Abstract
GREGOR MENDEL, A MORAVIAN FRIAR IN THE BIRTHPLACE OF GENETICS
Brno, the economic and academic capital of Moravia in the 19th century
According to his autobiography, his family relatives and informed biographers, Johann Mendel was born on 22 July 1822 (Iltis, 1954; Schindler, 1965; Van der Pas, 1972; Klein & Klein, 2013) in the village of Heinzendorf, located in Silesia close to the north border of Moravia, a province that was part of the Austro-Hungarian Empire, the capital of which, Brno, is close to the Austerlitz battlefield. As Vítĕzslav Orel indicates in his magisterial biography of Mendel (Orel, 1996), it is in Brno, as early as 1819, that the first empirical laws of genetics were published. They were formulated by Count Festetics at the request of the naturalist Christian Carl André, in response to the concerns of sheep farmers, who were eager to find ways to improve the quality of wool of their animals and had formed an Association for the Promotion of Agriculture (Orel & Wood, 1998; Poczai et al., 2014). The term ‘genetics’ appears here for the first time, well before the beginning of the 20th century. In this context, the question of inheritance was widely debated in Brno during the first half of the 19th century, notably by Cyrill František Napp, the abbot of the Augustinian monastery of the city. Napp chaired the local Association of Pomology created by André to address the issue of improving fruit trees through artificial pollination. This association was publishing the results obtained in Germany and England, among them the work of Thomas Andrew Knight, the President of the London Horticultural Society. Knight had initiated experiments on the hybridization of annual plants as early as the end of the 18th century and described in peas the phenomenon of dominance, the uniform appearance of the hybrids and the assortment of parental characters in the offspring.
Saint Thomas Monastery, a horticultural research and education organization
In 1854, Napp had installed an experimental greenhouse and a botanical garden within the monastery (Orel, 1996), whose members had the duty, by Imperial decree, to be actively involved in teaching at the secondary and higher education establishments of the city. Johann entered the monastery in 1843 under the name of Gregor and became a priest in 1847, allocated on emergency to the service of the Altbrünn parish after three of the priests died from an epidemic of infectious disease that Mendel also most probably contracted (Nivet, 2004).
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Gregor Mendel had already been identified by Napp as gifted for the sciences. Several monks of the monastery participated in the insurrection of 1848 against the imperial power. Among them was Matouš František Klácel, a professor of philosophy and polemist, who petitioned, with the support of Mendel, for the right of the monks to choose freely between pastoral service and the study and teaching of the sciences (Nivet, 2006); Klácel was indeed very influential to the young Mendel’s fate (Peaslee & Orel, 2007). Gregor Mendel was nominated in 1849 as a professor by Imperial decree. According to Nivet, Napp used these circumstances astutely to free Mendel from his parish duties and sent him to Vienna to follow a university course for 2 years, with the aim of qualifying for higher education teaching (Nivet, 2004).
In Vienna, Gregor Mendel was introduced to the cell theory and the experimental method by the botanist Franz Unger and the physicist Christian Doppler. Following the ideas of Unger, who was in favour of the concept of a particulate inheritance, Mendel stepped away from the dominating idea of inheritance by blending, according to which fluids coming from the parents would mix in their progeny, which was endorsed by his contemporary, Charles Darwin, who frequently refers to blended characters in his book on The Variation of Animals and Plants under Domestication (Darwin, 1868).
In 1856, when Gregor Mendel began his experiments on hybrid plants, he had acquired an excellent level of university training. Moreover, he worked in a favourable environment, in terms of both theoretical discussions and material conditions: he benefitted from half a century of active debates within the Brno learning associations and from the experimental infrastructures of the monastery. Furthermore, he was actively encouraged by his superior Napp who, as soon as 1836, had formulated the question, ‘what is transmitted, and how is it transmitted?’, as a subject for fundamental research on inheritance that had to be resolved using the experimental method (Serre, 1984; Orel, 2009).
Johann Mendel, aspiring botanist and researcher
According to one of his first biographers (Iltis, 1924), the young Johann Mendel had demonstrated since his early years in a peasant family an excellent aptitude for observation and had been introduced to botany and agronomy by his parents, his schoolmaster and the village priest, Schreiber, himself a correspondent of the Brno Agricultural Society. All had encouraged him to pursue his studies because of his brilliant results in the unique class of the village school. He joined the monastery in Brno in 1843 after completing a course at the Philosophical Institute in Olmütz, where he studied physics, mathematics and logic (Orel, 1996; Klein & Klein, 2013). The modest resources of his family were insufficient to support the full curriculum of higher education. In his early years living in a pleasant rural environment, he was identified as a gifted young boy by his schoolmasters, but owing to an accidental fall of his father at the farm, he had on several occasions to interrupt his curriculum to take care of the chores (Klein, 2000; Klein et al., 2009; Nivet, 2020).
Johann Mendel had therefore the right profile articulated prophetically in 1820 by G. Hempel, a member of the Agriculture Society in Brno, to describe the new type of natural scientist that would have to emerge in order to explain the laws of hybridization of sexual plants: ‘able to conduct demanding experiments; a researcher having a profound knowledge of botany and acute observation capabilities, who could, with a tireless and relentless patience, capture the subtleties of these experiments, firmly take them under control, and provide a clear explanation’ (Orel, 1996).
The legendary discoveries of a wrongly unknown genius
Thus, Gregor Mendel is not the ‘unknown genius’ described in the historical textbooks, who would have discovered the laws of heredity alone and without any help, guided only by his passion for peas (Blanc, 1984). As a matter of fact, most of the notions and knowledge on which Mendel’s work relies can be found in the scientific literature of his time. It is known that he had access to it through the books available in the excellent library of the monastery (Figs 1, 2). He was in no way isolated from the scientific and industrial community of his time, as testified by his numerous trips to congress and exhibits in Austria, England, France, Germany and Italy, as he had affiliations to learned societies.
Knight had proposed the pea as a particularly well-adapted experimental model for the study hybridization and had described the phenomenon of dominance, the uniform appearance of the hybrids, and the assortment of the parental characters in the offspring. These notions had been reinforced by other breeders, such as the British J. Goss and A. Seton, who worked on the same peas of the genus Pisum studied by Mendel, or the French A. Sageret working on the melon, when Mendel was still a schoolboy. Moreover, the German Gaertner had published in 1849 a monumental treatise, in which he described the artificial pollination method he had used no less than 10 000 times in 700 species of plants, including, in particular, its use to study the first four characters that Mendel included in his study. Mendel knew this work well, and refers to it in his report, because it was the topic of lessons given by F. Diebl at the Institute of Philosophy in Brno that Mendel attended (Orel & Wood, 1998). It is therefore clear that Mendel is not the discoverer of these notions, nor the inventor of the hybridization methods or the choice of Pisum as experimental model. One has to look elsewhere for what made his work an inescapable masterpiece for biology.
