RA Fisher, statistician and geneticist extraordinary: a personal view

Abstract

I was among the last of RA Fisher’s students and disciples and, as a result, he had an enormous influence both on my career and on my attitudes to science and scientific research. In the summer before I started taking Fisher’s lecture courses in statistical and mathematical population genetics, I was given a reading list that included Fisher’s three outstanding books, The Genetical Theory of Natural Selection,1Statistical Methods for Research Workers,2 and The Design of Experiments.3 These formed a little light recommended reading over a summer vacation! Later in that year, I went to see Fisher in the Genetics Department about the possibility of doing research with him. I then wrote in my diary.... ‘very promising, looks as though all will be well. I hope it’s the right subject.’ Well, it undoubtedly was and has remained with me for the following 47 years, and hopefully more to come. Fisher was very supportive of the young as is evident from Joan Box’s outstanding biography of her father.4 He was disparaging of authority for authority’s sake, and his dismissive statements about distinguished geneticists and statisticians were a lesson in appreciating scientists for their actual contributions rather than their, perhaps sometimes inflated, reputations. Towards the end of January 1956 I went to see him to get his support for applications for a research studentship stipend to do my PhD with him, starting later that year. In my diary I wrote, ‘He is a nice man. I should almost say “sweet”. Went for a long walk with him in pouring rain and talked. Then he dictated two rather good letters applying for a grant for me.’ This was characteristic of his charm and concern for those he wished to help. And yet, as Joan Box says in her biography: He seemed inhuman sometimes in his lack of consideration for the feelings of others.... Capable of rough handling those who opposed him with ready-made arguments that he treated with contempt: He was sometimes arbitrary and disagreeable: and he was recalcitrant to any form of coercion. (ref. 4, p. 430) It is this complexity of his character that needs to be understood in order to interpret his relations with other scientists, and so sometimes his attitude to scientific viewpoints that did not coincide with his own. Fisher is often portrayed as the supreme theoretician and analyst, without reference to his concern for practical applications, which he instilled in his students, including myself. This is a serious misapprehension, as the vast majority of his theoretical work was, as he himself often emphasized, devoted to an understanding of how to deal with real experimental data. He, for example, collected data in the field on the three forms of the primrose, Primula vulgaris, a subject that in the end formed a major part of my initial research in genetics under his guidance. Fisher remained throughout his life a keen observer of the natural world. Fisher’s conciseness and obscurity in some of his statistical and mathematical writing are legendary. In my exam at the end of my third year Fisher set a question on interpreting inbreeding by alternate parent offspring matings using his novel approach to handling problems in inbreeding, the theory of junctions. I made a vain attempt to answer the question as I felt I should, but was completely stumped. Later I asked Fisher’s colleague, ARG Owen, who was a lecturer in the department, what Fisher had intended. He said he had tried to dissuade Fisher from setting the question, and when he asked what sort of an answer was expected Fisher came back a few days later with three closely written pages of algebra! WS Gosset, the ‘Student’ of student’s t-test whom Fisher greatly admired, once wrote in a comment on Fisher’s writing, ‘when I come to “evidently” I know that it means two hours hard work at least before I can see why’.5 And yet at times, especially when explaining essentially non-mathematical concepts, he could be a model of clarity, as exemplified most famously in his discussion of the tea tasting experiment as described in The Design of Experiments.3 He there used as a model experiment the attempt to establish whether a lady could discern whether milk had been added to the cup before or after the tea. Fisher was a proud man in addition to his sensitivity, and this undoubtedly explained some of the antagonistic interactions he developed with scientific colleagues. Notable among these, and sadly, was the antagonism that developed with one of the other great founders of population genetics, Sewall Wright. Wright’s review of Fisher’s The Genetical Selection was extremely positive [4,11] and Fisher acknowledged that Sewall Wright may be one of the few people who could really understand what was in his book. However, Sewall Wright picked up a minor arithmetical error in one of Fisher’s transformations, a missed factor of two, and this I believe was the basis of the antagonism that eventually developed between them. Statisticians and those who know of Fisher largely through statistical applications often do not appreciate that Fisher’s contributions to genetics were in many ways as original, revolutionary, and important as his contributions to statistics. He founded the field of population genetics, together with Sewall Wright and JBS Haldane. Many a terse paragraph in his classical work The Genetical Theory of Natural Selection,1 a true successor to Darwin’s The Origin of Species, has been the basis for a whole new field of experimental and theoretical analysis. An example of this was his description of a model involving selective interactions between alleles at two linked loci that could favour closer linkage between the genes, a field to which I first contributed in the early 1960s and which became a major interest of mine.5 This is now the basis for the whole excitement about the way that the almost unlimited number of polymorphisms detectable at the DNA level can be used in the attempt to analyse the specific genetic basis for multifactorial disease susceptibility in human populations. His interests in genetics paralleled those in statistics from a very early age, following perhaps from his reading of Darwin’s work as a schoolboy. He was an active member of the Eugenics Society as a student in Cambridge. In the same year, 1922, for example, in which he published his monumental work On the Mathematical Foundations of Theoretical Statistics6 he also published his paper On the Dominance Ratio,7 in which he derived for the first time the classical result that, in a one locus two allele system, heterozygote advantage leads to a stable balanced polymorphism. His