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Commentary

Predicting the range of linkage disequilibrium
Jurg Ott

Laboratory of Statistical Genetics, Rockefeller University, 1230 York Avenue, New York, NY 10021-6399

A much pondered question in the Mid-dle Ages was, ‘‘How many angels can
dance on the head of a pin?’’ Today, we
pose more sensible questions but answers
are not necessarily getting easier.

A generally accepted strategy in the
mapping of a disease gene is to initially
apply linkage analysis for an approximate
estimate of the location of the trait gene
and to subsequently make use of linkage
disequilibrium (association) for a more
accurate localization. The thinking behind
this approach has been that disequilibrium
extends over much shorter distances from
a disease gene than does linkage. On the
other hand, biotechnology companies are
gearing up to develop large numbers of
single nucleotide polymorphism (SNP)
markers (1) to localize disease genes by
the disequilibrium mapping approach
alone, for example, in case-control studies.
It is then of interest to know how many
such markers will be required on a ge-
nome-wide basis. Thus, the question is,
how rapidly does disequilibrium decay as
one moves away from a disease locus? The
answer to this question is obviously of
more than academic interest. Whether
several 1,000 or several 100,000 SNP
markers are needed will have a major
impact on such association mapping stud-
ies. An early prediction was that in large
outbred populations, disequilibrium
should be detectable within 100 kb of a
disease locus (2). So, it is timely that an
extensive study addresses this important
point in a recent issue of PNAS (3).

Collins and colleagues (3) collected
information from the literature on auto-
somal haplotypes identified through
family studies. They focused on haplo-
types for pairs of loci, with the two
members of a pair being a disease and a
marker locus or two marker loci. Mark-
ers with multiple alleles were dichoto-
mized into two-allele systems for a
unique estimate of association desig-
nated by r. Distances (d in kb) between
loci were determined on the scale of the
physical map. For a disease gene with
uncertain map position, its map location
was estimated under the Malecot model
with the aid of the ALLASS program (4).
This approach prev iously has been
shown to provide excellent estimates for
the locations of trait genes (5). All in all,

approx imately 250 locus pairs were
worked up.

Different classes of locus pairs were
distinguished, in particular, those contain-
ing a disease locus and pairs of random
SNP loci. For closely linked loci, the Ma-
lecot model allowed for the multiple-
pairwise estimation of model parameters.
One of these parameters, «, depends on
the number of generations since forma-
tion of the haplotypes and on the ratio
between physical and genetic maps. The
so-called swept radius, 1y«, estimates the
distance in kb at which association falls to
approximately 1y3 of its original level.
Interestingly, this distance turns out to be
very similar for disease and random hap-
lotypes. For disease haplotypes, the swept
radius is estimated between 300 and 500
kb and for random haplotypes it is some-
what smaller than 300 kb. The study (3)
concludes with the suggestion that the
number of SNPs required for a genome
scan might be on the order of 30,000 or
less.

On the basis of computer simulations, a
recent progress report (6) predicted an
extremely short range of useful disequi-
librium, only about 3 kb. The report met
with widespread skepticism even though it
appeared in a so-called high-visibility
journal. These predictions are clearly con-
tradicted by observed data (3). The main
reason for the discrepancy appears to be
that the simulations were carried out un-
der the assumption of a continuously ex-
panding human population up to its
present size of 5 billion, which seems
unrealistic (3). A more likely scenario is
that various bottlenecks and cycles of ex-

pansion and contraction have occurred in
human history. Thus, it is reassuring that
the study in a recent issue of PNAS (3)
projects a required number of 30,000
SNPs rather than the figure of 500,000
resulting from the computer simulation.

Isolated populations often are consid-
ered advantageous for association map-
ping (7) but some examples have been
found in which the extent of linkage dis-
equilibrium is the same in small isolated
and large outbred populations (1). A pre-
vious investigation of this situation con-
cluded that isolated populations are to
some, relatively small degree favorable for
association analysis (8). On the other
hand, there are well-known instances of
strong disequilibrium in small populations
(9). It seems to depend very much on the
history of populations, be they large or
small, whether disequilibrium will be ex-
tensive around disease loci.

In their figure 1, Collins and colleagues
(3) show a graph of the association, r,
versus distance, d, between loci on a hap-
lotype. Visual inspection of the graph
reveals two interesting features. First, at
least at small distances, there seem to be
two clusters of haplotypes, one corre-
sponding to low and one with high asso-
ciation. Further, in each cluster, there
does not seem to be a strong relationship
between association and distance for ap-
proximate values of d , 150 kb. This
finding confirms previous observations
that disequilibrium and physical distance

See companion article on page 15173 in issue 26 of volume
96.

