D. Botstein, R. L. White, M. H. Skolnick, R. W. Davies, Am. J. Hum. Genet.
, 314 (
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.[PubMed][CrossRef][PubMed][CrossRef]
G. J. Dover et al., Blood
, 816 (
1992); S. L. Their et al.
, Am. J. Hum. Genet.
, 214 (1994).[PubMed][PubMed]
D. Easton, D. Ford, J. Peto, Cancer Surv.
, 95 (
1993); D. Ford et al.
, 692 (1994).[PubMed][PubMed]
S. T. Reeders et al.
, Hum. Genet.
, 348 (
1987); G. Romeo et al.
, 8 (1988); A. Turco, B. Peissel, L. Gammaro, G. Maschio, P. F. Pignatti, Clin. Genet.
, 287 (1991).[PubMed][CrossRef][PubMed][CrossRef]
J. Barbosa, H. Noreen, F. C. Goetz, E. J. Yunis, Diabete Metab., 160 (
1976); G. I. Bell et al., Proc. Natl. Acad. Sci. U.S.A., 1484 (1991); D. W. Bowden et al., Am. J. Hum. Genet., 607 (1992); P. Froguel et al., Nature, 162 (1992).
R. Fishel et al.
, 1027 (
1993); F. Leach et al.
, p. 1215; N. Papadopoulos et al.
, 1625 (1994); R. Fishel et al.
, 167 (1994); B. Liu et al.
, Cancer Res.
, 4590 (1994).[PubMed][CrossRef][PubMed][CrossRef]
E. A. De Weerd-Kastelein, W. Keijzer, D. Bootsma, Nat. New Biol.
, 80 (
S. Brul et al.
, J. Clin. Invest.
, 1710 (
1988); J. M. Tager et al.
, Prog. Clin. Biol. Res.
, 545 (1990); J. Gartner, H. Moser, D. Valle, Nat. Genet.
, 16 (1992); N. Shimozaun et al.
, 1132 (1992).[PubMed][CrossRef][PubMed][CrossRef]
R. Ward, in Hypertension: Pathophysiology, Diagnosis, and Management, J. H. Laragh and B. M. Brenner, Eds. (Raven, New York,
1990), pp. 81—100.
E. S. Lander and D. Botstein, Cold Spring Harbor Symp. Quant. Biol., 49 (
C. C. Li, Am. J. Hum. Genet.
, 517 (
1987); P. P. Majumder, S. K. Das, C. C. Li, ibid.
, 119 (1988); S. K. Nath, P. P. Majumder, J. J. Nordlund, ibid.
, in press.[PubMed][PubMed]
Bilineality has been thought to plague many genetic analyses, particularly those involving psychiatric disorders. See, for example, S. E. Hodge, Genet. Epidemiol.
, 191 (
1992); M. Durner, D. A. Greenberg, S. E. Hodge, Am. J. Hum. Genet.
, 859 (1992); K. R. Merikangas, M. A. Spence, D. J. Kupfer, Arch. Gen. Psychiatry
, 1137 (1989); M. A. Spence et al.
, Hum. Hered.
, 166 (1993).[PubMed][CrossRef][PubMed][CrossRef]
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.
D. C. Wallace, Annu. Rev. Biochem.
, 1175 (
1992); J. B. Redman, R. G. Fenwick Jr., Y. H. Fu, A. Pizzuti, C. T. Caskey, J. Am. Med. Assoc.
, 1960 (1993).[PubMed][CrossRef][PubMed][CrossRef]
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).
M. C. Neale and L. R. Cardon, Methodology for Genetic Studies of Twins and Families (Kluwer Academic, Boston,
L. S. Penrose, Acta Genet., 257 (
1953); J. H. Edwards, ibid., 63 (1960); Br. Med. Bull., 58 (1969); N. Risch, Am. J. Hum. Genet., 222 (1 990).
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, 399 (
1918); D. S. Falconer, Introduction to Quantitative Genetics (Longman, New York, 1981).
See also W. R. Williams and D. E. Anderson, Genet. Epidemiol.
, 7 (
1984); D. T. Bishop, L. Cannon-Albright, T. McLellan, E. J. Gardner, M. H. Skolnick, Genet. Epidemiol.
, 151 (1988); E. B. Claus, N. J. Risch, W. D. Thompson, Am. J. Epidemiol.
