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Am J Hum Genet. Oct 8, 2010; 87(4): 494–504.
PMCID: PMC2948802

Identification of Copy Number Variation Hotspots in Human Populations


Copy number variants (CNVs) in the human genome contribute to both Mendelian and complex traits as well as to genomic plasticity in evolution. The investigation of mutational rates of CNVs is critical to understanding genomic instability and the etiology of the copy number variation (CNV)-related traits. However, the evaluation of the CNV mutation rate at the genome level poses an insurmountable practical challenge that requires large samples and accurate typing. In this study, we show that an approximate estimation of the CNV mutation rate could be achieved by using the phylogeny information of flanking SNPs. This allows a genome-wide comparison of mutation rates between CNVs with the use of vast, readily available data of SNP genotyping. A total of 4187 CNV regions (CNVRs) previously identified in HapMap populations were investigated in this study. We showed that the mutation rates for the majority of these CNVRs are at the order of 10−5 per generation, consistent with experimental observations at individual loci. Notably, the mutation rates of 104 (2.5%) CNVRs were estimated at the order of 10−3 per generation; therefore, they were identified as potential hotspots. Additional analyses revealed that genome architecture at CNV loci has a potential role in inciting mutational hotspots in the human genome. Interestingly, 49 (47%) CNV hotspots include human genes, some of which are known to be functional CNV loci (e.g., CNVs of C4 and β-defensin causing autoimmune diseases and CNVs of HYDIN with implication in control of cerebral cortex size), implicating the important role of CNV in human health and evolution, especially in common and complex diseases.


Recent studies have shown that the presence of copy number variants (CNVs) in the human genome is substantial, and thousands of CNVs have been identified in human populations.1,2 CNV mutations can introduce unprecedented genomic instability in both germline and somatic cells, which would lead to Mendelian diseases and complex traits, including cancers.3,4 Investigation of the CNV mutation rate is, therefore, critical to unraveling the instability of the human genome and in turn the functional impact of CNVs underlying human traits and diseases.

The inbreeding across hundreds of generations made it accessible to study the mutation rate for spontaneous CNVs in the laboratory mouse strains.5 However, the direct estimation of germline mutation rate for CNVs in the human genome is technically challenging. Only a few copy number variation (CNV) loci have been studied individually by disease-prevalence calculation, pedigree analysis, sperm typing, or pooled sperm assay,6–11 but a systematic investigation of the CNV mutation rate across the genome has yet to be accomplished. The locus-specific mutation rates for CNV have been observed to be ~100 to 10,000 times higher than those for nucleotide substitution rates,3 which not only highlights the instability of CNV regions but also suggests large variation in CNV mutation rate.

In order to examine whether such a notable variance of mutation rate observed between CNV loci is potentially due to the inconsistency among various locus-specific investigatory mothods6–8,10,11 or instead reflects the presence of CNV mutational hotspots, a genome-wide analysis for estimation and comparison of CNV mutation rate is demanded. In this study, we developed a statistical method called “CNVMut” to evaluate CNV mutation rate across autosomes of the human genome by utilizing vast, readily available genotyping data from human populations. This proposed method was carefully evaluated and validated via simulation approaches, and it was applied to identifying mutational hotspots of CNVs in HapMap populations.

Material and Methods

An Algorithm for Approximately Estimating the CNV Mutation Rate by Using Flanking SNPs

CNVs can be classified as recurrent CNVs with common breakpoints and as nonrecurrent CNVs with variable breakpoints.3 A CNV region (CNVR) is usually defined to combine calls from different individuals as a grouping of CNVs overlapping or in close proximity to each other, regardless of the potential architectural complexity.2,12 In this study, a method was proposed for approximate estimation of the mutation rate for each CNVR. Each CNVR was treated as a simple marker with potentially multiple alleles, each with a distinct copy number (0, 1, 2, etc.). Each individual carries two such alleles in his or her diploid genome.

The SNPs flanking CNV loci often show strong linkage disequilibrium (LD) with the CNVs,1,12–14 therefore allowing one to trace CNV mutation events by using the phylogenies of flanking SNPs constructed by plausible ancestral recombination graphs (ARGs).15 ARGs can describe the relationship of chromosome sequences from a population back to its common ancestor through events of mutation, recombination, and coalescence, which are defined under a Wright-Fisher model with recombination. According to the impact of historical recombination events, a series of genealogical trees are embedded in the ARG. Each genealogical tree describes the phylogeny for each SNP, which is also called a “marginal tree.” Following each marginal tree for the flanking SNPs, we define the tree with the smallest number of CNV changes as a surrogate of the most parsimonious genealogical tree for the CNV locus according to the parsimony criterion. The number of CNV mutations (including both deletion and duplication) is summarized on the basis of the most parsimonious tree and can be converted to an approximate estimation of mutation rate for the CNV locus by simulations.

