© 2004 Nature Publishing Group http://www.nature.com/naturegenetics

LETTERS

Evidence for substantial fine-scale variation inrecombination rates across the human genome
Dana C Crawford1, Tushar Bhangale2, Na Li3,4, Garrett Hellenthal3, Mark J Rieder1, Deborah A Nickerson1,2 &Matthew Stephens3
Characterizing fine-scale variation in human recombination
rates is important, both to deepen understanding of therecombination process1 and to aid the design of diseaseassociation studies2,3. Current genetic maps show that rates varyon a megabase scale, but studying finer-scale variation using
pedigrees is difficult. Sperm-typing experiments4–6 havecharacterized regions where crossovers cluster into 1–2-kb hot
spots, but technical difficulties limit the number of studies7. An
alternative is to use population variation to infer fine-scalecharacteristics of the recombination process. Several surveys8–10
reported ‘block-like’ patterns of diversity, which may reflect
fine-scale recombination rate variation11–13, but limitations ofavailable methods made this impossible to assess. Here, weapplied a new statistical method, which overcomes theselimitations, to infer patterns of fine-scale recombination ratevariation in 74 genes. We found extensive rate variation bothwithin and among genes. In particular, recombination hot spots
are a common feature of the human genome: 47% (35 of 74) ofgenes showed substantive evidence for a hot spot, and many
more showed evidence for some rate variation. No primary
sequence characteristics are consistently associated with precise
hot-spot location, although G+C content and nucleotide
diversity are correlated with local recombination rate.
Population-level variation carries important information about finescale recombination rates14. Crossover events tend to reduce population-level association (commonly known as linkage disequilibrium;LD) among alleles on either side of the crossover, and so the expectedamount of LD between sites depends on the recombination rate
between them2. Until now, however, methods used to extract this information, such as plots of pair-wise LD measures, did not distinguishreliably between patterns that are due to recombination rate variationand patterns that could arise by chance, with no rate variation11,12. We
used a statistical method that can make this distinction and can reliably
predict the presence of recombination hot spots (defined as a small
region where crossovers occur more than ten times more frequently
than in surrounding sequence) from population data15.

To briefly describe the method: assume haplotypes are available orhave been estimated. The method considers each sampled haplotype
in turn and attempts to construct it as a mosaic of previously considered haplotypes. Under simplifying assumptions about population
demography, the method uses the average length of mosaic pieces toestimate the local background recombination rate, and the positionsof breaks in the mosaic to estimate the location and intensity of hot
spots. It also measures the strength of the evidence for a hot spot, usinga Bayes factor (BF), which is the probability of obtaining the data if a
hot spot is present divided by the probability of obtaining the data if a
hot spot is not present. The BF is akin to a likelihood ratio, but it integrates over (rather than maximizing over) the uncertainty in haplotypic phase and putative intensity and location of a hot spot. A BF of
10 indicates that the data are ten times more likely to be obtained if
there is a hot spot than if there is not, and we consider this substantive
evidence for a hot spot. In computing the BF, the method takes into
account chance clustering of recombination events, or recombinant
haplotypes drifting to high frequency, thus guarding against overconfidence that ‘block-like’ patterns of LD are due to recombination ratevariation.
To illustrate the approach, we applied it to previously publishedgenotype data from 50 individuals from the United Kingdom ofEuropean descent at five regions of the MHC where sperm typing identified recombination hot spots5. Polymorphism-based methods andsperm-typing methods measure different things. Sperm typing measures meiotic recombination rates in a few extant males, whereas patterns of polymorphism are shaped by recombination in ancestors ofsampled individuals and, therefore, reflect average recombination rates
in transmissions from many males and females over thousands of generations. Differences between results from the two approaches might
therefore point to such biological mechanisms as selection or sex-specific fine-scale recombination. For these data, however, results from thetwo approaches agree closely: four regions showed substantive evidence
in the polymorphism data for a hot spot (BF = 35, >100, >100, >100),and the fifth, suggested by sperm-typing results to have an intensity
close to our threshold of ten times the background rate, showed mild
evidence (BF ≈ 1.3). The estimated locations and intensities of hot

Departments of 1Genome Sciences, 2Bioengineering and 3Statistics, University of Washington, Box 354322, Seattle, Washington 98195, USA. 4Present address:
Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, Minnesota 55455, USA. Correspondence should be addressed to M.S.
(stephens@stat.washington.edu).
Published online 6 June 2004; doi:10.1038/ng1376

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Figure 1 Estimated locations and intensities ofhot spots from MHC polymorphism data5 (leftpanel, HLA-DNA; right panel, HLA-DMB). The
dotted, dashed and dotted-dashed green lines
show estimates from three independent
applications of our method; the thicker solid line
shows their average. In each interval between
consecutive SNPs, the plot shows the posteriormean of the intensity in that interval, relative tothe background rate of recombination. The steplike appearance of the plots therefore reflects
uncertainty in the estimated location of the hot
spot. The vertical black lines show theapproximate hot-spot center and the verticaldotted gray lines show the approximateboundaries of the hot spots, both estimated from
sperm-typing results5.

