Genetic Epidemiology 17:165–173 (1999)

© 1999 Wiley-Liss, Inc.

Effect of Inbreeding Avoidance on Hardy-Weinberg Expectations: Examples ofNeutral and Selected Loci

Andrea Robertson, 1 Deborah Charlesworth, 2* and Carole Ober 1

1Department of Human Genetics, The University of Chicago, Chicago, Illinois2Department of Ecology and Evolution, The University of Chicago,Chicago, Illinois

Although all human populations avoid close inbreeding, the effect of inbreedingavoidance on genotype proportions has not been formally considered. This paperexamines the expected proportions of genotype frequencies after adjusting the Hardy-Weinberg model for close inbreeding avoidance in an inbred population. This cor-rected model was used to evaluate genotype distributions for HLA haplotypes andhaplotypes created from three microsatellite loci on human chromosome 13 in asample of 315 married Hutterites. In this sample, there were five individuals whowere homozygous for an HLA haplotype and 15 individuals who were homozygousfor a chromosome 13 haplotype. The expected numbers of homozygotes were 21 forHLA and 26 for chromosome 13 haplotypes using a model adjusted for overall in-breeding (P = 0.00031 for HLA and P = 0.019 for chromosome 13) and 18 for HLAand 22 chromosome 13 haplotypes using a model adjusted for both overall inbreed-ing and close inbreeding avoidance (P = 0.0016 for HLA and P = 0.099 for chromo-some 13). The model that takes into account both overall inbreeding and inbreedingavoidance provided a better fit to the observed genotype distributions for chromo-some 13 haplotypes (P = 0.099), suggesting that nonrandom aspects of Hutteritemating structure, other than inbreeding and inbreeding avoidance, have small effectson genotype distributions in the population. The fact that significant deficiencies ofHLA homozygotes persist after taking into account inbreeding avoidance furthersuggests that factors related to the HLA haplotype per se influence the genotypeproportions at HLA loci in the Hutterites. Genet. Epidemiol. 17:165–173, 1999.© 1999 Wiley-Liss, Inc.

Contract grant sponsor: NIH; Contract grant number: HD21244.

*Correspondence to: Carole Ober, Ph.D., Department of Human Genetics, The University of Chicago,924 E. 57th Street, Chicago, IL, 60637. E-mail: carole@genetics.uchicago.edu

Deborah Charlesworth is currently at ICAPB, University of Edinburgh, Edinburgh, UK.

Received for publication 12 January 1998; revision accepted 7 October 1998

166 Robertson et al.

Key words: HLA; inbreeding avoidance; Hardy-Weinberg expectations; mating structure

INTRODUCTION

A deficiency of homozygotes for the 5-locus (serologically defined) HLA hap-lotype was previously reported in the Hutterites [Kostyu et al., 1993]. In that study,observed genotype proportions were compared to Hardy-Weinberg expectations thatwere adjusted for overall inbreeding. Using an average inbreeding coefficient of 0.0396in a sample of 852 adult Hutterites, the expected number of homozygotes for the 5-locus (serologically defined) HLA haplotype was 68 compared to 24 homozygotesobserved (P < 0.00001). Although the expectations were adjusted for overall inbreed-ing, otherwise random mating was assumed. However, all human populations avoidmating with close relatives, but the effect of such inbreeding avoidance on Hardy-Weinberg expectations has not been previously explored.

In the Hutterite community, marriages between first cousins are discouraged(and rare) and marriages between closer relatives are taboo. For example, in a sampleof 411 Hutterite spouses, there were no marriages among first cousins [Ober et al.,1997]. Because individuals who are related to each other as first cousins or closerwill share proportionally more of their genes than less related individuals, assumingrandom mating between this component of the population will increase the expectedproportion of homozygotes. The purpose of this study was to quantitate the effectsof inbreeding avoidance on homozygosity levels in the Hutterites and to determinewhether inbreeding avoidance per se could account for the previous observation ofdeficiencies of HLA homozygotes in this population. We first examined the effectsof such close matings on the frequency of homozygotes and then adjusted expecta-tions for inbreeding avoidance. To further test the effect of inbreeding avoidance ongenotype frequencies in the population, haplotypes were constructed from micro-satellite loci on chromosome 13 and used as an “internal” control that was assumedto be selectively neutral. We demonstrate that the Hardy-Weinberg model adjustedfor inbreeding avoidance provides a better fit to the observed genotype distributionsat a “neutral” locus but that a significant deficiency of HLA homozygotes persistsafter taking into account inbreeding avoidance. Thus, the deficiency of HLA ho-mozygotes previously observed in this population cannot be explained by close in-breeding avoidance and suggests that factors related to the HLA haplotype per seinfluence genotype distributions at these loci.

