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Archives of Sexual Behavior pp350-aseb-365186 December 28, 2001 8:30 Style file version July 26, 1999
Archives of Sexual Behavior, Vol. 31, No. 1, February 2002, pp. 63–71 (
C
°
2002)
How Many Gay Men Owe Their Sexual Orientation
to Fraternal Birth Order?
James M. Cantor, Ph.D.,
1
Ray Blanchard, Ph.D.,
1,2,5
Andrew D. Paterson, M.B., Ch.B.,
2,3
and Anthony F. Bogaert, Ph.D.
4
Received October 16, 2000; revision received March 11, 2001; accepted September 1, 2001
In men, sexual orientation correlates with the number of older brothers, each additional older brother
increasingtheoddsofhomosexualitybyapproximately33%.However,thisphenomenon,thefraternal
birth order effect, accounts for the sexual orientation of only a proportion of gay men. To estimate the
sizeof this proportion,wederivedgeneralized forms oftwoepidemiologicalstatistics, the attributable
fraction and the population attributable fraction, which quantify the relationship between a condition
and prior exposure to an agent that can cause it. In their common forms, these statistics are calculable
onlyfor2levelsofexposure:exposedversusnot-exposed.Wedevelopedamethodapplicabletoagents
with multiple levels of exposure—in this case, number of older brothers. This noniterative method,
which requires the odds ratio from a prior logistic regression analysis, was then applied to a large
contemporary sample of gay men. The results showed that roughly 1 gay man in 7 owes his sexual
orientation to the fraternal birth order effect. They also showed that the effect of fraternal birth order
would exceed all other causes of homosexuality in groups of gay men with 3 or more older brothers
and would precisely equal all other causes in a theoretical group with 2.5 older brothers. Implications
are suggested for the gay sib-pair linkage method of identifying genetic loci for homosexuality.
KEY WORDS: attributable fraction; attributable risk; birth order; homosexuality; H-Y antigen; logistic regres-
sion; sexual orientation; sib-pair linkage method.
Epidemiological studies have repeatedly shown that
older brothers increase the probability of homosexual-
ity in later-born males (Blanchard, 1997, 2001; Jones &
Blanchard, 1998). Older sisters, in contrast, do not af-
fect the sexual orientation of later-born males, and neither
older brothers nor older sisters affect the sexual orienta-
tionoflater-born females.Becausefemales are essentially
invisible to this process, we have called it the fraternal
birth order effect.
1
Centre for Addiction and Mental Health, Toronto, Ontario, Canada.
2
Department of Psychiatry, Faculty of Medicine, University of Toronto,
Toronto, Ontario, Canada.
3
Department of Genetics, The Hospital for Sick Children, Toronto,
Ontario, Canada.
4
Departments of Psychology and Community Health Sciences, Brock
University, St. Catharines, Ontario, Canada.
5
To whom correspondence should be addressed at CAMH—Clarke Di-
vision, 250 College Street, Toronto,Ontario, Canada M5T1R8; e-mail:
ray
blanchard@camh.net.
Thefraternalbirthordereffecthasbeendemonstrated
not only in ordinary homosexual community volunteers
(Blanchard & Bogaert, 1996a,b; Blanchard, Zucker,
Siegelman, Dickey, & Klassen, 1998; Ellis & Blanchard,
2001; Robinson & Manning, 2000; see also Blanchard &
Bogaert, 1997a; Purcell, Blanchard, & Zucker, 2000;
Williams et al., 2000), but also in atypical homosexual
groups who differ as widely as possible in their own char-
acteristics and in the characteristics of their desired part-
ners. Older brothers increase the probability that male-
to-female transsexuals will be sexually attracted to men
rather than women (Green, 2000; see also Zucker et al.,
1997), that pedophiles will be sexually attracted to boys
rather than girls (Blanchard et al., 2000; Bogaert, Bezeau,
Kuban,&Blanchard,1997),andthatsexoffendersagainst
adultsandpubescentswilloffendagainstmalesratherthan
females (Blanchard & Bogaert, 1998).