0

20

40

Estimated intensity

60
40

90,00095,00010,0000

Position

105,000

110,000

Position

35 genes occurred in hot spots, which covered ∼6% of the sequence.
Most hot spots were narrow (only two spanned >4 kb), but our method
assumed that most hot spots would be narrow, and hot-spot boundaries
are difficult to estimate precisely from polymorphism data. Indeed, thenotion of a hard boundary may itself be misplaced5. There was no obvious pattern of hot-spot location within a gene: estimated hot-spot centers lay in introns, exons and upstream regions.
Figure 3 shows the 90% credible intervals (CIs) for estimated hotspot intensities. Several genes without substantive evidence for a hot
spot nevertheless show evidence for some rate variation (CI excluding1). Others have CIs that cover almost the entire range of possible intensities, suggesting that their polymorphism data are uninformative. Few
genes show strong evidence against a hot spot (Figs. 2a and 3): no genes
have a BF <0.1 in either population, and only eight have CIs that exclude
intensities >10. On this basis, ∼90% of genes could contain hot spots.

spots from the polymorphism data (Fig. 1) were consistent with spermtyping results, although we limited intensities to <100, which hindereddirect comparison of estimated intensities.
We applied the same method to search for hot spots in 74 candidate
genes (Supplementary Table 1 online) that we resequenced in 23
European Americans and 24 African Americans. Although previous
simulation results15 suggested that the method is relatively robust to
population structure, we minimized potential effects by analyzing thetwo population samples separately. Thirty-five genes (47%) showed
substantive evidence for a hot spot in one or both samples: 19 in both
samples, 11 in African Americans only and 5 in European Americans
only (Fig. 2a). Estimated intensities in these genes ranged from 20 to 80,
although at least two-thirds had results suggestive of intensities >100.
Even with our conservative limit on hot-spot intensity and assumptionof no more than one hot spot per gene, ∼60% of recombinations in these

0.01

0.1

1

10

100

1,000

Strength of evidence (BF) for hot spot in AA sample

1

F3
F13A1
MMP3
FGB
F10
C2
SELE
HMGCR
PROS1
SMP1
TNFRSF1B
TFPI
NOS3
F2RL1
SFTPD
F2R
PPARG
F9 IL12B
TF
PLG
CSF3R
F11 IL1ASERPINA5
IL10RA
TGFB3
CD9
IL12A
SELP
ACE
PON2
PROC
IL1RN
MAP3K8
APOB
TRAF6
IRAK4
PPARA
PON1
IL15RA
STAT4
JAK3
AGT
REN
F2RL2
KLK1
PLAUR
F5
ABO
AGTR1
LDLR
IL21R
IL1R1
SERPINE1
VEGF
IL4
IL4R
BDKRB2VCAM1KLKB1IL1R2PROZ
SFTPA2
TIRAP
APOH
CD36
CYP4F2SFTPA1IL2RB
KNG
IL10RB

0.01

0.1

1

10

100

1,000

BF in sample from population without bottleneck

1,000
100
10
1

10

PLAT

F2RL2
VEGF
SFTPA2JAK3PLAUR
SFTPA1
IL21RIL2RB
CD36
PON1
IL4
IL10RB
IL15RA
TFPI
SELE
SELP
TNFRSF1B
LDLR
AGTR1
F2R
VCAM1
BDKRB2F5PPARA
PLG CSF3R
IL1A
IL4R
SERPIN
IL10RA
F10
F11
TIRAP
PPARG
KNG
TGFB3
F3
KLKB1
NOS3
TF
TRAF6
SFTPD
HMGCR
PROZ
F2RL1
KLK1
SMP1
SERPINE1
STAT4
F9
IL12B
MMP3
PROS1
MAP3K8C2FGB
CD9 IRAK4
IL12A
AGT
F13A1 ACE
F2
IL1R1
PLAT
PROC
APOB
IL1R2
IL1RN
PON2
ABO
REN
APOH
CYP4F2

