What about R.A. Fisher's statement of the "too good" data of J.G. Mendel's Pisum paper?

Mendel was accused by Fisher that his observed data, which corresponded to expectations, were too good to be true, and, further, that Mendel, growing only 10 plants per offspring, disregarded in his genotypical analysis the loss of recessives by assuming a ratio of 1:2 instead of 1.1126:1.8874. In contrast, it is proposed here that all chi-square statistics of genetic segregations fall short because the variance of genetic segregations is smaller and not of a binomial type as assumed. Furthermore, this variance and the corresponding chi-square statistics are not homogeneous in different segregation types. Consequently, it is not possible to summarize the different chi-square statistics as Fisher did. It is only in this way that he was able to obtain his unrealistic result (a probability of "seven times in 100,000 cases"). Regarding Fisher's second accusation, it should be taken into account that Mendel selected his 10 plants from offspring with a finite and not an infinite number of entities. Although this number is different from offspring to offspring, the average number is about 30. This means that the loss of recessives must be calculated by using a hypergeometric and not a binomial model as Fisher did. Consequently, the real deviation from the 1:2 ratio can be disregarded.     

L. H. Bailey's citations to Gregor Mendel

L. H. Bailey cited Mendel's 1865 and 1869 papers in the bibliography that accompanied his 1892 paper, Cross-Breeding and Hybridizing, and Mendel is mentioned once in the 1895 edition of Bailey's "Plant-Breeding." Bailey claimed to have copied his 1892 references to Mendel from Focke. It seems, however, that while he may have first encountered references to Mendel's work in Focke, he actually copied them from the Royal Society "Catalogue of Scientific Papers." Bailey also saw a reference to Mendel's 1865 paper in Jackson's "Guide to the Literature of Botany." Bailey's 1895 mention of Mendel occurs in a passage he translated from Focke's "Die Pflanzen-Mischlinge."     

What would have happened if Darwin had known Mendel (or Mendel's work)?

The question posed by the title is usually answered by saying that the "synthesis" between the theory of evolution by natural selection and classical genetics, which took place in 1930s-40s, would have taken place much earlier if Darwin had been aware of Mendel and his work. What is more, it nearly happened: it would have been enough if Darwin had cut the pages of the offprint of Mendel's work that was in his library and read them! Or, if Mendel had come across Darwin in London or paid him a visit at his house in the outskirts! (on occasion of Mendel's trip in 1862 to that city). The aim of the present paper is to provide elements for quite a different answer, based on further historical evidence, especially on Mendel's works, some of which mention Darwins's studies.     

Gregor Mendel's classic paper and the nature of science in genetics courses

The discoveries of Gregor Mendel, as described by Mendel in his 1866 paper Versuche uber Pflanzen-Hybriden (Experiments on plant hybrids), can be used in undergraduate genetics and biology courses to engage students about specific nature of science characteristics and their relationship to four of his major contributions to genetics. The use of primary source literature as an instructional tool to enhance genetics students' understanding of the nature of science helps students more clearly understand how scientists work and how the science of genetics has evolved as a discipline. We offer a historical background of how the nature of science developed as a concept and show how Mendel's investigations of heredity can enrich biology and genetics courses by exemplifying the nature of science.     

Role of de Vries in the rediscovery of Mendel's paper. II. Did de Vries really understand Mendel's paper?

In this paper, we discuss briefly three of the several lines of evidence that we believe demonstrate de Vries's lack of understanding of Mendel's paper. In our view, at least part of de Vries's failure of understanding derives from the fact that he appears to have viewed Mendel's paper as being mainly about the inheritance of characters that was his own interest. Therefore, he looked at it to see whether Mendel had found any laws of inheritance. Mendel had done his research for another purpose, to find the laws describing the formation of hybrids and the development of their offspring. Thus, de Vries started his examination of Mendel's paper with a very fundamental misunderstanding of what it was about.     

On the Origin of Mendelian Genetics

SYNOPSIS. An examination of research on heredity in the yearsbetween Mendel's scientific work and his multiple rediscovery(approximately 1850–1900) suggests that at the turn ofthe century the elucidation of the mechanism of the transmissionof hereditary traits from parent to offspring was inevitable.By 1900, a variety of different investigators were either attackingthe problem of genetic transmission directly and successfully,or were examining specific aspects of the issue. However, itappears that the identity of analysis used by Mendel and byhis rediscoverers was primarily the result of the latter allfollowing Mendel's formulation. Had Mendel not been rediscovered,the "Laws of Heredity" would likely have been formulated quitedifferently, and been discovered and refined over a period oftime rather than all being discovered and given their finalform at the very outset.     