Back to the source: Versuche über Pflanzen-Hybriden by Gregor Mendel
In this perspective, it is appropriate to refer to the small number of Mendel’s original publications and, in particular, to his paper, Versuche über Pflanzen-Hybriden, written in German, his native language. It was published in 1866 by the Society of Natural History of Brünn (the German name of Brno), on the basis of the two lectures presented by Mendel on 8 February and 8 March 1865, in which he reported the results of > 8 years of experimental work (Mendel, 1866; Bateson, 1902; Naudin et al., 1990). The two lectures were well attended and echoed in the local press (Zhang et al., 2017).
The first impression that comes to mind on reading this text is its modern and clear style, although there has been, since the ‘rediscovery’ of his work, a wealth of never-ending interpretations and speculations on what Mendel really discovered (Sturtevant & Lewis, 2001) or thought he had uncovered (Hartl & Orel, 1992; Orel & Wood, 2000). The reality of this rediscovery and its interpretation are subject to contradictory debates. In 1936, the mathematician and geneticist Ronald Fischer suggested that Mendel had, voluntarily or not, biased his observations, while refuting the view put forward by Bateson, who conjectured that Mendel’s paper was not a literal description of his work but a reconstruction (Fisher, 1936). Taking broader views, Jan Sapp has described ‘the nine lives of Mendel’ and the posthumous controversies that his work triggered and continue to feed (Sapp, 1990; Olby, 1997), while John Porteous, after showing that it is still not possible to account fully for Mendel’s observations, made the case for a rational use of Mendelian genetics that takes into account the discoveries of the last century dominated by the development of molecular biology (Porteous, 2004a, b).
A question of vocabulary: factors, elements and genes
The second striking fact when reading Mendel’s paper is the vocabulary that he uses or, more precisely, the words he does not use. There is no gene or genetics in sight and only one explicit but indirect mention of heredity. Indeed, the term ‘gene’ was introduced only in 1909 (Johannsen, 1909), simplifying the terminology of Hugo de Vries, one of the ‘rediscoverers’ of Mendel’s laws, who used the term ‘pangenes’ to designate the elementary units of heredity, in reference to Charles Darwin’s theory of pangenesis, in which he referred to gemmules, probably the equivalent of the exosomes that are the focus of intense research nowadays (Noble, 2020). Even more surprising, the term ‘factor’, taught to students as representing the gene for Mendel, appears only twice, with two distinct meanings: the first, ‘it remains more than probable that there is a factor in action for the variability of cultivated plants, which hitherto has received little attention’, probably refers to the fact that the different forms of the characters are transmitted separately (the law of independent assortment), whereas the second, ‘We must then treat it as necessary that the very same factors combine in the production of constant forms in the hybrid plant’, could designate the elementary units of heredity. Indeed, Mendel uses the term ‘element’ and not ‘factor’ on ten occasions in his conclusions, clearly indicating his standing in the framework of a particulate concept of heredity, in contrast to Darwin, who supported the blending hypothesis of heredity (Mayr, 1982).
Sexual reproduction and ‘development’ at the heart of Mendel’s interests
Hartl & Orel (1992) follow Mayr in using the argument of pedagogic repetition to discern in Mendel’s text the main idea he wants to convey: ‘The law of combination of the differing characters, by which the development of hybrids results, finds its foundation and explanation accordingly in the conclusive principle that hybrids produce germ and pollen cells corresponding in equal number to all constant forms that arise from the combination of the characters united through fertilization’. This idea is repeated six times in different forms. This vision contrasts, they say, ‘with the traditional presentation according to which Mendel discovered that hereditary characters are determined by cellular elements, now called genes, that exist in pairs, are submitted to independent segregation and assortment, and persist unchanged through the successive generations of hereditary transmission’ (Hartl & Orel, 1992).
This point of view insists on the fact that Mendel mostly endeavoured to establish explicitly the equal contribution of both sexes to the generation of offspring, with the underlying mechanism remaining implicit, because it was not accessible through his experimental means: chromosomes and nuclein were described after 1865, and their roles understood much later. Iris Sandler insists on the fact that Mendel uses, in different forms throughout his exposé, not less than 50 times the German term Entwicklung, usually translated as ‘development’, in the broad sense that prevails in the 19th century (Sandler, 2000), when the term ‘evolution’ was not yet widely used (Abbott & Fairbanks, 2016; Fairbanks, 2020). To her, this term is the central element of Mendel’s thought, reflecting his interest in the study of a biological process that includes the transmission of characters and their manifestation throughout the life of an organism and a species.
In order to convince ourselves of the relevance of this view, let us follow Gregor Mendel step by step in the different sections of his exposé. In the sections that follow, we use one of the most recent English translations of Mendel’s report because it takes into account the contextual relationships of Mendel’s and Darwin’s parallel and independent works and thoughts (Abbott & Fairbanks, 2016; Fairbanks & Abbott, 2016; Fairbanks, 2020); for another see Müller-Wille & Hall (2016).
GREGOR MENDEL’S METHOD: AN OBSERVATION, AN OBJECTIVE, AN EXPERIMENTAL PLAN
Introductory remarks
Whatever importance is given to what was formulated by Mendel implicitly or explicitly, his text is one of the foundations of modern biology because of the methodology he uses and the mathematical formalism he introduces, as was the case for William Harvey, the founder of physiology in the 17th century (Auffray & Noble, 2009). Even in his preliminary remarks, he indicated clearly the initial observations on which he founded his study:
The striking regularity with which the same hybrid forms reappeared whenever fertilisation took place between the same species was the stimulus for further experiments, whose objective was to follow the development of hybrids in their progeny.
