Fine Mapping in 94 Inbred Mouse Strains Using a High-Density Haplotype Resource

The genetics of phenotypic variation in inbred mice has for nearly a century provided a primary weapon in the medical research arsenal. A catalog of the genetic variation among inbred mouse strains, however, is required to enable powerful positional cloning and association techniques. A recent whole-genome resequencing study of 15 inbred mouse strains captured a significant fraction of the genetic variation among a limited number of strains, yet the common use of hundreds of inbred strains in medical research motivates the need for a high-density variation map of a larger set of strains. Here we report a dense set of genotypes from 94 inbred mouse strains containing 10.77 million genotypes over 121,433 single nucleotide polymorphisms (SNPs), dispersed at 20-kb intervals on average across the genome, with an average concordance of 99.94% with previous SNP sets. Through pairwise comparisons of the strains, we identified an average of 4.70 distinct segments over 73 classical inbred strains in each region of the genome, suggesting limited genetic diversity between the strains. Combining these data with genotypes of 7570 gap-filling SNPs, we further imputed the untyped or missing genotypes of 94 strains over 8.27 million Perlegen SNPs. The imputation accuracy among classical inbred strains is estimated at 99.7% for the genotypes imputed with high confidence. We demonstrated the utility of these data in high-resolution linkage mapping through power simulations and statistical power analysis and provide guidelines for developing such studies. We also provide a resource of in silico association mapping between the complex traits deposited in the Mouse Phenome Database with our genotypes. We expect that these resources will facilitate effective designs of both human and mouse studies for dissecting the genetic basis of complex traits.

P HENOTYPIC variation among inbred mouse strains exposed to a disease-causing agent (be it genetic, infectious, or environmental) provides potential insight into human disease processes that often cannot be practically achieved through direct human studies. Indeed, hundreds of phenotype measurements related to human diseases are available for dozens of inbred strains in common use over the past 50-100 years Grubb et al. 2009). As with the direct study of chronic disease in humans, key steps toward determining the genetic underpinnings of this phenotypic variation are to develop a catalog of the genetic variation among inbred mouse strains and to interpret the structure of variation patterns across the strains. Recent advances in high-throughput genotyping and DNA resequencing technologies are making it possible to rapidly uncover the genetic variation maps of many model organisms (Lindblad-Toh et al. 2005;Mackay and Anholt 2006;Borevitz et al. 2007;Frazer et al. 2007;International Hapmap Consortium 2007;Star Consortium 2008). A recent whole-genome resequencing study of 15 inbred mouse strains captured a significant fraction of the genetic variation among a limited number of strains, allowing researchers to infer patterns of genetic variation and to identify the ancestral origin of the genetic variation Yang et al. 2007). Yet the availability and common experimental employment of hundreds of inbred strains, including .190 stocks available from the Jackson Laboratory, motivates the need for a highdensity variation map for a larger set of strains. We have assembled the Mouse HapMap, a resource consisting of a dense set of genotypes for a total of 138,980 unique biallelic single nucleotide polymorphisms (SNPs) in 94 inbred mouse strains at an average spacing of 20 kb on chromosomes 1-19 and X.
This resource is ideal for performing high-resolution mapping studies under QTL peaks. We evaluate the feasibility and effectiveness of such studies by examining a typical study from the Mouse Phenome Database (MPD) Grubb et al. 2009) (http://www.jax. org/phenome) and measure the statistical power to detect genetic associations in regions of various sizes. We provide several resources to the mouse genetics community for supporting such studies and a webserver that can estimate the significance threshold, compute the statistical power of a proposed study, and perform in the fine mapping of measured phenotypes. In addition, we provide a database of associations for all phenotypes contained in the MPD. The web resources are available at http://mouse.cs.ucla.edu/.