The diversity of the samples in which this phenome-
non has been demonstrated makes fraternal birth order
63
0004-0002/02/0200-0063/0
C
°
2002 Plenum Publishing Corporation
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Archives of Sexual Behavior pp350-aseb-365186 December 28, 2001 8:30 Style file version July 26, 1999
64 Cantor, Blanchard, Paterson, and Bogaert
(ortheunderlying variableitreflects)the most widespread
factorinhomosexualdevelopmentthathasyetbeenidenti-
fied. There are, however, other measures of the theoretical
importance of this phenomenon, in particular, the propor-
tion of homosexual men who acquired their sexual ori-
entation from the fraternal birth order effect, as opposed
to some other agent. In this paper, we derive the general-
izedformsofepidemiologicalstatisticsneededto estimate
this proportion, and we apply the generalized approach to
a large, matched sample of homosexual and heterosexual
volunteers.
A statistical approach that is capable of answering
one empirical question is obviously capable of answer-
ing others that follow the same general form and satisfy
the same underlying assumptions. We therefore briefly
discuss the application of our method to similar research
problems. We also discuss the implications of our empir-
ical findings for genetic studies of sexual orientation.
THE ATTRIBUTABLE FRACTION AND
POPULATION ATTRIBUTABLE FRACTION
Theattributablefractionandpopulationattributable
fraction statistics provide intuitive measures of the mag-
nitude of the relationship between two dichotomous vari-
ables. As typically used in epidemiology, these two vari-
ables are disease state (present vs. absent) and exposure
toa pathogen(exposedvs. neverexposed).These statistics
are applied to diseases that can be caused by more than
one pathogen. They quantify the relationship between the
disease and any one specific pathogen, which we will call
the target pathogen.
These statistics may be explained as follows. The
population of all persons with a given disease can be di-
videdintothreegroups:thosewhowere exposedtothetar-
get pathogen and got the disease because of the exposure
(causally exposed), those who were exposed to the tar-
get pathogen but actually got the disease from some other
pathogen (coincidentally exposed), and those who were
never exposed to the target pathogen and therefore nec-
essarily got the disease from some other pathogen (never
exposed). The attributable fraction is the ratio of diseased
people who got the disease from the pathogen to the num-
ber of diseased people who wereexposedto the pathogen,
causally exposed/(causally exposed + coincidentally ex-
posed). The population attributable fraction is the ratio of
people who got the disease from the pathogen to the to-
tal number of diseased people, causally exposed/(causally
exposed + coincidentally exposed + never exposed). The
population attributable fraction can be thought of as the
percentage of cases of disease (potentially) preventable
by a total elimination of exposure in the entire population
(Gefeller, 1992).
The population attributable fraction may be equiv-
alently expressed as the product of the attributable frac-
tionandthe prevalenceof exposureamongdiseased cases.
This form makes it clear that exposure to a potent agent
may be strongly related to a disease, yet account for only
a small proportion of the existing cases because of the
rarity of exposure to it. The historical use of the term
“population” here is unfortunate, because it suggests that
“attributable fraction” refers to a sample characteristic,
and “population attributable fraction,” to the correspond-
ing population parameter. As just shown, however, the
population attributable fraction actually conveys a differ-
ent type of information.
Although the attributable fraction and population at-
tributablefraction aremostfrequentlyapplied in epidemi-
ological analyses of diseases and their causes, these statis-
tics may just as readily be applied to variables that do not
describe pathology. Therefore, neutral terms will be used
for interpretation here: agent rather than pathogen to de-
scribe the independent variable (IV), and condition rather
than disease to describe the dependent variable (DV). For
the same reason, we will refer to the statistics as attribu-
tablefractionsratherthanasattributablerisks,orthemany
other names that have been used (Greenland & Robbins,
1988; Walter, 1978).
The case of two dichotomous variables is usually
depicted with a 2 × 2 table (Fig. 1). The odds ratio in this
case may then be expressed as
ad
bc
,
and the attributable fraction may be expressed as
prevalence
exposed
− prevalence
unexposed
prevalence
exposed
or
d
c+d
−
b
a+b
d
c+d
.
