University of California

Formulas and tables to facilitate the calculation of recombination values in heredity


R. W. Allard

Author Affiliations

R. W. Allard was Associate Professor of Agronomy and Associate Agronomist in the Experiment Station, Davis.

Publication Information

Hilgardia 24(10):235-278. DOI:10.3733/hilg.v24n10p235. January 1956.

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This study provides the following aids for using the method of maximum likelihood to estimate recombination values and examine heterogeneity when complex genetic data are available:

Estimation equations for a variety of backcross, F2, and F3 situations, including equations for estimating linkage intensities between a member of a complementary or duplicate pair, or a gene pair producing a 13:3 ratio, and a third gene pair;

Tables of scores to facilitate the numerical solution of these equations;

Tables to facilitate the calculation of the standard error of the recombination value.

Since advance planning is important in linkage investigations, the use of the tables for this purpose is also described.

Literature Cited

Allard R. W. Inheritance of some seed coat colors and patterns in lima beans. Hilgardia. 1953a. 22:167-177. DOI: 10.3733/hilg.v22n05p167 [CrossRef]

Allard R. W. Inheritance of four morphological characters in lima beans. Hilgardia. 1953b. 22:383-389. DOI: 10.3733/hilg.v22n11p383 [CrossRef]

Fisher R. A. A system of scoring linkage data, with special reference to the pied factors in mice. Amer. Nat. 1946. 80:568-578. DOI: 10.1086/281475 [CrossRef]

Fisher R. A. Statistical methods for research workers. 1949. 11th ed. Edinburgh and London: Oliver and Boyd. xiv + 354p.

Fisher R. A., Balmukand Bhai. The estimation of linkage from the offspring of selfed heterozygotes. Jour. Genetics. 1928. 20:79-92. DOI: 10.1007/BF02983317 [CrossRef]

Hutchinson J. B. The application of the “method of maximum likelihood” to the estimation of linkage. Genetics. 1929. 14:519-537.

Immer F. R. Formulae and tables for calculating linkage intensities. Genetics. 1930. 15:81-98.

Immer F. R. Calculating linkage intensities from F3 data. Genetics. 1934. 19:119-136.

Immer F. R., Henderson M. T. Linkage studies in barley. Genetics. 1943. 28:419-440.

Kramer H. H., Burnham C. R. Methods of combining linkage intensity values from backcross, F2 and F3 genetic data. Genetics. 1947. 32:379-390.

Mather K. The combination of data. Ann. Eugenics. 1935. 6:399-410. DOI: 10.1111/j.1469-1809.1935.tb02121.x [CrossRef]

Mather K. Types of linkage data and their value. Ann. Eugenics. 1936. 7:251-264. DOI: 10.1111/j.1469-1809.1936.tb02144.x [CrossRef]

Mather K. The measurement of linkage in heredity. 1951. 2d ed. London: Methuen and Co., Ltd. 149p.

Stephens W. L. Tables of the recombination fraction estimated from the product ratio. Jour. Genetics. 1939. 39:171-180. DOI: 10.1007/BF02982823 [CrossRef]

Allard R. 1956. Formulas and tables to facilitate the calculation of recombination values in heredity. Hilgardia 24(10):235-278. DOI:10.3733/hilg.v24n10p235
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