A brief summary of our statistical method for indirectly estimating the CNV mutation rate is illustrated in Figure S1 (available online). First, the program Margarita15 was implemented for the construction of plausible ARGs by the SNPs flanking each CNV locus in one population. The corresponding marginal tree for each SNP was obtained in this step as well, the external nodes representing the inferred haplotypes of genotyped individuals, the internal nodes representing the ancestral haplotypes in previous generations, and the root representing the common ancestral haplotype. Second, an expectation-maximization (EM) algorithm was used for inferring haplotypes involving a CNV marker and its flanking SNPs as described by Kato et al.,16 and we also modified the algorithm to allow the input of phase-known data (i.e., the preinferred haplotypes of flanking SNPs obtained from ARG construction). Third, haploid copy numbers of a CNV marker were superimposed to corresponding external nodes that represented the preinferred haplotypes of flanking SNPs for each marginal tree, and they were inferred for each internal node by traversing all the binary tree units (BTUs; Figure S1D). Lastly, the number of mutation events was counted for all BTUs, the smallest count being taken as the most parsimonious estimator. In particular, deletion events and duplication events were counted separately along the most parsimonious marginal tree, with the assumption that a tree requiring fewer substitutions is better than one that requires more, for evaluation of the relative mutation rate between deletion and duplication. This detailed procedure is described in Appendix A.

Because the real phylogeny was unknown, the average of the estimator for R plausible ARGs (R = 100 here) was taken. For example, the cumulative mutation count, M, was estimated by taking an average of the inferred number of mutations over R (R = 100 here) plausible ARGs:


where Mrl is the estimator of the mutation number for the l-th marginal tree of the r-th plausible ARG, and N is the sample size.

The statistic M measures the minimum effective number of mutation events instead of mutation rate in a population, following the parsimony assumption; i.e., the estimation depends on the observed cumulative mutation events under an assumption of constant evolution rate. It allows an indirect comparison of mutation rates between CNV loci and between populations. The order of magnitude of the mutation rate could be converted from the M statistic with the use of a simulation approach.

Simulation in Evaluating the Algorithm Performance

Given that the aforementioned algorithm invoked several assumptions that may not biologically realistic, it was evaluated via a simulation approach. In particular, we interrogated the effect of several factors on the estimation of M, including mutation rate, effective population size, number of flanking SNPs, sample size, recombination rate between the CNV locus and its flanking SNPs, and that between adjacent SNPs. The program SIMCOAL217 was employed in simulating the neutral genetic diversity of a CNV marker and its flanking SNPs under different mutation rates and demographic models (see Appendix B).

Algorithm Implementation for Real Data

Genotype data for the unrelated samples from the HapMap Phase II project were included in our analysis: 60 Yoruba in Ibadan, Nigeria (YRI), 60 Utah residents with ancestry from northern and western Europe (CEU), and 89 Asians (45 Han Chinese from Beijing [CHB] and 44 Japanese from Tokyo [JPT]; CHB+JPT). First, 4330 genotyped CNVRs from 22 autosomes, identified by a previous study in HapMap populations, were investigated.2 Genotypes of the SNPs flanking CNV regions but not involved in CNVR were obtained from the HapMap website (NCBI build 36, release 24). Second, the genetic distance between each CNVR and its nearest upstream and downstream SNPs was calculated according to the local recombination rate estimation obtained from the HapMap website (NCBI build 36) (Figure S2). The CNVRs with a genetic distance of > 0.1cM to its flanking SNPs were excluded from further analysis, so as to minimize the effect of high recombination rate between a CNVR and its flanking SNPs on the estimation of M. Overall 4187 CNVRs were enrolled in the following analyses.

The proposed method, CNVMut, was implemented to estimate both the statistic M and the proportion of deletion mutation for each CNV locus by using a total of 20 flanking SNPs for each population, respectively. Pairwise comparisons of the estimates of M among three HapMap populations were conducted by Spearman's correlation test with the use of all of the CNVs and/or the exclusion of those CNVs with the largest decile of Fst defined by Weir and Cockerham.18 Fst was calculated according to allele frequencies estimated during the CNV allele inference by EM algorithm.