On the origins of the Mendelian laws

The two laws usually attributed to Mendel were not considered as laws by him. The first law, the law of independent segregation occurs in Mendel's paper as an assumption or hypothesis. Hugo de Vries refers to this as a law discovered by Mendel. This appears to be the first use of an expression equivalent to Mendel's law. In his paper de Vries did not associate the observable characters with structures having a causitive role. That was done by Correns, who transformed the law of segregation of characters into a law of the segregation of anlagen. The second law, the law of independent assortment, is present in embryonic form in Mendel's paper. Here the independent assortment of characters appears as a secondary conclusion to a series of experiments involving several pairs of traits. Mendel repeats the primary conclusion later in the paper but not the secondary one. This leads us to believe that he considered the secondary conclusion as of lesser importance. We note in this context that the 9:3:3:1 ratio commonly associated with the idea of independent assortment, and attributed to Mendel, also does not occur in his paper. A careful reading of the papers of his discoverers shows it was Correns who first drew attention to this ratio. However, he did not formulate the second Mendelian law even though it was clearly implied. Neither was it stated by de Vries. Indeed, the first clear separation of the two laws and the naming of the second law was by T. H. Morgan some 13 years later.     

R.A. Fisher's contributions to genetical statistics

R. A. Fisher (1890-1962) was a professor of genetics, and many of his statistical innovations found expression in the development of methodology in statistical genetics. However, whereas his contributions in mathematical statistics are easily identified, in population genetics he shares his preeminence with Sewall Wright (1889-1988) and J. B. S. Haldane (1892-1965). This paper traces some of Fisher's major contributions to the foundations of statistical genetics, and his interactions with Wright and with Haldane which contributed to the development of the subject. With modern technology, both statistical methodology and genetic data are changing. Nonetheless much of Fisher's work remains relevant, and may even serve as a foundation for future research in the statistical analysis of DNA data. For Fisher's work reflects his view of the role of statistics in scientific inference, expressed in 1949: There is no wide or urgent demand for people who will define methods of proof in set theory in the name of improving mathematical statistics. There is a widespread and urgent demand for mathematicians who understand that branch of mathematics known as theoretical statistics, but who are capable also of recognising situations in the real world to which such mathematics is applicable. In recognising features of the real world to which his models and analyses should be applicable, Fisher laid a lasting foundation for statistical inference in genetic analyses.     

Statistics is not enough: revisiting Ronald A. Fisher's critique (1936) of Mendel's experimental results (1866)

This paper is concerned with the role of rational belief change theory in the philosophical understanding of experimental error. Today, philosophers seek insight about error in the investigation of specific experiments, rather than in general theories. Nevertheless, rational belief change theory adds to our understanding of just such cases: R. A. Fisher's criticism of Mendel's experiments being a case in point. After an historical introduction, the main part of this paper investigates Fisher's paper from the point of view of rational belief change theory: what changes of belief about Mendel's experiment does Fisher go through and with what justification. It leads to surprising insights about what Fisher had done right and wrong, and, more generally, about the limits of statistical methods in detecting error.     

Mendel's experiments: A reinterpretation

Conclusion My conclusion is that Mendel deliberately, though without any real falsification, tried to suggest to his audience and readers an unlikely and substantially wrong reconstruction of the first and most important phase of his research. In my book I offer many reasons for this strange and surprising behavior,⁵³ but the main argument rests on the fact of linkage. Mendelian genetics cannot account for linkage because it was based on the idea of applying probability theory to the problem of species evolution. Central to the theory is the law of probability according to which the chance occurrence of a combination of independent events is the product of their separate probabilities. This is the common basis of Mendel's first and second laws, but this is why Mendel's second law on independent assortment is enunciated in too general a way. From Morgan's work we now know that characters may not always be independent if their genes are located very close one to the other on the same chromosome. And this was also the basis of Mendel's personal drama: he surely observed the effects of linkage, but he had no theoretical tools with which to explain it. So he presented his results in a logical structure consistent with the central idea of his theory. Had he described the real course of his experiments he would have had to admit that his law worked for only a few of the hundreds of Pisum characters — and it would thus have been considered more of an exception than a rule. This is why he insisted on the necessity of testing the law on other plants, and this is why in his second letter to Carl Nägeli he admits that the publication of his data was untimely and dangerous.⁵⁴.We can argue that already in 1866 Mendel was less confident that his so-called second law had the same general validity as the first — and that later he lost his confidence altogether. Contemporary testimony indicates that in the end he became as skeptical as all his contemporaries as to the scientific relevance of his theory.⁵⁵ But he was wrong. His research is in no way the fruit of methodological mistakes or forgery, and it remains a landmark in the history of science. He was only the victim of a strange destiny in which the use of probability theory was responsible, at the same time, for the strength and for the weakness of his theory. We must still consider him the father and founder of genetics.     

Mendel, the empiricist

In contemporary texts in biology and genetics, Mendel is frequently portrayed as a theorist who was the father of classical genetics. According to some authors, he created his theory of inheritance to explain the results of his experimental hybridizations of peas. Others have proposed that he designed and carried out his experiments to demonstrate the correctness of a theory of inheritance he had already developed. We disagree strongly with these views of Mendel. Instead, we have come to regard him as an empirical investigator trying to discover the empirical natural laws describing the formation of hybrid peas and the development of their offspring over several generations. We have supported our view with an analysis of portions of Mendel's paper and his letters to Carl N ageli.     