MATERIALS AND METHODS

Sample Composition

A sample of 434 married Hutterites was selected for this study from a largersample of Hutterites who have participated in studies of HLA and fertility [Ober etal., 1998]. All married individuals in our database who met the following criteriawere studied: (1) DNA was available for genotyping at three tightly linkedmicrosatellite loci on chromosome 13, (2) HLA haplotypes were known or could bedetermined, and (3) family data were available for the construction of haplotypes.Three hundred thirty-five individuals met this criteria.

Of these 335 adult Hutterites, 315 individuals could be assigned unambiguous

Effect of Inbreeding on Hardy-Weinberg Expectations 167

3-locus haplotypes for the chromosome 13 microsatellite loci, D13S318, D13S144,and D13S1324, by direct observation of alleles segregating in families. The remain-ing 20 individuals could not be assigned unambiguous haplotypes because of miss-ing family information and these individuals were eliminated from subsequentanalyses. HLA haplotypes comprised of 16-loci from HLA-G to HLA-DPB1 wereknown for 299 of the 315 subjects [Weitkamp and Ober, 1999]. In the remaining 16individuals, HLA haplotypes were determined using three HLA region microsatellites,D6S265, MICA, DQ.CAR [Foissac et al., 1997] and information on the HLAhaplotypes of their parents. Thus, our final sample included 315 married Hutterites(157 wives, 158 husbands) in whom haplotypes were known for both HLA and chro-mosome 13 haplotypes.

HLA and Chromosome 13 Haplotypes

The HLA region spans approximately 4 Mb [Campbell and Trowsdale, 1993]and 0.9 cM [Dawson et al., 1995]. A detailed description of 16-locus HLA haplotypedistributions and typing methods used in the Hutterites is reported elsewhere[Weitkamp and Ober, 1999]. Three microsatellite loci on chromosome 13 (D13S318,d13S144, D13S1324) were used to represent a control haplotype that was not linkedto HLA. Marker order for these three loci was determined by STS content mapping.Approximate physical distances were estimated based on YAC lengths. Recombina-tion fractions were determined by direct observation of recombinant events in aHutterite pedigree of 361 individuals who participated in our genetic studies of asthma[Ober et al., 1998] and genetic distances were determined using the CRIMAP soft-ware. Based on these studies, we determined that the three chromosome 13 loci spana distance of approximately 2.8 Mb and 3 cM.

Expectations of Homozygote Frequencies

The expected proportion of homozygotes for the HLA and chromosome 13haplotypes were calculated in two ways. First, the Hardy-Weinberg model, adjustedfor overall inbreeding but assuming otherwise random mating, was used to calculatethe expected frequency of homozygotes for each haplotype, using the equation:

pi2(1 – F) + piF

where pi = the frequency of haplotype i and F = the average inbreeding coefficient.In this sample of 315 adults, F = 0.0306. Expectations were summed over allhaplotypes and multiplied by the number of subjects in the study (N = 315) to deter-mine the expected number of homozygotes in the sample.

The second method included an additional correction for inbreeding avoidance.To determine the effect of avoidance of first cousin and closer marriages, we deter-mined the contribution that these matings would have on the frequency of homozy-gotes, if such matings existed. In finite populations, such as the Hutterites, the kinshipcoefficient between first cousins will be > 0.0625, because they are likely to havemore than two common ancestors. To estimate the proportion of the sample of 315Hutterites that was related to each other as first cousins or closer, kinship coeffi-cients were determined for all possible pairs of unlike sex individuals in the sampleusing the algorithm of Boyce [1983]. For the 46,689 possible pairs, the smallest

168 Robertson et al.

kinship coefficient observed between first cousins was 0.0795, suggesting that inthis population marriages between individuals with a kinship coefficient of ≥0.0795,would be avoided. This accounted for 5.37% of all possible unlike sex pairs in oursample. The median kinship coefficient among these “avoided” pairs was 0.10 (s.d.= 0.062) To determine the expected proportion of homozygotes taking into accountavoidance of close relatives, we determined the expected proportion of homozygotesproduced by first cousin or closer relatives and subtracted this contribution from theexpected proportion of homozygotes using a random mating model. The expectationwas calculated as:

(1 – Q) × [(pi2(1 – F) + piF)] – Q × [pi

2(1 – f) + pif],

where F is the average inbreeding coefficient in the population (= 0.0306), f is theaverage inbreeding coefficient among Hutterites related as first cousins and closer (=0.10), and Q is the proportion of marriages between first cousins and closer relativesthat are avoided (= 0.0537). Therefore, the expected proportion of homozygotes inour sample, adjusting for both inbreeding and inbreeding avoidance, is:

(1 – 0.0537) × [pi2(1 – 0.0306) + pi (0.0306)] – 0.0537 × [pi

2(1 – 0.1) + pi (0.1)]

RESULTS

In the 315 Hutterites in this sample, there were 52 unique HLA haplotypes and55 unique chromosome 13 haplotypes. The median haplotype frequency was 0.0188(range, 0.00167–0.0853) for HLA and 0.00635 (range, 0.00159–0.117) for the chro-mosome 13 haplotypes (Fig. 1). The medians and overall distributions of the HLAand chromosome 13 haplotype frequencies were similar (Median Test, P = 0.208;Kruskal-Wallis test, P = 0.087).

The expected frequencies of homozygotes for the HLA and chromosome 13haplotypes after correcting for inbreeding and inbreeding avoidance are shown inTable I. The overall expected and observed numbers of homozygotes for HLA andchromosome 13 haplotypes are shown in Table II. Among the 315 married Hutterites,21 homozygotes for HLA haplotypes were expected under a random mating model,whereas 18 were expected after correcting for inbreeding avoidance. In this sample,only five homozygotes for the HLA haplotype were observed (χ2 = 13.0, P = 0.00031for random mating model; χ2 = 9.96, P = 0.0016 for inbreeding avoidance model).Among the 315 subjects, 26 homozygotes for the chromosome 13 haplotype wereexpected under a random mating model; after correcting for inbreeding avoidance,22 were expected. In this sample, 15 homozygotes were observed (χ2 = 5.54, P =0.019 for random mating model; χ2 = 2.72, P = 0.099 for inbreeding avoidance model).

DISCUSSION

All human populations avoid close inbreeding, yet the effects of inbreeding avoid-ance on genotypic proportions have been largely ignored in the literature [for excep-tions, see Hartl, 1980; Jacquard, 1970]. We initiated this study to determine the effectsof close inbreeding avoidance on Hardy-Weinberg expectations and to determine

Effect of Inbreeding on Hardy-Weinberg Expectations 169

Fig. 1. Frequency distribution of HLA (a) and chromosome 13(b) haplotypes. N = 630 chromosomes;the numbers above each bar are the numbers of homozygotes for haplotypes in each frequency group.

TABLE I. HLA and Chromosome 13 Haplotype Frequencies and Homozygote Frequency Expectations*

HLA Chromosome 13

Expected ExpectedExpected after Expected after

under correcting for under corrected forFrequency random inbreeding Frequency random inbreeding

Haplotype (p) Number mating avoidance Haplotype (p) Number mating avoidance

1084 0.085 1 0.0097 0.0083 215 0.117 3 0.0170 0.01481012 0.065 0.0061 0.0052 514 0.106 0.0142 0.01231027 0.064 0.0059 0.0050 434 0.073 4 0.0074 0.00641013 0.047 0.0036 0.0030 534 0.067 0.0063 0.00541025 0.042 0.0030 0.0025 333 0.051 3 0.0041 0.00341041 0.042 1 0.0030 0.0025 214 0.048 1 0.0037 0.00311089 0.042 2 0.0030 0.0025 437 0.044 0.0033 0.00281034 0.040 1 0.0028 0.0023 614 0.044 1 0.0033 0.00281083 0.038 0.0026 0.0022 326 0.037 0.0024 0.00201030 0.037 0.0024 0.0020 414 0.037 0.0024 0.00201082 0.032 0.0020 0.0016 313 0.030 0.0018 0.00151008 0.030 0.0018 0.0015 135 0.027 0.0015 0.00131017 0.030 0.0018 0.0015 542 0.025 0.0014 0.00121019 0.030 0.0018 0.0015 111 0.022 0.0012 0.00101021 0.030 0.0018 0.0015 556 0.021 1 0.0010 0.00091088 0.028 0.0017 0.0014 412 0.019 0.0009 0.00081001 0.025 0.0014 0.011 536 0.019 0.0009 0.00081004 0.023 0.0012 0.0010 224 0.017 0.0008 0.00071015 0.018 0.0009 0.0007 334 0.017 0.0008 0.00071023 0.018 0.0009 0.0007 144 0.014 0.0006 0.00051014 0.017 0.0008 0.0006 516 0.014 0.0006 0.00051029 0.017 0.0008 0.0006 544 0.013 0.0005 0.00041037 0.017 0.0008 0.0006 714 0.013 0.0005 0.00041039 0.017 0.0008 0.0006 211 0.011 0.0005 0.00041042 0.017 0.0008 0.0006 142 0.010 1 0.0004 0.00031085 0.015 0.0007 0.0006 235 0.008 0.0003 0.00021026 0.012 0.0005 0.0004 433 0.008 1 0.0003 0.0002