interests in genetics and statistics did not, however, develop independently but interacted strongly with each other. The most notable of these interactions was the use of the word ‘variance’ and the development of the analysis of variance, and the stimulus for the ideas for factorial experimentation. His first substantial, and indeed seminal paper on genetics was that on The Correlation Between Relatives on the Supposition of Mendelian Inheritance.8 The paper opens with the sentence, ‘Several attempts have already been made to interpret the well-established results of biometry in accordance with the Mendelian scheme of inheritance’. That is indeed what this paper achieved. On the first page just a few sentences further down he says: It is therefore desirable in analysing the causes of variability to deal with the square of the standard deviation as the measure of variability. We shall term this quality the Variance of the normal population to which it refers, and we may now ascribe to the constituent causes fractions or percentages of the total variance which they together produce. Here in one sentence was the introduction of the word variance as it is now commonly used in statistics, and of the notion of the analysis of variance. This paper has an interesting history. It was first submitted for publication to the Royal Society of London some 2 years earlier, but rejected. It was eventually published by the Royal Society of Edinburgh through the intervention of Leonard Darwin, Charles Darwin’s youngest son and a strong influence and mentor of Fisher’s, who paid £50 towards the cost of the paper’s publication. Fisher later learnt that the referees were Karl Pearson, then Galton Professor of Eugenics at University College, and RC Punnett, the Arthur Balfour Professor of Genetics in Cambridge. He delighted to recount, as I heard him say myself, that these two rejected his paper, ‘both of whom I later succeeded’. In his Bateson Lecture, delivered in 1951, Fisher made clear the fact that his ideas on factorial experimentation had been stimulated by his knowledge of genetics. The title of the lecture was Statistical Methods in Genetics.9 He said: And here I may mention a connection between our two subjects which seems not to be altogether accidental, namely that the ‘factorial’ method of experimentation, now of lively concern so far afield as the psychologists or the industrial chemists, derives its structure, and its name, from the simultaneous inheritance of Mendelian factors. Fisher’s interests in randomization, and the development of his ideas on the design of experiments, grew out of his first appointment as a statistician at the Rothamsted Experimental Station. He was initially to spend 6 months or so there to find out whether useful analyses could be made of the extensive data on crop yields that had been obtained at Rothamsted over many years. The first specific explanation of the principle of randomization published by Fisher was in the first edition of Statistical Methods for Research Workers in 1925.2 Fisher said: The first requirement which governs all well planned experiments is that the experiment should yield not only a comparison of different manures, treatments, varieties, etc., but also a means of testing the significance of such differences as are observed. He then later says: For our test of significance to be valid the differences in fertility between plots chosen as parallels must be truly representative of the differences between plots with different treatment; and we cannot assume that this is the case if our plots have been chosen in any way according to a pre-arranged system; ... The direct way of overcoming this difficulty is to arrange the plots wholly at random. Thus, from this initial exposition of the principles of randomization it is clear that Fisher places an overwhelming emphasis on the need for randomization in order to obtain valid estimates of error so that a proper test of the significance of the effects of different treatments can be made. An extension of Fisher’s ideas on randomization, again emphasizing the need for valid estimates of error, but in an exemplary clear way without any use of formulae, was his classic paper on The Arrangement of Field Experiments.10 This was published in 1926 in the Journal of the Ministry of Agriculture as a rebuttal to his Director, Sir John Russell’s, advocacy of systematic designs. In this paper Fisher explains with great clarity the idea of using a 5% significance level, what is a variance, that the main purpose of replication is to provide a valid estimate of error and, as he puts it: One way of making sure that a valid estimate of error will be obtained is to arrange the plots deliberately at random, so that no distinction can creep in between pairs of plots treated alike and pairs treated differently. He also introduces the idea of blocks and randomization within blocks, gives an example of Latin squares, and emphasizes his view ‘... that large and complex experiments have a much higher efficiency than simple ones’. This is in line with his advocacy of factorial experimentation. Fisher’s ideas on experimental design and randomization and its applications were greatly enlarged in his book The Design of Experiments,3 the first edition of which appeared in 1935. It is perhaps only here that he first indicates clearly how randomization may avoid bias in his comment that: ... for the full procedure of randomisation, by which the validity of the test of significance may be guaranteed against corruption by the causes of disturbance which have been eliminated. Thus, in effect, his view appears to be that randomization to provide a valid estimate of error on the one hand, and to eliminate biases on the other, are really two sides of the same coin. It seems sometimes to be assumed that, because Fisher did not apply his ideas on randomization and experimental design to clinical trials, he had no interest in the analysis of human data. Nothing, of course, could be further from the truth. His major interests were in the experimental possibilities that were opened up by blood group serology, and the possibilities of using genetic polymorphisms to analyse patterns of inheritance of diseases in families. Fisher had had his attention called to the genetical interest of serological studies by JBS Haldane. His correspondence4,11 with the serologist, Todd, reveals that he was the first to suggest that the antigens detected by serological agglutination assays may be ‘the direct products of individual genes rather than have secondary reactions’. He suggested a wide variety of experiments to Todd, and expressed his impatience with the slow rate at