The starting point is the observation of a regularity, in the manner of the meteorologist Mendel also was, registering daily for many years the climate parameters in Brno and publishing in one of his nine papers in this field a careful description of a tornado. Indeed, Mendel published twice as many papers on meteorology as on biology, a fact that has been recognized by naming the Czech polar station after his name (‘Mendel Polar Station’, 2022). Mendel then precisely states the problem he proposes to study and resolve (i.e. the search for a law governing the development of hybrids):
That a generally standard law for the formation and development of hybrids has not yet been successfully given is no wonder to anyone who knows the extent of the subject and who realizes the difficulties with which experiments of this kind must struggle. A final determination will result only when detailed experiments on the most diverse plant families are available.
Referring to the breeders of the 18th and 19th centuries, such as Koelreuter, Gaertner, Herbert, Lecocq and Wichura, cited nominally, Mendel mentions the difficulties they encountered and introduces as a means to overcome them the objective of establishing the numerical ratios that exist between the hybrid forms in the successive generations. In other words, his objective is to establish a mathematical formalism, a model of the phenomenon of his study, the development of the hybrids:
Anyone who surveys the work in this area will be convinced that among the numerous experiments, none have been carried out in the extent and manner that would make it possible to determine the number of the various forms in which the progeny of hybrids appear, so that one could, with confidence, arrange these forms into the individual generations and determine their relative numerical relationships. Some courage is certainly required to undertake such an extensive work; nevertheless, it seems to be the only proper means to finally reach resolution of a question regarding the evolutionary history of organic forms, the importance of which must not be underestimated.
Notably, Mendel tackles the development of organisms in a global manner, without referring explicitly to the underlying questions of heredity and evolution. He concludes his preliminary remarks by introducing the notion of an experimental plan:
Whether the plan by which the individual experiments were arranged and carried out corresponds to the given objective may be determined through a benevolent judgment.
Such a concise and modest statement can only trigger admiration for what constitutes one of Mendel’s major contributions to biology. While following Mendel step by step in the exposé of his motives, his hypotheses, his results, and the practical and theoretical means he employs, one will see that he is not only at the origin of genetics, which should be considered as a by-product of his work developed by his successors, the geneticists, but he is, first and foremost, through his global approach to the development of organisms and the back-and-forth move between mathematical modelling to generate hypotheses and experimental exploration of these hypotheses, one of the founders of systems biology, together with William Harvey and Claude Bernard (Noble, 2008; Auffray & Noble, 2009). His research is integrative in nature and conducted iteratively to study and model biological systems as complex systems in interaction with their environment. His methodology should therefore be considered as a forerunner of the systems approaches that have become pervasive in biology, physiology and medicine since the beginning of the 21st century (Auffray et al., 2020).
Selection of the experimental plants
Gregor Mendel introduces his experimental plan by a sentence that would merit being posted at the entrance of all biological laboratories:
The worth and validity of any experiment are determined by the suitability of the materials as well as by their effective application.
He then defines the necessary and sufficient conditions to ensure that the observations made during his experiments would be protected from perturbations that would render their interpretation difficult or even impossible. He chooses from the outset to study individual characters that are easy to distinguish in the hybrids and to follow in their offspring, and he identifies uncontrolled pollination and fertility defects as potential obstacles to the discernment of the laws of development of hybrids:
The experimental plants must necessarily
1. Possess constantly differing characters.
2. At the time of flowering, their hybrids must be protected from the action of all pollen from other individuals or be easily protected.
3. The hybrids and their progeny in the succeeding generations must not suffer any noticeable disturbance in fertility.
Mendel pays particular attention to the role of pollinating insects. He then clarifies what he means by detailed experiments, which he underlined already in his preliminary remarks, by pointing to the necessity of an exhaustive description, insisting that all individuals must be observed:
To recognise the relationships of the hybrid forms to one another and to their original parents, it appears to be necessary that every member that develops in the series in every single generation be subjected to observation.
This concern about exhaustivity, in concordance with the fourth precept of Descartes’ Méthode, explains why Mendel’s approach could have been considered as strictly analytical and reductionist (Serre, 1984). However, in his project to study the development of the hybrids as a process, Mendel always pays attention to the context, the dynamic relationships and the conditions that determine the stable or unstable behaviour of the hybrids. He retains from his observations only what is pertinent in relationship to the question driving his study. From this point of view, he is more Cartesian than the early 20th century geneticists who developed his work further while ‘reducing’ it to the sole question of heredity, when Mendel dealt also with evolution and development. Indeed, he avoids ‘carefully precipitation and prevention’, and he divides the difficulties in how many parts ‘that would be necessary to better resolve them’. In other words, he works out what is necessary and sufficient to resolve his question of interest, without considering other facts that are not indispensable in the framework of the hypotheses he formulates. Thus, he verifies the adequacy of peas to his experimental plan, as the reading of his predecessors had suggested to him, and retains only the convenient varieties, probably because of their very distinct characters and robustness:
Experiments made with several members of this family (Leguminosae) led to the conclusion that the genus Pisum sufficiently meets the necessary requirements. Several completely independent forms of this genus possess uniform characters that are easily and certainly distinguishable, and they give rise to perfectly fertile hybrid progeny when reciprocally crossed. … From these, 22 (out of 34) were selected for cross-fertilisation and were cultivated annually throughout the duration of the experiments.
Finally, he considers that his work stands outside the debate on the question of the definition of species and varieties, and thus of the position of the hybrids in evolution, a question that sparked debates after the publications by Darwin and Wallace of their theories on the role of natural selection, which was the subject of the lecture given by Makowsky in January 1865, just before those by Mendel (Fairbanks, 2020):
The systematic classification is difficult and uncertain. … In any case, these systematic ranks are completely unimportant for the experiments described here.
Mendel thus develops a methodological but not an ontological reductionism; he intends to focus on a precise problem: to clarify the remarkable regularity he has observed in the development of the offspring of the hybrids.
W. Focke referred ~15 times to Mendel in his treatise on plant hybridization published in 1881, without completely understanding its meaning, because he mentions the work on Pisum only once. For him, Mendel’s work represented an isolated series, poorly significant when compared with the voluminous contributions of Koelreuter, Gaertner and Wichura, with studies that dealt with no less than 98 plant varieties … none of which had been organized with the rigor and precision of Mendel. Nonetheless, it is this single mention that would later draw the attention of the ‘rediscoverers’, first of all Carl Correns, who attributed ‘the laws of heredity’ to Mendel. This was an astute manner on his part to circumvent the priority battle that could have developed with Hugo de Vries, who had, like him, conducted experiments similar to those of Mendel, or with Erich von Tschermak-Seysenegg.