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1035 0.012 0.0005 0.0004 113 0.006 0.0002 0.00021043 0.010 0.0004 0.0003 442 0.006 0.0002 0.00021044 0.010 0.0004 0.0003 454 0.006 0.0002 0.00021024 0.008 0.0003 0.0003 515 0.006 0.0002 0.00021031 0.008 0.0003 0.0003 715 0.006 0.0002 0.00021090 0.008 0.0003 0.0003 112 0.005 0.0002 0.00011018 0.007 0.0002 0.0002 132 0.005 0.0002 0.00011032 0.007 0.0002 0.0002 415 0.005 0.0002 0.00011038 0.007 0.0002 0.0002 115 0.003 0.0001 0.00082005 0.007 0.0002 0.0002 213 0.003 0.0001 0.00081045 0.005 0.0002 0.0001 324 0.003 0.0001 0.00082001 0.005 0.0002 0.0001 435 0.003 0.0001 0.00081003 0.003 0.0001 0.0009 524 0.003 0.0001 0.00081028 0.003 0.0001 0.0009 546 0.003 0.0001 0.00081087 0.003 0.0001 0.0009 114 0.002 0.0005 0.00041091 0.003 0.0001 0.0009 234 0.002 0.005 0.00041016 0.002 0.0005 0.0004 237 0.002 0.0005 0.00041020 0.002 0.0005 0.0004 242 0.002 0.0005 0.00041022 0.002 0.0005 0.0004 335 0.0002 0.0005 0.00041072 0.002 0.0005 0.0004 337 0.002 0.0005 0.00041075 0.002 0.0005 0.0004 445 0.002 0.0005 0.00041080 0.002 0.0005 0.0004 447 0.002 0.0005 0.00041086 0.002 0.0005 0.0004 511 0.002 0.0005 0.00042003 0.002 0.0005 0.0004 537 0.002 0.0005 0.00042030 0.002 0.0005 0.0004 543 0.002 0.0005 0.0004

Sum 5 0.0712 0.0626 552 0.002 0.0005 0.0004633 0.002 0.0005 0.0004634 0.002 0.0005 0.0004

Sum 15 0.0877 0.0786

*In all calculations F = 0.0306, f = 0.1, Q = 0.0537. See text for details.

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172 Robertson et al.

whether inbreeding avoidance could explain the previously reported deficiency ofhomozygotes for the HLA haplotype in the Hutterites.

Using estimates derived from a sample of 315 married Hutterites, the modelthat takes inbreeding avoidance into account provided a better estimate of the ex-pected number of homozygotes at the chromosome 13 locus (P = 0.019 before cor-rection; P = 0.099 after correction). The chromosome 13 haplotype served as an“internal” control for non-random aspects of Hutterite mating structure (other thaninbreeding avoidance) that could influence genotype distributions in the population.For example, Hutterites marriages are nonrandom with respect to colony lineage andit is not uncommon for multiple marriages to occur between two sibships [see Oberet al., 1997, for a more detailed discussion of mating patterns]. These aspects of themating structure would be expected to affect all loci in a similar manner. The factthat the observed number of homozygotes for the chromosome 13 haplotype is notsignificantly different from the expected number derived from the inbreeding avoid-ance model suggests that other aspects of the Hutterite population structure havesmall, if any, effects on proportions of homozygous individuals in the population. Incontrast, deficiencies of homozygotes for the HLA haplotype remain highly signifi-cant (P = 0.0016) after correcting for inbreeding avoidance, suggesting that factorsrelated specifically to the HLA haplotype, and not to Hutterite population structure,result in a deficiency of homozygotes in this region.