0.1

1,000
100

BF in sample from population with bottleneck

0.01

ABO

F2

0.1

0.1

1

10

F10
TF
F13A1 IL2RB
IL1R1 PPARG
F3
STAT4
KNG
IL10RASFTPA1NOS3 F9LDLR
SELE
KLK1
PPARA
TRAF6
BDKRB2
F11
SMP1
IL4R
KLKB1
F2R
REN
TFPIC2
IRAK4
PROZ
F2RL1
PLAT
HMGCR
PROS1
SFTPD
CD9
F2
PON2
SERPINE1
TIRAP
IL1AIL1R2
IL12APROC
MAP3K8
FGB
ACE
AGT
TGFB3
IL12B
MMP3
CYP4F2
IL1RN
APOH

c

0.01

100

SERPINA5
VEGF
JAK3
VCAM1
SFTPA2PLAUR
IL10RBSELPTNFRSF1B
IL15RA
PON1 CD36
PLG
F5
IL21R
IL4
F2RL2
APOB
AGTR1
CSF3R

BF in sample from population with bottleneck

b
1,000

a

0.01

Estimated intensity

20
0
10,000 15,000 20,000 25,000 30,000 35,000 40,000

Strength of evidence (BF) for hot spot in EA sample© 2004 Nature Publishing Group http://www.nature.com/naturegenetics

80

100

LETTERS

0.01

0.1

1

10

100

1,000

BF in sample from population without bottleneck

Figure 2 BFs summarizing the strength of the evidence for a hot spot in each gene and each population sample. Colored background shading indicates regionsof the graph that correspond to genes with substantive evidence for a hot spot (BF >10) in one or both samples. All axes are on a log scale. (a) Results for real
data: x axis, BF for the African American (AA) sample; y axis, BF for the European American (EA) sample. (b,c) Results for simulated data without a hot spot(b) and with a hot spot (c). The gene name indicates which gene the simulated data matched for SNP density, length and background levels of recombination.
(b) The color of the gene name indicates the assumed ratio of rate of gene conversion to crossing-over (black, 0; magenta, 1; orange, 10). (c) The color of thegene name indicates the intensity of the simulated hot spot: black, 1–10 (i.e., no hot spot); red, 10–20; green, 20–50; blue, 50–100.

NATURE GENETICS VOLUME 36 | NUMBER 7 | JULY 2004701© 2004 Nature Publishing Group http://www.nature.com/naturegenetics