, 961 (1990).[PubMed][CrossRef][PubMed][CrossRef]
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., 165 (
1912); N. E. Morton, Am. J. Hum. Genet., 1 (1959); W. J. Ewens, ibid., 853 (1982); P. P. Majumder, Stat. Med.,163 (1985); W. J. Ewens and N. C. Shute, Ann. Hum. Genet., 399 (1986); M. R. Young, M. Boehnke, P. P. Moll, Am. J. Hum. Genet., 705 (1988).
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, 223 (
1916); S. Wright, Evolution and the Genetics of Populations: Genetic and Biometric Foundations (Univ. of Chicago Press, Chicago, 1968), pp. 373— 420.
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.
R. R. Williams et al.
, Arch. Intern. Med.
, 582 (
1990); J. V. Selby et al.
, J. Am. Med. Assoc.
, 2079 (1991); R. R. Williams et al.
, Ann. Med.
, 469 (1992).[PubMed][CrossRef][PubMed][CrossRef]
G. Carey and J. Williamson, Am. J. Hum. Genet.
, 786 (
1991); L. R. Cardon and D. W. Fulker, Am. J. Hum. Genet.
, in press; N. J. Schork et al.
, in preparation.[PubMed][PubMed]
E. S. Lander and D. Botstein, Genetics, 174 (
L. Groop and R. DeFranzo, personal communication.
G. A. Barnard, R. Stat. Soc. J., 115 (
1949); J. B. S. Haldane and C. A. B. Smith, Ann. Eugen., 10 (1947); J. Chotoi, Ann. Hum. Genet., 359 (1984).
N. E. Morton, Am. J. Hum. Genet., 80 (
A. W. F. Edwards, Likelihood (Johns Hopkins Univ. Press, Baltimore, MD,
J. Ott, Analysis of Human Genetic Linkage (Johns Hopkins Univ. Press, Baltimore, MD,
1991), pp. 65— 68.
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., 75 (1993); H. Chernoff and E. S. Lander, J. Stat. Plann. Inference, in press.
G. D. Schellenberg et al., ibid., 668 (1992); C. E. Yu et al., Am. J. Hum. Genet., 631 (1994).
E. S. Lander and D. Botstein, Proc. Natl. Acad. Sci. U.S.A.
, 7353 (
1986); N. J. Schork, M. Boehnke, J. D. Terwilliger, J. Ott, Am. J. Hum. Genet.
, 1127 (1993).[PubMed][CrossRef][PubMed][CrossRef]
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.
, 471 (
1984); G. E. Bonney, G. M. Lathrop, J. M. Lalouel, Am. J. Hum. Genet.
, 29 (1988); N. J. Schork, Genet. Epidemiol.
, 207 (1992).[PubMed][CrossRef][PubMed][CrossRef]
J. Ott, Clin. Genet.
, 119 (
1977); F. Clerget-Darpoux, Ann. Hum. Genet. 46, 363 (1982); ______, C. Bonaiti-Pellie, J. Hochez, Biometrics
, 393 (1986); F. Clerget-Darpoux, M. C. Babron, C. Bonaiti-Pellie, J. Psychiatr. Res.
, 625 (1987).[PubMed][PubMed]
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.
, 309 (
1990); C. I. Amos and J. A. Williamson, Am. J. Hum. Genet.
, 213 (1993); S. E. Hodge and R. C. Fiston, Genet. Epidemiol.
, in press.[PubMed][CrossRef][PubMed][CrossRef]
J. Ott, Am. J. Hum. Genet.
, 161 (
1979); J. Edwards, Cytogenet. Cell Genet.
, 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 (1992); R. W. Cottingham Jr., R. M. Idury, A. A. Schaffer, Am. J. Hum. Genet.
, 252 (1993).[PubMed][PubMed]
R. C. Elston and J. Stewart, Hum. Hered., 323 (
Since its introduction, the Elston-Stewart algorithm has been extended and modified in various ways; see, for example, J. Ott, Am. J. Hum. Genet.
, 588 (
1974); K. Lange and R. C. Elston, Hum. Hered.
, 95 (1975); C. Cannings, E. T. Thompson, M. H. Skolnick, Adv. Appl. Probab.