The distribution of HLA and chromosome 13 haplotypes were not statisticallydifferent, but there were differences between them that influenced the number ofhomozygotes expected (18 expected for HLA; 22 expected for chromosome 13). Thegreater genetic distance between chromosome 13 markers (3 cM) than across theHLA region (≈1 cM) and the higher mutation rate at microsatellite loci should pro-duce a larger number of rare haplotypes for the chromosome 13 loci compared withHLA. Indeed, 58% of chromosome 13 haplotypes had frequencies <1%, whereasonly 42% of HLA haplotypes had frequencies <1%. However, few individuals areexpected to be homozygous for rare haplotypes. In fact, only one of five HLA ho-mozygotes one of 15 chromosome 13 homozygotes were homozygous for one of therare haplotypes (Fig. 1). On the other hand, the presence of two chromosome 13haplotypes but no HLA haplotypes with frequencies >10% likely accounts for someof the differences in expected numbers of homozygotes. The differences in this endof the frequency distribution are more difficult to explain, but could be due to selec-tion against high-frequency HLA haplotypes or other nonrandom factors influencingHLA haplotype frequencies. Nonetheless, the differences with respect to high fre-quency haplotypes make it inappropriate to compare directly the observed number ofhomozygotes for HLA (N = 5) and chromosome 13 haplotypes (N = 15). On the

TABLE II. Expected and Observed Number of Homozygotes in 315 Married Hutterites for HLAand Chromosome 13 Haplotypes

Number expected Number expected afterNumber under random mating corrected for

Locus observed in an inbred population P value inbreeding avoidance P value

HLA 5 21 0.00031 18 0.0016Chromosome 13 15 26 0.019 22 0.099

Effect of Inbreeding on Hardy-Weinberg Expectations 173

other hand, the differences between the distributions should not influence how wellthe proposed models fit the individual data because the haplotype frequencies aretaken into account.

This study indicates that adjusting the Hardy-Weinberg model to take into ac-count close inbreeding avoidance provides a better fit to observed genotype propor-tions at a neutral locus in the Hutterites. This study also provides further evidencethat factors specifically related to the HLA haplotype influence the genotype propor-tions at these loci. Whether this is due to reduced overall fertility among Hutteritecouples matching for HLA haplotypes [Ober et al., 1998], avoidance of mates whomatch for an HLA haplotype [Ober et al., 1997], or other selective factors is cur-rently under investigation.

REFERENCES

Boyce AJ. 1983. Computation of inbreeding and kinship coefficients on extended pedigrees. J Hered74:400–404.

Campbell R, Trowsdale J. 1993. Map of the human MHC. Immunol Today 14:349–352.Dawson DV, Ober C, Kostyu DD. 1995. Extended HLA profile of an inbred isolate: the Schmiedeleut

Hutterites of South Dakota. Genet Epidemiol 12:47–62.Foissac A, Crouau-Roy B, Fauré S, Thomsen M, Combon-Thomsen A. 1997. Microsatellites in the

HLA region: an overview. Tissue Antigens 49:197–214.Hartl DL. 1980. Principles of population genetics. Sunderland, MA: Sinauer Associates, Inc.Jacquard A. 1970. The genetic structure of populations. New York: Springer-Verlag.Kostyu DD, Dawson DV, Elias S, Ober C. 1993. Deficit of homozygotes in a Caucasian isolate. Hum

Immunol 37:135–142.Ober C, Weitkamp LR, Cox N, Dytch H, Kostyu D, Elias S. 1997. HLA and mate choice in humans.

Am J Hum Genet 61:497–504.Ober C, Hyslop T, Elias S, Weitkamp LR, Hauck WW. 1998. HLA matching and fetal loss: results of a

10-year prospective study. Hum Reprod 13:101–106.Ober C, Cox N, Parry R, Abney M, DiRienzo A, Changyaleket B, Gidley H, Kurtz B, Lander ES, Lee

J, Pettersson A, Prescott J, Richardson A, Schlenker E, Summerhill E, Willadsen S, CSGA.1998. Genome-wide search for asthma susceptibility loci in a founder population. Human MolecGenet 7:1393–1398.

Weitkamp LR, Ober C. 1999. Ancestral and recombinant 16-locus haplotypes in the Hutterites.