For comparison of the mutation rate of CNVs between populations and detection of mutational hotspots of CNVs, coalescent simulations were employed in converting the estimates of M to different orders of the mutation rate. The simulated data with different mutation rates of CNVs at order of magnitudes (5 × 10−7, 5 × 10−6, 5 × 10−5, 5 × 10−4, and 5 × 10−3 per generation) were respectively produced by an extension of SIMCOAL2 under the proper selection of a demographic model for each population.19 The demographic model used in coalescent simulations for three populations (YRI, CEU, and CHB+JPT) is illustrated in Table S1. In each simulation under a proper demographic model, individuals (60 for the YRI model, 60 for the CEU model, and 89 for the CHB+JPT model) with a CNV at a given mutation rate and 20 flanking SNPs with a minor allele frequency (MAF) > 0.01 were simulated. The recombination rate of adjacent loci, including that between a CNV marker and its flanking SNPs and that between adjacent SNPs, was assumed to be 10−5 per generation, based upon the evidence including the following: (1) the estimation of M is robust when the recombination rate between adjacent loci is less than 10−3 per generation (Figures S3E and S3F); (2) the genetic distances between CNV loci to their flanking SNPs were less than 0.1cM and 3.96 × 10−3 cM on average; and (3) the average recombination rate of the human genome is ~10−8 per generation per bp,20,21 and the SNP density of HapMap Phase II is 1.14 per kb.22

Mutational hotspots for CNVs were identified according to the approximate estimation of the mutation rate converted from the estimates of M. Some potential differentiating features between mutational hotspots and the remaining loci, including the adjacency to segmental duplications (SDs; alternatively termed low-copy repeats [LCRs]),23,24 the recombination rate between the CNVR and its flanking SNPs, the CNVR size and the mechanisms underlying CNV formation, were compared by Fisher's exact test or the Mann-Whitney test. The location information of SDs was obtained from the UCSC Genome Browser (hg 18) for examining whether CNVs overlapped with SDs or not. The recombination rate between the CNVR and its flanking SNPs was obtained from the HapMap website (NCBI build 36). The genetic diversity of the CNVR was measured by the inferred heterozygosity according to allele frequencies estimated by the EM algorithm. The CNV formation mechanisms were obtained from Conrad et al.2

In addition, the potential association of the relative contribution of deletion versus duplication in the mutation rate with the different CNV formation mechanisms was also investigated by the Mann-Whitney test.


Evaluation of the Performance of the Estimation of M Using Simulated Data

The performance of the statistic M, under both circumstances of considering demographic events or not, was carefully evaluated and validated via simulation approaches. Simulations illustrated that the estimates of M increase with increasing mutation rates and can be affected by the demographic model. However, the number of flanking SNPs used in constructing ARGs, sample size, and recombination rate between adjacent loci (especially when recombination rate is < 10−3 per generation) has only very limited effects on the estimation of M (Appendix B and Figure S3).

The Estimation of M for the CNVRs Identified in HapMap Populations

A set of 4330 polymorphic CNVRs as recently identified in three HapMap populations,2 including 60 YRI, 60 CEU, and 89 CHB+JPT, was investigated in this study. A total of 4187 (96.7%) of these CNVRs have close flanking SNPs with a genetic distance of 0.1 cM or less and were included in the additional analyses. The estimates of M showed a very diverse distribution in all three populations (Figure 1). Notably, the estimates of M are significantly correlated in all pairwise comparisons among three continental populations (p < 10−5), especially when excluding the CNVRs with pairwise Fst in the largest decile (Figure S4), suggesting the consistency of the estimation of M among populations.

