Genetic Dissection of Complex Traits

References and notes

• 1 A. H. Sturtevant, J. Exp. Zool. 14, 43 (1913). Crossref, Google Scholar
• 2 W. Bender, P. Spierer, D. S. Hogness, J. Mol. Biol. 168, 17 (1983); P. Spierer, A. Spierer, W. Bender, D. S. Hogness, ibid., p. 35. Crossref, Google Scholar
• 3 T. D. Petes and D. Botstein, Proc. Natl. Acad. Sci. U.S.A. 74, 5091 (1977). Crossref, Google Scholar
• 4 D. Botstein, R. L. White, M. H. Skolnick, R. W. Davies, Am. J. Hum. Genet. 32, 314 (1980). Google Scholar
• 5 D. N. Cooper and J. Schmidtke, Ann. Med. 24, 29 (1992); V. A. McKusick, Mendelian Inheritance in Man: Catalogs of Autosomal Dominant, Autosomal Recessive, and X-Linked Phenotypes (Johns Hopkins Univ. Press, Baltimore, MD, 1992); F. Collins, personal communication. Crossref, Google Scholar
• 6 T. H. J. Huisman, Am. J. Hematol. 6, 173 (1979); M. H. Steinberg and R. P. Hebbel, ibid. 14,405 (1983). Crossref, Google Scholar
• 7 G. J. Dover et al., Blood 80, 816 (1992); S. L. Their et al., Am. J. Hum. Genet. 54, 214 (1994). Crossref, Google Scholar
• 8 D. Easton, D. Ford, J. Peto, Cancer Surv. 18, 95 (1993); D. Ford et al., Lancet 343, 692 (1994). Google Scholar
• 9 S. T. Reeders et al., Hum. Genet. 76, 348 (1987); G. Romeo et al., Lancet ii, 8 (1988); A. Turco, B. Peissel, L. Gammaro, G. Maschio, P. F. Pignatti, Clin. Genet. 40, 287 (1991). Crossref, Google Scholar
• 10 P. H. St. George-Hyslop et al., Nature 347, 194 (1990). Crossref, Google Scholar
• 11 J. Barbosa, H. Noreen, F. C. Goetz, E. J. Yunis, Diabete Metab. 2, 160 (1976); G. I. Bell et al., Proc. Natl. Acad. Sci. U.S.A. 88, 1484 (1991); D. W. Bowden et al., Am. J. Hum. Genet. 50, 607 (1992); P. Froguel et al., Nature 356, 162 (1992). Google Scholar
• 12 R. Fishel et al., Cell 75, 1027 (1993); F. Leach et al., ibid., p. 1215; N. Papadopoulos et al., Science 263, 1625 (1994); R. Fishel et al., Cell 77, 167 (1994); B. Liu et al., Cancer Res. 54, 4590 (1994). Crossref, Google Scholar
• 13 N. G. Jaspers and D. Bootsma, Proc. Natl. Acad. Sci. U.S.A. 79, 2641 (1982); E. Sobel et al., Am. J. Hum. Genet. 50, 1343 (1992). Crossref, Google Scholar
• 14 E. A. De Weerd-Kastelein, W. Keijzer, D. Bootsma, Nat. New Biol. 238, 80 (1972). Crossref, Google Scholar
• 15 L. M. Bleeker-Wagemakers et al., Genomics 14, 811 (1992); R. Kumar-Singh, P. Kenna, G. J. Farrar, P. Humphries, ibid. 15, 212 (1993). Crossref, Google Scholar
• 16 S. Brul et al., J. Clin. Invest. 81, 1710 (1988); J. M. Tager et al., Prog. Clin. Biol. Res. 321, 545 (1990); J. Gartner, H. Moser, D. Valle, Nat. Genet. 1, 16 (1992); N. Shimozaun et al., Science 255, 1132 (1992). Crossref, Google Scholar
• 17 R. Ward, in Hypertension: Pathophysiology, Diagnosis, and Management, J. H. Laragh and B. M. Brenner, Eds. (Raven, New York, 1990), pp. 81–100. Google Scholar
• 18 W. F. Dietrich et al., Cell 75, 631 (1993). Crossref, Google Scholar
• 19 K. Kajiwara, E. L. Berson, T. P. Dryja, Science 264, 1604 (1994). Crossref, Google Scholar
• 20 E. G. Puffenberger et al., Hum. Mol. Genet. 3, 1217 (1994). Crossref, Google Scholar
• 21 E. S. Lander and D. Botstein, Cold Spring Harbor Symp. Quant. Biol. 51, 49 (1986). Crossref, Google Scholar
• 22 C. C. Li, Am. J. Hum. Genet. 41, 517 (1987); P. P. Majumder, S. K. Das, C. C. Li, ibid. 43, 119 (1988); S. K. Nath, P. P. Majumder, J. J. Nordlund, ibid., in press. Google Scholar
• 23 Bilineality has been thought to plague many genetic analyses, particularly those involving psychiatric disorders. See, for example, S. E. Hodge, Genet. Epidemiol. 9, 191 (1992); M. Durner, D. A. Greenberg, S. E. Hodge, Am. J. Hum. Genet. 51, 859 (1992); K. R. Merikangas, M. A. Spence, D. J. Kupfer, Arch. Gen. Psychiatry 46, 1137 (1989); M. A. Spence et al., Hum. Hered. 43, 166 (1993). Crossref, Google Scholar