One is inclined to think that, without their late knowledge of Mendel’s work, all three would have encountered difficulties in making complete sense of their own results. Charles Darwin himself had conducted during 11 years crosses between self-fertilizing plants, which he published in 1876 (Darwin, 1876; Ruse, 2010), without discerning or understanding the meaning of the regularity on which Mendel focused: in one of his crosses, Darwin obtained a ratio of 3.6:1 between the second-generation characters, close to Mendel’s 3:1 ratio. Although he received an advance copy of Fockes’s 1881 book, Darwin passed it to a colleague without reading it, shortly before he died in 1882 (Sclater, 2006); this was a missed opportunity for two great minds to meet.
Arrangement and order of the experiments
In the following section, Mendel progressively accounts for the details of his experiments, while constantly referring to his aim and to the results of his predecessors on which he relies, particularly the uniformity of the first-generation hybrids:
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If two plants that are constantly different in one or more characters are united through fertilisation, the characters in common are transmitted unchanged to the hybrids and their progeny, as numerous experiments have shown; each pair of differing characters, however, unites in the hybrid to form a new character that generally is subject to variation in the progeny. To observe these variations for each pair of differing characters and to ascertain a law according to which they occur in succeeding generations was the objective of the experiment. This experiment, therefore, breaks up into just as many individual experiments as there are constantly differing characters in the experimental plants.
… the individual experiments, which had to be limited to characters that appear clearly and decidedly in the plants. A successful result would finally show whether they all are observed as portraying identical behaviour in hybrid union …
After the rediscovery of Mendel’s work, the reality of his experiments was questioned, on the pretext that the results were ‘too good to be true’. William Bateson, who was the first translator of Mendel’s work into English and was his active promoter (Bateson, 1902), thought that Mendel had not really conducted the experiments as reported in his paper, because he could not have had access to pure varieties for the seven characters he studied. According to him, Mendel would have proceeded through a reconstruction from experiments in which multiple characters would have co-existed in the same plants. This is curious for the person who proposed to designate the new discipline born from Mendel’s discovery by the term ‘Genetics’. Contemporary botanists have, on the contrary, demonstrated that Mendel had access to the biological material necessary (Fairbanks & Rytting, 2001; Kemp, 2002). Ronald Fisher, in his 1936 paper that had a resounding echo (Fisher, 1936), showed that Bateson wanted principally to attribute to the Darwinists the blackout on Mendel’s work that he was fighting. It is troubling that this pioneer of statistics and the theory of experimental plans had considered it appropriate to suppose that Mendel had, voluntarily or through an excessively zealous assistant, biased his results to set them in concordance with those expected from his theory; these suppositions have now been dismissed (Franklin et al., 2008). Fisher’s position is probably explained by his endorsement of the school of thought that rejected the Darwinian interpretation of Mendel’s work.
Mendel continues:
Of a larger number of plants of the same kind, only the most vigorous were selected for fertilisation. Feeble specimens always yield uncertain results …
Further, in all experiments reciprocal crosses were undertaken in this manner: One of the two kinds that served as seed plants for a number of fertilisations was used as the pollen plant for the other.
For each experiment a number of potted plants were placed in a glasshouse during the flowering period. They served as a control for the main garden experiment in case of possible disturbance by insects.
With more than 10 000 carefully examined plants, the case of such undoubted interference occurred only a few times.
One recognizes here Mendel’s concern to preserve his experiments from any undesirable interference, whether internal (the fecundity of the hybrids) or external (the intervention of insects), by taking the necessary controlling measures. Importantly, he introduces systematic cross-fertilization, clearly indicating his interest in measuring precisely the contribution of both sexes to the characters of the hybrid offspring. This is an essential point in Mendel’s observations and his working hypothesis, because the idea that had prevailed since antiquity was that of a female matrix stimulated, without a material contribution by the male; an Aristotelian concept reformulated in different forms by the preformationists of Mendel’s time.
Mendel has thus been able to take the best advantage of the knowledge and techniques he learned from his masters, in order to design an experimental plan suitable to reach his objective: to provide an explanation for the remarkable regularity during the development of hybrid plants. In contrast to his predecessors, he built his experiments on solid foundations, focusing on what was necessary and sufficient to reach his goal.
GREGOR MENDEL’S SYSTEMIC EXPERIMENTATION: CONTEXTUALIZATION, RELATEDNESS, CONDITIONALITY, PERTINENCE
During the 8 February 1865 session of the Natural History Society in Brno, after summarizing his motives and his method, already discussed in previous sessions, Mendel reports the results he has obtained, insisting on the numerical ratios observed between the different forms of the hybrids during the successive generations. Mendel thus formulates a first mathematical model that conforms to the precepts of systems biology. Indeed, although his approach is based on the Cartesian precepts of objectivity, division, causality and exhaustivity that characterize analytical reductionism, he completes it by adhering to the systemic precepts of contextualization, relatedness, conditionality and pertinence (Auffray et al., 2003).
The form of the hybrids
In the first section of his paper dealing with the experimental results, Mendel reports that he first verified, through what we would today call ‘pilot experiments’, that his experimental model does not fit with the idea of heredity by mixing that predominates, including in Darwin’s writings: ‘when two commingled breeds exist at first in equal numbers, the whole will sooner or later become intimately blended’ (Darwin, 1868). For him, the uniformity of the hybrids prevails as evidence. He then defines the notion of dominance by introducing the appropriate vocabulary:
The experiments conducted with ornamental plants in past years already produced evidence that hybrids, as a rule, do not represent the precise intermediate form between the original parents.
In the following discussion those characters that are transmitted wholly or nearly unchanged in the hybrid association, that themselves represent the hybrid characters, are defined as dominant, and those that become latent in the association are defined as recessive.
He then summarizes what is one of his major contributions: the equal contribution of the two sexes to the characters of the hybrids, transmitted by the sexual cells during pollination, and underlines the advantage of studying the seed characters that can be observed very rapidly:
Further, it has been shown through all the experiments that it is completely unimportant whether the dominant character belongs to the seed plant or to the pollen plant; the hybrid form remains exactly the same in both cases.
The hybrid forms of the seed shape and albumen develop directly after artificial fertilisation simply through the action of the pollen from another individual.
One can only recognize here Mendel’s extraordinary capacity for synthesis and concision, as he is able to summarize in the same sentence his theoretical and practical views.