遗传学第一个十年中的W.贝特森

在遗传学的第一个十年间,贝特森在捍卫、诠释、发展和推广孟德尔理论中作出了杰出贡献。他和孟德尔一样,是超越其时代的人。 Abstract：During the first decade of the history of genetics,B ateson made a notable contribution to the defending,interpreting,developing and spreading of Mendels laws.He,like Mendel,was ahead of his time.     

Scientific animal breeding in Moravia before and after the rediscovery of Mendel's theory

Leading Moravian sheep breeders, who joined with university professors and other educated citizens to form a Sheep Breeders' Society in 1814, looked to science to provide a reliable basis for breeding. Their activities reached a climax in the 1830s, when they defined and focused on heredity as the central research goal. Among the members taking part was Abbot Cyrill F Napp, who in 1843 would accept Mendel into the monastery. The contributions of Abbot Napp to the sheep breeders' view of heredity are here described. After 1900, when Moravian animal breeding sought to embrace Mendelism, in competition with other theories, a major influence was exerted by Jaroslav Krízenecky (1896-1964). In 1963, Krízenecky accepted responsibility for establishing the Mendel Museum (Mendelianum) in Brno as a vehicle for historical research into the origin and essence of Mendel's discovery.     

The Cold War Context of the Golden Jubilee,Or, Why We Think of Mendel as the Father of Genetics

In September 1950, the Genetics Society of America (GSA) dedicated its annual meeting to a "Golden Jubilee of Genetics" that celebrated the 50th anniversary of the rediscovery of Mendel's work. This program, originally intended as a small ceremony attached to the coattails of the American Institute of Biological Sciences (AIBS) meeting, turned into a publicity juggernaut that generated coverage on Mendel and the accomplishments of Western genetics in countless newspapers and radio broadcasts. The Golden Jubilee merits historical attention as both an intriguing instance of scientific commemoration and as an early example of Cold War political theatre. Instead of condemning either Lysenko or Soviet genetics, the Golden Jubilee would celebrate Mendel - and, not coincidentally, the practical achievements in plant and animal breeding his work had made possible. The American geneticists' focus on the achievements of Western genetics as both practical and theoretical, international, and, above all, non-ideological and non-controversial, was fully intended to demonstrate the success of the Western model of science to both the American public and scientists abroad at a key transition point in the Cold War. An implicit part of this article's argument, therefore, is the pervasive impact of the Cold War in unanticipated corners of postwar scientific culture.     

The real objective of Mendel's paper: A response to Monaghan and Corcos

Mendel's work in hybridization is ipso facto a study in inheritance. He is explicit in his interest to formulate universal generalizations, and at least in the case of the independent segregation of traits, he formulated his conclusions in the form of a law. Mendel did not discern, however, the inheritance of traits from that of the potential for traits. Choosing to study discrete non-overlapping traits, this did not hamper his efforts.     

Essence and origin of Mendel's discovery

In early 19th-century Moravia, breeders of animals and plants joined with other interested citizens in the Moravian and Silesian Agricultural Society to debate economic priorities. Several of the senior members had a profound influence upon breeding theory: J.K. Nestler, Professor of Natural History and Agriculture at the University of Olomouc, left a collection of influential writings. In the context of sheep breeding he defined 'inheritance capacity' (Vererbungsf?higkeit), 'hereditary history' (Vererbungsgeschichte) and 'developmental history' (Entwicklungsgeschichte). His linking of the last two terms, as two sides of the same coin, puts Mendel's use of the second one in context. Professor F. Diebl taught the same topics as Nestler at the Philosophical Institute in Brno, with a bias towards plants. Diebl's lectures were attended by Mendel who gained top marks in three examinations. Diebl stressed the importance of artificial pollination to produce new varieties and recognised peas and beans as suitable subjects for the procedure. Prelate Cyrill Napp, abbot before Mendel, had a deep interest in heredity and how it was transmitted through both sexes. He generously supported Mendel's research. A happy blend of economic and academic influences, together with original talent and inner drive, led to Mendel's great discovery.     

Reginald crundall punnett: first arthur balfour professor of genetics, cambridge, 1912

R. C. Punnett, the codiscoverer of linkage with W. Bateson in 1904, had the good fortune to be invited to be the first Arthur Balfour Professor of Genetics at Cambridge University, United Kingdom, in 1912 when Bateson, for whom it had been intended, declined to leave his new appointment as first Director of the John Innes Horticultural Institute. We here celebrate the centenary of the first professorship dedicated to genetics, outlining Punnett's career and his scientific contributions, with special reference to the discovery of "partial coupling" in the sweet pea (later "linkage") and to the diagram known as Punnett's square. His seeming reluctance as coauthor with Bateson to promote the reduplication hypothesis to explain the statistical evidence for linkage is stressed, as is his relationship with his successor as Arthur Balfour Professor, R. A. Fisher. The background to the establishment of the Professorship is also described.     

Crossing over...Markov meets Mendel

Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the mathematically more elaborate parts. I kept those as separate sections in the exposition.