As noted earlier, the population attributable fraction is
the simple product of the attributable fraction and the
Fig. 1. Organization of data for a dichotomous condition and dichoto-
mous exposure status. Cell values represent number of cases. Preva-
lence of the condition among cases without any exposure (i.e., baseline
prevalence), p
0
= b/(a + b). Prevalence of the condition among cases
experiencing exposure to the agent, p
1
= d/(c + d).
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Archives of Sexual Behavior pp350-aseb-365186 December 28, 2001 8:30 Style file version July 26, 1999
Sexual Orientation and Birth Order 65
prevalence of exposure to the agent among the cases with
the condition, or
Ã
d
c+d
−
b
a+b
d
c+d
!
µ
d
b + d
¶
.
Unfortunately, these calculations of the attributable
fractionsarelimitedto IVs that possess exactlytwo levels.
Thatis,dataregardingtheexposurestatusofacasemustbe
dichotomized into exposed versus not-exposed. Although
dichotomies appropriately capture information regarding
many factors, they require researchers to collapse multi-
level data into less precise, all-or-none categories.
Generalizedformsoftheattributablefractionthatcan
accommodate multilevel variables are required to utilize
the information inherent in multilevel data. Park (1981)
suggested a methodfor quantifying the relation between a
dichotomous IV and a multilevel DV. Park’s method does
not, however, apply to multilevel IVs. The problem of
multiple-levelIVs(i.e.,multipleexposures)wasdiscussed
by Denman and Schlesselman (1983). Their suggested
solution employed individual odds ratios, with a separate
ratioestimatedfor eachlevelof theIVrelativetothe unex-
posed group. Denman and Schlesselman’s approach does
notrequirealinearincrease inoddsbetween eachadjacent
level of the IV (i.e., a constant odds ratio for the sample).
When,however,therelationbetweenaconditionandnum-
ber of exposuresislinearintheodds—asappearstobethe
caseforsexualorientationand numberofolder brothers—
that approach may not be the most efficient or accurate.
Wethereforeundertook to derivean attributablefrac-
tion for multiple exposures, a statistic that would use the
odds ratio from a prior logistic regression analysis to di-
rectlycalculatetheattributablefractionforanygivennum-
ber of exposures. In this context, exposures refer broadly
to occurrences of the causal agent, whether they impinge
on the case directly or affect the case via their cumulative
effect on some intervening variable. The latter situation
is frequently encountered in birth order research, where
the probability of a fetus developing certain diseases in-
creases with the number of prior fetuses to which the ma-
ternal uterus is exposed. Children of later pregnancies are
more likely to develop macrosomia (e.g., Babinszki et al.,
1999), mental retardation (e.g., Flannery & Liederman,
1994), Down’s syndrome (e.g., Schimmel, Eidelman,
Zadka, Kornbluth, & Hammerman, 1997), and diabetes
(e.g., Tuomilehto, Podar, Tuomilehto-Wolf, & Virtala,
1995).Intheseexamples,priorfetuseswouldnotaffectthe
subsequent fetus—that is, the “case”—directly, but rather
through the intervening variable of cumulative changes in
the uterine environment.
DERIVATION OF THE ATTRIBUTABLE
FRACTION FOR MULTIPLE EXPOSURES
Where the attributable fraction for two dichotomous
variables may be depicted in a 2 × 2 table, situations in
whichcasesmayexperienceanynumberofexposuresmay
be depicted in a table with 2 × (N + 1) cells, where N
indicatesthemaximum numberof timesanycasehasbeen
exposed to the agent (Fig. 2). Let S be the odds ratio for
the overall set of exposure levels, with the assumption
of a constant increase in the odds of the condition be-
ing present between each level of the IV. Then, let odds
n
be the odds of the condition being present after n expo-
sures, with odds
0
being the odds of the condition being
present with no exposure to the agent. Note that odds
0
may also be thought of as the baseline odds of a case
having the condition or as the odds of having the condi-
tion because of a factor other than the agent represented
by the IV.