The first generation of the hybrids
By careful study of the fate of the different forms of the seven characters examined in the offspring of the hybrids, Mendel confirms the reappearance of the recessive forms, a fact established by his predecessors. This is the disjunction phenomenon that geneticists designated as ‘Mendel’s first law’. However, Mendel’s main contribution is his report of a ratio of 3:1 between the hybrid forms as a general rule observed in all crossings, independently of the contribution of the two sexes:
In this generation, along with the dominant characters, the recessive characters reappear in their full individuality and do so in the determinate and pronounced average ratio of 3:1, so that of every four plants from this generation, three produce the dominant and one the recessive character. This applies without exception for all characters included in the experiment.
Because the hybrids produced from reciprocal crosses acquired a wholly similar form and because no appreciable variation appeared in their further development, the results for each experiment could be combined.
Mendel lingers on the first two experiments concerning the form (round or wrinkled) and the colour (yellow or green) of the seeds, for which he reports ratios of 2.96:1 and 3.01:1, respectively. He also provides a numerical table of the features of ten out of 250 experimental plants, thus illustrating the variability of the results. He then generalizes his observations to all seven characters, reporting ratios varying between 2.85:1 and 3.15:1:
As in the individual pods, the distribution of characters varied similarly among individual plants.
These two experiments are important for ascertaining the mean ratios because they produce especially meaningful averages with a smaller number of experimental plants.
If the results of all experiments are summarised, there is an average ratio between the number of forms with dominant and recessive characters of 2.98:1 or 3:1.
Mendel presents his results as a mathematician, as for his meteorological observations, using numerical values and tables (Kemp, 2002). By doing this, he differs from his contemporary naturalists, whose treatise are richly illustrated by descriptive plates. In his paper, there is not a single representation of his plants or a scheme of the pollination procedures. Instead, he insists on the quantification and measurement of variability using the statistical methods he learned from his physicist teachers, which he uses in a very innovative manner for a naturalist.
A controversy was initiated by readers of Ronald Fisher’s paper (Fisher, 1936), leading to a statement that Mendel’s results were ‘too good to be true’ from a statistical point of view. Without going into the details of Fischer’s paper (whose intention was to support Mendel’s work), it is worth pointing out that he first considers that the variations observed in the individual experiments discussed here are within the expected norm, before noting a deviation he considers as abnormal in the following experiments (Fairbanks & Rytting, 2001; Rédei & Kang, 2001). Several authors have endorsed a view opposite to that of Fisher, denying the existence of a bias (Pilgrim, 1984, 1986; Corcos & Monaghan, 1985, 1993). Alfred Sturtevant, Thomas Morgan’s collaborator who established the first genetic maps in Drosophila, compared in his history of genetics the seven experimental series in which crosses of hybrid peas with yellow and green seeds were performed between 1896 and 1924 and collected by Johannsen, with that of Mendel (Sturtevant & Lewis, 2001). Tschermak, who counted half the number of seeds compared with Mendel, obtained results closer to the ideal proportion, whereas Lock, who counted four times fewer, reported the ratio with the largest deviation, and Darbishire, who counted 18 times more, obtained a ratio within average. It can therefore be concluded that Mendel’s experiments are clearly coherent between themselves and with established statistical laws, which has been confirmed by recent works (Franklin et al., 2008; Pires & Branco, 2010; Radick, 2015, 2022). In recent years, Gregor Mendel’s experimental design and methodology for data recording, analysis and mathematical modelling have inspired positive comments from scientists in many fields, praising his logical empiricism (Cohn, 2003; Birchler, 2015; Opitz & Bianchi, 2015; De Castro, 2016; Deichmann, 2019; Huminiecki, 2020; Berger, 2022; Mittelsten Scheid, 2022).
Let us come back to Mendel’s exposé, as he now introduces a contextual distinction and a prediction:
The dominant character can have a double signification here, namely that of the original parental character or that of the hybrid character.
An original parental character must be transmitted unchanged to all progeny, whereas the hybrid character must follow the same behaviour as observed in the first generation.
Mendel tells us that the dominant characters should not be endowed with an absolute value and that it is necessary to take into account the context in which they manifest themselves, a necessary condition in order to predict in a pertinent manner their transmission to the offspring. In doing so, Mendel acts as a precursor of systems biology by enforcing the systemic precepts: he understands the transmission of the dominant character in relationship to the environment in which it evolves, which is different in the pure and hybrid lines, and not only as an isolated object with particular properties. His quest is not about the structure of the gene, but rather about its behaviour in the different contexts in which it can manifest itself, principally in the successive generations.
The second generation of the hybrids
On the basis of his model of the behaviour of the characters in the course of generations, he formulates the hypotheses that form the basis for the design of a second series of observations for the characters studied:
Those forms that preserve the recessive character in the first generation do not vary in the second generation in relation to that character; they remain constant in their progeny. This is not the case for those that possess the dominant character in the first generation. Of these two-thirds yield progeny that carry the dominant and recessive character in the ratio 3:1 and thus show the same behaviour as the hybrid forms; only one-third remains constant with the dominant character.
The ratio 3:1, which results in the distribution of the dominant and recessive characters in the first generation, resolves then for all experiments into the ratio 2:1:1, if one simultaneously distinguishes the dominant character in its signification as a hybrid character and as an original parental character. Because the members of the first generation arise directly from the seeds of the hybrids, it now becomes apparent that the hybrids from each pair of differing characters form seeds, of which one-half again develops the hybrid form, whereas the other yields plants that remain constant and produce in equal parts the dominant and the recessive character.
This is the first part of his text that Mendel underlines extensively, in order to highlight the importance he attributes to this step in his work. He thus implements the systemic precepts of contextualization, relatedness and conditionality (Auffray et al., 2003), by showing his interest first and foremost about the dynamic relationship between the characters and the rules they follow in different contexts, and not only about their elementary causality. It is this systemic approach that leads him to the pertinent conclusion that the observed relationships result from the production of hybrid and pure seeds in equal numbers.
The subsequent generations of the hybrids
After indicating that he has verified his conclusion by following the fate of the characters during four to six generations, depending on the character, Mendel changes gear by introducing an algebraic formula to express his model of the development of the hybrids:
If A represents one of the two constant characters, for example the dominant, a the recessive, and Aa the hybrid form in which the two are united, then the expression A + 2 Aa + a shows the developmental* series for the progeny of the hybrids of each pair of divergent characters.