Figure 1
Distribution of the Estimates of M in Three HapMap Populations

Approximate Estimation of Mutation Rates for the CNVRs Identified in HapMap Populations

Considering the observation that the statistic M can be affected by the demographic history of human populations, we converted the estimates of M to the approximate mutation rate by using a simulation approach under the proper demographic model in each population and made M comparable across populations. The distribution of M according to each 1000 simulations under different demographic models19 and at different mutation rates (5 × 10−7, 5 × 10−6, 5 × 10−5, 5 × 10−4, and 5 × 10−3 per generation) is shown in Figure S5 (e.g., the mean ± SD of M is 0.258 ± 0.174 for YRI, 0.158 ± 0.157 for CEU, and 0.150 ± 0.151 for CHB+JPT under the mutation rate of 5 × 10−5 per generation; 1.10 ± 0.198 for YRI, 1.11 ± 0.152 for CEU, and 1.12 ± 0.153 for CHB+JPT under the mutation rate of 5 × 10−3 per generation). The range of mutation rates selected for simulation was based on the contention that locus-specific mutation rates for CNV are approximately 100 to 10,000 times greater than nucleotide substitution rates, i.e., ~10−6 to 10−4 per generation.3 The range of M (2.5–97.5 percentile) for a given mutation rate in each population (Figure 1) provides an approximate estimation of the order of magnitude of the CNV mutation rate.

Similar to the findings of a wide range of variability of mutation rates among different CNV loci in the laboratory mouse strain,5 the estimation of the CNV mutation rate in human populations also showed variances of orders of magnitude across the human genome. Among the 4187 CNVRs investigated in the estimation of M, the mutation rates for most loci were estimated at the order of 10−5 per generation. However, the mutation rates for CNVRs could reach the order of 10−3 per generation, and these CNVRs are likely mutational hotspots. A total of 104 (2.5%) potential hotspots were identified in three HapMap populations (Figure S6). All of the identified CNV mutational hotspots are listed in Table S2. Interestingly, 49 (47%) of these identified CNV hotspots involve known genes of the human genome, suggesting their implications in biological functions and human health (Table 1).

Table 1
The Potential CNV Mutational Hotspots Involving One or More Genes

Notably, these estimators of CNV mutation rate are in concordance with experimental observations at individual loci. For example, mutation rates of two CNVRs involving the α-globin genes (chr16:162,083–167,514 and chr16:164,519–165,801, NCBI build 36) were evaluated at the order of ~10−5 in this study, consistent with the molecular findings in two previous studies.7,8 In addition, the CNVR of human β-defensin genes (chr8:7,330,051–7,342,809, NCBI build 36) was suggested to be a mutational hotspot in all three populations in this study. Interestingly, this psoriasis-associated β-defensin locus25 was previously reported among the fastest-mutating CNVs, with a germline mutation rate of 7 × 10−3 per gamete, revealed by a pedigree-based approach.11

Genomic Architecture and Rearrangement Mechanisms Underlying Hotspots

We also studied some genomic features of CNV loci between candidate hotspots (72 in YRI, 37 in CEU, and 22 in CHB+JPT) and nonhotspots (3075 in YRI, 2323 in CEU, and 1593 in CHB+JPT) to investigate the potential cause of a CNV hotspot. We found that about 60% of hotspots overlap with SDs, whereas only < 20% of nonhotspot CNVRs involve SDs; p = 7.63 × 10−15 (Fisher's exact test) for YRI, p = 4.39 × 10−12 for CEU, and p = 7.62 × 10−9 for CHB+JPT (Figure 2A).

Figure 2
Comparison of CNVRs with Potential Hotspots and Nonhotspots

In addition, no significant differences between hotspots and nonhotspots were observed for the recombination rate between the CNVR and its flanking SNPs; p = 0.138 (Mann-Whitney test) for YRI, p = 0.971 for CEU, and p = 0.903 for CHB+JPT (Figure 2B). In contrast, the CNVR sizes at the mutational hotspots are larger than those at the remaining loci; p = 0.007 (Mann-Whitney test) for YRI, p = 0.042 for CEU, and p = 9.07 × 10−5 for CHB+JPT (Figure 2C). The genetic diversity of the CNVR, measured by the inferred heterozygosity, is significantly higher for hotspots than that for nonhotspots as well; p < 10−5 (Mann-Whitney test) for all of the populations (Figure 2D).

The CNV formation mechanism has been hypothesized to affect mutation rate. The nonallelic homologous recombination (NAHR) mechanism was previously proposed to be a major mechanism underlying CNV formation.23 For example, NHAR was shown to account for > 99% of the neuropathy-associated CNVs in the 17p12 region.26 In addition, the loci of NAHR-mediated CNVs have been regarded as “hotspots” in a previous study.27 Here, we studied the data of CNV formation mechanisms provided by Conrad et al.2 and found that the NAHR-mediated events were more frequent at CNV hotspots than at the remaining loci, but not significantly; p = 0.0518 (Fisher's exact test) for YRI, p = 0.154 for CEU, and p = 0.0629 for CHB+JPT (Figures 2E and 2F), suggesting the involvement of the NAHR mechanism in generating CNV hotspots.

