Biological Journal of the Linnean Society (1987) 31: 31 1-331. With 4 figures
Evolutionary genetics and HLA:
another classic example
PHILIP W. H E D R I C K
Division of Biological Sciences,
University of Kansas, Lawrence, KS 66045, U.S.A.
GLENYS T H O M S O N AND WILLIAM K L I T Z
Department of Genetics,
University of California, Berkeley, CA 94720, U.S.A.
Received 22 April 1987, acceptedfor publication 27 April 1987
CONTENTS
Introduction . . . . .
Association with diseases . .
Single-locus variation . . .
Two-locus variation . . .
Suggested modes of selection .
Segregation distortion
.
Maternal-foetal interactions
Viability selection
.
.
Non-random mating . .
Concluding remarks . . .
Acknowledgements
. . .
References. . . . . .
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311
313
314
316
319
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322
328
329
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INTRODUCTION
T h e classic examples of evolutionary genetics, melanism in Biston betularia,
shell colour and pattern in Cepaea nemoralis and sickle-cell anaemia in humans,
are familiar to the readers of this journal. I n recent years, a number of other
genetic systems have been extensively studied but the one having the most data,
including both the number of genes and most extensive population sampling,
and for which there is extensive molecular information is the major
histocompatibility complex ( M H C ) in humans, known as the HLA (human
leucocyte antigen) region. Because of the richness of data for this system and the
apparent importance of a number of evolutionary factors affecting variation a t
HLA, we feel that HLA has become an exemplary system for understanding
evolutionary genetics.
HLA was discovered as a blood-group-like system detected on the white cells
of the blood (Terasaki, 1980; Albert, Baur & Mayr, 1984). The impetus for the
investigation of the HLA system was the need to match donors and recipients
0024-4066/87/08031I + 2 1 $03.00/0
31 I
0 1987 The Linnean
Society of London
312
P. W. HEDRICK E T AL.
for the antigens important for tissue transplantation. Although this has turned
out to be much more difficult and complex than was at one time hoped, from
this effort has grown our knowledge of the HLA system and homologous systems
in other species. It is now known that these histocompatibility systems contain
many genes, and that these genes control a variety of functions. These functions
include determination of cell surface molecules, immune response differences,
components of the Complement system, and possibly other related functions
connected with cell-cell regulation, hormone receptors (Edinin, 1986) and
maternal-foetal interaction (Gill, 1983).
By a combination of family and somatic cell hybrid studies, the HLA system
was mapped to the short arm of human chromosome 6. A large number of loci
have been mapped within the HLA region as depicted in Fig. 1 (Strominger,
1985). The original serologically detected histocompatibility antigens of the
HLA system map to a two cM chromosomal segment. These antigens behave as
if they were controlled by multiple alleles a t the three Class I loci called
HLA-A, -B, and -C. Of the Class I1 loci, which includes genes DP,0% DR,
and O X , the DR locus has been the most extensively studied. Both the Class I
and the Class I1 loci determine membrane glycoproteins. Also in the HLA
region are found the genes determining factors C2, Bf, C4A, and C4B of the
complement system (these genes are called Class I11 loci), which is involved in
the destruction of foreign antigens, steroid 2 1-hydroxalase, and most recently
HLA?A
1’
HLA-C
HLA-8
t
0.7
I
C 4 8 , 218
C 4 A , 21A
0.3
I;
JI
HLA-DR
“‘*T
P2
p3
‘1’
a2
P2
HLA-DP
t
Il2
Glo I
Figure 1. Map of the HLA region located on the small arm of chromosome 6. Map distance in
centimorgans is shown on the left. The class I 1 loci, DR,D Q a n d DP,are heterodimers made up of
a and B chains, 21A and 21B are the two 21 hydroxylase loci, and GLOI is glyoxylase I
EVOLUTIONARY GENETICS AND HLA
313
discovered tumour necrosis factor (Muller, Jongeneel, Nedospasov, Fischer
Lindahl & Steinmetz, 1987).
ASSOCIATION WITH DISEASES
Over 40 diseases have been shown to be associated with HLA antigens
(Thomson, 1986). These diseases affect all organ systems, although a common
theme is that many have a suspected autoimmune aetiology. A list of a few of
the diseases known to be associated with specific HLA antigens is given in
Table 1. Association as used here means that the diseased population has a
Statistically significant increased frequency of a particular HLA antigen over a
control population. Data on the frequencies of particular HLA antigens in
patient and control populations are also given in Table 1 for several diseases.
The case of ankylosing spondylitis provides one of the most striking examples of
an HLA-disease association. The frequency of the antigen B27 in patients is
90% compared to 8% in controls.
T o determine whether or not an association between a disease and a
particular HLA antigen exists, HLA typing is performed on a group of
unrelated patients and a group of unrelated control individuals, all of the same
homogeneous ethnic origin. For each HLA antigen, a 2 x 2 table of antigen
presence or absence versus disease presence or absence is set up. An association
between a disease and a particular antigen is demonstrated if there is a
statistically significant deviation between the antigen frequencies in patients and
controls. The most commonly used measure of the strength of an association
which
between a disease and a particular HLA antigen is the relative risk (RR),
can be written as
FAD( 1 - FAP)
RR =
FAP( 1 - FAD)’
where FAD and FAP are the frequencies of the antigens in the patient group
with the disease and the general population, respectively. A relative risk higher
Table 1. Frequency of antigens in diseased and population samples for several
diseases and the resultant relative risk
Frequency in:
Disease
Antigen
Narcolepsy
Ankylosing spondylitis
Reiter’s disease
Coeliac disease
Idiopathir hemochromatosis
Insulin dependent diabetes mellitus
DR2
B2 7
B2 7
DR3
A3
B8
DR3
DR4
DR4
DR2
A1
Rheumatoid arthritis
Multiple sclerosis
Hodgkin’s disease
Diseased
(FAD)
Population
JFAP)
Relative risk
(RR)
1 .o*
0.16
0.08
0.08
0.26
0.28
0.22
0.28
0.32
0.19
0.26
0.32
Very high
88
36
15.4
8.2
2.1
3.3
6.4
4.2
4.1
1.4
0.90
0.81
0.79
0.76
0.37
0.56
0.75
0.50
0.59
0.40
*Some instances of DR2 negative narcoleptics have now been observed
314
P. W. HEDRICK E l A L
than 1 (a positive association) is seen when an antigen is more frequent in the
patients than in the controls (see Table 1 for a list of some of the diseases with a
high relative risk), whereas a risk below unity (a negative association) reflects a
decreased frequency in the patients (e.g. Thomson, 1981).
