to apply the same procedure (mass 255 pollination) next summer (1867) to Hieracium. In the summer of 1867 Mendel experimented further 256 with methods for producing artificial hybrids in Hieracium. A floret bud emasculation method, using a 257 magnifying lens and a sharp needle produced the first Hieracium hybrid and this was the method Mendel 258 used for all his later crosses. On the proposed mass-pollination Mendel did not write any more. 259

260
The most important result according to Mendel's third letter (Letter III, November 1867)

was an artificial 261
Hieracium hybrid between H. praealtum and H. stoloniflorum. This was obtained by emasculation of 262 florets in bud. Only four seeds developed, one of which was without doubt a hybrid on the basis of 263 morphology. The other three were identical to the maternal plant and Mendel suspected that selfing had 264 occurred before the flower was open. The hybrid was a "healthy, luxuriant plant" that produced 624 265 seeds in isolation, from which 156 offspring were obtained (Letter III, Stern and Sherwood 1966, p. 72, 266 73). As is clear from the opening paragraph of the main text, Mendel was very eager to find out whether 267 the plants would be uniform and identical to the mother hybrid plant. We used the Mann Lesley (1927)  268 translation because the Piternick and Piternick (1950) [Mendel's underlining] from each other 281 and agree with the hybrid mother-plant. I look forward to their further development with some 282 eagerness." This passage is translated by Piternick and Piternick (1950)  and another that vegetatively resembled H. praealtum which Mendel described as 'aberrant'; of the 301 flowers he commented "the flowers are definitely of hybrid color!" (Letter VI, Stern and Sherwood 1966, 302 p. 81). The exclamation mark indicates his surprise, and the beginning of the realisation that there were 303 multiple hybrid types. When more hybrids started to flower, it was clear that in each case where he 304 obtained two or more hybrid plants from a hybrid combination, these always were different from each 305 other (Mendel 1869(Mendel /1870. Two years later (letter VIII July 1870) Mendel reflected on this revelation: "In 306 Pisum and other plant genera I had observed only uniform hybrids and therefore expected the same in 307 Hieracium. I must admit to you, honored friend, how greatly I was deceived in this respect. Two 308 specimens of the hybrid H. auricula + H. aurantiacum first flowered two years ago [1868]. In one of 309 them, the paternity of H. aurantiacum was evident at first sight; not so in the other one. Since, at the 310 time I was of the opinion that there could be only one hybrid type produced by any two parental species, 311 and since the plant had different leaves and a totally different yellow flower color, it was considered to 312 be an accidental contamination, and was put aside. Thus, in last year's shipment I enclosed only the 313 specimen which closely resembled H. aurantiacum in flower color. But when three specimens, each of 314 the same hybrid produced from the fertilization in 1868, and also the hybrid H. auricula + H. pratense 315 (var.) later flowered, as three different variants, the correct circumstances could no longer escape 316 recognition" (Letter VIII, Stern and Sherwood 1966, pp. 88 and 89). Thus by autumn 1868 Mendel knew 317 that the Hieracium crosses generated a multiplicity of different constant hybrids (Supplemental Table  318 ST3) and knew that he had to find a way of reconciling this with the fact that the parents were true-319 breeding. This was an unanticipated problem that required further study. 320 only single terms in an unknown series which may be formed by the direct action of the pollen of one 337 species on the egg-cells of another." If these hybrids were terms of an unknown series, more hybrids 338 would be needed to clarify the series, and experiments would be needed just as Mendel had performed 339 in analysing the F2 for Pisum. Further on he wrote: "As yet the offspring produced by self-fertilisation of 340 the hybrids have not varied, but agree in their characters both with each other and with the hybrid plant 341 from which they were derived………If finally we compare the described result, still very uncertain, with 342 those obtained by crosses made between forms of Pisum, which I had the honour of communicating in 343 the year 1865, we find a very real distinction. In Pisum the hybrids, obtained from the immediate 344 crossing of two forms, have in all cases the same type, but their posterity, on the contrary, are variable 345 and follow a definite law in their variations. In Hieracium according to the present experiments the 346 exactly opposite phenomenon seems to be exhibited. 347 Mendel therefore knew that the behavior of the Hieracium hybrids was likely to be of general interest 348 and that they were different in their behavior from Pisum, but the methodology for trying to understand 349 the rules that governed this would likely be similar, and amounted to identifying the relevant 350 Mendel considered that they were likely to be able to be understood in a common framework. This 360 framework was established to some degree, but there remained the problem of understanding the 361 diversity of constant hybrids generated from a single cross. 362

