PMC

The North American sample (RAL) comprised 37 genomes, while the African sample (RG) comprised 22 genomes.

(Left): Wavelet coherence of the two maps for chromosome arm 2L. The cone of influence is shown in white. (Right): For each arm, the plot shows the fraction of the genome with significantly high coherence at the 5% level, at each scale.

Plotted for each chromosome arm are the estimated recombination maps using our method and the consensus experimental map hosted at FlyBase . To ease comparison each map is LOESS-smoothed using a span of 15%. LDhelmet estimates were converted into units of cM/Mb by normalizing them to have the same total genetic distance as the empirical map.

Black circles denote Kendall's rank correlation between pairs of detail coefficients at each scale. Crosses denote the correlation that would be required for significance at the 1% level in a two-tailed test; red crosses are those scales at which the correlation is in fact significant.

(Top): Estimated recombination rate for RAL (blue) and RG (red) in a 50 kb region of chromosome 3R, and their respective mean recombination rates in this region (dotted). (Bottom): Evidence of recombination hotspots in the same region, evaluated according to sequenceLDhot. The dotted line shows the likelihood ratio cutoff we used.

The telomere is at the left end of the region. The recombination rate between positions 10 kb and 20 kb is considerably higher than the rate in the subtelomeric region immediately to the right. This trend is much more pronounced in the North American X than in the African X, consistent with a previous study .

The experimental genetic map of Singh et al. is shown in black with confidence intervals. The LDhelmet estimate for the RAL sample is shown in blue, while the estimate for the RG sample is shown in red. The LDhelmet estimates were converted into units of cM/Mb by normalizing them to have the same total genetic distance as the empirical map for the region. The three maps demonstrate high correlation, especially near the center of the region, where they share the highest peak in the same interval.

The whole arm is shown on the left, and a detailed (central) 1 Mb is shown on the right, for RAL and RG. Black contours denote regions of significant power at the 5% level, and the white contour denotes the cone of influence. Color scale is relative to a white noise process with the same variance. Lower panels show estimates of the corresponding recombination maps.

In each study, the program MaCS was used to simulate data, with sample size 22, for a 1 Mb region with the variable recombination map shown in red. (We used ; output was postprocessed to incorporate an empirical quadra-allelic mutation model.) Estimated recombination maps are shown in blue. The same block penalty of 50 was used in both cases. (A) The average recombination rate for the region is per kb, representative of the interior of the North American X. (B) The average recombination rate for the region is per kb, representative of the interior of the African X.

(A) In a linear model for the detail coefficients of the wavelet transform of the recombination map of chromosome arm 2L, covariates are the detail coefficients of wavelet transforms of data quality, gene content, GC content, divergence, and diversity. Shown is the −-value of the regression coefficient at the given scale, as determined by a t-test. Colored boxes indicate significant relationships, with red positive and blue negative. Also shown in the adjusted . (B) As above, but with the recombination map of the other population as an additional covariate.

In each plot, different colors represent the results for different datasets. The left and right columns show the estimated recombination maps of LDhelmet and LDhat, respectively, using the same block penalty of 50. Our method LDhelmet generally produces less noisy estimates than that produced by LDhat. (First Row) Each dataset was simulated with a constant recombination rate of per bp. (Second Row) Each dataset was simulated with a hotspot of width kb starting at location kb. The background recombination rate was per bp, while the hotspot intensity was the background rate, i.e., per bp. The maps are shown in their entirety, including potential edge effects.

Diagonal plots show the global wavelet power spectrum of each feature of the RAL (blue) and RG (red) data. Off-diagonal plots show Kendall's rank correlation between pairs of detail coefficients at each scale, with respect to the wavelet decomposition of the two indicated features. Crosses denote the correlation that would be required for significance at the 1% level in a two-tailed test; red crosses are those scales at which the correlation is in fact significant. The bottom left and top right plots correspond to RAL and RG, respectively.

In each plot, different colors represent the results for different datasets. The left and right columns show the estimated recombination maps of LDhelmet and LDhat, respectively, using the same block penalty of 50. In each simulation, the selected site was placed at position kb and the population-scaled selection coefficient was set to . The fixation time of the selected site was coalescent unit in the past. Although the estimated recombination maps are in general noisier than that for the neutral case (c.f., ), LDhelmet is more robust than LDhat. As illustrated in the plots, LDhat produces false inference of elevated recombination rates near the selected site more frequently than does LDhelmet. The same scenarios of recombination patterns as in were considered: (First Row) with a constant recombination rate of per bp, and (Second Row) with a hotspot of width kb starting at location 11.5 kb. The background recombination rate was per bp, while the hotspot intensity was the background rate, i.e., per bp. The maps are shown in their entirety, including potential edge effects.