One explanation for an HLA-disease association is that disease susceptibility
is a direct result of the presence of the particular HLA antigen. This may be the
case for ankylosing spondylitis and some other B27 associated disorders. In the
case of ankylosing spondylitis, the association with B27 is very strong
(RR=88), most patients have the antigen, and the B27 association is found in
all racial groups. Another explanation for an HLA-disease association is that the
association of a particular antigen(s) with a disease is the result of gametic or
linkage disequilibrium (see below) between the antigen(s) and the alleles at a
nearby locus which confers susceptibility to disease. This is the most generally
accepted explanation of HLA disease associations and suggests that any
association found between an antigen and a disease indicates the existence of
disequilibrium between this antigen locus and the disease locus.
As we stated above, in many, but not all, of the HLA-associated diseases an
autoimmune aetiology has been either demonstrated or suggested. In addition,
theoretical studies in the development of models to determine the modes of
inheritance of the HLA-associated diseases have led to a better understanding of
the inheritance patterns in insulin dependent diabetes mellitus, rheumatoid
arthritis, multiple sclerosis, ankylosing spondylitis, homochromatosis, coeliac
disease and others. However, it is now clear that many of the HLA-associated
diseases may involve heterogeneity in their HLA components, as well as nonHLA genetic components.
SINGLE-LOCUS VARlATION
Although the relationship of HLA variants to particular diseases suggests that
selective forces have had substansive effects on the alleles in the HLA region, it
is important that we objectively examine the variation in this region, and not
make n priori assumptions about selective factors. T h e neutrality theory gives a
useful starting point for our analysis in that it assumes that different alleles at a
locus have equivalent effects on fitness. I n the neutrality model, the equilibrium
heterozygosity (or homozygosity) and multilocus associations in a population
are a function of the combined effects of genetic drift and mutation, thereby
providing theoretical predictions against which the observed genetic variation in
a population or a sample may be compared.
Ewens (1972) developed sampling theory to predict the distribution of alleles
observed in a sample of size n taken from a population a t equilibrium under
neutrality. Watterson (1978a,b) extended this approach and developed a test
that allows the comparison of the observed homozygosity expected in a sample
of size n containing k alleles to the homozygosity expected under neutrality. This
conditional homozygosity F is defined as
where p , is the frequency of the ith allele in the sample of size n. (Note that this
EVOLUTIONARY GENETICS AND HLA
315
Table 2. Number of alleles (k), sample size (n), expected and observed
homoz ygosity, and the significance level for different populations at the HLA-A
and B loci (from Hedrick & Thomson, 1983)
Homozygosity *
Population
HLA-A
Caucasian
American
French
Italian
African blacks
Japanese
H LA-B
Caucasian
American
French
Italian
African blacks
Japanese
k
n
Expected
Observed
P
ia
1734
874
1044
286
1878
0.2 15
0.233
0.233
0.204
0.233
0.134
0.139
0.1 13
0.100
0.2 17
<0.1
< 0.05
< 0.025
<0.01
1734
874
1049
286
1900
0.121
0.065
0.068
0.073
0.089
0.075
<0.01
<0.01
17
17
17
17
31
31
29
25
29
0.121
0.131
0.135
0. I30
-
< 0.025
~
<0.025
*Hardy-Weinberg homozygosity in a sample drawn from a population at equilibrium under neutrality
(expected) and the Hardy-Weinberg homozygosity found in different populations (observed).
test does not examine deviations from Hardy-Weinberg proportions but
examines the allelic frequency array expected under neutrality.)
Using this approach, Hedrick & Thomson (1983) compared the observed
conditional homozygosity in 22 samples a t both the A and B loci of the HLA
region (Terasaki, 1980) to neutrality expectations. In all cases, the observed
homozygosity was less (observed heterozygosity was more) than that expected
from neutrality and was statistically significantly less a t the 0.05 level in 25 of
the 44 cases (see Table 2 for some of these data). We then evaluated the
evolutionary factors that could be important in influencing the level of
homozygosity conditioned on n and k, particularly those factors such as gene
flow, population bottlenecks, unidentified alleles, and balancing selection that
could decrease conditional homozygosity (increase heterozygosity) relative to
neutrality expectations. After extensive consideration of these factors, we
suggested that some form of balancing selection is the explanation most
consistent with the level of conditional homozygosity a t the A and B loci in the
populations studied. We should note that the relatively high rate of gene
conversion in the HLA region should have an effect on conditional
homozygosity similar to an elevated mutation rate. As a result, gene conversion
should not increase conditional homozygosity, a value which is independent of
4Nu (Ewens, 1972; N i s the effective population size and u is the mutation rate).
