Linkage Disequilibrium in Human Ribosomal Genes: Implications for Multigene Family Evolution

Peter Seperack,*” Montgomery Slatkin+ and Norman Arnheim*.*

*Department of Biochemistry and Program in Cellular andDevelopmental Biology, State University of New York, Stony Brook, New York I 1794, ?Department of Zoology, University of California, Berkeley, California 94720, and *Department of Biological Sciences, University of Southern California, Los Angeles, California 90089-0371 Manuscript received January8, 1988 Revised copy accepted April 2 1, 1988

ABSTRACT Members of the rDNA multigene family withina species do not evolve independently,rather, they evolve together in a concerted fashion.Between species, however, each multigenefamily does evolve independently indicating that mechanisms exist whichwill amplify and fix new mutations bothwithin populations and within species. In order to evaluate the possible mechanisms by which mutation, amplification and fixation occurwe have determined thelevel of linkage disequilibrium betweentwo polymorphic sites in human ribosomal genes in five racial groups and among individuals within two of these groups.The marked linkage disequilibriumwe observe within individuals suggeststhat sister chromatid exchangesare much more important than homologousor nonhomologous recombination events in the concerted evolution of the rDNA family and further that recent models of molecular drive may not apply to the evolution of the rDNA multigene family.

HE human ribosomal gene family is composed of ferences among individualsin the geneticcomposition T approximately 400 members which arear- of the multigene family because they create linkage ranged in small tandem clusters on five pairs of chro- disequilibrium among different members of familythe mosomes (for reviews, see LONG and DAWID1980; (OHTA1980a, b;NAGYLAKI and PETES1982; SLATKIN WILSON1982). Each member (Figure 1) is approxi- 1986).Interactions between chromosomes break mately 45,000 bases in length. The spacerregion down linkage disequilibriumand reduce the extentof (NTS) which is adjacentto the coding region and differences among individuals. In the theory of “mo- transcription regulatory signals has no known func- lecular drive”(DOVER 1982) it has been suggestedthat tion. transposition, gene conversion, and unequal crossing There is already evidencethat the humanribosomal over are possibly more important than natural selec- gene family evolves in a concerted fashion. Individual tion for the evolution of multigene families because members of the family in humans are much more soon after a variant arises, molecular drive tends to similar to one another than they are to members of limit the amount of variation among individuals on the rDNA family in other primates (ARNHEIMet al. which natural selection can act. We will show here 1980).Several mechanisms havebeen proposed to that there are substantial differences among individ- explain the relative homogeneity of rDNA and other uals in the rDNA family which is consistent with the multigene families despitethe fact that individual idea that interactions within chromosomes are much family members would beexpected to accumulate morefrequent than interactions betweenchromo- mutations independently of the others (for reviews, somes and that natural selection could contribute to see ARNHEIM 1983;DOVER 1982). Gene conversion, frequency changes in newly arising variants. unequal crossing over, and natural selection could all account for concerted evolution in the rDNA family. MATERIALS AND METHODS Because rDNA is notinterspersed throughout the genome, transposition is probably notimportant. Samples and DNA analysis: ALLANC. WILSON(Univer- What is at present unknown is whether gene conver- sity of California, Berkeley) supplied the aborigine DNA sion and unequalcrossing over occur primarilywithin samples andHAIG KAZAZIAN (The Johns Hopkins University Medical School) provided the Asian Indian, black, Chinese achromosome (ie., sister chromatidexchanges) or andMediterranean DNA. All DNA werederived from primarilybetween either homologous or nonho- unrelated individuals. DNA were digested with restriction mologous chromosomes. Frequent interactions within enzymes accordingto the manufacturer’s recommendations. chromosomes would tend to produce substantial dif- Gel electrophoresis,Southern transfer and hybridization with a 28s ribosomal DNA probewere carried out as

I Present address: BRI-Basic Research Program, NCI-Frederick Cancer described previously (ARNHEIMet al., 1980). Research Facility, P. 0. Box B, Frederick, Maryland 21701. Quantitative determination of rDNA haplotype fre-