This formula triggered various interpretations, because Mendel does not display pairs of characters (AA and aa) in each of the terms corresponding to the pure forms, as geneticists would do later. In fact, at this stage of reasoning, in his logic he has only to care about the latent co-existence of the characters: he thus introduces the minimal hypothesis required to explain his observations, without attempting to explore exhaustively the underlying mechanisms that were inaccessible to his experiments, thus complying with the systemic precept of pertinence (Auffray et al., 2003).
*As pointed out by Iris Sandler (Sandler, 2000), Mendel used the German term Entwicklungsreihe, whereas the initial English and French translations bypassed the term ‘development’.
The progeny of the hybrids in which several different characters are combined
In order to test the validity of his model for the serial development of the hybrids in equiprobable combinations, Mendel the undertakes a more complex series of experiments, in which he combines the differential characters two by tow or three by three. We refer here only to his principal conclusions that were interpreted by the geneticists as Mendel’s second law of the independent assortment of the characters:
There is, then, no doubt that for all of the characters admitted into the experiments the following sentence is valid: The progeny of hybrids in which several essentially differing characters are united represent the terms of a combination series in which the developmental* (polynomial) series for each pair of differing characters are combined. Simultaneously it thus is shown that the behaviour of each pair of differing characters in hybrid association is independent of other differences between the two original parental plants.
Given that Mendel had studied seven characters in a species that has seven chromosomes, some considered he had been lucky, because his results would have been different if the characters had been linked on the same chromosomes. It is now established that Mendel could not have detected a linkage of the characters he studied because they are spread on five of the seven chromosomes in Pisum, with two on each of chromosomes 1 and 4, but too far away to appear as linked. Furthermore, certain biases in the distributions reported can be attributed to the fact that Mendel could not conduct all possible experiments and reported in his paper only a fraction of the results obtained (Fairbanks & Rytting, 2001). Mendel then generalizes the role of random combinations of the characters as a principle applicable to any character:
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Simultaneously, factual evidence is produced that constant characters occurring in different forms of a plant genus can, through repeated artificial fertilisation, occur in all possible combinations according to the rules of combination.
If we endeavour to summarise the results, we find that for those differing characters that admit easy and certain differentiation of the experimental plants, we observe completely identical behaviour in hybrid union. One-half of the progeny of the hybrids for each pair of differing characters is also hybrid, whereas the other half is constant in equal proportions for the characters of the seed and pollen plants.
The perfect identity shown by all characters tested in the experiment fully permits and justifies the assumption that the same behaviour applies to other characters that appear less sharply in the plants and thus could not be included in the individual experiments.
At this stage, Mendel has reached his first goal: to provide a law for the development of the hybrids corresponding to the ‘remarkable regularity’ observed initially and enabling ‘the establishment of numerical ratios existing between these forms’. He relied for this on a proven experimental model and the notions of uniformity of the hybrids, of disjunction and independent segregation of the characters established by his predecessors. His original contribution consists of the link he established between the precise numerical ratios observed in the diverse combinations of the characters in the offspring of the hybrids, on the one hand, and the random combination of the reproductive cells, on the other hand. His explanation is based on the experimental demonstration of the existence of an equal contribution of the two sexes, in contradiction to the views prevailing since antiquity.
Mendel’s next step is to validate his hypothesis through a new series of experiments.
GREGOR MENDEL’S MODEL: THE GENERAL EQUATION OF THE DEVELOPMENT OF HYBRIDS
At the end of the 8 February 1865 session of the Society of Natural History in Brno, Gregor Mendel has finished his exposé of the fate of the differential characters during the successive generations of the hybrids, thus providing an experimental proof that the regularity observed was not the fruit of his imagination. Moreover, he has given this regularity a numerical value grounded on statistical analysis and has placed it in relationship to the behaviour of the reproductive cells during fertilization.
During his next exposé during the 8 March 1865 session, Mendel reports his efforts to generalize his model, with the results of the experiments conducted in order to test it.
Contrary to the legend, Mendel’s exposés were presented to numerous and interested audiences, despite the unusual character of his presentation, as testified by the reports published in the local press. However, the understanding of the significance of his observations and thesis was beyond reach for even the most educated of his contemporaries. Nevertheless, continuing his investigations, Mendel presents the first general equation of biology that describes the development of hybrids.
The fertilizing cells of the hybrids
Mendel initiates a second iteration of his systemic approach, with the goal of testing the hypothesis he has derived from the model developed from his first series of experiments. For this, he designs a new experimental plan to perform reciprocal crosses of hybrids for two differential characters with the original pure lines, with the hybrid providing the male cells in the first cross and the female cells in the second cross:
The results of the initial experiments led to further experiments whose success appeared capable of throwing light on the nature of the germ and pollen cells of the hybrids.
We must then treat it as necessary that the very same factors* combine in the production of constant forms in the hybrid plant. Because the different constant forms are produced in one plant, even in one flower of the plant, it appears logical to assume that in the ovaries of the hybrids as many germ cells (germinal vesicles) and in the anthers as many pollen cells form as there are possible constant combination forms and that these germ and pollen cells correspond to the individual forms in their internal nature.
*This is the only occurrence in Mendel’s main text of the term ‘factor’ to designate the entities involved in the transmission of the characters, which is nowadays interpreted and used abusively as a reference to the gene in its modern sense.
In fact, it can be shown theoretically that this assumption would be thoroughly ample to account for the development of the hybrids in individual generations, if one were simultaneously allowed to assume that the different kinds of germ and pollen cells are, on average, formed in equal numbers in the hybrid.
Further, if the individual forms of the germ and pollen cells of the hybrid were formed on average in equal numbers, then in each experiment the four previously stated combinations necessarily would be equal in their numerical relationships.
Also, this assumption is limited in that the formation of the different germ and pollen cells merely approaches equality in numbers and not that every individual hybrid reaches such numbers with mathematical precision.
Here again, Mendel demonstrates his ability to delineate the conditions that are necessary and sufficient in his experiments and to predict the results that are pertinent with regard to his working hypothesis. Indeed, the five experiments he conducted produced an equal distribution of the four possible forms in the offspring of the crosses, in conformity with the prediction:
The yield corresponds to these requirements perfectly. … In all of the experiments, then, all forms appeared as this assumption required and, in fact, in nearly the same numbers. … The proposed theory finds ample confirmation in this experiment as well. … All combinations possible through the union of different characters appeared as expected and in nearly equal numbers.
