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Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. A Quarter Century of Linkage Papers
  5. Acknowledgements
  6. References

From its inception in 1925 through the almost 30 years that it carried the title of Annals of Eugenics, this journal published numerous articles on the statistical aspects of genetic linkage analysis and its applications to family pedigree data. This overview discusses 40 papers on linkage analysis published in the Annals.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. A Quarter Century of Linkage Papers
  5. Acknowledgements
  6. References

Volume I of the Annals of Eugenics was published in 1925 and was favorably reviewed in Science magazine (Holmes, 1926). In a foreword to the first issue of the Annals, Karl Pearson, its editor and the director of the Galton Laboratory for National Eugenics, and E. M. Elderton pointed out that the “development of Mendelism in recent years has been in the direction of a multiplicity of factors, even for apparently simple characters” (which sounds rather modern) and that “probability lies at the basis of our knowledge.” Thus, they invited researchers to publish papers (called “memoirs” at the time) on biology and genetics as well as mathematics and statistics. This was in stark contrast to journals issued by the Royal Society (soon to be headed by Paul Nurse, the current president of Rockefeller University (Kaiser, 2010), which is quoted as having issued a warning that “mathematics must not be mixed with biology.” In fact, the publications of the Galton Laboratory had been offered to the Royal Society Library but the offer was refused—a good reason for the laboratory to launch its own publication vehicle.

In this short review, I will outline what has been published in the Annals regarding linkage analysis. I found a total of 46 publications, mostly on methodology and a few on applications to family data. Perhaps not surprisingly, authors are mostly British, and male, particularly of methods papers. One outstanding female member of the Galton Laboratory was Julia Bell. She contributed an early 15-page paper on the inheritance of migraine to the Annals (Bell, 1933), but otherwise published mostly elsewhere (Harper, 2005).

A Quarter Century of Linkage Papers

  1. Top of page
  2. Summary
  3. Introduction
  4. A Quarter Century of Linkage Papers
  5. Acknowledgements
  6. References

This review focuses on the papers published in the Annals of Eugenics from its foundation in 1925 through 1954, when it changed its name to Annals of Human Genetics. Early issues of the Annals contained various reports on family pedigree data and considerations of the mode of inheritance of the trait segregating in these families. The first papers on linkage analysis are due to Haldane (Haldane, 1934) and Fisher (Fisher, 1934), published back to back. The two authors took issue with the problem of estimating the recombination fraction when offspring cannot simply be identified as recombinants or nonrecombinants. Haldane (Haldane, 1934) pointed out that Bernstein in the early 1930's had recognized for the first time that two-generation families (without grandparents) are useful for linkage analysis and had devised a scoring system relevant for such family data. Haldane then modified and improved this scoring system. Fisher applied his information measure to these data types and demonstrated that some of Bernstein's and Haldane's formulas are not fully efficient. He also demonstrated how his information measure could be applied to two parameters jointly (Fisher, 1935c).

In a pair of papers on dominant (Fisher, 1935a) and recessive (Fisher, 1935b) traits, Fisher proposed the use of u-scores as a more efficient way to score family data for linkage. Depending on parental mating types, these u-scores provide simple rules for combining offspring phenotype classes into a test statistic (u-score). Fisher demonstrated that his u-scores are fully efficient only for recombination fractions approaching 0.5 (no linkage) but are always much more efficient than Bernstein's y-statistics and are easy to apply. Haldane later showed that correcting for skewness in the distribution of u-scores improves their statistical properties (Haldane, 1947).

Haldane also investigated methods for detecting pseudo-autosomal linkage (then called incomplete sex-linkage) and provided a list of traits such as xeroderma pigmentosum and achromatopsia that he concluded to be due to genes in the pseudo-autosomal region of the X and Y chromosomes (Haldane, 1936). Fisher provided further analyses of these data by carrying out analyses of variance of u-scores, separating effects of linkage, and heterogeneity (Fisher, 1936b). His results confirmed significant evidence of linkage for some of Haldane's phenotypes. In a subsequent paper, Fisher fleshed out his approach to testing for heterogeneity by analysis of variance of his u-scores and applied it to data on Friedreich's Ataxia but “no significant linkage could be expected from so small a group of families, especially as diagnosis must have been very incomplete” (Fisher, 1936a). Together with Mather, Fisher then applied his methods to data on mice (Fisher & Mather, 1936); the authors concluded that some “suggestions of linkage … are not conclusive but are being followed up further.” At around the same time, Mather published a scholarly paper evaluating various family types and the information they provide on linkage (Mather, 1936), and Fisher evaluated statistical properties of the so-called product formula (odds ratio) for phenotypes of offspring of intercross matings (both parents are double heterozygotes) (Fisher, 1939).