Genetics 119: 943-949 (August, 1988) 944 P. Seperack, M.and Slatkin N. Arnheim quencies: After Southern transfer andhybridization the 1984; NEI and ROYCHOUDHURY1982; CANN,BROWN nitrocellulose filters were exposed for either 6, 18 and 48 and WILSON 1982; JOHNSON et al. 1983). The BglII hr or 18,48 and 96 hron XS-5 film (Kodak) without intensification. For each exposure each lane was scanned site most likely arose as a point mutationin one rDNA twice using a Zeineh SoftLaser scanning densitometer genethat contained aparticular length variant. (LKB) with a tungsten lamp. Peak heights (PH) for each Therefore, measuring the frequency of the BglII site fragment in each gel lane were measured and values for in association with the closely linked length variation duplicate scans were averaged. Deviations from linearity region within andamong populationscan directly seen in the three different exposures of the same gel (due to film saturation and detector saturation)were determined assess thetempo and mode of the mechanism of and corrected, based on exposure time. The frequency of concerted evolution. rDNA repeats in each band in each exposure was deter- Figure 1B shows diagramatically how a Southern mined as follows. The ratio of the peak heights (a,) for type blot of a BglII-Hind111 digest of human DNA can 1, 2 and 3 fragments relative to the constant bands in each reveal each of the 10 possible haplotypes that result lane was determined: fromthe combination of 5 lengthvariants a, = PH;/PHc. (LVO LV4)and the two formsof the BglII poly- The frequency of each band (F,) was then determined by morphism (+/-). Densitometric tracingsof these blots dividing the ratio of the peak height to the constant band can then be used to determine thefrequency of each of each fragment (ai)by the sum of all ratios of all bands in haplotype. each lane: The degree of linkage disequilibrium is measured E = a,/C a, by comparing the observed frequency of each haplo- 3 type with that expected if the two markers segregated Using this method we have corrected for variation be- independently in the population. To examinethe tween lanes due to loading errors and amount of probe degree of linkage disequilibrium in several popula- hybridization to differentially digestedDNA. The corrected tions we pooled DNA samples fromindividuals of frequencies for each band in each of the three different exposures were averaged to give the frequency for the bands each population. Altogether we examined 20 Austra- presented in Tables 1 and 2. lian aborigines (8000 genes), 14 Asian Indians (5600 genes), 17 individuals of African descent (6800 genes), RESULTS 16 Chinese (6400 genes) and 17 Mediterranean individuals (6800 genes). All of the individuals used in The approximately 400 rDNA genes in any given this study were unrelated. The results are seen in human are notidentical. A number of DNA polymor- Figure 2. Table 1 summarizesthe percentagesof each phisms involving restriction enzyme sites and length haplotype in each population. In general the distri- variation have been described (ARNHEIMand SOUTH- bution of length variant haplotypesare approximately ERN 1977; KRYSTALand ARNHEIM 1979; LAVOLPE the same in all populations with some notable excep- et al. 1985; WILSONet al. 1982; KRYSTALet al. 198 1; tions. The LVO length variant is found only in aborig- HIGUCHIet al. 198 1; RANZANI, BERNINI andCRIPPA 1984; SEPERACKand ARNHEIM 1982).The locations ine, Mediterranean and Chinese populationswhile the of several of thesepolymorphisms are shown in Figure LV3 variant is twice as common in blacks as in the 1A. We used two of these polymorphisms, a length other populations. The number of genes containing variation region and a restriction enzyme site to ex- the BglII site also varies among these groups (Table amine for thefirst time the degreeof linkage disequi- 1). librium between markers in members of a multigene These data were used to calculate the extent of family. In higher primates the length variation region linkagedisequilibrium between lengthvariants and is found in humans, chimpanzeesand pygmy chimpan- the BglII polymorphism. Because LV2 is in relatively zees (ARNHEIMet al. 1980). The BglII restriction high frequency in all population samples, a convenient enzyme site polymorphism, however, is human spe- way to quantify the extent of linkage disequilibrium cific (SEPERACKand ARNHEIM1982) and its increase is obtained by pooling the frequencies of the other in frequency in populations or in individuals could length variants and using the standard measure for only result by the mechanisms responsible for con- two alleles at each of two loci, D’, which is the ratio certed evolution in general (ARNHEIM 1983; SEPER- of the actual disequilibrium to the maximum possible ACK and ARNHEIM1982). Itis difficult to estimate the given those allele frequencies(LEWONTIN 1964). exact time at which the mutation generating theBglII Those values are also shown in Table 1. The values site in human rDNA occurred. Since the mutation is of D‘ indicatea nonrandom association of length human specific, it must have occurred after the hu- variants and the BglIl restriction site. Whether there man/chimpdivergence about 6-7 X lo6 yr before is a nonrandom association of different haplotypes on present,but before the divergence of the various chromosomes,cannot be assessed directly with our racial groups which is estimated to bebetween 50,000 methods (see however, DISCUSSION). and 500,000yr before present (SIBLEYand AHLQUIST That thevalue of D’ in each population is different L inkage DisequilibriumrDNA Linkage 945