MATERIALS AND METHODS
Array design: The Mouse HapMap genotypes were obtained using two Affymetrix genotyping arrays with 20 or 36 perfect match/mismatch probe pairs. SNPs were selected to be as evenly spaced as possible across the NCBI build 33 and mapped to NCBI build 37. Genotypes were called with the Affymetrix DM algorithm, and the genotypes with low confidence or with conflicting calls between replicated samples or any discovery strain were called as missing.
Analysis of shared segments: We assigned each segment in the 94 strains of the Mouse HapMap to a founder strain representing a different ancestral origin as well as identified shared segments among strains using a hidden Markov model following the approach presented in Frazer et al. (2007). The mapping with four founder strains was performed with a hidden Markov model with four reference strains representing possible founders with an additional state for unknown reference, learning the parameters from the genotype data using the expectation-maximization (EM) algorithm as described in the imputation method. A hidden Markov model with two states representing common and divergent regions was constructed for each pairwise comparison, with a recombination parameter u ¼ 10 À8 and a mutational parameter m ¼ 0.03, estimated from the distribution of maximumlikelihood parameters using the EM algorithm among all 4371 comparisons. The fraction of the genome with shared segments was computed as the fraction of genome-wide SNPs with the probability of shared segments .0.9. The number of distinct ancestral segments at a genomic position was computed by taking all the pairwise probabilities of shared segments and performing hierarchical clustering with a median agglomeration method by taking the pairwise probabilities as elements of a similarity matrix. Imputation of missing genotypes: We performed imputation using EMINIM (Kang et al. 2009) of the Perlegen/ National Institute of Environmental Health Sciences (NIEHS) data  in the 94 strains to increase the number of genotypes available for the 94 strains. Briefly, a hidden Markov model was constructed for each strain targeted for imputation with 16 1 1 states per SNP representing each of 16 resequenced reference strains and a state representing an equivocal reference strain. Unlike the previous methods (Scheet and Stephens 2006;Marchini et al. 2007), the maximum-likelihood parameters of genome-wide mutation and the recombination parameters were learned from the data using the EM algorithm and the forward-backward algorithm, independently for each strain. For the leave-one-out imputation for experimentally missing genotypes in the resequenced strains, 15 1 1 states were used, excluding the target strain for imputation.
Threshold estimation: To control the false-positive rate of in silico mapping, significance thresholds guaranteeing a 5% false-positive rate were estimated for regions of size 10, 20, and 30 Mb via simulation. For each size n-Mb region, the genome was split into non-overlapping bins of size n. For each of these bins, a random phenotype capturing background genetic effects was generated, and Efficient Mixed Model Association (EMMA) (Kang et al. 2008) was used to perform association between the phenotype and all SNPs within the region. The most significant association was recorded for each bin. The threshold was then determined by taking the P-value that was the maximum among the smallest 5% of all P-values within this set. A total of 10,000 simulations were performed.
Power simulation: Statistical power for in silico mapping was estimated for a set of mouse strains by utilizing a simulationbased framework. First, we generated a random phenotype with a correlation structure that is consistent with the genetic background by using a kinship matrix derived from the relatedness between the strains. Second, we adjusted the phenotypic values on the basis of a particular SNP having a genetic effect. That is, the phenotype values for strains that have one allele at the SNP were increased by a predetermined amount corresponding to the strength of the genetic effect. Finally, we used EMMA (Kang et al. 2008) to detect the association of this SNP with this phenotype and recorded whether or not EMMA reports an association stronger than the significance threshold. This type of simulation was performed over 10,000 SNPs chosen uniformly at random from a set of .100,000. The statistical power is then defined as the fraction of associations detected at the pre-determined significance threshold.