After a single exposure to an agent, the odds of de-
veloping a condition increase by a factor of S, that is,
odds
1
= odds
0
· S.
After a second exposure to an agent, the odds of de-
veloping the condition increase by a factor of S once
again:
odds
2
= odds
0
· S · S.
Fig.2. Organizationof data fora dichotomous conditionand anarbitrary
number of exposures. Cell values represent number of cases. Prevalence
of the condition among cases without any exposure, p
0
= b
0
/(a
0
+ b
0
).
Prevalence of the condition among cases experiencing n exposures to
the agent, p
n
= b
n
/(a
n
+ b
n
).
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66 Cantor, Blanchard, Paterson, and Bogaert
In general, the odds of the condition being present after n
exposures is expressible as
odds
n
= odds
0
· S
n
. (1)
However, the attributable fraction, whether for sin-
gle or for multiple exposures, is expressed in terms of
probabilities or prevalence rates, rather than odds. Equa-
tion (1) may be recast in terms of probabilities by not-
ing that odds = probability/(1 − probability). Replacing
odds
n
and odds
0
respectively with p
n
and p
0
, where p
n
is
the probability of the condition being present after n ex-
posures and p
0
is thebaselineprobabilityofthecondition,
yields, with simplification,
p
n
=
1
1 +
¡
1
p
0
− 1
¢±
S
n
. (2)
As noted earlier, the attributable fraction is the dif-
ference in prevalence (or probability) of cases between
the exposed and nonexposed groups, expressed as a pro-
portion of the prevalence among the exposed. This calcu-
lation is true in general. The attributable fraction for any
individual level of the IV, G
n
, is the difference in preva-
lence of cases between that level and the baseline level,
expressed as a proportion of the prevalence at that level of
exposure:
G
n
=
p
n
− p
0
p
n
= 1 −
p
0
p
n
.
G
n
may be expressed in terms of S and p
0
using Eq. (2) to
substitutefor p
n
,providinganequationfor theattributable
fraction for any n:
G
n
= 1 −
p
0
1
±£
1 +
¡
1
p
0
− 1
¢±
S
n
¤
G
n
= (1 − p
0
)
µ
1 −
1
S
n
¶
. (3)
Thus, each value of G
n
can be calculated directly with
Eq. (3), from only the baseline prevalence and overall
odds ratio.
The population attributable fraction can then be cal-
culated as the weighted average of each G
n
, with weights
assigned by the distribution of exposure levels in the pop-
ulation. If D
n
is the proportion of cases that have expe-
rienced n exposures to the agent, then the population at-
tributable fraction is
n=N
X
n=0
G
n
· D
n
, (4)
or, in vector notation, the cross product of the column
vectors G and D, D
0
G.
THE PROPORTION OF
“OLDER-BROTHER-TYPE” GAYS
The proportion of gay men who owe their sexual ori-
entationtothe fraternalbirthorder effectwasestimatedby
applying the foregoing method to unpublished data from
Blanchard and Bogaert (1996b). The participants in this
study were 302 homosexual men who were individually
matched on year of birth with 302 heterosexual men. All
participantsdescribedtheirraceasWhiteandreportedthat
they were single births. None was adopted, had any ma-
ternal half-siblings, or expressed any doubt that he knew
of all children born to his mother. Table I presents this
sample broken down by sexual orientation andby number
of older brothers.
Equation (3) requires two values, the baseline preva-
lence of the condition under investigation and the odds
ratio for its increase between each level of exposure to
the agent. The overall prevalence of homosexuality in the
adult male population is probably somewhere between
2 and 3% (e.g., ACSF Investigators, 1992; Billy, Tanfer,
Grady, & Klepinger, 1993; Fay, Turner, Klassen, &
Gagnon,1989;Johnson, Wadsworth,Wellings, Bradshaw,
& Field, 1992; Laumann, Gagnon, Michael, & Michaels,
1994), and so we have estimated the baseline prevalence
(or the prevalence of homosexuality among men with 0
older brothers) to be 2%. Logistic regression analysis of
TableIdatarevealsanoddsratioof1.33.Substitutingthese
values into Eq. (3) produces the attributable fraction val-
ues, G
n
, listed in Table II. Thus, for example, G
2
∼
=
0.43;
that is, 43% of the homosexual men with two older broth-
ers in this sample can attribute their homosexuality to the
older brother effect.