• 24 A simple application of the Hardy-Weinberg principle shows that the proportion of individuals who inherit D from a homozygous parent (as opposed to a heterozygous parent) is equal to the allele frequency of D. Suppose that allele D has frequency ρ and let q = 1 − ρ. The proportion of individuals in the population who inherit D from a homozygous parent is 2ρ2/(2ρ2 + 2ρq) = ρ. Google Scholar
• 25 M. A. Pericak-Vance et al., Am. J. Hum. Genet. 48, 1034 (1991). Google Scholar
• 26 E. H. Corder et al., Science 261, 921 (1993). Crossref, Google Scholar
• 27 D. C. Wallace, Annu. Rev. Biochem. 61, 1175 (1992); J. B. Redman, R. G. Fenwick Jr., Y. H. Fu, A. Pizzuti, C. T. Caskey, J. Am. Med. Assoc. 269, 1960 (1993). Crossref, Google Scholar
• 28 N. J. Schork and S. W. Guo, Am. J. Hum. Genet. 53, 1320 (1993). Google Scholar
• 29 M. J. Khoury, T. H. Beaty, B. H. Cohen, Fundamentals of Genetic Epidemiology (Oxford Univ. Press, New York, 1993); K. M. Weiss, Genetic Variation and Human Disease (Cambridge Univ. Press, Cambridge, 1993). Google Scholar
• 30 M. C. Neale and L. R. Cardon, Methodology for Genetic Studies of Twins and Families (Kluwer Academic, Boston, 1992). Google Scholar
• 31 L. S. Penrose, Acta Genet. 4, 257 (1953); J. H. Edwards, ibid. 10, 63 (1960); Br. Med. Bull. 25, 58 (1969); N. Risch, Am. J. Hum. Genet. 46, 222 (1 990). Google Scholar
• 32 N. Risch, Am. J. Hum. Genet. 46, 229 (1990). Google Scholar
• 33 ———, ibid., p. 242. Google Scholar
• 34 The concept of heritability has a long history in genetics, being one of the most widely used terms in all of biology; see, for example, R. A. Fisher, Trans. R. Soc. Edinburgh 52, 399 (1918); D. S. Falconer, Introduction to Quantitative Genetics (Longman, New York, 1981). Crossref, Google Scholar
• 35 B. Newman, M. A. Austin, M. Lee, M. C. King, Proc. Natl. Acad. Sci. U.S.A. 85, 3044 (1988). Crossref, Google Scholar
• 36 See also W. R. Williams and D. E. Anderson, Genet. Epidemiol. 1, 7 (1984); D. T. Bishop, L. Cannon-Albright, T. McLellan, E. J. Gardner, M. H. Skolnick, Genet. Epidemiol. 5, 151 (1988); E. B. Claus, N. J. Risch, W. D. Thompson, Am. J. Epidemiol. 131, 961 (1990). Crossref, Google Scholar
• 37 Problems that arise through the ascertainment of probands whose families are then used in genetic studies have been discussed at length in the genetics literature. Some articles of relevance are W. Weinberg, Arch. Rassen-Gesellschaftsbiol. 9, 165 (1912); N. E. Morton, Am. J. Hum. Genet. 11, 1 (1959); W. J. Ewens, ibid. 34, 853 (1982); P. P. Majumder, Stat. Med. 4,163 (1985); W. J. Ewens and N. C. Shute, Ann. Hum. Genet. 50, 399 (1986); M. R. Young, M. Boehnke, P. P. Moll, Am. J. Hum. Genet. 43, 705 (1988). Google Scholar
• 38 J. Ott, Am. J. Hum. Genet. 46, 219 (1990). Google Scholar
• 39 The number of major genetic factors segregating in a cross between inbred strains can be estimated under some circumstances; see (47); W. E. Castle, Science 54, 223 (1916); S. Wright, Evolution and the Genetics of Populations: Genetic and Biometric Foundations (Univ. of Chicago Press, Chicago, 1968), pp. 373– 420. Google Scholar
• 40 M. W. Feldman and L. L. Cavalli-Sforza, in Genetic Aspects of Common Diseases: Applications to Predictive Factors in Coronary Disease (Liss, New York, 1979), pp. 203–227. Google Scholar
• 41 K. W. Kinzier et al., Science 253, 661 (1991); G. Joslyn et al., Cell 66, 601 (1991). Crossref, Google Scholar
• 42 L. A. Aaltonen et al., Science 260, 812 (1993). Crossref, Google Scholar
• 43 R. R. Williams et al., Arch. Intern. Med. 150, 582 (1990); J. V. Selby et al., J. Am. Med. Assoc. 265, 2079 (1991); R. R. Williams et al., Ann. Med. 24, 469 (1992). Crossref, Google Scholar
• 44 R. F. Clark and A. M. Goate, Arch. Neurol. 50, 1164 (1993). Crossref, Google Scholar
• 45 M. E. Marenberg, N. Risch, L. F. Berkman, B. Floderus, U. de Faire, N. Engl. J. Med. 330, 1041 (1994). Crossref, Google Scholar