Table 1. Sample data on linkage disequilibrium (r) and distance (d, in kb) between
disease genes and nearby SNP markers

Disease gene Population r d x12

Huntington disease (14) Canada 0.14 175 12.15
0.11 175 8.05

Huntington disease (15) England 0.29 175 11.93
0.28 175 11.06

Cystic fibrosis (16) Caucasians 0.19 9 6.15
0.51 19 46.23

Limb girdle muscular dystrophy (17) Reunion Islands 0.66 50 25.02
Amish 0.80 50 33.63

Hemochromatosis (18) Utah 0.80 0 164.68

2–3 u PNAS u January 4, 2000 u vol. 97 u no. 1

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do not correlate significantly when d , 60
kb (10). My immediate reaction to these
two clusters was that they correspond to
isolated versus general populations. Thus,
I obtained data for a few examples of each
from the quoted web site (3). Table 1
shows the observed association values be-
tween disease and closest marker loci at
very small distances. At least on the basis

of this small sample, it appears quite con-
vincing that increasing population isola-
tion is more or less correlated with in-
creasing association.

Special applications of disequilibrium
mapping previously have furnished some
spectacular results. A much-quoted exam-
ple is that of the locus for diastrophic dys-
plasia, which was predicted to be 60 kb from

the best marker (11) and was localized at a
distance of 70 kb from it (12). On the other
hand, the same method has been much less
successful in other instances (13). A very
dense map of SNPs can be expected to yield
rather accurate results. Of course, if candi-
date genes are available for a trait, analysis
of SNP markers in or very near these genes
provides a cost-effective solution.

1. Jorde, L. B., Watkins, W. S., Kere, J., Nyman, D.
& Eriksson, A. W. (2000) Hum. Hered. 50, 57– 65.

2. Bodmer, W. F. (1986) Cold Spring Harb. Symp.
Quant. Biol. 51, 1–13.

3. Collins, A., Lonjou, C. & Morton, N. E. (1999)
Proc. Natl. Acad. Sci. USA 96, 15173–15177.

4. Collins, A. & Morton, N. E. (1998) Proc. Natl.
Acad. Sci. USA 95, 1741–1745.

5. Lonjou, C., Collins, A., Beckmann, J., Allamand,
V. & Morton, N. E. (1998) Hum. Hered. 48,
333–337.

6. Kruglyak, L. (1999) Nat. Genet. 22, 139 –144.
7. Peltonen, L. (2000) Hum. Hered. 50, 66 –75.
8. Lonjou, C., Collins, A. & Morton, N. E. (1999)

Proc. Natl. Acad. Sci USA 96, 1621–1626.

9. Laan, M. & Pääbo, S. (1997) Nat. Genet. 17,
435– 438.

10. Jorde, L. B. (1995) Am. J. Hum. Genet. 56, 11–14.
11. Hästbacka, J., de la Chapelle, A., Kaitila, I.,

Sistonen, P., Weaver, A. & Lander, E. (1992) Nat.
Genet. 2, 204 –211.

12. Hästbacka, J., de la Chapelle, A., Mahtani, M. M.,
Clines, G., Reeve-Daly, M. P., Daly, M., Hamilton,
B. A., Kusumi, K., Trivedi, B., Weaver, A., et al
(1994) Cell 78, 1073–1087.

13. Vesa, J., Hellsten, E., Verkruyse, L. A., Camp,
L. A., Rapola, J., Santavuori, P., Hofmann, S. L. &
Peltonen, L. (1995) Nature (London) 376, 584 –
587.

14. Andrew, S., Theilmann, J., Hedrick, A., Mah, D.,

Weber, B. & Hayden, M. R. (1992) Genomics 13,
301–311.

15. Snell, R. G., Lazarou, L. P., Youngman, S., Quar-
rell, O. W., Wasmuth, J. J., Shaw, D. J. & Harper,
P. S. (1989) J. Med. Genet. 26, 673– 675.

16. Kerem, B., Rommens, J. M., Buchana, J. A., Mark-
iewicz, D., Cox, T. K., Chakravarti, A., Buchwald, M.
& Tsui, L.-C. (1989) Science 245, 1073–1080.

17. Allamand, V., Broux, O., Richard, I., Fouger-
ousse, F., Chiannilkulchai, N., Bourg, N., Bren-
guier, L., Devaud, C., Pasturaud, P., Pereira de
Souza, A., et al (1995) Am. J. Hum. Genet. 56,
1417–1430.

18. Ajioka, R. S., Jorde, L. B., Gruen, J. R., Yu, P.,
Dimitrova, D., Barrow, J., Radisky, E., Edwards,
C. Q., Griffen, L. M. & Kushner, J. P. (1997) Am. J.
Hum. Genet. 60, 1439 –1447.

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