, 26 (1978); R. C. Elston, V. T. George, F. Severtson, Hum. Hered.
N. E. Morton and C. J. MacLean, Am. J. Hum. Genet.
, 489 (
1974); S. J. Hasstedt, Comput. Biomed. Res.
, 295 (1982); G. E. Bonney, Am. J. Med. Genet.
, 731 (1984); S. W. Guo and E. T. Thompson, IMA J. Math. Appl. Med. Biol.
, 171 (1991); ibid.
, p. 149; N. J. Schork, Genet. Epidemiol.
, 73 (1992).[PubMed][PubMed]
L. Kruglyak and E. S. Lander, in preparation.
S. W. Guo and E. T. Thompson, Am. J. Hum. Genet.
1992); D. C. Thomas, Cytogenet. Cell Genet.
, 228 (1992); A. Kong, N. Cox, M. Frigge, M. Irwin, Genet. Epidemiol.
, 483 (1993).[PubMed][PubMed]
For a discussion, see W. C. Blackwelder and R. C. Elston, Genet. Epidemiol.
, 85 (
1985); A. S. Whittemore and J. Halpern, Biometrics
, 118 (1994).[PubMed][CrossRef][PubMed][CrossRef]
N. E. Morton et al., ibid., 201 (1983); R. N. Hyer et al., ibid., 243 (1991); S. S. Rich, S. S. Panter, F. C. Goetz, B. Hedlund, J. Barbosa, Diabetologica, 350 (1991).
J. Davies et al., Nature, in press.
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., 842 (1990)].
K. Lange, Am. J. Hum. Genet.
, 148 (
1986); D. E. Weeks and K. Lange, ibid.
, 859 (1992).[PubMed][PubMed]
W. C. Blackwelder and R. C. Elston, Commun. Stat. Theor. Methods
, 449 (
1982); C. I. Amos and R. C. Elston, Genet. Epidemiol.
, 349 (1989); J. M. Olson and E. M. Wijsman, ibid.
, 87 (1993).[CrossRef][CrossRef]
0. F. Goldgar, Am. J. Hum. Genet.
, 957 (
1990); C. I. Amos, ibid.
, 535 (1994); D. W. Fulker and L. R. Cardon, ibid.
, p. 1092; N. J. Schork and S. Ghosh, submitted.[PubMed][PubMed]
L. P. Ryder, E. Andersen, A. Svejgaard, Eds., HLA and Disease Registry, Third Report (Munksgaard, Copenhagen,
W. E. Braun, HLA and Disease (CRC, Boca Raton, FL,
E. H. Corder et al.
, Nat. Genet.
, 180 (
1994); C. Singer et al.
, Arch. Neurol.
, 13 (1992); F. Schachter et al.
, Nat. Genet.
, 29 (1994); H. Schunkert et al.
, N. Engl. J. Med.
, 1634 (1994); F. Cambien et al.
, 641 (1992).[PubMed][CrossRef][PubMed][CrossRef]
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.
1986); V. T. George and R. C. Elston, Genet. Epidemiol.
, 193 (1987).[PubMed][CrossRef][PubMed][CrossRef]
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.
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.
K. M. Weiss, Genetic Variation and Human Disease (Cambridge Univ. Press, Cambridge,
C. T. Falk and P. Rubinstein, Ann. Hum. Genet.
, 227 (
1987); F. Clerget-Darpoux et al.
, 247 (1988); G. Thompson et al.
, Genet. Epidemiol.
, 43 (1989); J. Ott, ibid.
, p. 127; J. D. Terwilliger and J. Ott, Hum. Hered.
, 337 (1992); M. Knapp, S. A. Seuchter, M. P. Baur, Am. J. Hum. Genet.
, 1085 (1993).[PubMed][CrossRef][PubMed][CrossRef]
R. S. Spielman et al.
, Am. J. Hum. Genet.
, 506 (
1993); S. E. Hodge, ibid.
, 367 (1993).[PubMed][PubMed]
J. Gelemnter et al., ibid., 1801 (
1991); K. Blum et al., Alcohol, 59 (1993); J. Gelernter et al., J. Am. Med. Assoc., 1673 (1993).
D. Goldman et al.
, Alcohol. Clin. Exp. Res.
, 199 (
1993); B. K. Suarez et al.
, 12 (1994); C. N. Pato et al.