These findings shed light on the understanding of genome architecture and rearrangement mechanisms underlying CNV mutations in the human genome.

Reevaluation of the Relative Mutation Rate of Deletion versus Duplication

The CNV mutation rates associated with deletion and duplication (alternatively, loss and gain) can be interrogated separately in order to investigate the respective contribution of deletion and duplication in CNV mutation. It has been proposed that deletions occur more frequently than duplications for NAHR-mediated CNVs, reflecting the lack of intrachromatid NAHR events in duplication rearrangement.10 The deletion to duplication ratio of ~2:1 was observed consistently at three autosomal CNV loci in a pooled sperm PCR assay.10 At the 421 NAHR-mediated CNV loci (both hotspots and nonhotspots) investigated in this study, the proportion of deletion events was estimated to be 0.774 ± 0.395 (mean ± SD) for YRI, 0.715 ± 0.436 for CEU, and 0.667 ± 0.448 for CHB+JPT. In contrast, at the 182 VNTR-mediated CNV loci, the proportion of deletion events is 0.499 ± 0.472 for YRI, 0.352 ± 0.458 for CEU, and 0.394 ± 0.474 for CHB+JPT. The proportion of deletion mutation events was significantly different between NAHR-mediated CNVRs and VNTR-mediated CNVRs (Mann-Whitney test: p < 10−5 for YRI, p < 10−5 for CEU, and p = 2.71 × 10−5 for CHB+JPT). These observations suggested the predicted overrepresentation of deletion versus duplication at the CNV loci mediated by the NAHR mechanism.


Previous approaches for estimating the mutation rate for CNVs by using molecular assays or prevalence calculation are locus specific, and only a few CNV loci have ever been studied in the human genome. The statistical method of CNVMut proposed in this study makes it accessible to evaluate the CNV mutation rate across the human genome, though approximately, by using vast, readily available genotyping data of human populations.

In this method, we employed LD relationship between the CNV loci and their flanking SNPs in tracing CNV mutation events by the plausible genealogical histories reconstructed by the flanking SNPs. Because CNV alleles are not readily determined experimentally, we used the EM algorithm to infer haploid copy number with the assistance of the preinferred haplotypes of flanking SNPs. According to our evaluation, the accuracy of the CNV alleles' inference was comparable to that of the SNP haplotype inferred by the EM algorithm.28 The error rate can be controlled by less than 5%, especially with the help of flanking SNPs (data not shown). In order to eliminate the inflated estimation of the M statistics caused by the uncertainty of the CNV alleles' inference as much as possible, we conducted such inference for every plausible ARG and averaged the analysis (i.e., the M statistics). In addition, simulations were also conducted with genotype data when converting the statistic M to an approximate estimation of the CNV mutation rate.

The statistic M was proposed to measure the minimum effective counts of CNV mutation events based on plausible ARGs constructed by flanking SNPs. The estimation of M was based upon an assumption of the parsimony criterion with a constant evolution rate. Any violation of this assumption, such as different changes of different copies following different mutation rates, would lead to an underestimation of the statistic M.

In this study, actual mutation rates were obtained by rescaling M with the use of coalescent simulations. The genetic diversity of a CNV locus and its flanking SNPs was simulated under the assumption of neutrality. Because this estimate does not account for purifying selection, it probably represents a lower bound on the true rate. In addition, we examined the possible effect of varying local recombination rate on mutation rate estimation for the CNVRs involving the genes of α-globin and β-defensins in YRI population and found that the estimation of CNV mutation rate for both loci was unaffected (~10−5 and ~10−3 per generation, respectively), similar to those estimated under the assumption of a constant recombination rate (10−5 per generation). It has also been illustrated (Figure S3) that both the number of flanking SNPs (when > 10) used to construct plausible ARGs and the recombination rate between adjacent loci have limited and slight effects on the estimation of M. Therefore, it is proper to use 20 flanking SNPs and an assumed constant recombination rate of 10−5 per generation between adjacent loci for coalescent simulations to convert the estimates of M into mutation rate.