LETTERSOne potential concern is that deviations from the method’s simplistic characteristics across populations are not implausible. But patterns ofmodeling assumptions could lead to detection of hot spots where none LD reflect the average recombination process in the ancestors of a popexist. To test this, we applied the method to data sets simulated with con- ulation, and not the average over extant individuals. Because humanstant recombination rate and varying levels of gene conversion under a populations share much of their evolutionary history, even large difdemographic scenario in which one ancestral population splits into two ferences in the recombination landscape of extant populations may be
populations, one of which undergoes a bottleneck (mimicking a difficult to detect from LD data.
European American population) and the other of which undergoes an
Nonetheless, we assessed support for population differences in
expansion (mimicking an African American population), with limited three ways. First we examined, using simulations, how often we
recent migration from European Americans to African Americans should expect a BF >10 in only one population sample if the popu(mimicking admixture). We simulated 74 data sets to match actual lations share common hot-spot characteristics. Results (Fig. 2c)genes and population samples. In contrast to the real data, only one sim- suggest that this is not unusual for the sample sizes, densities of sinulated data set showed substantive evidence for a hot spot in either pop- gle-nucleotide polymorphisms (SNPs) and levels of population difulation, and many showed substantive evidence against a hot spot (Fig. ferentiation in our data. Second, for genes showing substantive2b). Further simulations under different assumptions showed similar evidence for a hot spot in only one population sample, we carriedpatterns (Supplementary Fig. 1 online). These simulations represent out a likelihood ratio (LR) test of the hypothesis that there is a hotsome of the most plausible deviations from the modeling assumptions spot of the same intensity in both populations. The most signifiunderlying the method2 and include scenarios previously shown to have cant difference was in CSF3R (LR = 11.3, P = 0.03). Finally, we
the largest effect15,16.
One factor not included in our modelingassumptions or simulations is selection.
SFTPA2SFTPA2
Unlike population demography, however,
F2RL2
F2RL2
VCAM1
VCAM1
selection will influence each locus differently,
PLAUR
PLAUR
IL21R
IL21R
and so is less likely to produce large-scale, sysVEGF
VEGF
SELP
SELP
TNFRSF1B
tematic distortion of the results. Furthermore, TNFRSF1B
APOH
APOH
PLG
PLG
we found no relationship between genes idenF5
F5
PPARG
PPARG
tified here as containing hot spots and thoseSERPINE1SERPINE1REN
REN
IL10RB
IL10RB
whose polymorphism data suggest strong
SERPINA5SERPINA5
JAK3
JAK3
selective pressure (J. Akey, personal commuIL1R1
IL1R1
KNG
KNG
nication), and genes with particular molecular
TGFB3
TGFB3
F10
F10
IL4
IL4
functions were no more likely to be identified
LDLR
LDLR
IL2RB
IL2RB
as containing a hot spot (Supplementary
PPARA
PPARA
IL15RA
IL15RA
Table 2 online). Thus, although we considered
CD36
CD36
PON2
PON2
F9
F9
genes from specific functional pathways, our
TF
TF
TRAF6
TRAF6
results should be representative of genes
MAP3K8
MAP3K8
F13A1
F13A1
across the genome.
PROZ
PROZ
F3
F3
PON1
PON1
The large number of hot spots identified in
IL1RN
IL1RN
NOS3
NOS3
our data seems not to be an artifact caused by
IL4R
IL4R
SMP1
SMP1
deviations from simplistic modeling assumpAPOB
APOB
CYP4F2
CYP4F2ABO
ABOtions, but rather reflects a genuinely high freIL1R2
IL1R2
AGTR1
AGTR1
quency of recombination hot spots throughout
SELE
SELE
C2
C2
the human genome. If we assume that the 35
F2
F2
SFTPA1SFTPA1
CSF3R
CSF3R
genes with substantive evidence for a hot spot
AGT
AGT
SFTPD
SFTPD
have a single hot spot, and no other genes have
ACE
ACE
PROS1
PROS1
hot spots, then the hot-spot frequency is one
PLAT
PLAT
FGB
FGB
TFPI
TFPI
per 63 kb. This estimate seems conservative, as
IL12B
IL12B
IL1A
IL1A
it ignores the possibility of multiple hot spots in
KLKB1
KLKB1
TIRAP
TIRAP
a gene5 or of genes containing hot spots but
BDKRB2
BDKRB2
F2RL1
F2RL1
IRAK4
IRAK4
having inconclusive LD data. Thus, in human
F11
F11
F2R
F2R
genes, hot spots are probably at least as frequent
IL10RA
IL10RA
HMGCR
HMGCR
as in the human MHC class genes (one every
STAT4
STAT4
MMP3
MMP3
PROC
PROC
60–90 kb) and may be as frequent as in
CD9
CD9
KLK1
KLK1
17
Saccharomyces cerevisiae (one every 50 kb) .
IL12A
IL12A
We identified several genes (11 in African
Americans and 5 in European Americans)
1
10
100
1
10
100
that show substantive evidence for a hot spot
Hot-spot intensity
Hot-spot intensity
in one population but not the other, whichraises the question of whether populations
Figure 3 Estimated 90% (symmetric) CIs for hot-spot intensity in each gene in each population sample
differ in their recombination landscape.
(red, African Americans; green, European Americans). Genes are listed, from top to bottom, in order ofBecause the recombination process varies decreasing BF in the African American sample. Dark shading indicates those genes with substantive
18,19
among individuals
and through evolu- evidence for a hot spot (BF >10) in Figure 2a. The vertical black line in each box indicates the mediantionary time20,21, differences in hot-spot of the posterior distribution of intensity. The x axis is on a log scale.

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LETTERS

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Estimated recombination rate / background recombination ratea0

