Population Admixture May Appear to Mask, Change or Reverse Genetic Effects of Genes Underlying Complex Traits

Corresponding author: Hong-Wen Deng, Creighton University, 601 N. 30th St., Ste. 6787, Omaha, NE 68131., deng{at}creighton.edu (E-mail)

Communicating editor: J. B. WALSH

	ABSTRACT

TOP ABSTRACT THEORY DISCUSSION LITERATURE CITED

Association studies using random population samples are increasingly being applied in the identification and inference of genetic effects of genes underlying complex traits. It is well recognized that population admixture may yield false-positive identification of genetic effects for complex traits. However, it is less well appreciated that population admixture can appear to mask, change, or reverse true genetic effects for genes underlying complex traits. By employing a simple population genetics model, we explore the effects and the conditions of population admixture in masking, changing, or even reversing true genetic effects of genes underlying complex traits.

ASSOCIATION studies have been widely used to help decipher the genetic basis of quantitative traits, such as the susceptibility to complex diseases. Despite extensive efforts, the results in the identification and inferences of genetic effects for complex traits from independent association studies often fail to reach consensus. One such example is the association between the vitamin D receptor (VDR) gene and bone mass (EISMAN 1995 ; PEACOCK 1995 ; GONG et al. 1999 ), a major determinant of osteoporosis (DENG et al. 2000A ). Association studies differ in their findings on the significance of the VDR gene on bone mass variation. Further, studies that found the VDR gene significant differed in their inferences on the allelic effects (HOUSTON et al. 1996 ; GONG et al. 1999 ).

Potential causes underlying the inconsistent association studies are complex, including a number of plausible factors (genotype-by-environment interaction, epistasis, population differentiation, etc.), although no specific cause(s) has been unambiguously identified for any special case. It is well known that one of the most important causes that may lead to the inconsistent results from association studies is population admixture, which may induce false positives for genes not underlying complex traits (CHAKRABORTY and SMOUSE 1988 ; DENG and CHEN 2000A ; DENG et al. 2001 ). It is much less well appreciated that population admixture can mask, change, or reverse true genetic effects for genes underlying complex traits. We employ a simple one-locus population genetics model to explore some of the potential effects of population admixture for association studies.

	THEORY

TOP ABSTRACT THEORY DISCUSSION LITERATURE CITED

Consider two large and randomly mating subpopulations, P₁ and P₂. Further assume that Hardy-Weinberg equilibrium holds at a biallelic marker locus (alleles Q and q) which, for the purpose of simple illustration, is assumed to be the functional mutation of a quantitative trait locus (QTL). The frequencies of the allele Q in P₁ and P₂ are f₁ and f₂, respectively. A large population P is formed by admixture of individuals from P₁ (with a proportion p) and P₂ (with a proportion 1 - p).

Let Q be the functional allele causing larger phenotypic values and a (>0) and d denote the additive and dominance effects at the QTL (respectively), which are assumed to be the same in subpopulations P₁ and P₂. Finally, let µ₁ and µ₂ denote the genotypic values of the genotype qq in P₁ and P₂. Assume, due to the complex determination of the phenotypic values from environmental factors and/or other genetic loci in the two subpopulations, that µ₁ µ₂. Without loss of generality, we assume µ₂ = 0; hence µ₁ represents the difference of the mean phenotypic values of the complex trait of the genotype qq in the two subpopulations. The genotypic values of the QQ, Qq, and qq are, respectively, µ₁ + 2a, µ₁ + a + d, and µ₁ in the subpopulation P₁, and 2a, a + d, and 0 in P₂. Letting µ_QQ, µ_Qq, and µ_qq denote the mean values of the genotypes QQ, Qq, and qq, respectively, in the admixed population P, we have

Clearly,

(1a)

(1b)

(1c)

Define

(2)

Note that k₁ - k₂ + k₃ = 0. It can be easily seen from Equation 2 that

(3)

and

In the following, we investigate the conditions under which the true genetic effects for a recessive, additive, and dominant QTL are incorrectly inferred, due to population admixture, as overdominant, underdominant, no effect (the three genotypes have the same mean phenotypic effect; i.e., the QTL effect is masked), or reversed (the allele q is associated with larger phenotypic values). Other genetic models (as reflected by different d values) can be easily investigated using the approach we outline below.