• 46 G. Carey and J. Williamson, Am. J. Hum. Genet. 49, 786 (1991); L. R. Cardon and D. W. Fulker, Am. J. Hum. Genet., in press; N. J. Schork et al., in preparation. Google Scholar
• 47 E. S. Lander and D. Botstein, Genetics 121, 174 (1989). Google Scholar
• 48 L. Groop and R. DeFranzo, personal communication. Google Scholar
• 49 G. A. Barnard, R. Stat. Soc. J. B11, 115 (1949); J. B. S. Haldane and C. A. B. Smith, Ann. Eugen. 14, 10 (1947); J. Chotoi, Ann. Hum. Genet. 48, 359 (1984). Google Scholar
• 50 N. E. Morton, Am. J. Hum. Genet. 8, 80 (1955). Google Scholar
• 51 A. W. F. Edwards, Likelihood (Johns Hopkins Univ. Press, Baltimore, MD, 1992). Google Scholar
• 52 J. Ott, Analysis of Human Genetic Linkage (Johns Hopkins Univ. Press, Baltimore, MD, 1991), pp. 65– 68. Google Scholar
• 53 J. Tomfohrde et al., Science 264, 1141 (1994). Crossref, Google Scholar
• 54 J. K. Ghosh and P. K. Sen, in The Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, L. M. LeCam and R. A. Olshen, Eds. (Wadsworth, Monterey, CA, 1985), pp. 807– 810; D. M. Titterington, A. F. M. Smith, U. E. Makov, Statistical Analysis of Finite Mixture Distributions (Wiley, London, 1985); J. Ott, in (52), pp. 194–216; J. Faraway, Genet. Epidemiol. 10, 75 (1993); H. Chernoff and E. S. Lander, J. Stat. Plann. Inference, in press. Google Scholar
• 55 J. M. Hall et al., Science 250, 1684 (1990). Crossref, Google Scholar
• 56 G. D. Schellenberg et al., ibid. 258, 668 (1992); C. E. Yu et al., Am. J. Hum. Genet. 54, 631 (1994). Google Scholar
• 57 R. Sherrington et al., Nature 336, 164 (1988). Crossref, Google Scholar
• 58 E. S. Lander and D. Botstein, Proc. Natl. Acad. Sci. U.S.A. 83, 7353 (1986); N. J. Schork, M. Boehnke, J. D. Terwilliger, J. Ott, Am. J. Hum. Genet. 53, 1127 (1993). Crossref, Google Scholar
• 59 C. S. Haley and S. A. Knott, Heredity 69, 315 (1992). Crossref, Google Scholar
• 60 P. J. Tienari et al., Genomics 19, 320 (1994). Crossref, Google Scholar
• 61 D. E. Weeks, T. Lehner, E. Squires-Wheeler, C. Kaufmann, J. Ott, Genet. Epidemiol. 7, 237 (1990). Crossref, Google Scholar
• 62 One way of avoiding the possible use of an incorrectly specified segregation model in a linkage analysis is to estimate linkage and segregation parameters simultaneously. Although computationally prohibitive in certain settings, this strategy appears to have some favorable features. See, for example, C. J. MacLean, N. E. Morton, S. Yee, Comput. Biomed. Res. 17, 471 (1984); G. E. Bonney, G. M. Lathrop, J. M. Lalouel, Am. J. Hum. Genet. 43, 29 (1988); N. J. Schork, Genet. Epidemiol. 9, 207 (1992). Crossref, Google Scholar
• 63 J. Ott, Clin. Genet. 12, 119 (1977); F. Clerget-Darpoux, Ann. Hum. Genet. 46, 363 (1982); ______, C. Bonaiti-Pellie, J. Hochez, Biometrics 42, 393 (1986); F. Clerget-Darpoux, M. C. Babron, C. Bonaiti-Pellie, J. Psychiatr. Res. 21, 625 (1987). Google Scholar
• 64 For a discussion of how robust linkage analysis might be in certain settings, see, for example, J. A. Williamson and C. I. Amos, Genet. Epidemiol. 7, 309 (1990); C. I. Amos and J. A. Williamson, Am. J. Hum. Genet. 52, 213 (1993); S. E. Hodge and R. C. Fiston, Genet. Epidemiol., in press. Crossref, Google Scholar
• 65 L. J. Eaves, Heredity 72, 175 (1994). Crossref, Google Scholar
• 66 J. Ott, Am. J. Hum. Genet. 31, 161 (1979); J. Edwards, Cytogenet. Cell Genet. 39, 43 (1982); N. J. Schork, in Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, Seattle, WA, 21–24 April 1994, E. M. Keramidas and S. M. Kaufman, Eds. (Interface Foundation of North America, Fairfax Station, VA, 1992); T. M. Goradia, K. Lange, P. L. Miller, P. M. Nadkarni, Hum. Hered. 42, 42 (1992); R. W. Cottingham Jr., R. M. Idury, A. A. Schaffer, Am. J. Hum. Genet. 53, 252 (1993). Google Scholar
• 67 N. J. Schork, Genet. Epidemiol. 8, 29 (1991). Crossref, Google Scholar
• 68 R. C. Elston and J. Stewart, Hum. Hered. 21, 323 (1971). Google Scholar