Using the data from the most recent histocompatibility workshop (Albert
et al., 1984), Klitz, Thomson & Baur (1986) have applied this approach to
samples for nine loci of the HLA region. As in the previous samples, loci A and
B had conditional homozygosities statistically significantly less than neutrality
expectations (Table 3). I n addition, the other loci that code for membrane
glycoproteins, C, 0% and DR, as well as locus Glo-I, had homozygosities
significantly less than expected. However, the four complement loci had
P. W. HEDRICK E T AL.
316
Table 3. Comparison of the observed homozygosity for nine loci in the HLA
region to that expected from neutrality. This is a summary of samples from four
to seven populations where the value in table is the level of statistical
significance (from Klitz et al., 1986)
Ohscrved minus
exprctrd
hornozygosity
-
Glo
DQ
DR
0.001
0.001
0.001
0
+
~
~
~
~
Complement
loci
~
ns, ns, ns
0.01
B
C
A
0.001
0.001
0.001
~
~
~
~
homozygosities either consistent with (Bf, C4B, and C4A) or exceeding (C2)
neutrality expectations. These results are particularly interesting because they
suggest that the complement loci, which are embedded in the HLA region, and
the Class I and I1 HLA loci display quite different evolutionary histories despite
their close linkage and the background of extensive disequilibrium in the region.
TWO-LOCUS VARIATION
Under neutrality, a population a t equilibrium has an expected association
between alleles at different loci. Even though there is no selection among
different alleles at a locus, the combined effects of genetic drift and mutation
result in an interlocus association which is highest when there is limited
recombination (e.g. Ohta & Kimura, 1969; Hill, 1975). We have extended the
approach of Ewens (1972) and Watterson (1978a,b) using the computer
simulation approach of Hudson ( 1983) to determine the extent of disequilibrium
expected in a sample of size n with k and 1 different alleles at two loci (Hedrick
& Thomson, 1986). These disequilibrium values also depend upon the amount
of recombination as measured by the quantity 4.1% where N is the size of the
population from which the sample is drawn and c is the rate of recombination
between the loci.
The extent of gametic disequilibrium can be measured in several ways for a
specific gamete or haplotype (e.g. Hedrick, Jain & Holden, 1978, for a review).
A widely used measure of gametic disequilibrium for a given gamete is
where xV is the observed frequency of gamete A,BJ,p , and qj are the frequencies
of alleles A , and BJ at loci A and B , and the expected frequency of gamete A,Bj is
p,qJ, assuming no association between the alleles. The range of this measure of
gametic disequilibrium is a function of the allelic frequencies, making a measure
that has the same range for all allelic frequencies desirable. For this reason,
Lewontin ( 1964) suggested using the normalized measure
where if D, < 0, D,,, is the lesser ofp,qJ and ( 1 --pJ ( 1 - qJ) and if D, > 0, D,,,
the lesser of p,( 1 - q,) and ( 1 -p,)qj.
is
EVOLUTIONARY GENETICS AND HLA
317
A number of different approaches have been suggested to measure the overall
gametic disequilibrium when there are multiple alleles a t both loci (Hedrick &
Thomson, 1986; Hedrick, in press). For all these different measures of
disequilibrium, when the observed disequilibrium between HLA loci A and B is
compared to that expected from neutrality, the observed values are generally
much larger (e.g. Hedrick & Thomson, 1986). However, even more instructive
is the pattern of disequilibrium values when they are examined in detail. For
such an analysis, we have developed an approach designed to examine the
distribution of disequilibrium values and identify patterns that are consistent
with past selective events (Klitz & Thomson, in press; Thomson & Klitz, in
press). A strength of this approach is that disequilibrium in multilocus gametic
frequencies may be retained for a number of generations, and decays in time
only as a function of the recombination rate between two loci, thereby reflecting
the effects of past evolutionary events.
The disequilibrium values for a pair of loci are constrained by the following
relationships
I n other words, the disequilibrium values for a given allele a t one locus and all
other alleles at the other locus sum to zero so that, for example, the negative
disequilibrium value(s) for a given allele(s) is exactly balanced by a positive
disequilibrium value(s) a t another allele(s).
Let us assume that selection favours a particular haplotype A , B , and
examine the resulting pattern of disequilibrium values. (The results obtained
generally apply whether the haplotype A , B , increases in frequency via a genetic
hitchhiking event or via selection for this haplotype.) T h e theoretical
development is given in Thomson & Klitz (in press) and is an extension to
multiple alleles of the hitchhiking models of Thomson, W. F. Bodmer & J.
Bodmer (1976) and Thomson (1977). If initially all disequilibrium values (D,)
between the alleles a t the two loci of interest are zero, or small (as they will be in
the case of newly arisen mutants), then the following simple relationships for the
disequilibrium values resulting from a selection event can be given.
First, the positive disequilibrium of the gamete or haplotype A , B , , which
increases in frequency as a result of the selection or hitchhiking event, and the
A,B, haplotypes, i = 2 , . . ., k, j = 2 , . . ., I , will be balanced by the negative
disequilibrium values of the A,B,, i = 2, . . ., k, and A , B,, j = 2, . . ., 1,
haplotypes. Further, the negative disequilibria of the A,B, haplotypes,
i = 2,. . ., k, will be proportional to the A, allele frequency, while the
normalized disequilibrium values D for all these haplotypes will be equal when
p,+ q , 6 1. For the A , B, haplotypes, j = 2, . . ., 1, the disequilibria will be
proportional to the B, allele frequency, and the normalized disequilibria values
will be equal for all these haplotypes when p , q, d 1, but in most cases these
will be different from the constant normalized disequilibrium values for the A,B,
haplotypes.