As an example to demonstrate our theoretical approach, we derive in detail the conditions under which the genetic effect at the QTL appears to be overdominant in the admixed population P. Under this scenario, we have µ_Qq > µ_QQ and µ_Qq > µ_qq. From Equation 1aEquation 1bEquation 1c and Equation 2,

(4)

Hence,

1. When f₂ < f₁, from Equation 3 and Equation 4, it is apparent that
   

   (5)

   When the true genetic effect is recessive at the QTL in subpopulations P₁ and P₂ (i.e., d = -a),
   

   (6)

   Since k₁ < 0 when f₂ < f₁ (Equation 3), the inequalities of Equation 6 cannot hold. Therefore, when the true genetic effect at the QTL is recessive in subpopulations P₁ and P₂, it is impossible for an overdominant genetic effect at the QTL to be manifested in the admixed population P.

2. When the true genetic effect is additive at the QTL in subpopulations P₁ and P₂, (d = 0), from Equation 5
   

   (7)

   Hence, we must first have -a/k₂ < a/k₁, implying from Equation 3 that
   

   (8)

   where w₁ is a function of the admixture proportion p (Equation 2). Fig 1A illustrates the function w₁ in Equation 8 to demonstrate intuitively the domain of p in which w₁ > 0 for a particular set of parameters (f₁ = 0.7 and f₂ = 0.4). It is apparent from Fig 1A that, even when the true genetic effect is additive at the QTL in subpopulations P₁ and P₂, there is a large range of p in which an overdominant effect can be incorrectly inferred in the admixed population P. In addition, the subpopulation mean µ₁ must also fall within the regions between the two plotted lines (µ₁ = and µ₁ = ) in Fig 1B when the true allelic effect a = 1.

   
   

   View larger version (9K): In this window In a new window Download PPT slide   Figure 1. The conditions for overdominant effects in the admixed population P when f2 < f1 · a = 1, f2 = 0.4, f1 = 0.7, and µ2 = 0. (a and b) Additive. (c) Dominance. Under additive effect, the parameter space for overdominant effects includes the area covered above the x-axis and under the curve shown in a and the area covered between the two lines drawn in b. Under dominant effects, the parameter space for overdominant effects includes the area covered between the x- and y-axes and the line drawn in c.

3. When the true genetic effect is dominant at the QTL in subpopulations P₁ and P₂ (d = a), from Equation 5,
   

   (9)

   Hence, we first must satisfy < 0, from which we must have k₂ > 0, which is satisfied for any value of p between 0 and 1 when f₂ < f₁ (Equation 3). Hence, as long as µ₁ is between the x-axis and the line µ₁ = in Fig 1C (where the additive effect a = 1), an overdominant genetic effect will be detected in the admixed population P even if the true genetic effect of the QTL is dominant in the large and randomly mating subpopulations P₁ and P₂. 2. When f₂ > f₁, it can be shown as above that, when the true genetic effect at the QTL is recessive in P₁ and P₂, it is impossible for an overdominant genetic effect at the QTL in the admixed population P to exist. When the true genetic effect is additive at the QTL in P₁ and P₂, we must have < µ₁ < and thus w₂ = k₁ + k₂ > 0 for overdominance. Finally, when the true genetic effect is dominant, we must have 0 < µ₁ < 2a/k₂ and thus 0 < -2a/k₂, which is satisfied for any value of p between 0 and 1 when f₂ > f₁ (Equation 3).

The conditions under which the genetic effect at the QTL in population P is manifested as underdominant, or is masked so that no genetic effect at the QTL is manifested, or is reversed so that the allele Q is associated with smaller phenotypic values can be similarly derived. These conditions are summarized in Table 1. Fig 2 and Fig 3 illustrate the conditions under two situations (f₂ < f₁ and f₂ > f₁) when the genetic effect at the QTL is masked or reversed by population admixture.

View larger version (10K): In this window In a new window Download PPT slide   Figure 2. The conditions under which the true allelic effect is masked by population admixture. a = 1 and f2 = 0.4. (a) f1 > f2. (b) f1 < f2. The situations under which f1 = 0.7 and 0.1 are studied, respectively. The parameter space includes the two lines drawn for d and µ1.

View larger version (9K): In this window In a new window Download PPT slide   Figure 3. The conditions under which the true allelic effect is reversed by population admixture. a = 1 and f2 = 0.4. (a) f1 > f2. (b) f1 < f2. The situations under which f1 = 0.7 and 0.1 are studied, respectively. The parameter space includes those under the curve drawn (when f1 > f2) in a and above the curve drawn (f1 < f2) in b.