• 69 Since its introduction, the Elston-Stewart algorithm has been extended and modified in various ways; see, for example, J. Ott, Am. J. Hum. Genet. 26, 588 (1974); K. Lange and R. C. Elston, Hum. Hered. 25, 95 (1975); C. Cannings, E. T. Thompson, M. H. Skolnick, Adv. Appl. Probab. 10, 26 (1978); R. C. Elston, V. T. George, F. Severtson, Hum. Hered. 42,16 (1992). Google Scholar
• 70 J. Ott, Am. J. Hum. Genet. 28, 528 (1976). Google Scholar
• 71 G. M. Lathrop, J. M. Lalouel, C. Julier, J. Ott, Proc. Natl. Acad. Sci. U.S.A. 81, 3443 (1984). Crossref, Google Scholar
• 72 N. E. Morton and C. J. MacLean, Am. J. Hum. Genet. 26, 489 (1974); S. J. Hasstedt, Comput. Biomed. Res. 15, 295 (1982); G. E. Bonney, Am. J. Med. Genet. 18, 731 (1984); S. W. Guo and E. T. Thompson, IMA J. Math. Appl. Med. Biol. 8, 171 (1991); ibid., p. 149; N. J. Schork, Genet. Epidemiol. 9, 73 (1992). Google Scholar
• 73 M. C. King, G. M. Lee, N. B. Spinner, G. Thompson, M. R. Wrensch, Annu. Rev. Public Health 5, 1 (1984); E. A. Thompson, Stat. Med. 5, 291 (1986). Crossref, Google Scholar
• 74 E. S. Lander and P. Green, Proc. Natl. Acad. Sci. U.S.A. 84, 2363 (1987). Crossref, Google Scholar
• 75 L. Kruglyak and E. S. Lander, in preparation. Google Scholar
• 76 S. W. Guo and E. T. Thompson, Am. J. Hum. Genet. 51,1111 (1992); D. C. Thomas, Cytogenet. Cell Genet. 59, 228 (1992); A. Kong, N. Cox, M. Frigge, M. Irwin, Genet. Epidemiol. 10, 483 (1993). Google Scholar
• 77 For a discussion, see W. C. Blackwelder and R. C. Elston, Genet. Epidemiol. 2, 85 (1985); A. S. Whittemore and J. Halpern, Biometrics 50, 118 (1994). Crossref, Google Scholar
• 78 D. E. Weeks and K. Lange, Am. J. Hum. Genet. 42, 315 (1988). Google Scholar
• 79 B. K. Suarez, J. Rice, T. Reich, Ann. Hum. Genet. 42, 87 (1978). Crossref, Google Scholar
• 80 L. R. Weitkamp, N. Engl. J. Med. 305, 1301 (1981); M. Knapp, S. A. Beuchter, M. P. Baur, Hum. Hered. 44, 37 (1994). Crossref, Google Scholar
• 81 P. Holmans, Am. J. Hum. Genet. 52, 362 (1993). Google Scholar
• 82 N. E. Morton et al., ibid. 35, 201 (1983); R. N. Hyer et al., ibid. 48, 243 (1991); S. S. Rich, S. S. Panter, F. C. Goetz, B. Hedlund, J. Barbosa, Diabetologica 34, 350 (1991). Google Scholar
• 83 D. Owerbach and K. H. Gabbay, Am. J. Hum. Genet. 54, 909 (1994). Google Scholar
• 84 J. Davies et al., Nature, in press. Google Scholar
• 85 D. H. Hamer, S. Hu, V. L. Magnuson, N. Hu, A. M. L. Pattatucci, Science 261, 321 (1993). Crossref, Google Scholar
• 86 In principle, one could either explicitly use the expected value of the IBD statistic or work with the probability distribution over the IBD statistic. The former approach has the difficulty that it is hard to derive an expression for the variance of the statistic. It has been done in some simple cases, such as inbred crosses (L. Kruglyak and E. S. Lander, submitted). The latter has been applied in numerous cases [for example, (79); C. I. Amos, D. V. Dawson, R. C. Elston, Am. J. Hum. Genet. 47, 842 (1990)]. Google Scholar
• 87 K. Lange, Am. J. Hum. Genet. 39, 148 (1986); D. E. Weeks and K. Lange, ibid. 50, 859 (1992). Google Scholar
• 88 X. Jeunemaitre et al., Cell 71, 169 (1992). Crossref, Google Scholar
• 89 J. K. Haseman and R. C. Elston, Behav. Genet. 2, 3 (1972). Crossref, Google Scholar
• 90 W. C. Blackwelder and R. C. Elston, Commun. Stat. Theor. Methods 11, 449 (1982); C. I. Amos and R. C. Elston, Genet. Epidemiol. 6, 349 (1989); J. M. Olson and E. M. Wijsman, ibid. 10, 87 (1993). Crossref, Google Scholar
• 91 C. I. Amos et al., Genet. Epidemiol. 3, 255 (1986). Crossref, Google Scholar
• 92 D. G. Marsh et al., Science 264, 1152 (1994). Crossref, Google Scholar
• 93 N. A. Morrison et al., Nature 367, 284 (1994). Crossref, Google Scholar
• 94 0. F. Goldgar, Am. J. Hum. Genet. 47, 957 (1990); C. I. Amos, ibid. 54, 535 (1994); D. W. Fulker and L. R. Cardon, ibid., p. 1092; N. J. Schork and S. Ghosh, submitted. Google Scholar