Mapping resolution simulations: Mapping resolution was estimated in each of the strain sets by utilizing a simulationbased framework. Phenotype data were generated in a similar manner as in the power simulations by using a randomly chosen SNP with a genetic effect. EMMA was used to detect the associations for all SNPs within 10 Mb of this SNP. For any simulation where any SNP in the region exceeded the significance threshold, we recorded the genomic distance between the causal SNP and the SNP with the most significant P-value in the region. This type of simulation was performed over 10,000 SNPs chosen uniformly at random from a set of .100,000. The mapping resolution was then defined as the average of the distance between the most significant SNP and the SNP simulated to have a genetic effect.
Additional strain selection: Using the Paigen2 mouse strain set (Svenson et al. 2007) from the Mouse Phenome Database as a starting point, we determined a new set of 33 inbred strains that would provide an increase in power when compared with the Paigen2 set. Our strain set was selected by first removing both wild-type and some genetically similar strains from the original Paigen2 strain set of 42 strains [for high-density lipoprotein (HDL) cholesterol]. The resulting 27 strains were used as a template to build a new inbred panel. We used a subset of Mouse HapMap strains as a candidate panel and iteratively selected mice that were genetically dissimilar to the template set. We selected candidate strains on the basis of their maximum genetic correlation with all strains in the growing template panel. The strain that had the maximum correlation, which was minimum among all candidate strains, was selected, and the procedure was repeated.
In-silico association mapping database: We downloaded the individual phenotype measurements of the Mouse Phenome Database (MPD) from the Jackson Laboratory and selected 474 quantitative phenotypes containing phenotype measurements in at least 20 strains. We applied EMMA (Kang et al. 2008) as an implementation of linear mixed models to correct for population structure and genetic relatedness, using the kinship matrix generated as a genotype similarity matrix. The variance component was based on a restricted maximumlikelihood estimate, and a standard F test was performed as previously suggested (Yu et al. 2006;Zhao et al. 2007). The false discovery rate (FDR) significance level was estimated using the q-value R package (Storey and Tibshirani 2003). The males and females were mapped for association separately. The genomic control inflation factor was computed by taking the median P-value and computing the corresponding x 2 statistic divided by 0.455 (Devlin and Roeder 1999).

RESULTS
The Mouse HapMap resource: We have assembled a dense set of genotypes for a total of 138,980 unique biallelic SNPs in 94 inbred mouse strains at an average spacing of 20 kb on chromosomes 1-19 and X. We selected the most commonly used inbred laboratory strains-especially targeting priority strains from the Mouse Phenome Database Grubb et al. 2009)-and 19 wild-derived strains both as reference out-groups and to help identify ancestry of genomic segments (Table 1). Our data set is a composite of 121,433 SNPs discovered and genotyped at the Broad Institute by comparing data from the two inbred mouse genome sequencing projects (Mouse Genome Sequencing Consortium 2002; Mural et al. 2002), with additional discovery in a wild-derived strain in regions of low marker density. In addition, we included 7570 SNPs covering physical gaps in the Broad Institute map revealed by examining data from the concurrent NIEHS/Perlegen effort to resequence 15 inbred strains ) and 13,094 SNPs discovered and genotyped at the Wellcome Trust Center for Human Genetics (WTCHG) that could be mapped to Build 37 of the mouse genome.
To evaluate the quality of these resources, we examined SNPs typed in common by Broad and WTCHG and compared each resource to the genotypes of strains produced from the NIEHS/Perlegen sequence data. SNPs overlapping between the Broad and WTCHG sets demonstrate a discordance rate of 0.00058, while SNPs overlapping WTCHG and NIEHS/Perlegen sequencebased genotypes demonstrate a discordance rate of 0.00688. The extremely high concordance of the Broad and WTCHG data and significantly higher accuracy than the array-based sequence genotypes are unsurprising; the Broad and WTCHG utilized established SNP genotyping techniques and need distinguish only between two homozygous genotype classes. An interesting disparity in discordance rate is observed between Perlegen and WTCHG genotypes. When the WTCHG genotype is the reference strain allele (C57BL/6J), the disparity with Perlegen genotype is 0.00335 and is 0.0106 otherwise. This is consistent with the variant discovery strategy employed by Perlegen, which emphasized low false-positive variant discovery at the expense of a higher false negative rate . Figure 1 summarizes the genotype resources for each of the 94 strains.