, Am. J. Med. Genet.
, 78 (1993); A. Parsian et al.
, Arch. Gen. Psychiatry
, 655 (1991); T. Arinami et al.
, Biol. Psychiatry
, 108 (1993); D. Goldman et al.
, Acta Psychiatr. Scand.
, 351 (1992); S. Schwab et al.
, Am. J. Hum. Genet.
(suppl.), 203 (1991); D. Goldman et al.
, Alcohol. Clin. Exp. Res.
, in press.[PubMed][CrossRef][PubMed][CrossRef]
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.
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.
E. A. Carbonell, T. M. Gerig, E. Balansard, M. J. Asins, Biometrics
, 305 (
1992); Z. W. Luo and M. J. Kearsey, Heredity
, 236 (1992); Z. B. Zeng, Genetics
, 1457 (1994); S. A. Knott and C. S. Haley, ibid.
, 1211 (1992); R. C. Jansen and P. Stam, ibid.
, 1447 (1994); Z. B. Zeng, Proc. Natl. Acad. Sci. U.S.A.
, 10972 (1993); R. C. Jansen, Genetics
, 205 (1993); Theor. Appl. Genet.
, 252 (1992).[CrossRef][CrossRef]
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.
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).
P. C. Groot et al.
, FASEB J.
, 2826 (
1992); C. J. Moen, M. Snoek, A. A. Hart, P. Demant, Oncogene
, 563 (1992).[PubMed][PubMed]
M. Festing, Inbred Strains in Biomedical Research (Oxford Univ. Press, New York,
J. A. Egeland et al.
, 783 (
1987); J. L. Kennedy et al
, 167 (1988); S. D. Detera-Wadleigh et al.
, 391 (1989); J. R. Kelsoe et al.
, 238 (1989); M. Baron et al.
, Nat. Genet.
, 49 (1993).[PubMed][CrossRef][PubMed][CrossRef]
E. Feingold, P. 0. Brown, D. Siegmund, Am. J. Hum. Genet.
, 234 (
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.
A. Rebai, B. Goffinet, B. Mangin, Genetics
, 235 (
1994); W. N. Frankel et al.
, in press.[PubMed][PubMed]
K. K. Kidd and J. Ott, Cytogenet. Cell Genet., 510 (
J. Ott, Proc. Natl. Acad. Sci. U.S.A.
, 4175 (
1989); J. D. Terwilliger and J. Ott, Cytogenet. Cell Genet.
, 142 (1992); M. N. Chiano and J. R. W. Yates, Ann. Hum. Genet.
, 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.
, 803 (1989); A. Kong, M. Frigge, M. Irwin, N. Cox, ibid.
, 1413 (1992).[PubMed][CrossRef][PubMed][CrossRef]
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.
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.
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.
M. Boehnke, Am. J. Hum. Genet.
, 513 (
1986); D. E. Weeks, J. Ott, G. M. Lathrop, ibid.
, A204 (1990).[PubMed][PubMed]
D. Brown, M. B. Gorin, D. E. Weeks, ibid., 544 (
C. Cannings and E. T. Thompson, Clin. Genet.
, 208 (
1977); M. Boehnke, M. R. Young, P. P. Moll, Am. J. Hum. Genet.
, 336 (1988); A. E. Pulver et al.
, Am. J. Med. Genet.
, 36 (1994); E. A. Thompson, Theor. Popul. Biol.
, 39 (1983); Am. J. Hum. Genet.
, 968 (1981); Biometrics
, 313 (1981); M. Boehnke, K. H. Omoto, J. M. Arduino, Am. J. Hum. Genet.
, 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).[PubMed][PubMed]
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.
D. T. Bishop and J. A. Williamson, Am. J. Hum. Genet.
, 254 (
A. Darvasi, A. Weinreb, V. Minke, J. I. Weller, M. Soller, Genetics
, 943 (
1993); Z. B. Zeng, ibid.
, 1457 (1994).[PubMed][PubMed]
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.
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.
, 853 (
1985); M. Boehnke, ibid.
, 379 (1994).][PubMed][PubMed]
N. Risch, Am. J. Hum. Genet.
(suppl.), abstract 185 (
1993); L. Kruglyak and E. S. Lander, submitted.[PubMed][PubMed]
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.)
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).
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.
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,
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.).