The Rutgers Map v.2 also provides three novel features that are not generally offered by other publicly available maps. First, we have estimated approximate 95% confidence intervals for the size of all 24,145 map intervals, both on the sex-averaged and sex-specific maps. This feature may be useful for assessing sensitivity of an analysis to map uncertainty and for combining the information in the Rutgers Map v.2 with map estimates derived from independent studies. In addition, we have applied local regression to create a smoothed version of the Rutgers Map that separates all markers by non-zero map distances. Overall, this alternative map should provide better estimates of map distance since nearly half of the map intervals in the Rutgers Map v.2, while physically distinct, show no evidence of recombination. Third, the smoothed map facilitates interpolation of map positions for markers that are not on our map. For example, a cM-scale map position can be easily estimated for any of the millions of SNP markers that have not been genotyped in the CEPH reference pedigrees and hence are not present on any of the CEPH-based linkage maps.

Table 1. Description of the second-generation Rutgers combined linkage–physical maps

Rutgers Map v.2 spans a total of 2925.8 Mb (2,925,822,157 bases), covering 96.8% of the Build 36.1 assembled genome. The physical coverage varies by chromosome. While the average percentage of physical length spanned by these maps is 94.7%, 15 of the chromosomes have >99.5% coverage. The acrocentric chromosomes (13, 14, 15, 21, 22) have considerably lower coverage, ranging from 68.6% (chromosome 22) to 83.8% (chromosome 13), due to the presence of large regions of heterochromatin that result in sequencing gaps.

These maps are 7.5 Mb longer than our Rutgers Map v.1 (when compared to the B35 versions of our maps, which were updated on our website post-publication), indicating that the additional SNPs added to the mapping set provide greater coverage of most chromosomes. For example, the map coverage of chromosome 20 increased by 2.17 Mb due to the addition of 11 SNPs on the map’s q-telomere end. Similarly, map coverage of chromosome 13 increased by 1.19 Mb due to the addition of 12 SNPs at the beginning of the map.

This second-generation Rutgers combined linkage–physical map (Rutgers Map v.2) has almost double the number of markers as the previous version and provides a unique and valuable map for several types of genetic analysis. The data have been carefully cleaned, and the position of each marker on the map is supported by both physical and recombination-based data. The smoothed maps provide a non-zero map distance between all markers and facilitate interpolation of additional markers not already on the map.

We used CRIMAP (Lander and Green 1987), an extremely fast map estimation program, to estimate our linkage maps. However, CRIMAP can yield biased estimates in the presence of missing data (Stewart and Thompson 2006; Stewart 2007). To assess the accuracy of our map estimates, we used LM_MAP, a program that generates the maximum likelihood estimate (MLE) of the map in the presence of missing data, for comparison. Differences between our map and the MLE were negligible, confirming that the bias (if any) in our map is minimal.

The confidence intervals provided with this map could be used in two ways: (1) to quantify the effect of map uncertainty on a genetic analysis; and (2) to combine the information in the Rutgers Map v.2 with independent map estimates obtained from individual studies. First, in critical regions it may be helpful to repeat any genetic analysis using a small number of different maps, where the maps are selected so that their variance is representative of the sampling error of the map estimate. This is important since, despite the fact that many investigators ignore the effect of map uncertainty, several studies have shown the potential of incorrect map distances to negatively impact multipoint linkage analysis (Halpern and Whittemore 1999; Daw et al. 2000). Furthermore, many other analyses (e.g., genotype error detection and haplotype inference) could also be negatively affected by map uncertainty. Second, since LM_MAP provides direct estimates of variability for arbitrary linkage mapping datasets, the information in our Rutgers Map v.2 could easily be combined with the information in independent linkage mapping datasets via meta-analysis. Stewart (2007) showed that a meta-analysis of independent map estimates can yield less-variable maps with increased resolution, relative to the variability and resolution of any of the independent maps used in the meta-analysis.