B 8-1 I 8-2 H!nd Ill "1xxxxx LUO -LUO -LUl -LU2 - LU3 -J-xxxxx- A Hlnd II -LUO :// €eo R I 991 II MS I -LUi - xxx 8-2 Hind Ill LU2 + I. I - LU I -LU3 + LUi + \I-- \,-x- FIGURE1 ."A. Representation of a rDNA family member including the position of restriction sites that are polymorphic in the human population. ETS, external transcribed spacer; 18,I 8s gene: ITS, internal transcribed spacer; 28,283 gene; NTS. nontranscribed spacer. The polymorphic restriction enzyme sites are indicated. The BglIl site, originally thought to be monomorphic (KRYSTALand ARNHEIM1979) has recently been documented as being polymorphic (SEPERACKand ARNHEIM1982). The region of length variation in the NTS is denoted by XXX. B, Diagram of how the HindlII-Bglll double digest pattern of rDNA can reveal all 10 length variant-BgllI polymorphism haplotypes. The positions of the monomorphic Hind111 site 3' to the polymorphisms and the monomorphic Bglll site (B-1) 5' of them in the 28s gene are indicated. The positions of monomorphic BamHI sites are also shown (*). For any particular one of the 5 length variants, double digestion with RgllI and Hindlll will release either one of two fragments; the longer represents those genes without the B-2 site, while the shorter must be derived from genes with the site. The difference in length is equal to the number of bases between B-2 and the Hindlll site. Fach length variant differs from the next larger and smaller one by about 700 base pairs (KRYSTALand ARNHEIM1979; LA VOLPEet al. 1985; SCHMICKELet al. 198 1). Thus digestion of a DNA sample with equal amounts of all 5 length variants will produce two sets of bands. One represents the 5 length variants without the BglII site and forms a ladder with rungs 700 bases apart. The second set of rungs, also 700 bases apart, will represent those genes without a BglII site. Because the Bglll (B-2) and Hind111 sites are only 2.5 kb apart the two sets of rungs overlap slightly. In this figure the digestion products of the largest (LVO) and smallest (LV4) length variants and the position that the LVO+. LVO-. LV4+ and LV4- products take in the gel relative to the products of the other length variants is shown.

