Jurg Ott / 5 Jan 2013
Rockefeller University, New York

Notes to Analysis of Human Genetic Linkage

These notes are intended to complement and update the third edition of this book (Johns Hopkins University Press, Baltimore, Maryland). Errors and misprints are listed in a separate document. For line numbers, up is shorthand for from the bottom.

Page 8, bottom paragraph: Inheritance of the mitochondrial genome appears not to be completely maternal. See Awadella et al. (1999) "Linkage disequilibrium and recombination in hominid mitochondrial DNA", Science 286, 2524-2525; Strauss (1999) "mtDNA shows signs of paternal influence", Science 286, 2436.

Page 16, paragraph on pseudoautosomal regions: Additional reference — Graves AM, Wakefield MJ, Toder R (1998) The origin and evolution of the pseudoautosomal regions of human sex chromosomes. Hum Mol Genet 7:1991-1996

Page 16, line 10 up: The term syntenic is used here as originally defined by Renwick. That is, it means located on the same chromosome. However, more and more, syntenic is used to mean (what previously was called) homologous. That is, it refers to two loci (in different species) that are of the same evolutionary origin. As an example, see the abstract of Paperna et al. (1998) "Genes for the CPE receptor (CPETR1) and the human homolog of RVP1", Genomics 54:453-459.

Page 77, point-wise and global (genome-wide) significance levels associated with a maximum lod score observed in the genome: Equations (3.92) and (3.93) in Pak Sham's book, Statistics in Human Genetics, provide the relationships between these three quantities. For a genome of length 33 Morgans, I applied these equations to compute a corresponding table of values for maximum lod scores of 5 and smaller.

Page 147, line 13, "True peaks wider than false peaks": An interesting and illuminating comment on this phenomenon may be found in a letter (Knapp [1998] Discriminating between true and false-positive peaks in a genomewide linkage scan, by use of the peak length. Am J Hum Genet 62:1561-1562).

Page 164, append to paragraph "Estimating Age-of-Onset Curves": A recent analysis has applied sophisticated statistical methods for an unbiased estimation of penetrance in BRCA1 and BRCA2. Satagopan JM, Offit K, Foulkes W, Robson ME, Wacholder S, Eng CM, Karp SE, Begg CB (2001) The lifetime risks of breast cancer in Ashkenazi Jewish carriers of BRCA1 and BRCA2 mutations. Cancer Epidemiol Biomarkers Prev 10, 467-473

Page 177, section 8.5 -- An early paper describing a variance components approach to the mapping of quantitative trait loci is: Jayakar SD (1970) On the detection and estimation of linkage between a locus influencing a quantitative character and a marker locus. Biometrics 26:451-464

Page 190: Another  program for multipoint linkage analysis is Allegro (Gudbjartsson et al. [2000] Allegro, a new computer program for multipoint linkage analysis. Nat Genet 25:12-13).

Page 223: Properties of testing for heterogeneity under the model discussed here have been addressed by Whittemore and Halpern (2001) "Problems in the definition, interpretation, and evaluation of genetic heterogeneity." Am J Hum Genet 68:457-465.

Page 226, top: Additional references to the irregularitiy of mixture models are, for example:
        Chernoff H, Lander E (1995) Asymptotic distribution of the likelihood ratio test that a mixture of two binomials is a single binomial. J Statist Plann Inference 43:19-40
        Chen J (1998) Penalized likelihood-ratio test for finite mixture models with multinomial observations. Canadian Journal of Statistics 26:583-599

Page 278: See note for page 190.

Page 286: An extended version of this program is available as EHPLUS. It has simpler input requirements and approximates p-values by a computer simulation algorithm. Based on EH, EHPLUS was developed by and is available at http://www.iop.kcl.ac.uk/IoP/Departments/PsychMed/GEpiBSt/software.stm.
The reference is Zhao et al. (2000) Model-free analysis and permutation tests for allelic associations. Hum Hered 50, 133-139.

Page 286: There has been a debate as to the relative efficiency of estimating haplotype frequencies based on (phase-unknown) genotype data versus that based on (phase-known) haplotype data. For a lucid discussion of this matter with analytical solutions, see P.M. McKeigue (2000) Efficiency of estimation of haplotype frequencies: Use of marker phenotypes of unrelated individuals versus counting of phase-known gametes. Am J Hum Genet 67:1626-1627.

Page 287, top: A useful program on linkage disequilibrium, MLD, may be found at ftp://statgen.ncsu.edu/pub/zaykin/ (a brief manual is contained in the "readme.txt" file in that directory).

Page 289, bottom: Cattle represent a population in which it is most likely genetic drift that generates much disequilibrium — estimates for effective population size are as low as 50. See Farnir et al. (2000) Extensive genome-wide linkage disequilibrium in cattle. Genome Res 10:220-227

Page 302, last paragraph in section 14.1: Dr. Michael Knapp (Bonn, Germany) pointed out to me that absence of main effects (i.e., at each of the two loci, IBD sharing is , , ) and presence of interaction effects are incompatible. He argues on the basis of inequalities (12) in Cordell et al. (Am J Hum Genet 57: 920-934, 1995) and Knapp et al. (Am J Hum Genet 57 suppl: A165, 1995) as follows: All joint IBD distributions at two loci are subject to the conditions

(1) z1j ≤ z0j + z2j for all j
(2) zi1 ≤ zi0 + zi2 for all i
(3) 2 z0j ≤ z1j for all j
(4) 2 zi0 ≤ zi1 for all i.

From (z2., z1., z0.) = (z2, z1, z0) = (, , ) (i.e., no main effects), one concludes that z22 = 1/16, z12 = 1/8, etc. (i.e., no interactions).

Page 318, paragraph "Ideally": An example of factor analysis carried out on symptoms may be found in Maziade et al. (1995) Negative, psychoticism, and disorganized dimension in patients with familial schizophrenia or bipolar disorder: continuity and discontinuity between the major psychoses. Am J Psychiatry 152:1458-1463

Page 308, middle, refers to the nature/nurture question. Myopia is quoted as an example. But ("scientific correspondence") this question is still far from being resolved for myopia. Quinn et al. (1999) Myopia and ambient lighting at night. Nature 399:113-114.

Page 309, bottom: Genetic effects on longevity in the fly are described in Science 290:2048 and Science 290:2137-2140 (2000).

Page 323, paragraph "Because of": It is stated that no problem exists with nonparametric multipoint linkage analysis. As pointed out to me by Dr. Joseph Terwilliger, this is only so in an ideal world — in reality, marker genotypes have errors so that looking at many markers jointly is subject to many errors. If so, twopoint analysis is still a more prudent way to proceed.