• 95 W. H. Berrittini et al., Proc. Natl. Acad. Sci. U.S.A. 91, 5918 (1994). Crossref, Google Scholar
• 96 L. P. Ryder, E. Andersen, A. Svejgaard, Eds., HLA and Disease Registry, Third Report (Munksgaard, Copenhagen, 1979). Google Scholar
• 97 W. E. Braun, HLA and Disease (CRC, Boca Raton, FL, 1979). Google Scholar
• 98 E. H. Corder et al., Nat. Genet. 7, 180 (1994); C. Singer et al., Arch. Neurol. 49, 13 (1992); F. Schachter et al., Nat. Genet. 6, 29 (1994); H. Schunkert et al., N. Engl. J. Med. 330, 1634 (1994); F. Cambien et al., Nature 359, 641 (1992). Crossref, Google Scholar
• 99 Some of these methods have generally fallen under the heading of “measured genotype” analyses. Relevant articles include E. Boerwinkle, R. Chakraborty, C. F. Sing, Ann. Hum. Genet. 50,181 (1986); V. T. George and R. C. Elston, Genet. Epidemiol. 4, 193 (1987). Crossref, Google Scholar
• 100 An exception would be if there were so many disease-causing alleles that the association could not be easily detected, or if the trait were predominantly due to a different cause in some populations. Google Scholar
• 101 This could happen if the ancestral disease-causing chromosome carried both the Eco RI and the Bam HI sites, but many normal chromosomes also had the Eco RI site but not the Bam HI site. Google Scholar
• 102 K. M. Weiss, Genetic Variation and Human Disease (Cambridge Univ. Press, Cambridge, 1993). Google Scholar
• 103 C. T. Falk and P. Rubinstein, Ann. Hum. Genet. 51, 227 (1987); F. Clerget-Darpoux et al., ibid. 52, 247 (1988); G. Thompson et al., Genet. Epidemiol. 6, 43 (1989); J. Ott, ibid., p. 127; J. D. Terwilliger and J. Ott, Hum. Hered. 42, 337 (1992); M. Knapp, S. A. Seuchter, M. P. Baur, Am. J. Hum. Genet. 52, 1085 (1993). Crossref, Google Scholar
• 104 C. Julier et al., Nature 354, 155 (1991). Crossref, Google Scholar
• 105 R. S. Spielman et al., Am. J. Hum. Genet. 52, 506 (1993); S. E. Hodge, ibid. 53, 367 (1993). Google Scholar
• 106 K. Blum et al., J. Am. Med. Assoc. 263, 2055 (1990). Crossref, Google Scholar
• 107 J. Gelemnter et al., ibid. 266, 1801 (1991); K. Blum et al., Alcohol 10, 59 (1993); J. Gelernter et al., J. Am. Med. Assoc. 269, 1673 (1993). Crossref, Google Scholar
• 108 D. Goldman et al., Alcohol. Clin. Exp. Res. 17, 199 (1993); B. K. Suarez et al., Genomics 19, 12 (1994); C. N. Pato et al., Am. J. Med. Genet. 48, 78 (1993); A. Parsian et al., Arch. Gen. Psychiatry 48, 655 (1991); T. Arinami et al., Biol. Psychiatry 33, 108 (1993); D. Goldman et al., Acta Psychiatr. Scand. 86, 351 (1992); S. Schwab et al., Am. J. Hum. Genet. 49 (suppl.), 203 (1991); D. Goldman et al., Alcohol. Clin. Exp. Res., in press. Crossref, Google Scholar
• 109 Indeed, a perfect association between two loci linked at 1% recombination decays with a “half-life” of about 70 generations, because (0.99)70 ≈1/2. This corresponds to about 1500 years for humans. Google Scholar
• 110 R. Plomin et al., Behav. Genet. 24, 107 (1994). Crossref, Google Scholar
• 111 R. Chakraborty and K. M. Weiss, Proc. Natl. Acad. Sci. U.S.A. 85, 9119 (1988). Crossref, Google Scholar
• 112 QTL analysis is included under the heading of polygenic trait analysis, despite the fact that a quantitative trait could, in principle, be monogenic. In practice, quantitative traits are nearly always polygenic, and the methodology is the same in any case. Google Scholar
• 113 H. Jacob, Cell 67, 213 (1991). Crossref, Google Scholar
• 114 T. Serikawa et al., Genetics 131, 701 (1992). Google Scholar
• 115 E. A. Carbonell, T. M. Gerig, E. Balansard, M. J. Asins, Biometrics 48, 305 (1992); Z. W. Luo and M. J. Kearsey, Heredity 69, 236 (1992); Z. B. Zeng, Genetics 136, 1457 (1994); S. A. Knott and C. S. Haley, ibid. 132, 1211 (1992); R. C. Jansen and P. Stam, ibid. 136, 1447 (1994); Z. B. Zeng, Proc. Natl. Acad. Sci. U.S.A. 90, 10972 (1993); R. C. Jansen, Genetics 135, 205 (1993); Theor. Appl. Genet. 85, 252 (1992). Crossref, Google Scholar