Using this method, we identified 104 potential mutational hotspots for CNVRs in three HapMap populations (YRI, CEU, and CHB+JPT). The hotspots were defined as CNVRs with an approximate estimation of mutation rate at ~10−3 per generation. Figure S6 illustrates the consistency of 104 potential hotspots among three populations. More than one-half of the potential hotspots identified in CEU and CHB+JPT can be confirmed in another population. However, more specific hotspots were observed in YRI. It should be noted that ancient CNV mutations are more likely to be observed in Africans than in other populations, given that non-Africans experienced extreme genetic drift, especially during their migration out of Africa.

Genetic diversity for hotspots is significantly higher than that for nonhotspots (Figure 2D), which is consistent with the observation, gathered from CNVs on the human Y chromosome, that high mutation rate has driven extensive structural polymorphism on Y.29 High genetic diversity is expected to be the consequence of high mutation rate, rather than a cause for mutational hotspots, because mutation is regarded as a force underlying genetic diversity. The enrichment of SDs at hotspots supports the contention that SDs act as mutation seeds during genome evolution and that SD-rich regions are vulnerable to genome rearrangements mediating CNVs.23,24 Interestingly, more CNVs at hotspots than at nonhotspots are found to be mediated by the NAHR mechanism taking place between two homologous SDs (Figure 2E). It has also been shown that the other known mechanisms underlying CNV formation, including DNA repair by joining of double-strand break ends, as well as DNA replication errors, are incident to genomic regions rich in repeat and repetitive sequences,30–33 reflecting the regional genome architecture inciting genomic instability and mutational hotspots of CNV.

Some disease-associated loci were identified as CNV mutational hotspots in this study (Table 1). Besides the psoriasis-associated CNVs of β-defensin genes mentioned above, we also identified a CNV hotspot involving the gene of complement component C4 (with isotopes C4A [MIM 120810] and C4B [MIM 120820]) in association with human systemic lupus erythematosus (SLE [MIM 152700]).34 In addition, two mutational hotspots involve a glutathione conjugation gene, GSTM1 [MIM 138350], with implication in cancer risk and drug resistance.35 The homozygous deletion of RHD (MIM 111680) can cause RhD-negative blood type.36 The CNVs at the RHD locus were reported to be highly polymorphic in human populations2,37 and were also identified as CNV hotspots in this study. The IGF1R locus (MIM 147370) is also among CNV hotspots, and its deletion CNVs can cause gene haploinsufficiency in association with short status and other developmental defects in children born small for gestational age.38 Notably, genomic instability was also shown in some CNVs mediating neuropsychiatric traits, including the GRM8 [MIM 601116] and HYDIN [MIM 610812] loci. GRM8 encodes the glutamatergic receptor 8, and the patient with CNV-mediated GRM8 gene rearrangement presented autism and severe mental retardation.39 The instable locus of hydrocephalus-associated HYDIN in 16q22.2 experienced an event of duplication and insertion into 1q21.1 during primate evolution, and the CNVs at both of these HYDIN loci can lead to abnormal brain size, i.e., microcephaly or macrocephaly.40 These findings of functional CNV loci as mutational hotspots suggest an important role of CNV in human diseases and evolution.

In addition, though we applied this method to the published CNV genotyping data provided by Conrad et al.2 and to genotypes of SNPs from HapMap database, various genotyping data produced by current prevailing whole-genome SNP arrays, e.g., Affymetrix Genome-Wide Human SNP Array 6.0 and Illumina Human1M-Duo DNA Analysis BeadChip, can also be applied to this method.

In summary, we propose a statistical method, CNVMut, to achieve an approximate estimation of CNV mutation rates using genotyping data of human populations and to identify potential CNV mutational hotspots. The enrichment of repeat sequence at mutational hotspots sheds light on the understanding of genome architecture and rearrangement mechanisms underlying CNV mutations in the human genome, and the observation of functional CNV loci in hotspots implicates an important role of CNV in human health and evolution.


We are grateful to M.E. Hurles and D.F. Conrad for their kind providing of the data for CNV formation mechanisms. The project was supported by the National Natural Science Foundation of China (NSFC) (30890034 and 31000552), NSFC for the Young Distinguished Scholar (30625016), and the Program of Shanghai Subject Chief Scientist (09XD1400200). F.Z. is supported by the Shanghai Pujiang Program (10PJ1400300) and a Ministry of Education of China grant (NCET-09-0322).