Let us compare these expectations to that observed for a large (5202
individuals) and relatively homogeneous sample for the A and B loci from
Denmark (Hansen, Larsen, Ryder & Nielsen, 1979). Figure 2 gives the observed
distribution of (A) disequilibrium and (B) normalized disequilibrium values for
+
P. W . HEDRICK E'T AL.
0.025
0.020
15
40
0.015
35
0.010
5
27
18
17
X
0.005
13
10
2
21
3938
454$,
p'
4'
I
I
37
z
c
0
2
D
-:
U
B
V
nl
+
0
nl
::
W
7
0.025 -
44
8
0.020
-
0.015
-
40 '5
35
0.010
27
X
0,005 -
22
13
14 39
38 45
41
I
I
0 -47
-1.0
I7
18
-0.8
-0.6
37
I
-0.4
I
-0.2
I
o
0.2
1
I
I
0.4
0.6
0.8
1.0
D'
Figure 2. A plot of all haplotypes containing the allele A1 where the numbers indicate the antigen
designation at the B gene for: (A) the disequilibrium measure D and (B) the normalized mcasure
D'.
allele A1 and all alleles at the B locus, a pattern most easily explained by
selection (see Klitz & Thomson, in press). Haplotype AlB8, has the highest
positive disequilibrium (and normalized disequilibrium) value in the population
(D= 0.0766, D = 0.728). I n Fig. 2A, A1B8 is the main haplotype in the
positive space with two low frequency haplotypes having low positive
EVOLUTIONARY GENETICS AND HLA
319
disequilibrium, while the rest of the related haplotypes (88 not A l ) fall in a
linear array in the negative space with disequilibrium values approximately
proportional to the frequency of the unshared A allele. The graph of normalized
disequilibrium values shown in Fig. 2B for A1 haplotypes reveals an alignment
of the negative values for the commoner haplotypes. T h e values fall between
-0.6 and -0.8. Rarer haplotypes, for example, AlB47, AlB38 and AlB13
depart furthest from this alignment apparently due to sampling effects. The
misalignment of A 1BX probably occurs because the blank allele BX is probably
an unidentified mixture of B locus alleles.
There are six haplotypes that have disequilibrium patterns consistent with a
past selective event, the most striking being A1B8 and A3B7. Many of the other
haplotypes have disequilibrium distributions completely different from these
expectations. The theoretical distribution of disequilibrium from a neutrality
population or from admixture is quite different from that expected from a
selective event (Thomson & Klitz, in press).
SUGGESTED MODES OF SELECTION
A distinctive feature of the HLA data at the single-locus level is the high
degree of polymorphism of the loci in combination with a relatively even
distribution of allele frequencies for the Class I and I1 loci, HLA-A, B, C, D Q
and DR loci, as well as the Glo-I (glyoxylase) locus. These observations are
compatible with the notion that the high levels of variation a t these HLA loci
are maintained by a selective mechanism, and that possibly all the HLA alleles
have been subject to some degree of selection. A variety of selection models have
been suggested to be important for genes in the M H C region, including
frequency-dependent selection models based on host-pathogen interactions,
selection for particular haplotype combinations and genetic hitchhiking models.
In addition to viability selection, other agents have been proposed to influence
the evolution of the M H C region, including maternal-foetal effects (e.g., Clarke
& Kirby, 1966; Warburton, 1968), segregation distortion (Alper, Awdeh, Raun
& Yunis, 1985), and non-random mating (Yamazaki, Boyse, Mike et al., 1976).
Here we will summarize our work on segregation distortion (Hedrick, unpubl.
a ) and maternal-foetal interactions (Hedrick, unpubl. b; Hedrick & Thomson,
unpubl.), and introduce how selection may operate through viability differences
resulting from infectious diseases and selective mating.
Segregation distortion
Segregation distortion occurs when heterozygous individuals produce unequal
proportions of their constituent gametes. For example, alleles at the t locus in
Mus musculus which maps close to the mouse M H C system, termed H2, are
favoured in males by segregation distortion but also are generally recessive
lethals. There is some suggestion that humans may have a locus near the HLA
region that causes segregation distortion, a putative t homologue, (e.g. Awdeh,
Raum, Yunis & Alder, 1983) although a detailed study by Klitz, Lo,
Neugebauer et al. (1987) found no evidence for segregation distortion in the
HLA region. I n addition, there are a number of reports that alleles at loci linked
to the t loci are in gametic disequilibrium with alleles at segregation distortion
P. W. HEDRICK E T A L .
320
loci, or that alleles at loci linked to segregation distortion loci are non-randomly
associated.
A number of factors may be important in influencing gametic disequilibrium
between loci in or near the segregation distortion region. For example, crossingover is greatly reduced between the t locus and the linked H 2 loci in t locus
heterozygotes because t alleles appear to be associated with an inversion (e.g.
Silver, 1985). I n other words, gametic disequilibrium generated by factors such
as mutation or genetic drift, would decay very slowly due to low recombination
between t chromosomes (or haplotypes) and non-t chromosomes.
It has recently been implied that segregation distortion may also be an
important factor generating or maintaining gametic disequilibrium (e.g. Alper
et al., 1985), begging the following questions. How are the observations of
gametic disequilibrium in the M H C region related to the phenomenon of
segregation distortion? Can segregation distortion generate gametic
disequilibrium or can it influence the rate of decay of gametic disequilibrium?
To investigate these questions (see Hedrick, unpubl., has for a more complete
treatment), let us assume that the t locus in mice or a homologous locus in
and the variant t, and that the
another species has two alleles, the wildtype
+ t and tt have the fitnesses 1, 1, and 1 -s, respectively. Assume
genotypes
that segregation distortion occurs only in heterozygous males, resulting in a
proportion m (where m > f) of gametes with the t allele and a proportion 1 -m
of gametes with the
allele. Let p, and p2 be the frequencies of the
and t
alleles, respectively, and PI ,, P, 2 , and P Z 2 be
, the frequencies of genotypes
+ t , and tt, respectively.
If s = 1, i.e. the t allele is a recessive lethal, then the equilibrium for the t
allele is
+
+ +,
+
+
(Bruck, 1957) assuming
p2e = 1/3.
