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Comments on C. C. Li's paper on measuring genetic distance

Comments on C. C. Li's paper on measuring genetic distance Comments on C. C. Li’s paper on measuring genetic distance BY CEDRIC A. B. SMITH Galton Laboratory, University College London Li defines a measure d,, of genetic distance between populations 1 and 2 by Two comments about this seem appropriate. I n the first place it is not really symmetrical (as Li states) but antisymmetrical; that is, d,, = - a,,. To get a symmetrical measure we would have t o take d:,. Secondly, suppose the two populations differ only a little, so that we can write P =p+4 I 2 =p-& % q1= Q2 q-8, =4+& where p = Q(pl+p2), = $(q1+q2); q and S is small. Then (if we interpret ‘log’ t o mean natural logarithm) the formula reduces to dl2 2: - 26/PP, neglecting terms in J2,or in other words, d;, N 4S2/p2q2. This is clearly appreciably different from most of the usual forms of ‘genetic distance’ which would equal S2/pq, or some simple multiple of this for small 6. But the two forms will not differ very much in order of magnitude (unless either p or q are near zero). Unfortunately this form suggests no very obvious generalization t o more than two populations. REFERENCE LI,C. C. (1978). On measuring genetic distance by selection intensity. Ann. Hum. Genet., Lond. 41, 501-4. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Human Genetics Wiley

Comments on C. C. Li's paper on measuring genetic distance

Annals of Human Genetics , Volume 41 (4) – May 1, 1978

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References (1)

Publisher
Wiley
Copyright
Copyright © 1978 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0003-4800
eISSN
1469-1809
DOI
10.1111/j.1469-1809.1978.tb00923.x
Publisher site
See Article on Publisher Site

Abstract

Comments on C. C. Li’s paper on measuring genetic distance BY CEDRIC A. B. SMITH Galton Laboratory, University College London Li defines a measure d,, of genetic distance between populations 1 and 2 by Two comments about this seem appropriate. I n the first place it is not really symmetrical (as Li states) but antisymmetrical; that is, d,, = - a,,. To get a symmetrical measure we would have t o take d:,. Secondly, suppose the two populations differ only a little, so that we can write P =p+4 I 2 =p-& % q1= Q2 q-8, =4+& where p = Q(pl+p2), = $(q1+q2); q and S is small. Then (if we interpret ‘log’ t o mean natural logarithm) the formula reduces to dl2 2: - 26/PP, neglecting terms in J2,or in other words, d;, N 4S2/p2q2. This is clearly appreciably different from most of the usual forms of ‘genetic distance’ which would equal S2/pq, or some simple multiple of this for small 6. But the two forms will not differ very much in order of magnitude (unless either p or q are near zero). Unfortunately this form suggests no very obvious generalization t o more than two populations. REFERENCE LI,C. C. (1978). On measuring genetic distance by selection intensity. Ann. Hum. Genet., Lond. 41, 501-4.

Journal

Annals of Human GeneticsWiley

Published: May 1, 1978

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