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XXXIV.—The Significance of the Correlation Coefficient when applied to Mendelian Distributions

Published online by Cambridge University Press:  15 September 2014

John Brownlee
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Extract

1. At the present moment there is much discussion regarding the means by which properties are hereditarily transmitted from a parent organism to its offspring, and of the extent to which the Mendelian theory is capable of accounting for the facts. In this note it is not proposed to discuss the general question but to investigate the conditions under which the theory of correlation may be applied to Mendelian groupings. Two important papers on this subject have already been published: one by Professor Pearson, entitled “A Generalized Theory of Mendelian Inheritance”; the other, which is largely a criticism of this, by Professor Udny Yule. In Professor Pearson's paper the results produced when two organisms with any number of pairs of different zygotes mate indiscriminately are fully considered. He finds that such a population once established is stable, and he then deduces the parental and fraternal correlation coefficients.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 30 , 1910 , pp. 473 - 507
Copyright
Copyright © Royal Society of Edinburgh 1910

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References

page 473 note * Royal Soc. Trans., 1903, p. 53.

page 473 note † “On the Theory of Inheritance of Quantitatively Compound Character on the Basis of Mendel's Laws,” by G. Udny Yule. Report of Conference on Genetics, published by Royal Horticultural Society of London.

page 475 note * ProfessorPearson, , Royal Soc. Trans., vol. cxcv. p. 119 Google Scholar, Table IX., “Exclusive Inheritance.”

page 482 note * r f.o. signifies correlation of father and offspring.

rf.m. signifies correlation of father and mother.

page 487 note * r s.o. signifies the correlation of the selected parent and offspring.

r n.o. signifies the correlation of the non-selected parent and offspring.

page 497 note * Roy. Soc. Trans., vol. cxcv. p. 92. Biometrika, vol. i. p. 361; vol. ii. p. 230 et seq.

page 497 note † Biometrika, vol. iii. p. 245 et seq.

page 497 note ‡ ibid., vol. iv. p. 427 et seq.

page 498 note * Bateson, Mendel's Principles of Heredity, p. 124.

page 498 note † Roy. Soc. Trans., vol. clxxv. p. 35.

page 500 note * Biometrika, vol. ii. p. 255.

page 500 note † Cf. also par. 4.

page 501 note * These and the subsequent correlations have been obtained by the fourfold method though not by the full process. They have been calculated by the formula,

and where the fourfold division is

This formula gives results very near the truth. When those coefficients, previously calculated in this paper by the full method, were checked by the method here referred to, the result has been so close that in the present instance where many coefficients are required the extra labour of calculation has not seemed necessary.

page 502 note * According to the method in which the population of parents is adjusted.