Haplotype structure among the strains: By using these genotype resources, we are able to examine the fine-level haplotype structure among the strains. For example, a comparison of the six 129 strains shows that they share the vast majority of their genomic segments, but there are several notable differences. In particular, there is a large disparity between 129P2/OlaHsD and 129X1/SvJ from 35 to 100 Mb on chromosome 7, and there are also differences specific to 129S6/SvEv on chromosomes 3, 5, and 12 (supporting information, Figure S1). Similarly, comparisons between the 15 C57 strains revealed significant discrepancies between C57BL/6J and the other C57 strains ( Figure S2). We also identified that some strains appear to result from recent hybridizations between two or more strains. We observed that HTG/GoSfSnJ shares .99.9% of the genome with either BALB/cByJ or C57BL/6J ( Figure  S3) and that NOR/LtJ shares .99.9% of segments with either NOD/LtJ or C57BLKS/J, confirming the annotated genealogical history (Beck et al. 2000) ( Figure S4). We also observed that two strains (RBA/DnJ and SOD/ EiJ) are ''hybrid'' strains with genetic content from both classical inbred and wild-derived strains. ( Figure S5). When comparing the fraction of the genome shared by any of the 12 classical inbred resequenced strains, there is a clear difference between the rates of sharing with the wider set of classical inbred strains (97% of the genome on average and 81% minimum) and with the wildderived strains (28% on average, 56% maximum) ( Figure 2). We allocated ancestry of local genomic regions to one of the four ''founder'' strains using the methods described previously for resequencing data . For each of the remaining 90 strains, we identified the fractions of genomic regions unequivocally close to the domesticus, musculus, castaneus, and molossinus strains. On average, these ancestral strains contribute 32. 3%, 9.19%, 4.52%, and 11.8%, respectively; 42.2% of the observed total genomic regions are ambiguous for ancestry, meaning either that the ancestry is not precisely represented by any of the four founder strains (37.3%) or that two or more ancestral subspecies share haplotypes in these regions (4.86%). The fractions of regions identified as having domesticus or unknown ancestry differ from previous studies ) due to the sparser resolution of the SNP map and the SNP ascertainment bias inherent in both current and former data sets. We note that these ancestry estimates make many assumptions, one of which is that the founder strains represent the true ancestral populations of the strains. Other studies that make slightly different assumptions such as Yang et al. (2007) differ in their ancestry estimates. All of the classical inbred strains and hybrid strains share predominantly domesticus ancestry [with Yang et al. (2007) having a higher estimate of the percentage of domesticus ancestry compared to Frazer et al. (2007)], while the wild-derived strains are divided into four groups corresponding to their respective ancestral subspecies: this is also reflected in the phylogeny derived from the Mouse HapMap data (Figure 3). To investigate the average sizes of shared haplotype segments among strains, we identified common (low SNP density) and divergent (high SNP density) ancestral segments across the genome for each pair of inbred strains using a hidden Markov model . Among the 4371 possible pairwise comparisons of the 94 strains, an average of 32.5% of the genomic regions are shared between any pair of strains ( Figure  4). The average number of shared ancestral segments genome-wide is 280 per comparison, which is about one segment per 10 Mb. On average, there are 176 segments C57BL/6J is not included in the 15 resequenced strain, but it is the reference strain that has been fully sequenced. O, included; X, excluded. HY, hybrid strain; IN, inbred strain; WI, wild-derived strain.
Fine Mapping in 94 Inbred Mouse Strains .1 Mb covering 28.8% of the genome, and 39 segments longer than 5 Mb covering 15.6% of the genome, which is reflective of the tight recent co-ancestry of these strains. Given a cross between any of the two parental strains, it is possible to estimate the genomic region excluded from mapping variations associated with phenotype traits due to the shared segments between them. For example, in mapping studies using BXD recombinant-inbred strains, 48.6% of genomic regions are shared between parental strains, and loci in these regions will not be mapped to traits.