A I B C M from 1 .O indicates that both polymorphisms have been 12345878910 present for sufficiently long in humans that there has been time for recombination to partially disassociate the length variants from theBgZII polymorphism. This is not unexpected given that the rDNAfamily evolves in a concerted fashion (see ARNHEIM 1983; DOVER I 1982) by means of genetic interactions. Thus recombination between two rDNA arrays thatare unequally aligned would contribute not only to the concerted evolution of the family but to a reduction in the level of disequilibrium if the event occurred in the DNA segment between the lengthvariant and the BgZII polymorphism (OHTA1980b). FIGURE2.-Analysis of rDNA haplotypes in 5 racial groups. A, Our population data however suggest that such a Australian aborigines; I, Asian Indians; B. blacks, C, Chinese; M, Mediterranean. DNA from all of the individuals studied in each simple interpretation cannot be correct.The fact that group were pooled by adding equal weights. Five to seven micro- the signs of the D' values are different in different grams of DNA from each pool was digested with BglII and Hind111 populations (for example D' = +0.233 for aborigines and run in the odd numbered lanes. An equal amount from each and D' = -0.249 for blacks) is totally unexpected if pool was digested with BamHI and runin the even numbered lanes. After southern transfer, hybridbation was carried out with a 28s linkage disequilibrium were being broken down in the RNA probe. The BamHl digestion products reveal the frequency same way in all populations. of the length variants independent of the EglII polymorphism. Linkage disequilibrium at the population level may Theseare the type 1 fragments. The lowest molecular weight be due in part to linkage disequilibrium within each fragment (C) in both odd and even lanes is a portion of the 28s individual. To examine this possibility two of the gene which hybridizes to the probe. The 28s piece in the Bglll- Hindlll digest is slightly smaller than the BamHl product. In the populations were studied in more detail. We examined odd numbered lanes two sets of fragments are seen above the 28s the DNAs ofindividual blacks and Asian Indians. The piece. The type 3 fragments represent the length variants without results for 12 Asian Indian individuals are shown in the BglII site while the type 2 fragments came from genes containing Figure 3. To test for linkage disequilibrium within the B-2 site. each individual, we calculated a x' on thecontingency table of gamete types. The x* value is closely related 946 P. Seperack, M. Slatkin and N. Arnheim TABLE 1 Percentages of haplotypes in DNAs from five populations

Lvo+/Lvo- LV I +/LV 1 - Lvz+/LVz-Lv3+/Lv3-Lv4+/Lv4- bgI+ D'

Aborigine 1.115.6 4.818.7 36.7119.7 8.416.8 4.514.80.233 55.5 Indian 010 7.913.6 46.119.6 17.015.8 7.512.30.192 78.7 Black Africans 010 8.7510 40.816.2 31.514.1 8.610 89.7 -0.249 Chinese 3.4511.45 12.113.7 49.715.8 17.512.05 4.810 0.192 87.0 Mediterranean 4.110 7.610 48.719.9 13.416.8 9.510 83.3 -0.0 16 Average 1.7311.41 44.4110.248.2313.2 17.5615.10.121 1 78.86.9811.42 The percentage of each of the ten haplotypes among the total numbers examined is given in each row. The averages for all populations and the frequencies of all haplotypes with Bglll site 8-2 (bgl+)are also given. D' is the measure of the linkage disequilibrium as described in the text. Thesedata were obtained from densitometric tracings of autoradiographs as explained in MATERIALS AND METHODS.

FIGURE3.-Analysis of rDNA haplotypes in individual Asian Indians. The mmples in the even numbcrcd lanes were digested with BamHl. The Bglll-Hind111 digests were run in the odd numbered lanes. tothe pairwise linkage disequilibrium coefficients. ent individuals correspond to samples from different When there are only two alleles at each locus, x2 = populations. ND/(p~g~p:!q:!),where D is the linkage disequilibrium, Linkage disequilibrium between single-copy loci in N is the number of individuals sampled and the p's subdivided populations has been examined in detail and 9's are the allele frequencies. To compute a x2 by PROUT (1973) and others. For simplicity, we will value for each individual, the percentages of each discuss only the case with two alleles at each of two haplotype were converted into counts by assuming loci. Let one locus have alleles A and a and the other that every individual had exactly 400 copies of the B and b. Let xy be the frequency of four gametic types rDNA gene, and then the countswere treated asbeing (AB, Ab, aBand ab) in the jth population (i = 1 - -4, in a 2 X n contingency table, where n is the number j = I. - .m,where m is number of local populations). of length variants in nonzero frequency in that indi- Let pj and 9, be the frequencies of A and B in popu- vidual. These values and the appropriate numbersof lation j (pj = xIj + xzj, 9, = xIj + x3,), and let xi. be the degrees of freedom are shown in Table 2 and indicate gamete frequencies averaged overpopulations: that there is significant linkage disequilibrium among 1" repeats within every individual. Most of the x2 values xi. = - xij. were sufficiently large that the tests would indicate m significant linkage disequilibrium even if an individual The linkage disequilibrium between these two loci in had many fewer than 400 copies of the rDNA gene. population j is Dj = x1jx4j - ~2~x3,and the linkage We also could test whether the linkage disequi- disequilibrium in the collection of populations is DT = librium detected in each population was due entirely x1.x.I. - x:! x3. In the present study, DT corresponds to linkage disequilibrium within individuals or to the linkage disequilibrium estimated from the pop- whether there is an among-individual component as ulation data (Table 1). well. To doso, we used the existing theory of linkage The main results from the theory of linkage dise- disequilibrium between two single-copy loci in a sub- quilibrium in a subdivided population is that the net divided population. For our purposes,a sample of linkage disequilibrium DT can be expressed as the sum haplotypes from a single individual corresponds to a of components due to linkage disequilibrium within sample from one population and samples from differ- each population, Dw, and a component due to covar- rD N A Linkage Disequilibrium Linkage rDNA 947