• 116 Work on gene-mapping schemes in experimental organisms is ongoing and a topic of great interest in statistical genetics. For example, L. Kruglyak and E. S. Lander (submitted) have developed a nonparametric method for QTL mapping; N. J. Schork (submitted) has shown how to use interval mapping for dichotomous traits; and N. J. Schork (submitted) has described methods for detecting epistatic interaction. Google Scholar
• 117 The key reason is that the meioses in experimental crosses are all equivalent (that is, they involve segregation of the same alleles in a fixed phase relationship, with each parent being heterozygous for a “high” and “low” allele at a QTL in, for example, F2 progeny), whereas the meioses in different human families are not directly comparable (that is, the configuration of “high” and “low” alleles varies among each set of parents, and only a subset of parents segregate for different alleles at a QTL). Accordingly, QTL analysis in experimental crosses allows one to compare means (for example, the mean phenotype of progeny inheriting allele A versus the mean phenotype of progeny inheriting allele B), whereas QTL analysis of human families requires one to compare variances (for example, squared differences Δ2 between sib pairs inheriting two IBD alleles versus between sib pairs inheriting no alleles IBD, as in the Haseman-Elston method). Google Scholar
• 118 P. C. Groot et al., FASEB J. 6, 2826 (1992); C. J. Moen, M. Snoek, A. A. Hart, P. Demant, Oncogene 7, 563 (1992). Crossref, Google Scholar
• 119 A. H. Paterson et al., Nature 335, 721 (1988). Crossref, Google Scholar
• 120 M. L. Rise, W. N. Frankel, J. M. Coffin, T. N. Seyfried, Science 253, 669 (1991); P. Hilbert et al., Nature 353, 521 (1991). Crossref, Google Scholar
• 121 S. D. Tanksley, Annu. Rev. Genet. 27, 205 (1993); J. C. Crabbe, J. K. Belknap, K. J. Buck, Science 264, 1715 (1994). Crossref, Google Scholar
• 122 M. Festing, Inbred Strains in Biomedical Research (Oxford Univ. Press, New York, 1979). Google Scholar
• 123 S. Ghosh et al., Nat. Genet. 4, 404 (1993); N. Risch, S. Ghosh, J. A. Todd, Am. J. Hum. Genet. 53, 702 (1993). Crossref, Google Scholar
• 124 H. J. Jacob et al., Nat. Genet. 2, 56 (1992). Crossref, Google Scholar
• 125 J. A. Egeland et al., Nature 325, 783 (1987); J. L. Kennedy et al., ibid. 336, 167 (1988); S. D. Detera-Wadleigh et al., ibid. 340, 391 (1989); J. R. Kelsoe et al., ibid. 342, 238 (1989); M. Baron et al., Nat. Genet. 3, 49 (1993). Crossref, Google Scholar
• 126 E. Feingold, P. 0. Brown, D. Siegmund, Am. J. Hum. Genet. 53, 234 (1993). Google Scholar
• 127 The factor [C + 2ρGh(T)] approximately converts a single-point significance level aT to a genome-wide significance level αT*, both for lod scores and allelesharing statistics. The factor is asymptotically correct for large values of T and thus small values of αT and αT*. The significance-level αT can also be regarded as the expected number of distinct regions in which the statistic X exceeds T. The significance level can be one-sided or two-sided. For a normally distributed statistic, h(T) = T2. For a lod score statistic, h(T) = T(2loge10). The constant ρ measures the crossover rate. If R(d) denotes the covariance function between genotypes (or allele-sharing status) at distance d (measured in Morgans), then ρ is defined by the equation ρ= − R′ (0)/2, where R′ (0) denotes the derivative at zero taken as a limit from above. In the simple case of individual informative meioses in a nuclear family or a single-generation cross, R(d) = exp(−2d). More generally, R(d) is of the form a1exp(−b1d) + a2exp(−b2d) +… + akexp(−bkd). For example, first-cousin allele sharing has R(d) = exp(−4d)/2 + exp(−6d)/3 + exp(−8d)/6. One can show that ρ = 1 for