To ascertain whether intervening genotypes might be successfully imputed from the resequencing data, we counted how many distinct haplotypic segments exist for each genomic region and compared this with the numbers derived from the resequencing data by combining the shared segment analysis using hierarchical clustering. The average number of distinct segments within any region is estimated to be 4.70 over 73 classical inbred strains. This limited diversity likely reflects recent bottlenecks, where a limited number of chromosomes from the founder strains gave rise to the modern inbred strains (Wade et al. 2002;Frazer et al. 2004Frazer et al. , 2007. Among the 12 resequenced classical inbred strains, an average of 3.46 ancestral segments were identified. Like the analysis of shared segments, these results suggest that most of the genetic variation existing among the classical inbred strains can be explained by the variation present in the resequenced strains. Integrating NIEHS/Perlegen resequencing and Hap-Map data: Now confident that we could identify segment ancestry by reference to the 16 resequenced strains, we proceeded to impute genotypes for the 8.27 million NIEHS/Perlegen SNPs on the 78 genotyped strains using a hidden Markov model that determines genome-wide transition and mutation parameters using the EM algorithm (Dempster et al. 1977;Kang et al. 2009). A feature of the technique that we used for imputation is the ability to obtain confidence levels for each prediction (Kang et al. 2009). We were able to call the majority of SNPs (79.2%) with high confidence (posterior probability .0.98) when genotypes were successfully called in all 16 resequenced strains (see Table 2 for details). We found that confidence scores vary greatly, with 11 wild-derived strains having no highconfidence imputed genotypes because their estimated mutation rates were very high. In contrast, all 9 strains with the C57BL/6 prefix have .99.7% with a highconfidence call rate, due to their genetic proximity to the reference strain C57BL/6J. We were also able to impute genotypes missing in the 16 resequenced strains, but only 17.2% of these with high confidence due to poor probe quality resulting in unreliable data (Table 2). We estimated the accuracy of our imputed genotypes in two different ways. First, we used a leaveone-out cross-validation approach to impute genotypes for each of the 16 resequenced strains using the remainder. When considering the SNPs with complete data in the resequenced strains, the average leave-oneout imputation error over the 12 classical inbred resequenced strains was 1.59%, dropping to 0.27% when only high-confidence genotypes were used (Table  3, Table S1). We found that these rates varied substantially among the 12 classical inbred strains (range: 1.17-3.63%; high-confidence genotype error range: 0.21-0.67%). These errors increase when considering the four wild-derived strains, with the total imputation error ranging from 13.0% to 34.1% (Table S2). These   (100) The percentage of imputed genotypes in each category is shown within parentheses. The confidence level corresponds to the predicted posterior probability of the imputation method. The level of resequencing corresponds to the number of missing genotypes in the 16 resequenced strains. error differences likely reflect the divergent ancestry of the imputed strains because the marker set remains biased toward the strains used for SNP discovery. Next, we estimated accuracy by comparing our imputed genotypes to data previously generated by the WTCHG on 47 of the 78 genotyped strains (Table 4) and found a total error rate of 4.86% (2.26% when excluding the 11 wild-derived and hybrid strains). Restricting our sample to the 71.7% of the imputed genotypes called at highconfidence genotypes reduces this error to 0.37%, .10 times smaller than recently published results for this marker subset using a different method (Szatkiewicz et al. 2008). As in the previous error estimate, the imputation error again differs greatly by strain, ranging from 0.065% to 20.9% (0.019% to 4.41% for highconfidence imputed genotypes) (Table S3).