Appendix A: An Algorithm for Estimating CNV Mutations by Using Flanking SNPs

General Description of the Algorithm

A brief summary of the algorithm is illustrated in Figure S1 and uses an example of a CNV (0 for homozygous deletion, 1 for heterozygous deletion, 2 for homozygous wild-type) and five SNPs (0 and 1 for homozygotes, H for heterozygote) flanking the CNV. For each CNV locus, the genotypes of both the CNV and its flanking SNPs for individuals from a population are used for analysis. The ARG is constructed by using genotypes of flanking SNPs with the haplotypes inferred simultaneously (step 1). An EM algorithm is employed in determining the phase of CNV alleles with the assistance of the inferred haplotypes of flanking SNPs in step 1 (step 2). The marginal trees describing the genealogical history of each SNP are then obtained according to the ARG constructed in step 1 (step 3). Each inferred CNV allele in step 2 is then superimposed to an external node of each marginal tree as step 4 (e.g., solid and open circles for deletion and wild-type, respectively). The CNV states for the internal nodes are then inferred on the basis of the rules as defined in the subsequent section (step 5), and the number of CNV mutation events is counted (step 6). Because the real ARG is unknown, steps 1–6 are repeated R times, and a statistic M is defined as the arithmetic average of the event counts of CNV mutation in the R plausible ARGs. We have developed a program called CNVMut, which is available online, to implement the algorithm.

ARG Inference Algorithm

A method of ARG was previously proposed for reconstruction of the phylogeny on the basis of mutation, recombination, and coalescence.15 Figure S1B illustrates an ARG of SNP haplotypes. Haplotype 2 and haplotype 4 are respectively derived from the recombination of haplotype 3 and haplotype 5. Haplotype 5 and haplotype 6 are conjunct by a mutation at site 4. When two haplotypes are identical for all SNPs, they can be conjunct by a coalescence event. For each site of the haplotype, there is a genealogical tree, called a “marginal tree,” embedded in the ARG according to the impact of historical recombination events. Figure S1D illustrates the marginal trees for sites 1–3, site 4, and site 5 from left to right, respectively.

In this study, we employed the software Margarita15 to infer ARGs and marginal trees on the basis of the genotypes of SNPs flanking a CNV. Margarita uses a heuristic algorithm to infer plausible ARGs by minimizing the number of involved recombination locally. This algorithm allows rapid computation and can handle both unphased and missing data.

Haplotype Inference Algorithm

An EM-based algorithm for inferring haplotype was proposed by Excoffier and Slatkin41 for the analysis of SNP data. Kato et al.16 extended the algorithm for CNV data. The difference between the algorithm for CNV and that for SNP is in the initial step during the generation of the possible haplotype pairs for a given genotype. As for the genotype of a SNP marker with its alleles coded as 0 and 1, a haplotype containing allele 0 and another containing allele 1 are the possible haplotype pair at this site. The alleles of a CNV loci are not readily distinguishable, because the possible allele/haplotype pair for a CNV with diploid copy number of 4 can be either [0 copies/4 copies], [1 copy/3 copies], or [2 copies/2 copies] at this locus.

To superimpose CNV alleles to the marginal tree requires the inference of CNV alleles with the assistance of the preinferred haplotypes of flanking SNPs provided by the software Margarita. In particular, all possible haplotypes encompassing the CNV and its flanking SNPs were enumerated, and an EM algorithm was applied to calculate and update the frequencies of haplotypes in order to obtain the maximum likelihood estimation, following the iteration previously described.16,41 In the end, the most probable haplotype pair for each individual is obtained for subsequent analysis.

Counting CNV Mutations

Each CNV allele could be superimposed to the external nodes of each marginal tree based on the inferred haplotypes, including CNV and flanking SNPs. Then, we infer the haploid copy number at each internal node of the tree. Let a binary tree unit (BTU) be denoted as a subtree with three nodes (two ends and one vertex) as shown in Figure S1D. The haploid copy number of each node is referred to as its state hereafter, and the state of each internal node is inferred according to the following rules: (1) Only when the states of both ends of the BTUs have been inferred can the state of the vertex be inferred. (2) If the state of any end is ancestral (“1” is set as the ancestral state here), the state of the vertex is set as the ancestral one. (3) If none of the states of two ends is ancestral and they are mutually exclusive, the union of the states of two ends is taken as the state of the vertex. (4) If none of the states of two ends is ancestral but not mutually exclusive, the intersection of the states of two ends is taken as the states of the vertex and both ends. (5) The procedure continues until all nodes of the marginal tree are updated.