backcrosses or intercrosses in which only an additive component is fit (1 df); ρ= 1.5 for intercrosses in which an additive and dominance component is fit (2 df); ρ= 1 for grandparent-grandchild pair allele sharing; ρ= 2 for half-sib pair allele sharing (as well as for sib pairs regarded as the sum of two half-sib pairs) and for recombinant inbred lines produced by selfing; ρ= 2.5 for uncle-nephew pair allele sharing; ρ= 8/3 for first-cousin pair allele sharing; and ρ= 4 for recombinant inbred strains produced by brother-sister mating. The analysis has also been modified by D. Siegmund (personal communication) for sib pair allele sharing in which the significance test is based on the possible triangle method (81). The calculated values in Table 1 are from L. Kruglyak, D. Siegmund, E. S. Lander, in preparation. Google Scholar
• 128 A. Rebai, B. Goffinet, B. Mangin, Genetics 138, 235 (1994); W. N. Frankel et al., ibid., in press. Google Scholar
• 129 K. K. Kidd and J. Ott, Cytogenet. Cell Genet. 37, 510 (1984). Google Scholar
• 130 J. Ott, Proc. Natl. Acad. Sci. U.S.A. 86, 4175 (1989); J. D. Terwilliger and J. Ott, Cytogenet. Cell Genet. 59, 142 (1992); M. N. Chiano and J. R. W. Yates, Ann. Hum. Genet. 58, 129 (1994); N. J. Schork, in Exploring the Limits of the Bootstrap, R. LePage and L. Billard, Eds. (Wiley, New York, 1991); and M. A. Schork, Am. J. Hum. Genet. 45, 803 (1989); A. Kong, M. Frigge, M. Irwin, N. Cox, ibid. 51, 1413 (1992). Crossref, Google Scholar
• 131 To illustrate the flexibility of permutation tests, suppose that a genome scan detects two loci on chromosomes 1 and 2 that appear to affect a trait in an additive fashion, with the first explaining twice as much variance as the second. To determine whether the second locus makes a significant contribution over and above the first, one could permute the genotypes for chromosome 2 among the progeny. The likelihood ratio statistic for a two-locus effect can be computed for each such permutation and the empirical distribution used to make inferences about the significance of the effect of the second locus. Google Scholar
• 132 See, for example, E. S. Edgington, Randomization Tests (Dekker, New York, 1987); E. W. Noreen, Computer Intensive Methods for Testing Hypotheses (Wiley, New York, 1989); B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, New York, 1994), pp. 220–236. Google Scholar
• 133 J. K. Belknap, Behav. Genet. 22, 677 (1992). Crossref, Google Scholar
• 134 Informative meioses are those in which one can definitively tell if the disease-causing allele has been transmitted from an obligate heterozygote. For a fully penetrant monogenic dominant trait, all meioses occurring in an affected individual are informative. For a fully penetrant monogenic recessive trait, meioses occurring in an obligate carrier are informative if they produce an affected child or if they produce an unaffected child who inherits the disease-causing allele from the other parent. This latter situation occurs in one-third of unaffected children and can be recognized by the use of close flanking markers. Google Scholar
• 135 M. Boehnke, Am. J. Hum. Genet. 39, 513 (1986); D. E. Weeks, J. Ott, G. M. Lathrop, ibid. 47, A204 (1990). Google Scholar
• 136 D. Brown, M. B. Gorin, D. E. Weeks, ibid. 54, 544 (1994). Google Scholar
• 137 C. Cannings and E. T. Thompson, Clin. Genet. 12, 208 (1977); M. Boehnke, M. R. Young, P. P. Moll, Am. J. Hum. Genet. 43, 336 (1988); A. E. Pulver et al., Am. J. Med. Genet. 54, 36 (1994); E. A. Thompson, Theor. Popul. Biol. 24, 39 (1983); Am. J. Hum. Genet. 33, 968 (1981); Biometrics 37, 313 (1981); M. Boehnke, K. H. Omoto, J. M. Arduino, Am. J. Hum. Genet. 46, 581 (1990). In cases involving a disease-causing allele D with high frequency, one may also wish to avoid families with “too many” affected individuals, because there is a high probability that one or both parents is homozygous for D (L. Kruglyak and E. S. Lander, in preparation). Google Scholar