The frequency distribution of older brothers among
homosexual men is estimated by the distribution in the
sample and is expressed in Table II as a proportion of
the total size of the sample of homosexual participants.
The sum of the products of these pairs of elements yields
a population attributable fraction of 15.1%. Thus, about
Table I. Sexual Orientation and Number of Older Brothers
a
Sexual orientation
Older brothers Heterosexual Homosexual
0 198 165
17586
21934
3812
414
5+11
a
From Blanchard and Bogaert (1996b).
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Sexual Orientation and Birth Order 67
TableII. AttributableFraction ofHomosexualityfor OlderBrothers and
the Frequency Distribution of Older Brothers in the Homosexual Group
No. of older Attributable Frequency
brothers, n fraction, G
n
distribution, D
n
0 .000 .546
1 .243 .285
2 .426 .113
3 .563 .040
4 .667 .013
5+ .745 .003
one out ofeverysevenhomosexual men in this samplecan
attribute his homosexuality to the older brother effect.
Additional calculations showed that variation in the
baselineprevalence—at leastwithinthe range of plausible
values—makes very little difference in the results. Re-
estimatingthepercentageofolder-brother-typegaysusing
a baseline prevalence of 1% yields a figure of 15.2%; re-
estimatingwith abaselineprevalenceof 4%yieldsafigure
of 14.8%.
The precise form of the function relating the odds of
homosexuality to a proband’s number of older brothers is
another issue that should be examined. Our estimate of a
33% increase in the odds per older brother was based on
the assumption that this function is linear. This assump-
tion is justified by the results of the following reanalysis
of raw data from Blanchard and Bogaert (1996b). This
reanalysis involvedrerunning the logistic regression anal-
ysis from that study. As in the original study, the criterion
variable was sexual orientation, coded dichotomously as
heterosexual or homosexual. In the reanalysis, the pre-
dictor variables were the participant’s number of older
brothers, the squared number of older brothers, and the
cubed number of older brothers (i.e., the linear, quadratic,
and cubic terms for older brothers, respectively). With
the linear term already entered into the regression equa-
tion,additionofthequadratictermproducednosignificant
improvement, χ
2
(1) = 0.24, p = .62; and with the linear
and quadratic terms already entered into the equation, ad-
dition of the cubic term produced no significant improve-
ment, χ
2
(1) = 0.23, p = .63. Very similar results were
obtained with a reanalysis of raw data from Blanchard
etal.(1998). It thereforeappearsthat a linearfunctionbest
describes the relation over the range of values observed.
Itseemslikelythatinasampleincludinga substantial
proportion of participants with many older brothers, the
functionwouldprovecurvilinear;thatis,after8or10older
brothers, additional older brothers would produce less or
no further increase in the odds of homosexuality. Such a
sample would not, however, be expected from a modern,
industrialized population, either now or in the imaginable
future. It is therefore reasonable to model the relation as
a linear one, at least for contemporary samples.
THE AF
50
The development of Eq. (3), a continuous function
for the attributable fraction at any n, makes possible an-
other useful metric by which to describe the association
between a condition and an agent associated with it. Be-
cause baseline frequency (p
0
) is a positive constant, and
because the contribution of exposures to the agent (G
n
)
is zero at n = 0 and increases as n increases, there will
eventually be a point at which the fraction attributable to
the exposures to the agent equals (and then exceeds) the
fractionattributableto alltheother (baseline)factors.That
is, at some n, p
n
= 2p
0
. For cases at this n, the agent has
contributed as much to the prevalence of the condition as
did all the other effects that were present at baseline (i.e.,
at n = 0). We term this point the AF
50
, because 50% of
the cases are attributable to the agent. The AF
50
is located
by setting Eq. (3) to 2p
0
and solving for n, that is,
(1 − p
0
)
µ
1 −
1
S
n
¶
= 2p
0
and thus,
n =
log
(
2 − 2p
0
)
− log
(
1 − 2p
0
)
log S
. (5)
Using the previous example estimating the baseline
prevalence of homosexuality as 2% and the odds ratio
of 1.33 from Table I, substitution into Eq. (5) yields an
n of 2.503 older brothers. That is, among gay men with
more than 2.5 older brothers, sexual orientation is more
attributable to the fraternal birth order effect than to all
other possible effects combined.