In summary, we were able to impute 657,300,201 genotypes across 8.27 million markers in 94 inbred strains, including 14,622,883 experimentally missing genotypes in the resequencing strains and 1,265,768 genotypes missing in the combined genotype sets (Table 2). This creates a near-comprehensive snapshot of variation in commonly available mouse strains.
To estimate the cost effectiveness of expanding this resource, we evaluated the potential imputation coverage made possible by increasing either the number of resequenced strains or the number of SNPs in the HapMap as discussed in File S1, Figure S6, and Table S4.
Trait mapping with the Mouse HapMap resource: This detailed picture of haplotype diversity in the mouse allows us to map traits in the inbred strains by correlat-ing genomic ancestry to trait measurements, rather than generating de novo experimental crosses. This in silico association mapping has two advantages: (1) it allows us to capture the full spectrum of diversity in the inbred strains rather than a subset used as progenitors of an experimental cross and (2) phenotypic noise can be minimized by performing replicates on genetically identical individuals. In particular, this approach should complement traditional QTL linkage mapping (often successful at locating large chromosomal segments) by providing a higher resolution, association-based component and indeed has already yielded several positive results (Grupe et al. 2001;Liao et al. 2004;Pletcher et al. 2004;Guo et al. 2006;Liu et al. 2006;Moran et al. 2006;Cervino et al. 2007;Guo et al. 2007;Liu et al. 2007;McClurg et al. 2007;Tang et al. 2008). The basic idea behind this type of study is that a region is first identified through a genetic cross or some other means, resulting in a large QTL region typically in the tens of megabases in length that contains many genes. Several dozen inbred strains are then phenotyped, and association analysis is performed in this region.
The association analysis requires two steps. The first is to determine an appropriate significance threshold that depends on the size of the QTL region. The second is to perform the association on each marker within this region. The key idea increasing the power of this approach is that since only the markers under the QTL are examined, the significance threshold will be much less conservative than a genome-wide significance threshold. We perform simulations to evaluate the  (100) The percentage of imputed genotypes in each category is shown within parentheses.  (100) The percentage of imputed genotypes in each category is shown within parentheses.
Fine Mapping in 94 Inbred Mouse Strains statistical power and mapping resolution of such an approach as well as provide insights into the design of such studies. Statistical power of in silico association: As has been previously shown by several studies (Payseur and Place 2007;Manenti et al. 2009), data sets consisting of several dozen strains do not have enough statistical power to detect weak effects (5% variance explained) with genome-wide significance. We evaluate the feasibility and effectiveness of mapping in a localized region the size of a typical QTL peak. One complication in our analysis is that the high degree of relatedness between strains described above introduces a systematic bias in association mapping in silico: an inflation of test statistics leading to false-positive associations, caused by population structure and genetic relatedness among the strains (Aranzana et al. 2005;Yu et al. 2006;Zhao et al. 2007;Kang et al. 2008). For example, among the 180 phenotypes deposited in the Mouse Phenome Database at the Jackson Laboratory with .30 distinct strains, 59% (106) of them have .50% of the interstrain phenotypic variance explained by population structure and genetic relatedness measured by using a variance component test ( Figure 5). At an FDR level of 0.05, 51% (91) of the phenotypes are significantly associated with population structure. We and others have shown that these issues can effectively be corrected using linear mixed models (Yu et al. 2006;Zhao et al. 2007;Kang et al. 2008). To evaluate the effectiveness of fine mapping through in silico association, we use the Paigen2 study as a typical study representative of the types of studies in the MPD study (Svenson et al. 2007). The Paigen2 study contains phenotype measurements for HDL cholesterol in 42 strains-33 classical inbred strains and 9 wild-derived strains-and contains an average of 21 replicates per strain (Table 5). While this study is somewhat larger than most of the studies in the MPD, we chose this study    to examine because it contained many phenotypes and included both wild-derived and classical inbred strains, which allowed us to explore study design choices in terms of the strains chosen.