Given that the states or haploid copy numbers of all nodes are inferred, the number of mutations can be counted for each marginal tree by traversing all of the BTUs of the marginal tree. If the states of the two ends are different, one mutation is added to the count. If L SNPs are used in ARG construction, L marginal trees and L estimators of the number of mutation are obtained. The smallest count is taken as the estimator of the plausible ARG, which can be considered as an approximate estimator of the most parsimonious mutation process. Notably, deletion mutation events and duplication mutation events can be counted separately along this parsimonious marginal tree, in order to compare mutation rates between deletion and duplication. Because the real ARG is unknown, the average of the estimator for R plausible ARGs (R = 100 here) is taken. For example, the statistic describing a CNV mutation can be expressed as


where Mrl is the estimator of the mutation number for the l-th marginal tree of the r-th plausible ARG and N is the sample size.

Appendix B: Evaluation of the Performance of the Estimation of M with the Use of Simulated Data

Simulation Data

The program SIMCOAL217 was employed in simulating the neutral genetic diversity of a CNV marker and its flanking SNPs under variable mutation rates and different demographic models. Because SIMCOAL2 allows short tandem repeat (STR) markers but not CNVs, simulations were conducted by using a STR marker as a surrogate of CNV. The most common allele of STR was converted to the ancestral allele with a haploid copy number of 1. The STR alleles shorter than the common one were set as 0 for the CNV, and the STR alleles larger than the common one were set as 1 + d for the CNV, where d is the difference of copy number between the STR alleles and the common allele.

In the simulation, a constant population with an effective population size (Ne) of 5000 was assumed and the sample size was set to 100 individuals. A haploid consisting of a CNV along with 20 flanking SNPs with an MAF greater than 0.01 was generated. The mutation rate for CNV was set to 5 × 10−5 per generation, and the rate of recombination between adjacent loci (including that between the CNV locus and its flanking SNPs and that between adjacent SNPs) was 10−5 per generation. However, when the effect of an individual factor was interrogated, numerous values were taken in simulation. The genotype of a diploid individual was then generated by combining two randomly selected haploids.

The Estimates of M Increase along with Increasing Mutation Rates

The estimates of M increase along with the increasing mutation rate of CNV (5 × 10−7, 5 × 10−6, 5 × 10−5, 5 × 10−4, and 5 × 10−3 per generation) for simulated data (Figure S3A), indicating that M could allow a comparison of the mutation rates among CNV loci. For example, the distributions of M are significantly (p < 10−5; Mann-Whitney test) different between the mutation rates of 5 × 10−5 and 5 × 10−3 per generation.

Effect of Demographic Models on the Estimation of M

Simulation analysis showed that the estimates of M increase along with increasing effective population size, even under the same mutation rate. For example, the estimates of M increase along with the increasing effective population size (2500, 5000, and 10,000) under a given mutation rate (Figure S3B). These observations suggest that population demographic profiles must be taken into consideration when converting the estimates of M to mutation rate.

The Estimation of M Is Not Affected by the Number of Flanking SNPs or the Sample Size

We also investigated the possible effect of the number of flanking SNPs (10, 20, 30, 40, and 50) and the sample size (50, 100, 150, 200, and 250) on the estimation of M. The simulation results showed that neither an increasing number of flanking SNPs nor increasing sample size would affect the estimation of M, besides a slight reduction of variance (Figure S3C and S3D).

Effect of Recombination Rate between a CNV and Its Flanking SNPs on the Estimation of M

The LD relationship between CNVs and flanking SNPs was employed in our proposed method. The impact of recombination rate (10−6, 10−5, 10−4, 10−3, 10−2, and 10−1 per generation) between a CNV locus and its flanking SNPs on the estimation of M was evaluated. Our observations indicated that the estimation of M was robust when the recombination rate was less than 10−3 per generation and that a recombination rate of 10−3 per generation or above can inflate the estimates of M (Figure S3E).

Effect of Recombination Rate between Adjacent SNPs on the Estimation of M

The effect of recombination rate (10−7, 10−6, 10−5, 10−4, and 10−3 per generation) between adjacent SNPs on the proposed algorithm for estimating M was also examined by simulation. It was illustrated that the estimation of M was robust to varying recombination rates between adjacent SNPs (Figure S3F).

Supplemental Data

Document S1. Six Figures and Two Tables:

Web Resources

The URLs for data presented herein are as follows:


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