DISCUSSION
Ourmainfindingisthatroughlyonegaymaninseven
owes his sexual orientation to the fraternal birth order ef-
fect. This shows that the contribution of fraternal birth
order to the sum total of gay men is more than negligible.
Alternative strategies for quantifying the magnitude
of the fraternal birth order effect in intuitively compre-
hensible terms treated number of older brothers as if it
were a continuous variable, that is, as if someone could
have fractions of an older brother. These analyses showed
that a boy with 2.5 older brothers would be twice as likely
to be gay as a boy with 0 older brothers and that, for
mathematically related reasons, half of all gay men with
2.5 older brothers would not have been gay if they had
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68 Cantor, Blanchard, Paterson, and Bogaert
had 0 older brothers (i.e., the attributable fraction equals
50% when the number of older brothers is 2.5). This also
means that among men with 2.5 older brothers, the frater-
nal birth order effect would equal all other causes of ho-
mosexuality combined. Previous work along these lines,
which used informal methods and whichhappened to pro-
duce values that closely approximated integers, showed
that a boy with 4 older brothers would be three times as
likely to be gay as a boy with 0 older brothers (Blanchard,
2001).
The foregoing conclusions rest on the assumption
that older brothers cause homosexuality, whether directly
or indirectly. This assumption seems to us justified on a
variety of logical and empirical grounds. From a purely
mathematical standpoint, the observed correlation bet-
weenhomosexualityandolderbrotherscouldariseinthree
basically differentways:the former could cause the latter;
the latter could cause the former; or both could be caused
by some third variable. We can eliminate the first possi-
bility on logical grounds—a man’s homosexuality cannot
operate backwards in time to give him additional older
brothers. That leaves only one competing interpretation,
namely, that homosexuality and older brothers are corre-
lated only because bothare caused by some thirdvariable.
The question then arises: What third variable?
One possibility might seem, at least at first glance, to
beparentalage.Aman’sfraternalbirthordernaturallycor-
relates substantially with the age of his parents at the time
of his birth. This raises thepossibility that the seeming as-
sociation of fraternal birth order and sexual orientation is
merely a statistical artifact arising from the correlation of
both with parental age, and that the important connection
is between parental age and sexual orientation. A genetic
explanation along these lines was suggested by Raschka
(1995), who argued that a higher paternal age might re-
flect an increased mutation rate in the spermatogenesis of
older fathers. The first problem with positing parental age
as the hypothetical third variable is that several empiri-
cal studies have shown directly that the relation between
numberofolderbrothersandmalehomosexualityisnotan
artifact of higher maternal or paternal age (Blanchard &
Bogaert, 1996a,b, 1997b, 1998; Blanchard & Sheridan,
1992; Bogaert et al., 1997). The second problem with
positing parental age as the hypothetical third variable
is logical (Jones & Blanchard, 1998). Parents’ ages at the
birth of a boyandthatboy’s birth order among his siblings
are, as already noted, strongly correlated. The correlation,
however, is essentially the same for both sexes. Hence, if
homosexuality is directly related to advanced maternal or
paternal age, gay men should tend to be born late with
respect to both their brothers and their sisters. They are
not, however; they are born late only with respect to their
brothers. It therefore appears that parental age cannot ex-
plain the relation between fraternal birth order and sexual
orientation.