10,00020,00030,00040,000

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b

5,000

10,00015,00020,00025,000

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(LR = 9.2, P = 0.04). A similar analysis of CD36 suggested that it
might also have two hot spots and that the intensity of the righthand hot spot might differ between populations (LR = 12.7; P =0.02). These LR and P values must be interpreted carefully (seeSupplementary Methods online), but they provide a useful guideto the evidence for differences among populations and suggest
genes for further investigation by sperm typing.
Our method also estimates a background recombination rate foreach gene, and these varied substantially among genes (Supplementary
Table 3 online). As expected, estimates from the two population samples were highly correlated (correlation = 0.79). Estimates for European
Americans were typically substantially lower than for African
Americans (median ratio = 0.29), emphasizing the tendency for LD toextend over greater distances in European Americans. Consistent withprevious reports22,23, nucleotide diversity (African Americans,
P = 0.001; European Americans, P = 0.0005) and pedigree-based
recombination rate estimates (African Americans, P < 0.0001;
European Americans, P < 0.00005) were positively correlated with estimated local background recombination rates, as was G+C content(African Americans, P < 0.0001; European Americans, P = 0.02;
Supplementary Tables 1 and 3 online). In contrast, there was no relationship between recombination rate and frequency of interspersed
repeat elements (African Americans, P = 0.59; European Americans,
P = 0.75). When we used multiple linear regression to control for pedigree-based estimates, the effects of both G+C content and nucleotide
diversity remained significant in African Americans, and diversity
remained significant in European Americans (Table 1). This suggeststhat the effects of nucleotide diversity and G+C content operate on afiner scale than the megabase scale on which pedigree-based estimates are obtained. (The generally larger P values in European
Americans may reflect lower precision of estimates due to lower SNP
density; Supplementary Tables 1 and 3 online.) Although G+C content has been correlated with recombination rates in humans on amegabase scale18,24, this is the first observation to our knowledge offiner-scale correlation.
G+C content and diversity have been previously associated with theexistence of hot spots: high G+C content is associated with presence of
hot spots in S. cerevisiae25, and the TAP2 (ref. 21) and β-globin26 hotspots in humans coincide with regions of higher nucleotide diversity.
But we found no evidence for either effect in our data. There were nodifferences in G+C content of genes with substantive evidence for a
hot spot versus genes without (t-test: African Americans, P = 0.34;
European Americans, P = 0.36), and for genes with substantive evidence for a hot spot, there was no significant difference in the G+C
content inside versus outside of estimated hot-spot boundaries (bootstrap: African Americans, P = 0.45; European Americans, P = 0.46).
Similarly, we found no evidence for increased diversity in hot spots(paired t-test based on nucleotide diversity: African Americans,
P = 0.32; European Americans, P = 0.75; paired t-test based on SNP
density: African Americans, P = 0.06; European Americans, P = 0.65).
This suggests that, in humans, although G+C content and diversity
may influence the background recombination rate on a scale of tens ofkilobases, any effect they have on the existence of narrow hot spots is
subtle or inconsistent across genes.

20

Estimated recombination rate / background recombination ratec0

© 2004 Nature Publishing Group http://www.nature.com/naturegenetics

visually inspected estimated hot-spot locations in genes showing
substantive evidence for a hot spot (Supplementary Fig. 2 online)
to identify genes where estimated hot-spot locations differed
between samples. Although most genes had similar estimated hotspot locations across samples (e.g., Fig. 4a and Supplementary Fig.
2 online), a few did not, including PLAUR (Fig. 4b) and CD36 (Fig.
4c). Analysis with a two-hot-spot model, however, suggested that
PLAUR has two hot spots in both populations and that the intensityof the left-hand hot spot might differ between populations

0

5,000

10,00015,00020,00025,000

Position (bp)

NATURE GENETICS VOLUME 36 | NUMBER 7 | JULY 2004

30,000Figure 4 Estimated intensity and location of hot spots based on the African
American sample (red) and the European American sample (green) for three
genes. See legend to Figure 1 for details on interpretation. Estimatedlocations for the two population samples are similar in many genes,
including SELP (a). Exceptions include PLAUR (b) and CD36 (c). See
Supplementary Figure 2 online for similar plots for other genes.

703© 2004 Nature Publishing Group http://www.nature.com/naturegenetics

LETTERSWe searched genes for DNA sequence Table 1 Results of multiple linear regression of estimated background recombination rateelements previously hypothesized to influ- on G+C content, nucleotide diversity and pedigree-based estimates of recombinationence hot-spot existence. None was consisCoefficientStandard error
P valuetently associated with the presence of hot
spots (Supplementary Table 4 online), African American sample
supporting previous suggestions that any Intercept
–3.79
0.79
–
5.56
1.68
0.0015relationship between primary sequence and G+C content
586.52246.800.020
hot-spot location is complex1,25. Although Diversity
0.34
0.13
0.012
the hot spots identified here substantially Pedigree-based estimates
increase the number of human hot spots European American sample
available for analysis, absolute numbers Intercept
–4.40
1.05
–
3.19
2.28
0.167
remain small. Analyses of population data G+C content
886.35356.590.015
provide both a valuable resource for sug- Diversity
0.54
0.18
0.003
gesting regions for future sperm-typing Pedigree-based estimates
experiments and a fast, cheap and reliable
method for identifying the large numberof hot spots that may be necessary to unravel the complex, and haplotypic phase of our data is unknown, we incorporated the estimation ofperhaps highly heterogeneous, mechanisms underlying the recombination parameters into the PHASE v2.1 software for haplotype estimation27,28 (see Supplementary Methods online). To compute BFs, we used therecombination process.