TABLE 2

Percentages of haplotypes in individual samples

Indians Indiv. NO. LVO+/LVO- Lvi+/Lvi- LV~+/LV~- LV~+/LV~- LV~+/LV~- bgl+ X2 d.f.

1 010 8.110 46.410 18.9113.5 11.911.3 85.2 113.1** 3 2 1.810 14.419.5 34.410 24.317.0 8.610 83.5 4 76.0** 3 7.910 6.010 28.017.1 32.919.6 10.510 83.3 4 24.9** 4 010 12.110 54.112.7 6.616.9 8.2111.1 79.3 141.3** 3 5 010 010 75.316.9 17.710 010 93.1 6.4* 1 6 010 014.2 44.4112.5 16.710 15.017.1 76.2 78.5** 3 7 010 4.6510 63.216.11 2 .o/o 6.610 93.9 11.9* 3 8 010 5.7512.95 49.915.1 25.010 10.711.65 90.5 34.8** 3 9 5.610 17.713.8 39.6112.4 15.810 5.1/0 83.8 29.6** 4 10 010 2.710 36.8110.0 23.610 26.7/0 90.0 3 50.4** 11 010 3.518.5 29.712 1.5 15.1111.8 5.1/4.9 53.33 13.5* 12 010 24.610 56.310 15.510 3.7/0 100.0 0 Ave. 1.2710 8.2912.41 46.517.02 19.4314.07 9.3412.17 84.83 Blacks 1 010 016.45 31.118.75 25.310 28.3410 84.8 188.1** 3 2 010 19.810 33.8510 28.05118.3 010 81.7 103.7** 2 3 010 7.810 42.916.1 17.810 12.410 493.9 28.1 4 6.310 9.610 40.115.95 27.410 6.610 94.05 29.6**b 5 5 010 010 22.3122.7 34.917.9 12.310 69.4 66.9** 2 6 7.0510 010 49.5118.1 19.116.15 01010.0* 75.75 2 7 010 6.610 38.510 38.314.3 12.210 95.7 24.2** 3 8 010 010 28.6119.6 36.710 15.610 80.4 105.1** 2 9 010 010 36.717.35 23.011 1.3 2 1.610 81.35 2 38.7** 10 010 010 34.410 35.7517.6 23.210 92.4 43.3** 2 11 010 15.410 29.9116.7 25.410 12.610 82.3 91.9** 3 12 010 1 1.910 53.018.6 15.010 1 1.410 91.4 3 23.4** 13 010 25.910 29.510 22.918.9 9.010 91.1 83.7** 3 Ave. 1.0310 7.7410.50 36.1818.76 26.8914.96 12.7110 86.20" These data were obtained from autoradiographs in the same manner as described for the data in Table 1. The degree of linkage disequilibrium as measured by the x' value from the 2 X n table (see MATERIALS AND METHODS) and the significance levels are shown. The individuals represented in this table are not those represented in Table 1 but the extent of linkage disequilibrium as measured by D' is consistent with the corresponding values in Table 1. The values of D' computed from the average haplotype frequencies in this table are 0.158 for Indians and -0.305 for black Africans, which are close to the values of 0.1 92 and -0.249 in Table 1. *P<0.01;**P<0.001. a Includes a unique length variant at 17.6%. Includes unique length length variant at 3.95%. ' Includes both unique length variants. iation in allele frequencies in different populations: quencies of length variants and the BgZII recognition site we computed the correlation coefficient between DT = Dw + cov(p,q), (1) the frequency of the LV2 lengthvariant with the where presence or absence of the BglII site. We computed the product moment correlation coefficient, r, as the 1" Dw = - D, ratio of the covariance computedfrom (2) tothe n j=l product of the standard deviations of the frequencies. For both the Indian andblack populations, r was small is the linkage disequilibrium within each population, (r = 0.066 for Indians, and r = -0.052 for blacks) 1" and indicates that there is no significant association cov(P,q) = - C (P, - j)(qj - B), (2) between LV2 and either the presence or absence of n j=l the BglII restriction site. Therefore, the linkage dise- and j and 4 are the frequencies of A and B averaged quilibrium found at the population level, the values over populations. These results were first derived in of D' in Table 1, are probably due entirely to linkage general form by PROUT(1 973). disequilibrium within each individual. Our analysis of the data in Table 2 shows that there It is important to realize that the contribution of is significant linkage disequlibrium within each indi- the covariance between individuals in allele frequen- vidual. To test for significant covariation of the fre- cies to the total linkage disequilibrium