which the experimental results were produced. Fisher had an enormous influence on the development of blood group research in Britain, stimulating the pioneering researches of Rob Race and Ruth Sanger with their Medical Research Council support. He formulated an of the blood and it was perhaps largely through the stimulus of this that I came to my with my on the human Fisher indeed up work on human genetics because he that the development of the serological ... is to to a both theoretical and in the problems of human genetics than can be expected from any further work on or Fisher’s other great to practical human genetics was his analysis of linkage in human which paralleled that of JBS Haldane. In a at an on in and the of he what is now called he said: It is therefore of great that these linkage should be in order that and may be used to the inheritance and the of other of individual such as those forms of and other He the of using polymorphisms in human for linkage but could not then have been of the possibilities that have opened up more through our knowledge of the human This has to the of essentially unlimited of polymorphisms to each other to linkage and so the of that genetic from genetic linkage analysis in I whether the fact that the ideas of factorial experimentation have clinical was to Fisher’s lack of interest in this Fisher’s that factorial experiments can much more including that on than simple experiments seems not to have been by the On the other hand, perhaps it was emphasis on and in out clinical trials, in order to which to this lack of of the principles of factorial experimentation in clinical clearly indicates that Fisher and remained on well after the publication in of book on The of Medical In all with I became of the to which he appeared to be by his with Fisher and not in any way antagonistic to him. It is clear that from their in the Fisher was supportive of He had to him for as a of the Eugenics Society and then about 2 years him a at The fact that the down did not, influence their Fisher on his appointment as Galton Professor at University College, and in doing so said: I shall to within a I hope it will come to and within when my statistical are much for and me is clearly a as to their of was the and clearly Fisher a theoretician mathematical were well his must have the first edition of Fisher’s Statistical Methods for Research Workers and could not have to have of Fisher’s arguments for It is that in a of he Fisher of his to a ... on statistical as to statistics, in a vain attempt to in of one for the of the of we have to with He the by I do not for a it on as is far more than any I hope to Fisher in his for to use the that he wished to use in his opens by are about the character of the who have made Statistical Methods a book. are practical who I the that it is an book as an about by and deliberately by and Fisher’s remained and indeed became more over the years. In of it was who Fisher that he had been the of the Royal Statistical to In a from Fisher to towards the end of in to his about to a Royal Statistical Society Fisher I have developed the ... of a as a of and I do not to my at this sort of This is perhaps a comment how could be Fisher’s on those with whom he did not perhaps a of their later It is clear from the starting towards the end of that the between Fisher and as a result of and studies on the between and Fisher’s on not from any indeed the but at least in part because of his as to the then and He himself was an but did not, to my Fisher’s antagonistic to the data on the between and was by two strong The and perhaps came from his developed on the of statistical and scientific Correlation must not be as of He causes such as genetic but without at the time really of the of the and the of it to a rather than a direct His was on his He strongly that people should be to come to their and be given the data. He was strongly against the that was out about the of In an for the published in he ... an published by the Medical up to the almost that it was that of should be to to the at large this He was for to their that they should up but this in the of what he data of a Many have Fisher of a of interest in these arguments because in 1956 he had already the of the to be their scientific However, as Joan Box out in her Fisher was to believe that he was to in way he and that for so doing should not influence the of this clinical when testing a new were first and following that had almost to was there really a need for a more example be the of and The clinical were then not whether or not to but how to do I believe that both Fisher and were well of this Thus, in his 1926 paper on The Arrangement of Field Fisher says at one ‘... if he had only he out a if could that on the the had come to This an for the use of when an is large that it is to be to the biases that could be in in the of on page of his book on The of Medical the results of such a measure are in the light of all then clearly the will not need to be This was written in the of a clinical on the of as a result of the of our knowledge of the human be an enormous variety of treatments, often to a much of then will not be or to subject all treatments independently to clinical And yet, arbitrary on which should be given an extensive may those treatments that are to be most I therefore believe that, in making the of treatments to be tried on more emphasis must be given to can now be much more for example, and to an understanding of the of of any or I believe that it will be to Fisher’s advocacy of complex multifactorial experiments so that treatments can be at the same time with higher and with the added of I believe that it will be to do initial studies which may only randomization, but which will on an of perhaps of only those treatments an of large effects in such studies will be the that are submitted to clinical this must be with the strong as by that as as there is an level of forms of for example, on but at a level, need to be The last time I Fisher was when he University in on his way back to He had as the of his planned the theory of in inbreeding and I was to suggest that this be of interest and that perhaps he should a on his on and However, my diary was a for on far for most of I Fisher to the the following In for we a lively discussion about a test I had for two in a set of time went by I that the was to and in a went to the to the it was The great man had missed his and I was He, however, was He it in his with which we and this time he did not his our son to this Fisher’s and and the description

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 13 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.