Variation discovery. As part of the National Heart, Lung, Blood Institute’s
Program for Genomic Applications, we resequenced 126 candidate genes
involved in lipid metabolism, inflammation and blood pressure regulation tolook for variation in 47 individuals from two populations: 23 unrelated
European Americans from CEPH pedigrees (NA06990, NA07019, NA07348,
NA07349, NA10830, NA10831, NA10842, NA10843, NA10842–NA10845,
NA10848, NA10850–NA10854, NA10857, NA10858, NA10860, NA10861,
NA12547, NA12548, NA12560) and 24 African Americans from the AfricanAmerican Human Variation Panel (NA17101–17116 and NA17133–NA17140).
All DNA samples are anonymous and are available to the public throughCoriell Cell Repository. This study received a Human Subjects exemption fromthe University of Washington (no. 00-3300-X).
For a typical gene, we resequenced the genomic region spanning the longest
reference transcript in LocusLink, including the exons and introns, as well as
2.5 kb upstream and 1.5 kb downstream on average. We designed overlapping
primers for PCR to span the gene and then sequenced PCR products using
Applied Biosystem’s Big Dye sequencing protocol on ABI3700 and ABI3730
machines. Data analysts assembled the sequence data for each gene onto a reference genomic sequence using Phred and Phrap and edited the resulting alignments for accuracy using Consed. We then identified polymorphisms using
PolyPhred 4.0 from pair-wise comparisons of individual sequence chromatograms in regions with an average Phred quality score >40. Analysts
reviewed all polymorphisms identified by PolyPhred for false positives associated with features of the surrounding sequence or biochemical artifacts. If thepolymorphism identified was an insertion-deletion polymorphism, analysts
manually genotyped each sample and designed primers from the other strand
to sequence past the polymorphism. Comparison of genotype calls from thisprotocol with calls on the TaqMan platform showed error rates to be <1%. We
deposited all genetic variation identified, and corresponding allele frequencies
and genotypes, into GenBank and dbSNP.
To reduce computational demands, we ignored sites with minor allele frequency (MAF) <0.05. To reduce the chances of imprecise estimates from uninformative data, we analyzed only those genes that had, in both populations, atleast 20 biallelic sites with MAF ≥ 0.05. We also excluded the two genes >100 kb
in overall length (ITGA2, 106 kb; ITGA8, 206 kb), as the assumption of a single
hot spot seemed least likely to hold for these longer genes. Of the initial pool of
126 genes, 74 genes met these requirements. A list of the 74 genes and GenBank
accession numbers can be found in Supplementary Table 1 online. The molecular function of all 74 genes based on level 1 classification using PANTHER islisted in Supplementary Table 2 online.

simple hot-spot model15, which assumes that there is a single hot spot of constantintensity λ. Crossovers occur as a Poisson process of constant rate r (per kilobase,per meiosis) outside the hot spot and of constant rate λr inside the hot spot (soλ = 1 corresponds to a constant recombination rate). The model has four parameters: the background population recombination parameter ρ (which equals
4Ner, where Ne is the effective population size); the intensity of the hot spot, λ;and the hot-spot center and width. The prior distribution for ρ was uniform on
log10(ρ) in the range ρ = 10–5–106 per kb, spanning several orders of magnitude
on either side of the expected average value for humans (0.4 per kb, assuming
Ne = 10,000 and r = 1 cM Mb–1). We assumed a priori that the center of the hot
spot was equally likely to be anywhere along the length of the sequence and thatthe width of the hot spot was ∼200–4,000 bp (specifically, that the width had anormal distribution, with mean 0 bp and standard deviation 2,000 bp, truncatedto lie above 200 bp). For each population sample and each gene, we assumed that
there was no recombination rate variation (i.e., λ = 1), that there was a ‘warm
spot’ (1 < λ < 10) or that there was a hot spot (10 < λ < 100), with longer genes
being less likely to show no variation. Specifically, for a gene of length L we
assumed that λ = 1 with probability q = exp(–L/50,000); otherwise log10(λ) is
uniformly distributed on (0, 2). This corresponds to a prior assumption that hot
spots and warm spots each occur as a Poisson process of average rate 1 per 100 kb.
We then used Markov Chain Monte Carlo (see Supplementary Methods online
for further details) methods to obtain a sample of size 1,000 from the joint posterior distribution of all the parameters and the unknown haplotypes, given the
genotype data G. From this, we estimated p10 = Pr(λ >10 | G), the posterior probability of a hot spot given the data. The BFs in Figure 1 are Pr(G | λ > 10) / Pr(G |λ < 10), which, by Bayes theorem, equals p10 (q + 0.5(1 – q))/(1 – p10)(0.5(1 – q)).
To allow for potential problems with convergence of the Markov Chain Monte
Carlo algorithm, we ran the algorithm three times for each analysis, using different seeds for the pseudorandom number generator, and used the mean of thethree estimates of p10 in computing the BFs. (We used the mean so that the BF islarge only if all three estimates of p10 are large.) Similarly, to estimate the locationand intensity of the hot spot, we used the posterior mean in each run and thenused the median of the values obtained from the three runs. The CIs in Figure 3
and Supplementary Table 3 online are based on the sample of size 3,000 obtainedby pooling the results from the three independent runs. Although combining
results from independent runs in this way has no theoretical justification, we view
it as a pragmatic way of avoiding gross errors due to poor convergence of the sampler in a single run. Supplementary Figure 2 online gives some idea of variability
across runs.
Computational times for each application of the method varied from 4 min(C2 in African Americans) to 5.5 h (F5 in African Americans) on a 2.4-GHz
processor with 4 Gb of RAM.