may be small 948 P. Seperack, M. Slatkin and N. Arnheim even though there is a significant variation among interchromosomal events substantial linkage disequi- individuals in those allele frequencies. A significant librium between polymorphic sites would be main- covariance indicates a nonrandom association of al- tained by a balance between genetic drift and recom- leles in different individuals. In Table 2 we see that bination. there is substantial variation among individuals in the Direct evidence showing that a single human chro- frequencies of both the length variants and the pres- mosome can in fact have only one repeat type comes ence or absence of the BglII restriction site yet the from the analysis of mouse-human hybrid cells which small values of the correlation coefficients we found carry only a single human rDNA containing chromo- indicate that these two polymorphisms are randomly some (KRYSTALet al. 1981; SCHMICKELet al. 1981; associated in different individuals. NAYLORet al. 1983). Since any one individual has no The observation of linkage disequilibrium within morethan 10 such blocks or nucleolus organizers, black and Asian Indian individuals provides more some haplotypes may not be represented in a partic- information about the possible mechanisms responsi- ular individual, anddifferent individuals will have ble for that linkage disequilibrium and possibly for different combinations of these blocks. Asian Indian the past spread of both of these polymorphisms in #5 is missing 3 of the 5 length variants. Blacks #3 and humans. Table 2 shows that thelinkage disequilibrium #4 each containa different novelclass of length within individuals is due primarily to the absence of variant which accounts for 3.95% of the former's and haplotypes that would be present if there were com- 17.6% of the latter's rDNA genes. plete linkage equilibrium. For example, Asian Indian Our data do not allow us to determine whether the individual #1 is missing both the LV1- and LV2- interactions between sister chromatids result primarily haplotypes. Assuming 400 repeats per individual, the from gene conversion or from unequal crossing over. expectednumber of LV2- haplotypes is approxi- However, a single gene conversion event will affect mately 27, and theabsence of any repeats of that type only one or a few repeats whereas unequal crossing is largely responsible for the large x' value for that over can result in the duplication or elimination of individual. We estimate that 4-6 copies of any haplo- several repeats at once. Consequently we suggest that type would be easily detected in our assay system. unequal crossing over has been a far more important process in primate rDNA evolution.The rDNA family DISCUSSION as a whole evolves in aconcerted fashion because Our analysis of linkage disequilibrium in popula- rarer recombinationevents between homologs and tions led to the finding that the disequilibrium was between rDNA blocks on nonhomologous chromo- based upon variation within rather than between in- somes will homogenize the entire rDNA family on a dividuals. This needs to be explained within the con- longer time scale (ARNHEIM 1983). text of the concerted evolution of the rDNA family Our data would seem to exclude natural selection as a whole. There are several kinds of genetic inter- as being responsible for linkage disequilibrium within actions that must contribute to the concerted evolu- individuals. Different individuals are missing different tion of the ribosomal RNA familyin man and the haplotypes, suggesting that there is no haplotype that higher apes. In these taxa rDNA has a multichromo- is highly deleterious. Most of the missing haplotypes soma1 distribution, so interactions between family are