We performed simulations to obtain both the significance threshold and statistical power. As described in Kang et al. (2008), the statistical power depends on the background genetic effect or intuitively on how much the intrastrain relatedness explains the phenotypic variance. In our framework, this relatedness is modeled with a variance component defined by the genetic similarity between the strains. We performed our simulations by varying the background genetic effect from 25% to 75% to capture the wide range of potential phenotypes. For actual phenotype values, the background genetic effect can be estimated from a phenotype by comparing the interstrain variance to the intrastrain variance after fitting the variance component model. Using simulations (see methods), we computed the 0.05 level of significance for 10-, 20-, and 30-Mb regions (see Table 6). We found that the level of the background genetic effect did not affect the significance threshold (data not shown), but the choice of strains had a significant effect. We can observe this phenomenon by comparing the significance threshold of the full set of 43 strains to the significance threshold of using just 33 classical inbred strains.
Using these thresholds, we performed an additional set of simulations to compute the power to detect various genetic effect sizes under the different backgrounds and region sizes shown in Table 7. The results show that the statistical power of a study of this size is high either for phenotypes where the background genetic effect is low or for strong genetic effects. Since both the threshold and power depend on the strain set and are estimated using computationally intensive simulations, we provide a webserver resource (http:// mouse.cs.ucla.edu/) for performing these simulations and threshold estimation.
We note that any set of strains is able to map only traits linked to variation that is polymorphic within the set of strains. Since the Mouse HapMap consists mostly of  (33)    We removed the wild-derived strains and 6 inbred strains that are very genetically similar to other strains in the study and replaced these strains with more distant classical inbred strains. The number of strains in the new set, 33, is equal to the number of classical inbred strains phenotyped in Paigen2.
SNPs that are polymorphic among the laboratory strains (not wild-derived), there is little power to detect SNPs that are polymorphic only among the wild-derived strains. Our simulation framework essentially ignores this problem since the possible set of simulated genetic variants are, by necessity, within the set of data used to generate the simulation. Alternative strategies for mapping traits, such as genetic crosses that include wild-derived strains or inbred strains with significant proportions of wildderived strain ancestry [such as the Collaborative Cross (Churchill et al. 2004)], will have higher power to map traits to loci polymorphic among wild-derived strains. Furthermore, the statistical power to map a trait to a specific locus greatly depends on the number of strains carrying the minor allele of the locus, which is similar to the effect of minor allele frequency on the power of human association studies.
Resolution of in silico association mapping: The main advantage of the in silico approach is the increased resolution compared to traditional QTL approaches. To evaluate the resolution, we again performed simulations using the set of strains in the Paigen2 study. We performed 10,000 simulations, and for each simulation we generated phenotype data assuming a randomly selected causal variant and then performed association mapping over the generated phenotypes and recorded the difference between the genomic location of the most associated marker and the causal variant. The resolution experiments demonstrate that the median distance between the actual causal variant and the closest marker is $3 Mb (Table 8), a significant improvement over a traditional cross.
Design of in silico association studies: Interestingly, as shown in Table 8, there was only a moderate power loss when we considered using only the 33 classical inbred strains from the Paigen2 study. Part of the reason for this is that, for the SNPs that are unique to the wildderived strains and are not polymorphic in the classical inbred strains, the power to detect associations at these SNPs is low since there are relatively few wild-derived strains included in the study.
We further explored how the choice of strains included in the study affects statistical power. We note that among the strains included in the Paigen2 study, there are several strains from the C57 group that are very genetically similar. A total of 6 strains of the 33 inbred strains are very similar to other strains in the set. We constructed a new set of inbred strains, removing these similar strains and replacing them with more distant classical inbred strains (Table 9). Using power simulations, we observed that this set of 33 strains has more power than the set of classical inbred strains included in the Paigen2 study and, surprisingly, has comparable power to the complete Paigen2 set of (43) strains (Table 7). These simulations are computationally intensive, and as a resource for the community, we provide a webserver (http:/ /mouse.cs. ucla.edu) for performing these simulations.