Estimation of background rates of recombination and identification of hot
spots. To assess the support in the polymorphism data for a recombination hot
spot, we used the ‘product of approximate conditionals’ model15. Because the

MHC data. We obtained the MHC polymorphism data from the Jeffreys lab
website. We divided the data into five nonoverlapping contiguous regions, eachcontaining one of the hot spots identified by sperm typing. We analyzed eachregion independently, as described above.

METHODS

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LETTERS
Simulations. We simulated the data used to produce Figure 2b,c andSupplementary Figure 1 online using coalescent-based software29. For
Figure 2b,c, we assumed that an ancestral population of size 9,000 split 2,800
generations ago into two populations, whose sizes instantaneously changed
to 9,000 and 10,000, respectively. The first population experienced exponential growth from 9,000 to 10,000 individuals starting 2,000 generations ago.
The second population experienced a bottleneck 400–600 generations ago,during which its size reduced to 500 individuals, before returning to its prebottleneck size. Finally, 20 generations ago, one-way gene flow started fromthe second population to the first, at a rate of 0.25 migrants per generation.
These parameters were provided by J. Akey and were chosen to match
approximately the real data in various summary statistics, including thedivergence between the populations (measured by FST), and Tajima’s D ineach population (J. Akey, personal communication). For the data used to
produce Supplementary Figure 1 online, we simulated data for two populations independently, under two different demographic scenarios: expansion,and bottleneck followed by expansion. For each scenario, we assumed anancestral population size of 8,600, which grew exponentially from 500 generations ago to a present size of 100,000. For the bottleneck scenario, thepopulation was also assumed to undergo a bottleneck 900–2,000 generations
ago, during which its size was reduced to 860 individuals. After the bottleneck, the population returned to its prebottleneck size of 8,600 individuals
before expanding as in the expansion scenario. The parameters of the bottleneck simulation were chosen to reduce expected SNP density to ∼60% of thelevels of the expansion scenario, approximately mimicking the reduction in
our European American (as compared with African American) samples.
In each case, we simulated data for 74 genes that matched the data on the 74
real genes with respect to numbers of individuals, numbers of SNPs with MAF>5%, physical length and background levels of LD. This last was accomplishedby using kρA as the value of ρ = 4N0r for the simulations, where ρA is the estimated value of ρ from the real data from African American samples and k is aconstant chosen to account for the fact that the software requires ρ to beentered in terms of the current population size N0 rather than the effective population size (we used k = 4/3 for Fig. 2; k = 10 for Supplementary Figure 1
online). For the simulations in Figure 2, we also matched the number of SNPs
that were shared across populations, by first simulating a large number of total
SNPs and then randomly selecting a subset of these SNPs such that the numberof SNPs that exceeded MAF >0.05 in (i) both populations, (ii) the first population only or (iii) the second population only matched our real data. For eachsimulated gene, gene conversion was assumed to occur uniformly across thegene, with average tract length of 250 bp and at a rate of zero, one or ten times
the crossover rate, with roughly equal numbers of genes in each rate category30.
To create data with recombination hot spots (Fig. 2c and Supplementary
Fig. 1 online) we used a previously described algorithm15. For each gene, wechose the location and intensity of the hot spot to match the corresponding
estimates from the real data from European American (for Fig. 2c) or African
American samples (for Supplementary Fig. 1 online).
LR computations. For genes showing substantive evidence for a hot spot in
only one population sample, we computed the LR to test the null hypothesisthat the intensity of the hot spot is the same in each population. We first
fixed the hot-spot location at the position estimated from the sample with
substantive evidence for a hot spot and used a Markov Chain Monte Carlo
scheme as above to sample from the posterior distribution for log10(λ), independently for each sample, using a uniform prior distribution onlog10(λ) = 0–2 and the prior distribution on ρ given above. We then usedkernel density estimation (from the R statistical package) to estimate theposterior density for log10(λ) for each sample. Because of our uniform priordistribution, this posterior density is proportional to the likelihood. We
computed LRs under the assumption that the data in the two samples wereindependent and were therefore equal to LRA(λA) LRE(λE) / LRA(λ0)
LRE(λ0), where LRA(.) is the likelihood for the African American sample,
LRE(.) is the likelihood for the European American sample, λA is the value of
λ that maximizes LRA(λ), λE is the value of λ that maximizes LRE(λ) and λ0
is the value of λ that maximizes LRA(λ)LRE(λ). All maximizations were done
over a dense grid of λ values. In some cases, the likelihood seemed to be
maximized above log10(λ) = 2, in which case we repeated the process with a