Mendel then attempts to refine his model and to test his hypothesis repeatedly, before completing the formulation of his law for the development of the hybrids through a general equation:
Thus, through experimental means the assumption is justified that pea hybrids form germ and pollen cells that, according to their nature, correspond in equal numbers to all the constant forms that arise from the combination of characters united through fertilisation.
The simplest case is offered by the developmental series for each pair of differing characters. It is known that this series is defined by the expression A + 2Aa + a, in which A and a signify the forms with constant differing characters and Aa signifies the hybrid form of both. It includes four individuals among the three different classes. In their formation, pollen and germ cells of the forms A and a occur in equal proportions on average in fertilisation, and thus each form appears twice, since four individuals are formed. Therefore, participating in fertilization are the pollen cells, A + A + a + a; and the germ cells, A + A + a + a. It is a matter of chance which of the two kinds of pollen unites with each individual germ cell.
Given that Mendel cannot distinguish the pure line characters through observations or experiments, he introduces the minimal hypothesis that the co-existence of the similar pure characters in a hybrid is equivalent to a fusion, whereas he makes the necessary and sufficient distinction for the differential characters. In other words, he does not yet perform a complete distinction between the notions of genotype and phenotype introduced later by Johannsen and Bateson that the geneticists would use later. However, in order to account for the mode of intervention of the sexual cells in the development of the hybrids, he includes in his model the pairing of the different forms of the characters as a fraction, which leads him to the general equation for the development of the hybrids:
The result of fertilisations can be clearly illustrated if the designations for united germ and pollen cells are shown as fractions, with the pollen cells above the line, the germ cells below. Thus, in this case: A/A + A/a + a/A + a/a. In the first and fourth classes the germ and pollen cells are the same, so the products of their association must be constant, A and a. With the second and third classes, however, once again a union of the two differing original parental characters takes place, and hence the forms that appear from this fertilisation are completely identical to the hybrid from which they are derived. Consequently, a repeated hybridization takes place. This accounts for the striking phenomenon that the hybrids are able, like the two original parental forms, to produce progeny that are identical to themselves; A/a and a/A both produce the same combination Aa, because, as alluded to earlier, it makes no difference for the result of fertilization which of the two characters belongs to the pollen or germ cells. Thus A/A + A/a + a/A + a/a = A + 2Aa + a. This is the average course for the self-fertilisation of hybrids when two differing characters are united in them.
The formulation of the law for the development of the hybrids in the form of an algebraic equation is the crowning of Mendel’s systemic approach: after two iterations, he has placed in apposition his mathematical model (the development of a binomial series) with the reality he has been able to perceive through his experiments (the development of the hybrids), thanks to a pertinent experimental plan. This is a revolutionary action that brings biology into the era of quantification through mathematics, as William Harvey did earlier for physiology (Auffray & Noble, 2009). The geneticists would later be the first to step through this opening when they realized the immense consequences of Mendel’s method and model. They would be followed and joined by the evolutionary and developmental biologists only after the quarrels over precedence and authority were overcome at the beginning of the 20th century. Mendel ends this long section with a new formulation of his law for the development of the hybrids:
The law of combination of the differing characters, by which the development of hybrids results, finds its foundation and explanation accordingly in the conclusive principle that hybrids produce germ and pollen cells corresponding in equal number to all constant forms that arise from the combination of the characters united through fertilisation.
In other words, Mendel claims to have found the explanation for the regularity in the appearance of the different forms of the hybrids in the course of successive generations in the equal contribution of the two sexes during fertilization.
CONCLUDING REMARKS
In this last part of his paper, Mendel continues the generalization of his model by extending it to other cases and refining it. After a section reporting preliminary studies on other plants (beans of the genus Phaseolus), which lead him to generalize the law established in Pisum, Mendel attempts to explain the phenomenon he observed, by using no less than ten times the term ‘elements’ (notably, a plural that we have highlighted in bold in Mendel’s text whenever he uses Elemente). This is the section that refers to the notion of the gene in its modern sense of an elementary substrate of heredity. Mendel refers explicitly to the most recent and still controversial results of his time about the cell theory in the physiology of fertilization and to the particulate vision of heredity:
According to the view of famous physiologists, in phanerogams, for the purpose of reproduction, one germ cell and one pollen cell unite into a single cell* that is able to develop into an independent organism through the uptake of matter and the formation of new cells. This development takes place according to a constant law that is founded in the material nature and arrangement of the elements, which succeeds in a viable union in the cell.
This is where Mendel introduces a footnote, marked by an asterisk, in which the first mention of elements appears. It is possible that this corresponds to an addition following his presentations and the initial versions of his manuscript, reflecting the evolution of Mendel’s thought and his will to consolidate the validity of his model further, without ignoring its limits:
*With Pisum it is shown without doubt that there must be a complete union of the elements of both fertilising cells for the formation of the new embryo. How could one otherwise explain that among the progeny of hybrids both original forms reappear in equal number and with all their peculiarities? If the influence of the germ cell on the pollen cell were only external, if it were given only the role of a nurse, then the result of every artificial fertilisation could be only that the developed hybrid was exclusively like the pollen plant or was very similar to it. In no manner have experiments until now confirmed that. Fundamental evidence for the complete union of the contents of both cells lies in the universally confirmed experience that it is unimportant for the form of the hybrid which of the original forms was the seed or the pollen plant.
In the next three paragraphs of the concluding remarks, Mendel uses the term ‘elements’ eight times, suggesting that it might have been, like his footnote, a late addition:
If the reproductive cells are the same and if they accord to the foundational cell of the mother plant, then the development of the new individual will be governed by the same law that applies to the mother plant. If there is a successful union of a germ cell with a dissimilar pollen cell, we must assume that between the elements of both cells that determine their reciprocal differences, there is some sort of counterbalance. The intervening cell that arises becomes the foundation of the hybrid organism whose development necessarily follows another law than for the two original parents. If the balance is assumed to be complete in the sense that the hybrid embryo is formed from similar cells in which the differences are completely and permanently connected, then it can be further concluded that the hybrid, like every other autonomous plant species, will remain constant in its progeny. The reproductive cells that are formed in the ovaries and the anthers are the same and are identical to the underlying intervening cell.