Mouse Phenome Association Database: To enable the research community to have access to the populationstructure-corrected associations, we have developed a corrected association database in conjunction with the MPD, in which we find that 71/180 phenotypes collected in .30 strains have at least one significant association (P , 1 3 10 À6 ). The database contains results for both the genotyped and the imputed SNPs. Among the phenotypes, 11 (6.1%) phenotypes showed significant associations across .20 different genomic regions, which may indicate residual bias from other sources generating false positives. This may be compared to 24 (13%) phenotypes showing association without population structure correction to .20 different genomic regions, while the total number of phenotypes with significant associations is similar (Figure 6). When comparing the ''inflation factor'' suggested by genomic control between different statistical tests, the t-test showed much higher overall inflation (l ¼ 2.08 6 1.29) compared to the linear mixed model (l ¼ 1.15 6 0.18) over the 180 MPD phenotypes, confirming that the rates from the conventional t-test were overly inflated false-positive rates (Figure 7). DISCUSSION We have described a high-density genotype resource for 94 inbred mouse strains and have demonstrated the viability of applying such a resource to fine mapping using in silico association. Our genotype data are available at http://mouse.cs.ucla.edu/mousehapmap/. In addition, we have established a website (http://mouse. cs.ucla.edu/) at which researchers can download genotype data and access a genome browser that allows the visualization of the haplotype and shared segment analyses. The website also supports inbred association mapping, allowing users to upload their collected phenotypes, and computes the significance thresholds and estimated statistical power. The website (http:// mouse.cs.ucla.edu) includes association results using the genotypes and all collected phenotype data in the Mouse Phenome Database.
A major concern for in silico association mapping has been that the effect of population structure potentially causes false positives. We have shown previously that EMMA corrects for this population structure using a linear mixed model (Kang et al. 2008) with a variance component using a kinship matrix obtained from the genetic similarity between strains. However, even with the correction, there is a slight inflation of statistics observed for some phenotypes in the associations in the Mouse Phenome Database. This inflation may be caused by a variety of factors, including different amounts of phenotypic variance in each strain, the kinship matrix not completely capturing the background genetic effects, and other confounding effects such as ''cage effects,'' which are correlated with the strains. We report the genomic control l-values (Devlin and Roeder 1999) as a means of quantifying the amount of inflation, and we urge users of the association database to take this inflation factor into account when interpreting the results of the phenotype associations.
Our study is one of several recent efforts for developing genetic and genomic resources for inbred mouse strains. Recently, Yang et al. (2009) developed a novel high-density genotyping array, which includes many SNPs chosen from both the Mouse HapMap and the Perlegen resequencing data ). In addition, the Wellcome Trust Sanger is currently sequencing 17 mouse genomes (Sudbery et al. 2009) (http:/ /www.sanger.ac.uk/resources/mouse/genomes/). Both of these efforts in combination with existing resources will lead to more dense and accurate genetic maps for laboratory strains.
Fine mapping of QTL loci by performing in silico association using inbred strains is just one of several approaches recently proposed to increase the mapping resolution of traditional QTL approaches. Alternate strategies include using the Collaborative Cross (Churchill et al. 2004), which contains a large number of inbred strains derived from eight parental inbred strains; using a breeding strategy to avoid population structure; using the Hybrid Mouse Diversity Panel (Bennett et al. 2010), which combines classical inbred strains with recombinant inbred strains; and using outbred stock (Valdar et al. 2006). Each of these strategies has advantages and disadvantages.
The mouse community is just one of many communities developing genetic and genomic resources for mapping complex traits. Similar efforts are being undertaken for many model organisms including Arabidopsis (Borevitz et al. 2007), Drosophila (Mackay and Anholt 2006), dog (Lindblad-Toh et al. 2005), and rat (Star Consortium 2008).