NATURE GENETICS VOLUME 36 | NUMBER 7 | JULY 2004

uniform prior distribution on log10(λ) = 0–3. We calculated P values withthe assumption that under the null hypothesis, 2log(LR) has an asymptotic
χ2 distribution on 1 degree of freedom.
Sequence motif search. We searched each gene for the sequence motifs
hypothesized to affect recombination rates (listed in Supplementary Table 4
online) and for microsatellites and ‘words’ (with alphabet A,C,G,T) to determine whether they are over-represented in the hot-spot regions.
Microsatellites were defined by a minimum number of repeats for each unit
size: ten repeats for a mononucleotide repeat, six repeats for a dinucleotide
repeat, five repeats for a trinucleotide repeat, three repeats for a tetranucleotide repeat or greater. We searched the sequence of each gene for words
as long as 15 letters. To determine whether sequence motifs, microsatellites
or words were significantly associated with hot spots, we counted the number of occurrences in the hot-spot region and the number of occurrences
outside the hot-spot region for each population separately. We then carriedout a boot-strap analysis to calculate the P values for tests of significance. For
the boot-strap procedure, for each gene, we independently simulated thepresence or absence of a hot spot with the probability of a hot spot being thenumber of genes with BF >10 for each population divided by 74. For eachgene assigned a hot spot in the simulation, we chose the hot-spot width atrandom from the empirical distribution of width estimates in each population. The position of the hot spot in the gene was selected uniformly along
the DNA sequence, conditional on the hot spot being contained entirely
within the DNA sequence. We counted the number of occurrences of thesequence motifs, microsatellites or words in the simulated hot spots. The
simulations were repeated 10,000 times. We carried out a similar boot-strap
analysis to determine whether G+C content was significantly associated withthe presence of hot spots.
To investigate association between the estimated background recombination
rate (ρ) and G+C content, nucleotide diversity, repetitive elements, sequencemotifs and map-based estimates of recombination rate, we carried out multiple
linear regressions of log(ρ) against these variables for each population sample
separately, using R. We calculated nucleotide diversity as the average number of
pairwise sequence differences across each gene (Supplementary Table 1
online). Repetitive elements were identified using RepeatMasker Map-based
estimated of recombination rates were deCode estimates18 obtained from the
University of California Santa Cruz Genome Browser.
URLs. The Program for Genomic Applications from SeattleSNPs is available at
http://pga.gs.washington.edu. Phred, Phrap and Consed are available at
http://www.phrap.org. Polyphred 4.0 is available at http://droog.mbt.washington.edu./PolyPhred.html. PANTHER is available at http://panther.appliedbiosystems.com/about.jsp. PHASEv2.1 is available at http://www.stat.washington.
edu/stephens/software.html. The Jeffreys lab website is http://www.le.ac.uk/ge/
ajj/HLA/index.html. The R statistical package is available at http://www.R-project.org. The University of California Santa Cruz Genome Browser is available at
http://genome.ucsc.edu/cgi-bin/hgGateway. RepeatMasker is available at http://
www.repeatmasker.org/.
Note: Supplementary information is available on the Nature Genetics website.
ACKNOWLEDGMENTS
We thank members of the SeattleSNPs team and the laboratory of D.A.N.
(M. Ahearn, B. Borrayo, E. Calhoun, M. Chung, S. Da Ponte, L. Daniels,
M. Daniels, C. Hastings, B. Howie, P. Keyes, P. Lee, B. Livingston, R. Mackelprang,
M. Montoya, C. Nguyen, D. Nguyen, C. Poel, N. Rajkumar, P. Robertson,
W. Schackwitz, T. Shaffer, A. Sherwood, K. Sherwood, J. Sloan, R. Torskey, E. Toth,
L. Witrack. M. Wong and Q. Yi) for their efforts in variation discovery and
M. Przeworski for critical reading of this manuscript. This work was supported by
grants from the National Heart Lung and Blood Institute Program for Genomic
Applications (D.A.N. and M.J.R.), the National Institute for Environmental Health(D.A.N and M.J.R.) and the National Human Genome Research Institute (M.S.).
COMPETING INTERESTS STATEMENT
The authors declare that they have no competing financial interests.
Received 3 February; accepted 13 May 2004
Published online at http://www.nature.com/naturegenetics/705

© 2004 Nature Publishing Group http://www.nature.com/naturegenetics

LETTERS
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