+ +,
+ < m < 1. For example, if m = 0.9 and s = 1.0, then
Because the frequency of alleles is different in the gametes of the two sexes,
there is an excess of heterozygotes over Hardy-Weinberg expectations (e.g.
Robertson, 1965; Purser, 1966). If we assume that at equilibrium
P: = P , = P I then
' 1 qc
= [2P,ePze+ ( m - ! ~ )(P i e - P z e ) P i
,el/['
-s(P;e+p2e(m-+)Pi
zel!
which simplifies to the quadratic
For example, if rn = 0.9 and s = 1.0, so that PZe= 1/3, solving this equation,
then P I z e= 2/3. The Hardy-Weinberg expectation is 2pIep2,= 4/9 so that there
is a 50% excess of heterozygotes over Hardy-Weinberg expectations. When
s = 1 , the ratio of the equilibrium proportion of heterozygotes to the
Hardy-Weinberg proportions increases as m increases, approaching a maximum
of 2 when m approaches 1.
Now let us assume that a locus linked to the t locus or its homologue, either
an H2, HLA or other homologous or linked locus, has two alleles, A , and A , ,
with frequencies, q , and q,, respectively, and that the rate of recombination
EVOLUTIONARY GENETICS AND HLA
32 1
between the t locus and the histocompatibility locus is c. There are then four
possible gametic types, + A , . , + A , , t A , , and [ A , , present in the population.
First, after some algebra it is possible to show (Hedrick, unpubl. a ) that the
gametic disequilibrium in generation t is
Therefore, if there is initially no disequilibrium, i.e., D o= 0, then D,= 0
demonstrating that segregation distortion cannot be the de novo cause of gametic
disequilibrium.
The dynamics in the change of disequilibrium given D o# 0 are more
complicated. Perhaps the simplest case is when a new mutant for a t allele arises
in a population. When such a new mutant occurs, then there is initially
maximum gametic disequilibrium as measured by the gametic disequilibrium
measure D’. For example, assume the frequencies of the gametes + A , and + A ,
before mutation are q , and q 2 , respectively. After mutation of a
allele on a
+ A , gamete to a t allele, the gametic frequencies become q , , q , -p2, 0, and p,
for gametes + A , , + A , , LA,, and tA,, respectively, and
+
=1
(e.g. Hedrick, 1983).
As an example, let s = 1.0, rn = 0.95, and the initial frequency of the gamete
tA, be 0.01. Figure 3A shows the decline of D’over 50 generations to a value of
about 0.46 (solid line). In Figure 3B, the measure D is plotted for the same
parameter combination. Because it is frequency-dependent, D increases from an
initial value of zero to a maximum near generation 20, approximately the time
when the t-allele has reached its equilibrium and stopped changing frequency,
and then declines monotonically. Also given in Fig. 3A is the decline of D’when
there is no segregation distortion and no selection (broken line). Note that it
declines more slowly than when these factors are present.
First, from these results it appears that segregation distortion cannot de novo
generate gametic disequilibrium between a segregation distortion allele and
alleles at another locus. This becomes more intuitive when we note that if rn is
rescaled, then the effect of segregation distortion is equivalent to that for haploid
selection (e.g. Hedrick, 1980a). As Thomson (1977) has shown, gametic
disequilibrium cannot be generated between a selected locus and a neutral locus
by change at the selected locus.
Second, segregation distortion results in a faster rate of decay of standing
disequilibrium between the segregation distortion locus and a neutral locus than
if there is no segregation distortion. The excelled rate of decay occurs because
the difference in allelic frequencies between male and female gametes results in
an excess of double heterozygotes causing a faster rate of decay than if there
were Hardy-Weinberg proportions.
Finally, how would we expect segregation distortion to influence the
disequilibrium between a pair of linked loci. I n other words, could a t-allele
with segregation distortion generate disequilibrium between a pair of
histocompatibility genes? In fact, given the proper initial gametic frequencies a
P. W. HEDRICK E T A L .
322
I
0
10
20
30
40
50
Generation
Figure 3. T h e decay of D and D in (A) and (B) respectively when there is segregation distortion
( m = 0.95) and selection s = 1.0, given the introduction of a new t allele mutant (solid lines) and for
D when there is no segregation distortion or selection (broken line).
t-allele mutant could, via genetic hitch-hiking, increase the disequilibrium
between linked neutral loci (e.g. Thomson, 1977; Hedrick, 1980b). However,
segregation distortion should still serve to hasten the decay of disequilibrium.
Klein and his coworkers (e.g. Figueroa, Golubik, Nizetic & Klein, 1985)
suggest that t haplotypes in mice are associated with particular H2 alleles (see
also Nadeau, 1983, 1986). Such an association suggests that the recombination
between t- and non t-haplotypes must be quite low (or some other factors are
important), particularly given that segregation distortion appears to hasten the
decay of disequilibrium as suggested above. Overall then, unlike the contention
of Alper et al. (1985) that male transmission bias can maintain disequilibrium, it
appears that segregation distortion will increase the rate of decay of gametic
disequilibrium.
Maternal-foetal interactions
Approximately 30% of the couples having two or more spontaneous abortions
do not have a demonstrable basis, such as a chromosomal or anatomical
abnormality, for the foetal loss (Thomas, Harger, Wagener, Rabin & Gill,
1985). A number of studies indicates that such couples often share antigens for
EVOLUTIONARY GENETICS AND HLA
323
Table 4. The prevalence of shared antigens at different HLA loci for normal
couples or for couples having a history of recurrent spontaneous abortions with
sample size in parentheses (after Thomas et al., 1985)
Locus (loci)
A*
B*
C*
Normal couples
0.422
0.243
0.219
0.072
0.220
(408)
(408)
(114)
(83)
(150)
Aborting couples
0.505 (325)
0.314 (325)
0.504 ( 1 15)
0.230 (152)
0.505 (109)
*Share one or two antigens.