363
The Cirsium hybrids behaved very differently from the Hieracium hybrids. In April 1869 Mendel wrote: 364 "Cirsium would be an excellent experimental plant for the study of variable hybrids, if it required less 365 space." (Letter VII, Stern and Sherwood, 1966, p. 84). In Geum Mendel produced F1 hybrids, but no 366 information exists about the variation in their progenies. In contrast to Hieracium, apomixis has not been 367 found in Cirsium and Geum. 368 369 Phase 2 -different constant hybrids from true breeding parents! 370 On July 3rd 1870 Mendel wrote to Nägeli: "As a matter of fact, variants appeared in all those cases in 371 which several hybrid specimens were obtained. I must admit to having been greatly surprised to observe 372 that there could result diverse, even greatly different forms, from the influence of the pollen of one 373 species upon the ovules of another species, especially since I had convinced myself, by growing the 374 plants under observation, that the parental types, by self-fertilization, produce only constant progeny." 375 (Letter VIII, Stern and Sherwood, 1966, pp. 88, 89). In the lecture of June 1869 Mendel had mentioned 376 that the different forms were only single terms in an unknown series. To dissect this series into its terms, 377 as he had done in Pisum, Mendel needed much larger numbers of hybrids. We think that this was the 378 reason why Mendel needed to increase the efficiency of his crosses and started to use a mirror with a 379 convex lens, since "diffuse daylight was not adequate for my work on the small Hieracium flowers" 380 (Letter VIII, Stern and Sherwood 1966, p. 86). In this long letter of July 3 rd 1870 we read that after 381 Mendel made a large number of crosses in May and June 1869 he had serious problems with his 382 eyesight, caused by the very intense light. Although he stopped immediately, it was well into the winter 383 before he was able to read longer texts and perform Hieracium crosses without concentrated light. 384 Before the eye problems began, Mendel had fertilized more than 100 emasculated flower heads of 385 Hieracium auricula with pollen from H. praealtum, H. cymosum and H. aurantiacum. The hybridisation 386 procedure was optimized by placing the emasculated plants for 2-3 days in a damp atmosphere in the 387 greenhouse after cross pollination (Mendel 1869 Nowadays we know that these species are highly apomictic. Overall Mendel must have carried out 397 thousands of emasculations and pollinations in May and June 1869, an incredible and painstaking task. 398 Ostenfeld (1906) commented: "This method, however, is so difficult and gives so small results, as the 399 Mendel's nephew who had visited the monastery, had his notes burned (Kříženeck 1965). Only two 448 sheets of Mendel's notes survived (Notitzblatt 1 and 2), and both have been dated after 1874 (Orel 449 1996). The first note is about segregation ratios of seed coat color in Pisum (Heimans 1969) species and 450 in the second it is written that Hieracium produces several hybrids in contrast to a single hybrid in 451 Wichura's Salix (see Supplemental Figure SF3). Neither form a cumulative series of combinations after 452 selfing as variable hybrids do (Heimans 1969, Allen 2016. Interestingly in this second note, Mendel 453 wrote 'Bei Veränderliche Ausgleichung' (in a varying compromise) i.e., the temporary equilibrium that 454 Mendel hypothesized in variable hybrids and indicating that he was still thinking in terms of gamete 455 formation. This supports our view that variable and constant hybrids were both parts of Mendel's 456 integrated research activities on the rules of heredity. The place where a paragraph ends can be identified by a line of text that does not run to the right margin 477 but a paragraph start must be inferred in the following line, because Mendel did not indent new 478 paragraphs. This inference is easily achieved for paragraphs on the same sheet of paper, because of their 479 physical connectedness. However, this connection is missing when a paragraph ends at the bottom of an 480 even numbered page and a new paragraph starts (or appears to start) on the next sheet, at the top of an 481 odd numbered page. For example, paragraph 5 of Letter I appears to begin at the top of page 3, but this 482 appearance is entirely dependent on the paragraph end at the bottom of page 2. Page 3 begins with a 483 capital letter in "Für", so this starts a new sentence, but not necessarily a new paragraph. 484