The search for a third variable must therefore turn to
other possibilities. These are rather difficult to envision,
even if one permits the positing of hitherto unobserved
phenomena. Imagine, for example, there exists some con-
dition that causes a man to produce extraordinarily suc-
cessful Y-bearing sperm. Such men sire large numbers of
sons, both in relation to other men and in relation to their
own number of daughters. The condition also, however,
predisposesthemtosirehomosexualsons. Thegaysonsof
such fathers would, in fact, have an excess of older broth-
ers. Thus, this imaginary condition (a hypothetical third
variable)does seemcapableof accounting for the data un-
til one reflects that such gay sons would have an equally
large excess of younger brothers. It could not, therefore,
explain the crucial finding that gay men have an excess
only of older brothers. It seems to us, in summary, that al-
ternative explanations of the correlation between fraternal
birth order and homosexuality are either so clearly incor-
rect or else so difficult to conceive that the most plausible
interpretation is the simple one that older brothers make
some causal contribution to homosexuality in later-born
males.
Dissimilar theories of the fraternal birth order effect
converge on the conclusion that our estimates of its mag-
nitude are likelytobeontheconservativeside.Thereason
for this, which we discuss below, is that these theories im-
ply that the variable of real interest is not a man’s number
of live-born older brothers but something slightly differ-
ent, for which his number of live-born older brothers is an
imperfect measure. One theory implies that the variable
of real interest is the number of prior male fetuses carried
by a man’s mother, whether these resulted in a live birth
or not. A second theory implies that the variable of real
interest is the number of older brothers that were actually
in a man’s environment when he was growing up, not his
total number of older brothers.
BlanchardandBogaert(1996b)hypothesizedthatthe
correlation of fraternal birth order with sexual orientation
in males reflects the progressive immunization of some
mothers to Y-linked minor histocompatibility antigens
(H-Y antigens) by each succeeding male fetus, and the
concomitantly increasing effects of anti-H-Y antibodies
on the sexual differentiation of the brain in each suc-
ceeding male fetus (Blanchard & Bogaert, 1996b). This
hypothesis rests partly on the argument that a woman’s
immune system would appear to be the biological sys-
tem most capable of “remembering” the number of male
(but not female) fetuses that she has previously carried
and of progressively altering its response to the next fetus
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Sexual Orientation and Birth Order 69
according to the current tally of preceding males. It also
rests on the finding that sexualorientationinfemales,who
do not express H-Y antigens and would therefore not be
targetsofanti-H-Yantibodiesinutero, isunrelated totheir
number of older brothers. Various lines of animal experi-
mental evidence and human clinical evidence that bear on
the plausibility of this hypothesis have been summarized
by Blanchard and Klassen (1997). Recently, Blanchard
and Bogaert’s basic assumption that the fraternal birth or-
der effect operates in the prenatal environment has been
bolstered by the finding that homosexual males with older
brothersweigh substantiallylessatbirththanheterosexual
males with older brothers (Blanchard, 2001; Blanchard &
Ellis, 2001).
Ifthematernalimmunehypothesisiscorrect,andif—
as animal evidence suggests (Epstein, Smith, & Travis,
1980;Krco &Goldberg,1976; Shelton&Goldberg,1984;
White, Anderson, & BonDurant, 1987; White, Lindner,
Anderson, & BonDurant, 1983)—male fetuses begin ex-
pressing H-Y antigens very early in development, then
spontaneously aborted male fetuses might also immunize
the mother and thereby augment the probability of homo-
sexuality in her subsequent male offspring. That would
mean that a calculation based on the observed relation
between a man’s sexual orientation and his number of
(live-born) older brothers underestimates the proportion
of gays who owe their orientation to the fraternal birth
order effect, or more precisely, to the mechanism under-
lying that effect. On that basis, one might argue that the
true percentage of older-brother-type gays is more likely
to lie above than below our present estimate.