In relation to those hybrids whose progeny are variable, one might perhaps assume that there is an intervention between the differing elements of the germ and pollen cells so that the formation of a cell as the foundation of the hybrid becomes possible; however, the counterbalance of opposing elements is only temporary and does not extend beyond the life of the hybrid plant. Because no changes are perceptible in the general appearance of the plant throughout the vegetative period, we must further infer that the differing elements succeed in emerging from their compulsory association only during development of the reproductive cells. In the formation of these cells, all existing elements act in a completely free and uniform arrangement in which only the differing ones reciprocally segregate themselves. In this manner the production of as many germ and pollen cells would be allowed as there are combinations of formative elements.
This attempted ascription of the essential distinction of either a permanent or a temporary association of the differing cell elements in the development of the hybrids can, of course, be of value only as a hypothesis for which a wide scope of interpretation is possible given the dearth of reliable data. Some justification for the stated view lies in the evidence given for Pisum that the behaviour of each pair of differing characters in hybrid union is independent of the other differences between the two original plants and, further, that the hybrid produces as many types of germ and pollen cells as there are possible constant combination forms. The distinctive characters of two plants can ultimately rest only on differences in the nature and grouping of the elements that are present in their foundational cells in living interaction.
Mendel reaches here the limit of what his experimental plan and model allow him to capture in the development of the hybrids. The convoluted formulation of his argument shows that he does not manage, in the framework of his hypotheses, to account through a common mechanism for the differences between the combinations of elements associated with constant and variable characters. However, he opens the way for his successors who, empowered by the indispensable supplementary knowledge, will take charge of developing genetics in the 20th century, verifying and confirming his hypotheses and thus responding to his invitation to repeat his main experiments in order to validate his laws.
The validity of the set of laws suggested for Pisum requires additional confirmation and thus a repetition of at least the more important experiments would be desirable, for instance the one concerning the nature of the hybrid fertilising cells.
The main reason why Mendel’s invitation was not followed by his colleagues is most probably that his conception and his method were not immediately intelligible for his contemporaries. The endorsement of the dominant theory of heredity by mixing by the Swiss naturalist Carl von Nägeli (and Darwin) explains Mendel’s failure to convince him, despite extensive attempts in correspondence, to reproduce his experiments. Nägeli was principally a specialist in hawkweed of the genus Hieracium, multicoloured flowering plants endowed with a partly asexual mode of reproduction that does not allow a direct application of Mendel’s experimental plan. Indeed, Mendel reported in a second paper, presented at the Society of Natural History in Brno in 1869, and in his correspondence with Nägeli the extensive and detailed results he had obtained in Hieracium (Nogler, 2006; van Dijk & Ellis, 2016), before shifting his attention to bees.
Having taken the charge of abbot of the monastery after the death of Napp in 1868, Mendel was increasingly absorbed by many administrative duties and could no longer spend the time required to develop his research further. It would take until the beginning of the 20th century and the rise of genetics for better-prepared minds to demonstrate the fecundity of Mendel’s work.
Gregor Mendel died in 1884 from a crisis of uraemia resulting from the chronic nephritis he suffered, without encountering in his lifetime the recognition he would have deserved (Cox, 1999; Allen, 2003). We still have a number of lessons to draw from the work of a man who was a systemic precursor of genetics and developmental biology (Auffray, 2002, 2004) and from the pertinent manner in which his experiments have been conceived, conducted, exposed, ignored, rediscovered, criticized, exploited and revisited. Gregor Mendel has been praised as a ‘man of God and science’ (Tan & Brown, 2006), remembered by family relatives as ‘a human, a catholic priest, an Augustinian monk, and abbot’ (Richter, 2015). Others have debated whether Mendel was forgotten or ignored in his lifetime, to conclude that he was both ignored and forgotten, then rediscovered (Kessel, 2002; Keynes, 2002; Keynes & Cox, 2008). In an attempt to set the record straight, Fairbanks has recently endeavoured at ‘demystifying the mythical Mendel’ through a comprehensive biographical review (Fairbanks, 2022). The French naturalist and writer Jean Rostand summarized Mendel’s life and scientific achievements beautifully in an eloquent portrait (Rostand, 1979):
It would require, in order to conduct such a long-term study, the marvellous, tireless patience of Mendel, who, alone, without help, with no collaboration, performs several hundred artificial pollinations, and examines no less than ten thousand plants. … In the end it required independence, dedication, solitude. … Mendel in the cloister silence has duration in his favour. He does not fear to engage into experiments that will take him years to complete. It is for his pleasure that he cultivates his peas, and even though they might not provide him with truths, he is satisfied to see them grow and flourish. His time is not precious, avariciously counted. He has no book to write, no masters to flatter, no reputation to sustain, no intrigues to conduct, no application to prepare. … For this priest, there is only his peas, after God.
The myth and the legend are still alive 200 years after Mendel’s birth. As physiologists and geneticists and systems biologists, we follow in the footsteps of Mendel who, together with William Harvey and Claude Bernard, pioneered the development of systems biology and physiology (Noble, 2008; Auffray & Noble, 2009). Let us celebrate him during the 2022 Mendel.Brno festival (Mendel.Brno – Mendel opted for Brno, available at: https://mendel.brno.cz/en/, 2022; Eckardt et al., 2022), together with the geneticists from around the world gathering at the International Mendel genetics conference (Mendel Genetics Conference, available at: https://www.mendel22.cz/about-conference/, 2022) and make good use of his contributions for the benefit of future generations.
ACKNOWLEDGEMENTS
C.A. thanks Dr Manlio Vinciguerra of Masaryk University and Dr Ondřej Dostál, Director of the Mendel Museum in Brno, Czech Republic for organizing a lecture and a private visit to Mendel’s library at Thomas Monastery on 9-10 May 2017 (Fig. 3; all pictures from C.A.’s private collection). We thank Dr Bertrand De Meulder, Senior Scientist at the European Institute for Systems Biology & Medicine (EISBM), for assistance in formatting the references, and two referees who provided very relevant and insightful comments that helped to correct historical mistakes and improve the accuracy of our paper. The authors have no conflict of interest to declare.
DATA AVAILABILITY
This paper is an updated and expanded version of a two-part online essay in French by C.A., posted in 2005 at the Observatory of Genetics in Montréal, Canada (now closed) and translated into English on the occasion of Gregor Mendel’s bicentenary. An overview for the general public was broadcast in French by Radio Prague on 8 February 2015 on the occasion of the 150th anniversary of his two 1865 lectures in Brno (Auffray, 2015).
REFERENCES
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