485
We counted the number of paragraphs (excluding final paragraphs) that coincided with a page break. Six 486 out of 63 paragraphs ended at a page break (35 pages; 4 complete letters, 2 letter fragments, 3 487 paragraphs at the bottom of an odd numbered page and 3 at the bottom of an even numbered page: 488 6/63 = 0.095). Since both sides are written on, the probability of a break at an even page is half of this 489 value, thus the probability that this paragraph configuration occurs by pure chance is estimated as 0.5 x 490 0.095= 0.048. Because paragraphs rarely end at the bottom of an even numbered page, this paragraph 491 structure likely represents an intentional change of subject. Furthermore, when we ask if it is likely that 492 page three of Letter I begins with a new paragraph, the answer is 'no' (p=0.048). 493

494
If there is a missing sheet (2 pages), then the first missing page must begin with a new paragraph, as is 495 assumed for the current page 3. If the current page 3 does in fact begin with a new paragraph, then the 496 second (missing) page has to have a paragraph end at the bottom. We can estimate p, the frequency of 497 pages with a paragraph end at the bottom, from those we can observe, thus p = 6/35 = 0.17 and 498 estimate the standard deviation as √(pq/N) = 0.064. Thus the chance that the second page of the 499 proposed missing sheet has a paragraph end at the bottom is p, so roughly 10% to 25% of pages selected 500 at random from Mendel's letters would have the properties required for this proposed missing page. 501 Therefore we cannot rule out the original existence of a page that is now lost. 502 503 504 Since the pages are not numbered, obvious reasons for missing pages would be if the sheet were lost, or 505 inserted in another letter in the wrong place. Mendel's handwritings have not been published 506 completely and we have no information about where the originals are now located. We checked 507 Correns' publications for strange junctions/twists, but could not find any that were clear. On the other 508 hand, given the history of Mendel's letters (Supplemental file 1), it would not be surprising if some were 509 incomplete. As a matter of fact, we know that the correspondence is incomplete (see Supplemental file 510 1). 511

512
The two missing pages (one sheet) could also explain why Mendel did not write about the other species 513 with which he already had started crossing experiments in 1865 and 1866 (Linaria, Calceolaria, Zea mays, 514 Ipomoea, Cheiranthus, Antirrhinum and Tropaeoleum), and which were much more suitable for testing 515 his Pisum findings than Hieracium, Cirsium and Geum. In his second letter to Nägeli, Mendel reported on 516 the progress of the crossing experiments in these species as though the subject was already known to 517 Nägeli. Only the last four pages of Nägeli's answer to Mendel's first letter have survived, but an 518 important passage is: "your plan to include other plants in your experiments is excellent and I am 519 convinced that with many different forms you will obtain essentially different results" (with respect to 520 the inherited characters 3 ) "It would seem to me especially valuable if you were able to effect hybrid 521 fertilizations in Hieracium for this will soon be the genus about whose intermediate forms we shall have 522 the most precise knowledge" (transcription: Hoppe 1971, our translation). "Many different forms" 523 suggests more than three (i.e. Hieracium, Cirsium and Geum) and is likely the list of species with which 524 Mendel had started crossing experiments to test the Pisum findings; it is surprising these are not 525 palustre x rivulare that were found in the wild, some more resembling one and some the other of the 549 parental species (von Niessl 1867). In 1866 Mendel had cultivated one of these Cirsium hybrids which 550 was highly fertile and produced offspring in the same year. Adolph Olborny (a member of the board), 551 also a specialist in Hieracium, took care of the Hieracium section of the society's herbarium. 552

553
Hieracium was a notoriously difficult genus for taxonomists. Besides morphologically distinct forms 554 ("Haubtformen"), Hieracium was characterized by many intermediate forms ("Mittelformen") which 555 formed a continuum between the Haubtformen. The question was whether these intermediate forms 556 were hybrids, site modifications (environmentally conditioned variants), or transient forms in the process 557 of speciation (as Nägeli believed). Fries categorically denied the existence of hybrids in Hieracium. 558