• 138 J. S. Beckman, in Gene Mapping Techniques and Applications, L. B. Schook, H. A. Lewin, D. G. McLaren, Eds. (Dekker, New York, 1991), pp. 201–229. Google Scholar
• 139 D. T. Bishop and J. A. Williamson, Am. J. Hum. Genet. 46, 254 (1990). Google Scholar
• 140 A. Darvasi, A. Weinreb, V. Minke, J. I. Weller, M. Soller, Genetics 134, 943 (1993); Z. B. Zeng, ibid. 136, 1457 (1994). Google Scholar
• 141 R. C. Elston, in Proceedings of the 16th International Biometric Conference, Hamilton, New Zealand, 7–11 December 1992 (Ruakura Conference Center, Hamilton, New Zealand, 1992), pp. 39–51. Google Scholar
• 142 Crossovers are randomly distributed with density N per centimorgan, where N is the number of informative meioses. It follows trivially that the expected distance to the nearest flanking crossover on either side is (1/N) cM. [See also, K. Lange, L. Kunkel, J. Aldridge, S. A. Latt, Am. J. Hum. Genet. 37, 853 (1985); M. Boehnke, ibid. 55, 379 (1994).] Google Scholar
• 143 J. Hastbacka et al., Cell 78, 1073 (1994). Crossref, Google Scholar
• 144 N. Risch, Am. J. Hum. Genet. 53 (suppl.), abstract 185 (1993); L. Kruglyak and E. S. Lander, submitted. Google Scholar
• 145 B. Kerem et al., Science 245, 1073 (1989); J. Hastbacka et al., Nat. Genet. 2, 204 (1992). Crossref, Google Scholar
• 146 In a population founded N generations ago, linkage disequilibrium should be detectable over distances on the order of (100/N) cM. By studying k affected chromosomes, one should be able to localize a disease gene to a region on the order of (100/kN)) cM. (Exact numbers would depend on the precise definition of detection of linkage disequilibrium and localization of a disease gene, but these estimates reflect the scaling with population age and number of affected chromosomes.) Google Scholar
• 147 Traditional construction of congenic strains by repeated backcrossing relies on the fact that an average of 50% of the undesired genome is lost at each generation. By using a complete genetic linkage map, however, one can identify those backcross progeny that have fortuitously lost a larger proportion of the undesired genome and breed them to create the next generation. In only three to four generations, it is possible to eliminate essentially all of the undesired genome. For example, this has been performed to construct congenic strains for the Mom-1 region of mouse chromosome 4 (A. Moser and W. F. Dietrich, personal communication). Google Scholar
• 148 Complementation tests can be performed only between two alleles causing the same recessive phenotype. Accordingly, knockout experiments should target an allele A1 that causes a dominant (or partially dominant) phenotype when placed in trans to a second allele A2; the knockout allele would then be expected to fail to yield the dominant phenotype in the complementation test. Because current gene knockout protocols are limited to a few mouse strains such as 129, one may first need to construct a congenic carrying the desired allele in such a strain before one can construct the appropriate knockout. Google Scholar
• 149 For an insightful historical account of the criticisms of Mendelian theory on the grounds that it cannot explain variation observed in nature, see W. B. Provine, The Origins of Theoretical Population Genetics (Univ. of Chicago Press, Chicago, 1971). Google Scholar
• 150 We thank L. Kruglyak and D. Siegmund for assistance concerning thresholds for significance and C. Amos, M. Boehnke, A. Chakravarti, F. Collins, R. Elston, W. Frankel, D. Fulker, S. Ghosh, S.-W. Guo, H. Jacob, J. Ott, A. Weder, A. Lynn, and members of the Lander laboratory for helpful comments on the manuscript. This work was supported in part by a grant from NIH (HG00098 to E.S.L.). Google Scholar