missing the BglII site because that is in much lower members on homologous as well as non-homologous frequency butthere are a fewmissing haplotypes chromosomes must occur (ARNHEIMet al. 1980). Our which do contain the site. The same argument sug- linkage disequilibrium data suggest that genetic inter- gests that biased gene conversion doesnot signifi- actions between sister chromatids occur much more cantly contribute to the observed patterns of linkage frequently than interactions among homologous and disequilibrium. nonhomologous chromosomes. The reason is that Our observation of variation in haplotype frequen- only interactions within chromosomes (i.e., between cies among individuals is inconsistent with one of the sister chromatids) can account for the within-individ- tenents of the hypothesis of molecular drive (DOVER ual linkage disequilibrium we have found. Recombi- 1982). In this theory it is supposed that when a new nation events occurringbetween sister chromatids will variant arises in a member of a multigene family any homogenize each tandem array independently of the increase in frequency of the variant gene in the family others, thus tending to create blocks primarily con- will occur in all of the individuals of the population in tainingone of the length variant-BglII haplotypes. a parallel fashion thus minimizing any potential effect The results of OHTA (1 980b) supportour conclusion. of natural selection on the frequency of the variant She modeled the effects of unequal and reciprocal when it is rare in the population. Therefore onewould crossing over in a multigene family on a single chro- not expect between-individual differences in the fre- mosome and found that when the rate of intrachro- quency of a variant gene. Our results show clearly mosomal events was muchhigher than the rate of that such differences do exist in the case of the human rD NA Linkage Disequilibrium Linkage rDNA 949 rDNA family and in fact that some individuals can A. DE FALCOand E. BONCINELLI,1985 Molecular analysis of possess significant frequencies of variants very rare in the heterogeneity region of the human ribosomal spacer. J. Mol. Biol. 183: 213-223. the population as a whole (Table 2, black individuals LEWONTIN, R. C.,1964 The interaction of selection and linkage. 3 and 4). Thus natural selection may in principle be I. General considerations, heteroticloci. Genetics 49 49-67. able to alter the frequency of variant members of a LONG,E. O., and 1. B. DAWID,1980 Repeated genesin eucaryotes. multigene family not long after their appearance in Annu. Rev. Biochem. 49 727-764, the population. NACYLAKI,T., andT. D. PETS, 1982 Intrachromosomalgene conversionand the maintenance of sequence homogeneity We thank ALLANC. WILSONand HAIC KAZAZIAN for generously among repeated genes. Genetics 100: 315-337. supplying DNA. We thankG. J. THOMPSONfor helpful discussions NAYLOR,S. L., A.Y. SAKACUCHI,R. D. SCHMICKEL,M. WOOD- and T. OHTA,J. B. WALSHand L. VAWTERfor helpful comments WORTH-GUTAIand T. B. SHOWS,1983 Organization of rDNA onthe manuscript. P. K. S. alsothanks NANCY RICE (BRI-Basic spacer fragment variants among human acrocentric chromo- Research Program NCI-FCRF) for supplying laboratory space dur- somes in somaticcell hybrids. J. Mol. Appl. Genet.2: 137-146. ing the completion of this project. This workwas supported in part NEI,M., and A. K. ROYCHOUDBURY,1982 Geneticrelationship by a National Institutes of Health grant (N. A.) and in part by a and evolution of human races. Evol. Biol. 14: 1-59. National Science Foundation grant (M.S.) OHTA,T., 1980a Evolutionand Variation of MultigeneFamilies (Lecture Notes in Biomathematics, No. 37). Springer-Verlag, New York. 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