?Share two or more antigens.
HLA loci (see Table 4 for a summary of 14 studies). Note that the frequency of
shared antigens is higher for aborting couples in all comparisons but when two
or three loci are examined simultaneously, it is much higher for couples with a
history of recurrent spontaneous abortion than for control couples. There are,
however, reports not consistent with this trend (e.g. Oksenberg, 1984).
Two main hypotheses have been suggested to explain the association between
HLA antigen-sharing in couples and recurrent spontaneous abortion. First, the
genetic hypothesis suggests that recurrent spontaneous abortions in couples that
share HLA antigens are the result of homozygosity of recessive detrimental
alleles statistically associated with HLA antigens (e.g. Schacter, Weitkamp &
Johnson, 1984, and references therein). Second, the immunological hypothesis
suggests that the presence of an immune response occurring when the mother
and foetus differ at the HLA loci is necessary for proper implantation and foetal
growth (e.g., Gill, 1983, and references therein). I n other words, sharing of
HLA antigens in a parental couple results in a foetus similar to the mother and
consequently an immune response by the mother to the foetus that is abnormal
in some way.
First, let us examine the genetic hypothesis and give the expected proportion of
foetal deaths in couples that share HLA antigens. Let us begin by assuming the
most extreme situation, i.e. a different non-complementary recessive lethal is in
absolute gametic disequilibrium (sensu Clegg, J. F. Kidwell, M. G. Kidwell &
Daniel, 1976) with each HLA antigen. In other words, if we give the complete
gamete (or haplotype), then the only gametes present would be A , I,,
A , I , , . . A , / , where A iis an allele at a HLA locus and l j is a recessive lethal at a
linked locus. Therefore, all individuals homozygous at one or more HLA
genotypes are inviable and all individuals heterozygous for all the HLA loci are
equally viable.
First, assume that the parental couple share either 0, 1 or 2 antigens at a
single locus, say A . Of course, when they do not share any antigens, e.g. the
mating is A , A , x A , A , , all progeny are viable, resulting in no selection or
so = 0, where the subscript refers to the number of antigens shared. When the
parents share one antigen, e.g. A , A , x A A , , three-quarters of the progeny are
viable so that s, = +. When the parents share two antigens, e.g., A , A , x A , A , ,
half the progeny are viable so s2 = +.
Let us define the proportion of A , gametes having I , alleles as .z. By
,
P. W. HEDRICK E T AZ.
324
Table 5. The mating types, their frequencies, and the proportion of lethal
progeny assuming that allele A , is shared and there is association with lethal
allele I,
Mating type
Frequency
Proportion
progeny 1, I ,
-
r,
r;
A,l,/X, x A , l,/A,<
A , I , /X, x A , </2,
i;
A , 17 12, x A , </A,
<
<
Z2
I
4
2 4 1 -2)
0
( 1 -z)*
0
substitution
Because the maximum value of D' is 1, we can calculate the maximum
1.
proportion z for given allelic frequencies using this expression. I f p , = q,, then
2 = D',,. Such a high frequency of a lethal would generally be unlikely. More
likely, the frequency of an associated lethal would be much lower than that for a
typical HLA antigen. For example, i f p , = 0.1, a typical frequency for alleles at
HLA loci A or B and q l = 0.01, a typical frequency for a recessive lethal, then
.i = 0.1.
How much will gametic disequilibrium that is not absolute, lower the
expected proportion of recessive lethal progeny? Let us examine the single-locus
HLA situation in which the parents share one antigen. Because there are two
types of gametes with A 1 , A , I , and A ,( (where the overscore means 'not'),
there are three possible mating types where both parents have A , alleles (see
Table 5). Using these mating-type frequencies and the expected segregation
proportions, then
J
I
E L 2
4z
.
(Note that i t is assumed that the frequency of gamete 31, is negligible.) In this
case, if z = 0.1, then s, is only 0.0025, two orders of magnitude below that for
absolute disequilibrium.
When there is partial disequilibrium between the antigen and a lethal, the
proportion of recessive lethal progeny may be higher when there is inbreeding.
If we define the proportion of matings that share one allele due to inbreeding as
f, (generallyf, = 4f), then the overall expected proportion of recessive lethal
progeny is
$1
= ~r[f,(l-C)"+S(l-fi)],
where ( 1 - c ) ~ is the probability of no recombination (Hedrick, unpubl. a ) . If the
parents are first cousins, then f = 1/16, f,= $, and n = 4. As an example,
assume that .z = 0.1 and c = 0.0, making s, = 0.0081. Although this is over
threefold that when f = 0, still less than 1% of the progeny would die resulting
EVOLUTIONARY GENETICS AND HLA
325
from homozygosity at lethals linked to the HLA gene. The impact would
become even less if the consanguinity is more remote.
It has been suggested that alleles at a t-locus homologue linked to the HLA
region can cause segregation distortion (see Alper et al., 1985, and discussion
above). If there are such alleles, then segregation distortion may influence the
proportion of lethal offspring for couples sharing HLA alleles. As an example,
let us assume that there is absolute disequilibrium between the A , alleles and an
allele causing segregation distortion. As in mice, assume that segregation
distortion takes place only in males so that the male heterozygote A , A ,
produces a proportion m of A , sperm and 1 - m of A , sperm. I n a mating
A , A , x A , A , with one shared antigen, then s, = +m, i.e. this proportion of the
progeny should be A , A , . If m = 0.8, then s, = 0.4, greater than the for no
2
segregation distortion. However, for two shared antigens s, = tm +( 1 - m ) = 1
as it would be for no segregation distortion.
