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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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