A very different class of explanations assumes that
the fraternal birth order effect operates postnatally, in the
environment of rearing. The most popular example of
these is the hypothesis that sexual interaction with older
males increases a boy’sprobabilityofdevelopingahomo-
sexual orientation, and that a boy’s chances of engaging
in such interactions increase in proportion to his number
of older brothers (Jones & Blanchard, 1998). If this hy-
pothesis is correct, then one should only count, as older
brothers, prior-born brothers who had the opportunity to
interact sexually with the subject. Older brothers who left
the family home or died before the subject was born, or
while the subject was still an infant, represent statistical
error that would reduce the apparent correlation between
fraternal birth order and sexual orientation. There is no
way to reliably identify and exclude such brothers in the
dataof Blanchardand Bogaert(1996b) orinanyotherdata
set known to us, however. Therefore this explanation, like
most other psychosocial explanations, also implies that
the available data underestimate the true percentage of
older-brother-type gays.
As indicated in the beginning of the paper, our find-
ings have implications for the gay sib-pair linkage method
ofidentifyinggeneticlocifor homosexuality(e.g., Hamer,
Hu, Magnuson, Hu, & Pattatucci, 1993; Hu et al., 1995;
Rice, Anderson, Risch, &Ebers, 1999). The present study
shows that older-brother-type gays (in genetic terminol-
ogy, phenocopies) add a considerable amount of noise
to gay sib-pair analyses, and they add it nonrandomly.
In the best-case scenario (best case for the geneticist), a
gay sib-pair would consist of the first two boys born in
a family. Table II shows, however, that the younger of
the pair already has a 24% chance of being gay for non-
geneticreasons.Ifagaysib-pair consistsofthesecondand
third boys born in a family, the elder has a 24% chance
of being gay for nongenetic reasons, and the younger
has a 43% chance of being gay for nongenetic reasons.
This analysis assumes, of course, that the fraternal birth
order and familiality effects are independent; there are
little data that bear on this assumption, but what there
are suggest that the effects are independent (Blanchard
& Bogaert, 1997a). It therefore appears that the fraternal
birth order phenomenon may significantly increase the
difficulty of finding genetic linkage using a gay sib-pair
design.
The foregoingproblemmight be approached in para-
metric linkage analyses of gay sib-pair data by specifying
different liability classes (specifically, phenocopy rates)
for different individuals. This is usually used to provide
age- and sex-dependent penetrances, but it could also be
used to assign different phenocopy rates to sibs with dif-
ferent birth orders (Ott, 1991). An analogous adjustment
might be made in so-called nonparametric analyses of
gay sib-pair data, by incorporating covariates or using a
weighting factor based on the birth orders of the indi-
vidual sibs (Dawson, Kaplan, & Elston, 1990; Flanders &
Khoury, 1991; Greenwood & Bull, 1999;Yang & Khoury,
1997).
Three assumptions underlying the attributable frac-
tion for multiple exposures and the AF
50
should be made
explicit, for the benefit of researchers who might con-
sider applying these statistics to other problems. First is
the assumption of a constant odds ratio (i.e., a linear in-
creaseinodds)overincreasinglevelsof theIV.Aswehave
shown, this assumption can readily be tested by examin-
ingthestatisticalsignificanceofthe higher order terms for
theIVinthe logistic regressionequation.Second is the as-
sumption that the odds of thecondition occurring increase
rather than decrease with each exposure to the agent,
that is, S > 1. Agents that are associated with decreased
odds of developing the condition, that is, S < 1, are re-
ferred to as protective factors; the statistics developed
here cannot be meaningfully interpreted for instances of
P1: GVG
Archives of Sexual Behavior pp350-aseb-365186 December 28, 2001 8:30 Style file version July 26, 1999
70 Cantor, Blanchard, Paterson, and Bogaert
protective factors. Third is the assumption that the case of
zero exposures, p
0
, provides a meaningful baselinepreva-
lence of the condition.
ACKNOWLEDGMENTS
The authors thank J. Michael Bailey, Scott
Hershberger, and Edward Miller for their comments on
earlier drafts of this paper. This research was supported
by Social Sciences and Humanities Research Council of
Canada Grant 410-99-0019 to Ray Blanchard and by a
postdoctoral fellowship award from the CAMH Founda-
tionandtheOntarioMinistryofHealthtoJamesM.Cantor.
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