Penrose (Penrose, 1935) came up with the revolutionary idea that even a single generation of individuals can be used to test for linkage. He considered two phenotypes (presumably under some form of genetic control), each with two levels of expression. This allows the representation of sib-pair data in four classes displayed in a 2 × 2 table. Penrose showed that in the presence of linkage the two classes, in which sib-pairs are either both alike or both unlike with respect to the two phenotypes, will occur in higher frequencies than expected by chance. He demonstrated his new method on the basis of 60 sib-pairs scored for red hair, blue eyes, and A and B agglutinogens. He concluded that linkage may exist for genes influencing red hair and agglutinogen. Penrose later extended his method to the analysis of quantitative traits (Penrose, 1938) and applied improvements of it (Penrose, 1946, 1953) to the phenotypes red hair versus ABO blood types (Penrose, 1950) and phenylketonuria versus ABO and MN blood types (Penrose, 1951). While the latter investigation furnished inconclusive results, results for red hair versus ABO seemed “highly unlikely to be a chance variation” (Penrose, 1950).

The simplicity of the sib-pair test for linkage led to a flurry of publications on all kinds of linkage investigations. In the Annals, 500 pairs of sibs were scored for such phenotypes as presence of hair in the mid-digital regions of the fingers, ability to taste phenyl-thiocarbamide (PTC), and various blood types (Boyd & Boyd, 1941). The authors of this investigation mentioned that they have been “informed by Fisher and his co-workers that the method of Penrose does not by any means utilize all of the information relative to linkage,” so they published the raw data in addition to analysis results. Another sib-pair linkage investigation reported that “one hundred and seventy one possible linkage relations were tested from data involving nineteen traits and 903 sib-pairs” (Kloepfer, 1946), and an attempt to replicate previous linkage findings concluded that “no signs of linkage were found between ‘strikingly red hair’ and the blood groups ABO, MN, P, Lewis, Duffy, Kell and Rhesus, taste sensitivity to PTC., eye colour, and sex” (Hauge & Helweg-Larsen, 1954). Another publication on allergy versus blood groups and eye color also “failed to reveal any evidence of linkage among the genes determining these traits” (Zieve et al., 1936). In those exciting times of applying the new tool of linkage analysis, it was evidently commonplace to report positive as well as negative linkage findings.

Clearly, the 1930's were a decade with many methodological advances in linkage analysis. Leading into the 1940’s, Finney published an analysis of human stature (Finney, 1939). Based on linkage analysis alone, he found evidence that a sex-linked gene for stature “may be present, but not giving a definite conclusion.” When he took into account parental statures, he observed strong correlations between parents and offspring but no evidence for linkage. The author concluded that “in view of the various seeming contradictions found in the data, it would be undesirable to place trust in any results derived therefrom without first testing them on other records” (Finney, 1939). This analysis reminds me of a recent population-based study showing that a genomic profile of 54 loci explains only ∼5% of the variance of stature but mid-parent values explains 40% of the variance (Aulchenko et al., 2009). Building upon Fisher's previous work, Finney then went on to publish a series of papers on the detection of linkage allowing for incompleteness of parental genotyping and for combining data from matings of known and unknown phase (Finney, 1940, 1941a, b, 1942a, b, 1943). Also in the mid 1940’s, Kosambi published his well-known recipe on converting recombination fractions into map distances (Kosambi, 1944).

On the basis of 17 pedigrees segregating color blindness and hemophilia, two X-linked genes previously known to be linked, Haldane and Smith undertook a thorough analysis of the data employing several methods including that of maximum likelihood (Haldane & Smith, 1947). They found a maximum likelihood estimate of the recombination fraction of 9.8%. This is an interesting paper, even today, as it demonstrates how linkage analysis by maximum likelihood may be carried out.

Towards the late 1940's and early 1950’s, several methodological papers addressed varying aspects of linkage analysis. Haldane showed that in the presence of inbreeding, two recessive traits are expected to be associated even in the absence of linkage, and that linkage increases this association further, but these effects are not strong enough to be useful for linkage analysis (Haldane, 1949). He also derived an expression for the frequency of recessive offspring of a cousin marriage when a number of ancestors are known to be unaffected by the trait. In 1951, Bailey published two papers on u-statistics, simplifying their use and applying them to traits with incomplete penetrance (Bailey, 1951a, b). Smith simplified the test for heterogeneity by omitting negligible terms (Smith, 1952). A few years later he showed how male and female recombination fractions could be estimated separately and provided a test for the difference in these two recombination fractions (Smith, 1954).

Mostly in the 1950’s, the methodological developments of preceding years bore fruit and led to linkage analyses applied to several traits (Race, 1942; Cotterman & Falls, 1943; Houston, 1950; Jackson & Lawler, 1951; Leese et al., 1952). Elliptocytosis received considerable attention through its linkage to Rh (Chalmers & Lawler, 1953; Goodall et al., 1953, 1954; Lawler & Sandler, 1954). On the basis of 53 Danish families with 212 children, Mohr confirmed the linkage between Duffy and Rh previously found in British families (Mohr, 1954).

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. A Quarter Century of Linkage Papers
  5. Acknowledgements
  6. References

This work was supported by grants from the Natural Science Foundation of China (project numbers 30730057 and 30700442).

References

  1. Top of page
  2. Summary
  3. Introduction
  4. A Quarter Century of Linkage Papers
  5. Acknowledgements
  6. References