This map contains virtually all of the polymorphic markers that have been genotyped in the CEPH standard reference pedigrees, and to our knowledge it is the most dense linkage map published to date. Other polymorphisms that investigators may be using can be localized onto our map using interpolation. Alternatively, as described above, meta-analysis could be used to combine our map with localized maps produced using genotype data from disease studies.

Files providing limited details about each marker (e.g., marker heterozygosity, number of informative meioses, Build 36 physical position) along with map positions (sex-averaged, female, male, smoothed) and confidence intervals are available on the Rutgers Map website at http://compgen.rutgers.edu/maps.

In total, 899 SNPs were genotyped by two or more companies. For each of the redundant SNPs, we retained only the genotypes that were assayed in the largest sample, leaving 13,666 nonredundant SNPs. The genotypes at the 13,666 nonredundant SNPs were analyzed for genotyping errors, identified using the PedCheck (O’Connell and Weeks 1998) program as non-Mendelian transmission events. We checked linkage groups using two-point linkage analysis to confirm that each SNP was linked to its corresponding chromosome with a lod score of ≥3.0, since unlinked markers cannot be used for map construction. We pooled the genotypes at the nonredundant SNPs with the genotypes that were used to construct the Rutgers Map v.1 to obtain our working data set that contains 28,425 markers.

To understand the adjusted Wald method and how it applies to map estimation, consider a single map interval and a set of n independent, fully informative meioses. If nonrecombinant and recombinant intervals are labeled as zero and one, respectively, then the standard estimate of the recombination rate p is the sample mean x, and the standard 95% confidence interval for p is x ± 2/. Note that (x) = x(1 − x) is a function of x, and that genetic distance is a function of p. The adjusted Wald method replaces x by (Σx_i + 2)/(n + 4), which permits construction of nondegenerate confidence intervals when x and (x) are both zero. Although most of the meioses in our linkage mapping data set are not fully informative, the information in our data is equivalent to some number of independent, fully informative meioses, denoted by n. In this sense, the degenerate confidence intervals have Σx_i = 0. We estimate the value of n separately, for the sex-averaged, female, and male maps using only the nondegenerate confidence intervals whose corresponding map distances are also non-zero.

In principle, our confidence intervals could be used in conjunction with Rutgers Map v.2 to posit realistic multivariate distributions for linkage maps, which would make it easy for investigators to quantify the effect of sampling error on their analyses. This is important since almost all multipoint genetic analyses contain an added, but often ignored, layer of variability that is attributable to uncertainty in the map.

Map distances were smoothed with local regression using a quadratic fit, as implemented in the Locfit package in R (Loader 1999). The smoothed fit can be done to an arbitrarily dense grid; we used a grid with double the density of the number of markers on each chromosome map. The smoothing parameter, which determines the degree of smoothing applied to each chromosome, was selected by the Akaike information criterion (AIC) (Akaike 1974). Because of the desirability of applying the same degree of smoothing to the male and female maps, a common value for the smoothing parameter was selected as the one that minimized, over the two individual maps, the maximum increase of the AIC over its respective optima. Selection of the smoothing parameter is equivalent to selecting the number of markers used in the sliding window to determine the local smoothed fit. Under certain circumstances it was possible for the local regression to develop negative slope, an undesirable artifact of smoothing. Consequently, the next step was to monotonize the local regression fit as implemented in the monoproc package in R (Dette et al. 2006). The result was a dense, smoothed, nondecreasing map.

Map positions on the centimorgan scale can be interpolated for markers not present on our map. Given a marker’s physical position, linear interpolation from the dense grid is used to identify a corresponding cM map position.

We thank Dr. Linda Brzustowicz for helpful discussions. This work was partially supported by National Institutes of Health grants GM080221, HG003229, and MH068457 (T.C.M.), HG00040, HG002651 (W.C.L.S.), and AA015346 (S.G.B.) and by March of Dimes grant 12-FY02-108 (T.C.M.).