	DISCUSSION

TOP ABSTRACT THEORY DISCUSSION LITERATURE CITED

Through a simple one-locus population genetics model, we demonstrate that there is a large range of parameter space in which population admixture changes the genetic effects of genes underlying complex traits. In particular, the parameter space in which population admixture may mask or reverse the genetic effects of genes underlying complex traits is not trivial. The parameters that are relevant in our simple one-locus genetics model include the mean phenotypic values in different subpopulations, the genetic effects (the magnitude such as the additive and dominance effects a and d), the allele frequencies at the QTL, and the admixture parameter p. It should be noted that when we investigate the effect of population admixture in masking the true genetic effects of a QTL, we explore the conditions under which the genotypic effects of all the genotypes of the QTL are exactly the same in the admixed population. In practice, the conditions under which population admixture may mask genetic effects of a QTL may be much less stringent. This is because as long as population admixture reduces the difference of the genotypic effects of a QTL to an extent that is difficult to be detected powerfully by sample sizes regularly employed in association studies, true genetic effects of the QTL will likely be masked by population admixture. Although some similar phenomena may have been noted in epidemiology studies (see example 12.5 in ARMITAGE and BERRY 1987 ), there has been no study like this one that explicitly addresses the effects of population admixture in changing, masking, or reversing the genetic effects of genes underlying complex traits.

Population association studies have certain advantages such as being powerful and relatively easy to recruit study subjects and thus are currently promoted (RISCH and TENG 1998 ; MORTON and COLLINS 1999 ) and commonly employed for seemingly large and randomly mating populations (DENG et al. 1999 ). However, population admixture is often difficult to detect (DENG et al. 2001 ). This study suggests that in addition to the potential false-positive (significant) effects that are often emphasized for population admixture studies (CHAKRABORTY and SMOUSE 1988 ; DENG and CHEN 2000A ; DENG et al. 2001 ), false-negative (nonsignificant) results inducible by population admixture should not be ignored. This is particularly important in metaanalyses of inconsistent association results, where negative association results have (incorrectly) been regarded as robust (to population admixture) and positive results have been regarded as potentially being confounded by population admixture. Our result should also be noted in QTL fine mapping studies based on robust linkage study results using the association study approach (DENG and CHEN 2000B ; DENG et al. 2000B ). This is because a true QTL in a genomic region identified via robust linkage studies may not be detected in fine mapping studies using the association approach, since the genetic effects may be masked in the collected sample due to potential population admixture.

It is not unusual that reverse genetic effects have been found in some association studies. For example, in the genetic studies of the VDR gene for osteoporosis, some studies find that the b allele is associated with higher bone mass than the B allele, while others found the opposite effect (HOUSTON et al. 1996 ; DENG et al. 1999 ). The reverse genetic effects are generally attributable to different phases (repulsion vs. coupling) of linkage disequilibrium between a marker locus and a functional mutation locus (HOUSTON et al. 1996 ). While this may be plausible, our study shows that this is not the only explanation and that population admixture may induce reverse genetic effects at the QTL per se. It is a common practice to infer the genetic effects (such as dominant, additive, or recessive) at candidate genes when significant effects are found in population association studies (e.g., DENG et al. 1999 ). It can be foreseen that, since population association studies are powerful in fine mapping genes underlying complex traits, when a true QTL is identified with the association approach, the results may be used to infer the allelic and mutational effects. Such inference may be critical for subsequent molecular studies in studying the function and the regulation of the gene and its product. However, a correct inference of allelic effects may be compromised by the results from the population association alone due to the potential effect of population admixture in reversing the genetic effects of the QTL. Therefore, approaches robust to population admixture in testing association and linkage (e.g., SPIELMAN et al. 1993 ; ALLISON 1997 ) may need to be used for the results to be confirmed.

	ACKNOWLEDGMENTS

Research assistance from graduate student Y. Li is appreciated. I thank Professor B. Walsh and two anonymous reviewers for their constructive comments that helped to improve this article. H.-W. Deng was partially supported by grants from Health Future Foundation, National Institutes of Health grants (R01 GM60402-01A1, K01 AR02170-01, R01 AR45349, and P01 DC01813-07), grants from State of Nebraska Cancer and Smoking Related Disease Research Program, U.S. Department of Energy grant DE-FG03-00ER63000/A00, a grant (30025025) from National Science Foundation of China, and a grant from HuNan Normal University.

Manuscript received May 3, 2001; Accepted for publication August 16, 2001.

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