Now let us examine the immunological hypothesis of selection resulting from
maternal-foetal interactions. Let the frequency of allele Ai at the A locus be pi
and assume in this discussion that the genotypes occur in Hardy-Weinberg
proportions. Examining the possible mating types and their progeny, there are
three different mating types or maternal-foetal combinations. Table 6 gives the
different types of matings when there are two alleles at the A locus. The first
type of mating, e.g. A , A , x A , A , , occurs when the male has no (zero) alleles
that are different from the female in other words, complete sharing of alleles in
the parents. As a result, all progeny have alleles that are present in the female.
The second type of mating, e.g. A , A , x A , A , , occurs when the male shares one
allele with the female but has one that is different so that half the progeny from
this mating have an allele different from the mother and half do not. Note that
the reciprocal of this mating type, A , A , x A , A , , has different consequences
because the male has no alleles that are not present in the female. The third
type of mating, e.g. A , A , x A , A , , occurs when both alleles in the male are
different from those in the female. In this case, all progeny have an allele that is
different from the mother.
Let us now calculate the expected change in allelic frequency and the
equilibrium allelic frequency from the frequencies given for progeny in Table 6.
+
+
Table 6. The different mating types and the relative fitness of
progeny for the single locus, two-allele immunological model
Progeny
Female
Male
'41'41
AIA2
4 - 4 2
1-5
1 -s
-
1 -.r
1-5
-
-
-
1
1
1 -s
1 -s
1- s
1
1
-
.~
1-5
1 -.r
1 -s
1 -.r
P. W. HEDRICK E'T A L
326
Using these fitnesses given in Table 6 and summing the three progeny columns,
then
where
e = 1 -s(
1 -@,/I,).
The only stable, polymorphic equilibrium occurs when P l e = 0.5. The same
approach can be used to examine different numbers of alleles given the same
general selection scheme (Hedrick & Thomson, 1987). When there are k alleles,
the only stable, polymorphic equilibrium is when p,?= 1/k. Figure 4 gives the
change in the frequency of allele A , when it is below the equilibrium frequency
for 2, 4, and 8 alleles. Here the frequency of all the other alleles is assumed to be
( 1 - p l ) / ( k - 1). T h e change in frequency as expected is positive between 0 and
p l Cand declines in magnitude as the number of alleles increases.
Assume that a second locus B has alleles B , and B , with frequencies q I and q2
and that gametes A , A , , A , B , , A , B , , and A , B , have frequencies x I , x 2 , xg, and
x4, respectively. Let c be the rate of recombination between the two loci,
D = x , - p , q l , and G,, be the frequency of the genotype composed of gametes i
and j , e.g. GI is the frequency of genotype A , B , / A , B , .
Let us extend selection to include both loci. Since there are 100 mating types
and 10 progeny types we will only describe the case in which the female is a
double homozygote (A,B,/A,B,). As a further shorthand, we will just give the
male gamete rather than the complete male genotypes. Table 7 gives the four
resulting categories with the number of antigens shared between the female and
the male gamete. For example, in the first row when a female A,B,/A,B,receives
a male gamete A,B,, i.e. both antigens in the male are in the female, all progeny
are A,B,/A,B, and share alleles with the mother at both loci so that we can
designate the fitness in general as wAB.I n the second row, one allele in the male
gamete is shared with the female genotype ( A , ) and one is not (B,) making the
fitness wA. As we will see below, it is useful to use the right-hand fitness
parameterization given in Table 7.
When s # it, then the solutions at equilibrium given c = 0 are
xIr = 0
Xle
=I
xlr =
-+ +
4
with D
= -$,
with D = 0,
with D = +.
The equilibria with D =
or are stable when t > 0 and t < 2s. O n the other
hand if t > 2s, then only the D = 0 equilibrium is stable.
When t = 2s, then we obtain the expression
XI
X
- (4-34 = 2 (4-3t).
4
4
In other words, there is no solution, i.e. there is a neutral curve, whatever the
initial gametic frequencies are, they remain there.
Now let us assume that c > 0. I n this case, we must iterate the expressions for
the genotypic frequencies given above. Using the results from c = 0 as a
background we can organize the results with recombination in a similar
EVOLUTIONARY GENETICS AND HLA
327
Table 7. The different ‘mating types’ and the resulting progeny
with their fitness for the two-locus immunological model when the
female is a double homozygote
Fitness
Male
gamete
Number of
antigens shared
Progeny
genotype
2
AiBjIAiB,
AiBJ/AiB,
x
A,?
A;B,
K.B.
x
A,Bj
Female
genotype
AiB,/A;B, x
X
-1
1
1
1
(a)
WA%
1-1
W%
1-5
WA
1-5
A;B,IA.B-1
1
Ai BJ/AiBj
0
(b)
1
1
Table 8. The recombination level (c) necessary to generate an equilibrium with
D # 0 for given selective values, below these values, D = 0 equilibrium is
present
S
0.1
0.2
0.4
t>25
1 = 2s
*
*
*
*
*
*
t = I-(l-s)Z
t = 3/25
<0.002
< 0.008
< 0.008
t = s
<0.014
< 0.03 1
< 0.080
<0.018
< 0.055
<0.047
*Only D = 0 equilibrium present.
Table 9. The level of disequilibrium, D ,expected for given s and t values for the
recombination amount between HLA loci A , B, and DR
t = 3/2s
C
0.008 ( A - B )
0.010 (B-DR)
0.018 (A-DR)
s
t = s
0.1
0.2
0.4
0.1
0.0
0.0
0.0
f0.183
z0.161
k0.231
f0.226
70.205
+ 0.13 1
0.0
f0.162
0.0
0.2
0.4
f0.216
k0.240
f 0.234
k0.221
z
0.206
k0.162
manner. When t > 2s, then the only equilibrium present is D = 0. I n addition,
when t = 2s, the only equilibria is D = 0, unlike the c = 0 case. If t <2s, then
there is D # 0 equilibrium if the recombination is low enough. Table 8 gives
several such cases, including t=;s and t = s . The middle column gives the
multiplicative case, i.e., if wAB= (1 - J ) ~ = 1 - t , then t = 1 - (1 - s ) ~ . For
example, in the case analogous to multiplicative fitness values and assuming
s = 0.1 (making t = 0.19), then if c < 0.002 there is D # 0 equilibrium. When
t = s = 0.1, then if c < 0.014, there are D # 0 equilibria.
How large are the D values generated by these values? Table 9 gives these D
values (remember because p , = q 1 = 3, D’ = 4 0 here) for the map distances
between the three main HLA loci. For example, when t = +s, s = 0.2, and
c = 0.008, then D = f0.183. I n other words, for these parameters which are not
much different from the value of c necessary for D # 0 equilibria, there is 73.2y0
of the maximum possible disequilibrium generated.
P. W. HEDRICK E T A L
328
0.0
0. I
0.2
0.3
0.4
0.5
PI
Figure 4. T h e expected change in aIlelic frequency when there are two, four or right equivalent
alleles under the immunological maternal-foetal model of selection.
Viability selection
Typically, exposure to an infectious agent in humans results in an immune
response which controls the infection or there is an acute infectious disease. In
contrast, a small proportion of the population may be genetically susceptible to
an autoimmune disease after exposure to certain infectious agents (Pollack &
Rich, 1985). These are the HLA associated autoimmune diseases discussed
above. Because most of these diseases are fairly uncommon and generally affect
individuals after reproduction, their impact on genetic variation at the HLA loci
may not be great.
On the other hand, a major function of M H C histocompatibility molecules is
in presenting foreign antigen to stimulate a n immune response to invading
pathogens (Zinkernagel, 1979). Histocompatibility alleles have been shown to
differ in their ability to create an immune response to a variety of infectious
agents, (van Eden, de Vries & van Rood, 1983) suggesting that the epidemic
diseases of the human past may have played a central role in determining the
HLA haplotype and allele frequencies observed in human populations today.
Let us briefly discuss how HLA types having different susceptibility to
pathogens may maintain genetic variation by examining a two-allele model.
Table 10 gives the relative fitness of the three genotypes given two alleles in the
four possible environments resulting from combinations of the presence and
absence of two pathogens. The fitnesses here assume complete dominance of the
resistant allele, i.e. one dose of the antigen (they are codominant in expression)
is enough to result in resistance. If we assume that there is no correlation in the
presence of the two pathogens and their frequencies are a , and a,, then the
frequency of the four environments are given in Table 10.
EVOLUTIONARY GENETICS AND HLA
329
Table 10. T h e relative fitnesses of the three genotypes when pathogens 1 and 2
are both absent ( -, - ) only 1 is present ( , - ), only 2 is present ( -, ) and
both are present (+, + )
+
+
Table 11. The proportion of females in two experiments that return to oestrus
after mating given exposure in an adjacent compartment to the same male
(stud), a genetically identical male (syngeneic) or a male differing only in the
H2 region (congenic) (from Yamazaki et al., 1983)
Male Syngeneic
Stud
Congenic
I
0.110 (73)
0.118 (76)
0.579 (76)
I1
Average
0.149 (47)
0.086 (58)
0.473 (55)
0.125
0.104
0.534
Let us assume that the environments vary over time. Haldane & Jayakar
(1963) showed that the conditions for a stable polymorphism in a temporally
variable environment are that the geometric mean over environments for the
heterozygote must be larger than that of the two homozygotes. I n the example
given in Table 10 the geometric means are (1-s,)'~, 1, and (l-s2)'i for the
genotypes A , A , , A , A , , and A 2 A 2 ,respectively, illustrating that as long as s,, s 2 ,
a , , and a2 > 0 that there should be a stable polymorphism. I n fact, these
conditions are very broad and are similar to the reversal of dominance models
developed by Gillespie (e.g. 1976) and discussed by Maynard Smith & Hoekstra
(1980), Hoekstra, Bijlsma & Dolman (1985) and Hedrick (1986).
Non-random mating
Although there does not appear to be any evidence for non-random mating
for HLA types, there does appear to be some general evidence from
experimental studies for the H2 types in mice (e.g. Yamazaki et al., 1976, 1978).
I n these studies males generally mate preferentially with females of a different
M H C type although sometimes the preference is for their own haplotype.
There is substantial evidence that mice (and other organisms) can distinguish
M H C types, an ability that could easily result in non-random mating. For
example, Yamazaki et al. (1983) mated females with males of a given MHC
type. These females were then exposed (in an adjacent compartment) to the
same male (stud male), another male of the same genotype as the first (a
syngeneic male), or another of the same genotype except for the H2 region (a
congenic male) (see Table 1 1 ) . T h e proportion offemales that returned to oestrus
330
P. W. HEDRICK E T AL.
was low (around 10%) when the second male was the stud or a syngeneic male
but was fivefold higher when the second male differed in the H2 region.
CONCLUDING REMARKS
‘The aim of our studies is to identify in general the evolutionary factors
influencing HLA genetic variation and in particular determine the nature and
extent of selective events acting in the HLA region. Obviously many different
types of selective pressures may be operating on the HLA loci. O u r theoretical
studies will help delineate the contributions of each of these forces to the genetic
variation at the single locus level and the disequilibrium at the multilocus level.
These population studies also help us understand the mechanisms by which
disease predisposing genes have become common in a population.
ACKNOWLEDGEMENTS
This research was supported by NIH grants GM 35326 and HD 12731.
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