Homosexuality as a Consequence of Epigenetically Canalized Sexual Development Author(s): William

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Homosexuality as a Consequence of Epigenetically Canalized Sexual Development Author(s): William R. Rice, Urban Friberg and Sergey Gavrilets Source: The Quarterly Review of Biology, Vol. 87, No. 4 (December 2012), pp. 343-368 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/10.1086/668167 . Accessed: 23/10/2014 11:13 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to The Quarterly Review of Biology. http://www.jstor.org This content downloaded from 24.48.51.83 on Thu, 23 Oct 2014 11:13:11 AM All use subject to JSTOR Terms and Conditions

Transcript of Homosexuality as a Consequence of Epigenetically Canalized Sexual Development Author(s): William

Homosexuality as a Consequence of Epigenetically Canalized Sexual DevelopmentAuthor(s): William R. Rice, Urban Friberg and Sergey GavriletsSource: The Quarterly Review of Biology, Vol. 87, No. 4 (December 2012), pp. 343-368Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/10.1086/668167 .

Accessed: 23/10/2014 11:13

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

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HOMOSEXUALITY AS A CONSEQUENCE OF EPIGENETICALLYCANALIZED SEXUAL DEVELOPMENT

William R. RiceDepartment of Ecology, Evolution and Marine Biology, University of California

Santa Barbara, California 93106 USA

e-mail: [email protected]

Urban FribergDepartment of Evolutionary Biology, Uppsala University

Norbyvägen 18D, 752 36 Uppsala, Sweden

e-mail: [email protected]

Sergey GavriletsDepartment of Ecology and Evolutionary Biology and Department of Mathematics, National Institute for

Mathematical and Biological Synthesis, University of TennesseeKnoxville, Tennessee 37996 USA

e-mail: [email protected]

keywordshomosexuality, androgen signaling, canalization, epigenetic,

gonad-trait-discordance, Jost paradigm

abstractMale and female homosexuality have substantial prevalence in humans. Pedigree and twin studies

indicate that homosexuality has substantial heritability in both sexes, yet concordance between identicaltwins is low and molecular studies have failed to find associated DNA markers. This paradoxical patterncalls for an explanation. We use published data on fetal androgen signaling and gene regulation vianongenetic changes in DNA packaging (epigenetics) to develop a new model for homosexuality. It is wellestablished that fetal androgen signaling strongly influences sexual development. We show that an unappreciatedfeature of this process is reduced androgen sensitivity in XX fetuses and enhanced sensitivity in XY fetuses, andthat this difference is most feasibly caused by numerous sex-specific epigenetic modifications (“epi-marks”)originating in embryonic stem cells. These epi-marks buffer XX fetuses from masculinization due to excess fetalandrogen exposure and similarly buffer XY fetuses from androgen underexposure. Extant data indicatesthat individual epi-marks influence some but not other sexually dimorphic traits, vary in strength acrossindividuals, and are produced during ontogeny and erased between generations. Those that escape erasurewill steer development of the sexual phenotypes they influence in a gonad-discordant direction in opposite

The Quarterly Review of Biology, December 2012, Vol. 87, No. 4

Copyright © 2012 by The University of Chicago. All rights reserved.

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sex offspring, mosaically feminizing XY offspring and masculinizing XX offspring. Such sex-specificepi-marks are sexually antagonistic (SA-epi-marks) because they canalize sexual development in theparent that produced them, but contribute to gonad-trait discordances in opposite-sex offspring whenunerased. In this model, homosexuality occurs when stronger-than-average SA-epi-marks (influencingsexual preference) from an opposite-sex parent escape erasure and are then paired with a weaker-than-average de novo sex-specific epi-marks produced in opposite-sex offspring. Our model predicts thathomosexuality is part of a wider phenomenon in which recently evolved androgen-influenced traitscommonly display gonad-trait discordances at substantial frequency, and that the molecular featureunderlying most homosexuality is not DNA polymorphism(s), but epi-marks that evolved to canalizesexual dimorphic development that sometimes carryover across generations and contribute to gonad-trait discordances in opposite-sex descendants.

Introduction

THE COMMON occurrence of homo-sexuality is perplexing from an evolu-

tionary perspective. Simple logic suggeststhat a fitness-reducing phenotype should beselected against, but homosexuality is none-theless surprisingly common in human pop-ulations—e.g., a prevalence of about 8% inboth sexes was reported in a large and sys-tematic sample in Australia (Bailey et al.2000). Existing genetic models for the evo-lution of human homosexuality can be sep-arated into two major classes: one based onkin selection (Wilson 1975) and anotherbased on sexually antagonistic alleles and/oroverdominance (Camperio-Ciani et al. 2004,2008; Gavrilets and Rice 2006; Bailey and Zuk2009; Iemmola and Camperio-Ciani 2009).These models are all based on special cases ofselection that directly, or indirectly, maintaingenetic variation at loci contributing to thehomosexual phenotype. However, despite nu-merous studies over the last decade searchingfor polymorphisms associated with homosexu-ality, no convincing molecular genetic evi-dence has been found despite the fact thatpedigree and twin studies clearly show that ho-mosexuality is familial (reviewed in Ngun etal. 2011). Homosexuality has also been hy-pothesized to be caused by nongenetic fac-tors such as maternal antibodies againstmale-specific antigens (reviewed in Bogaertand Skorska 2011). This hypothesis may in-deed explain some cases of homosexuality,but cannot account for most cases in menand none in women (Cantor et al. 2002).The poor correspondence between currentmodels and data calls for a new conceptual

framework to understand the evolution ofhomosexuality.

Here we integrate theory from evolution-ary genetics with recent developments in theregulation of gene expression and 50 yearsof research on androgen-dependent sexualdevelopment. We first find that the existingparadigm of mammalian sexual develop-ment is incomplete, with the missing compo-nent being a system to canalize androgensignaling during fetal development such thatthe response to circulating testosterone isboosted in XY fetuses and blunted in XXfetuses. We integrate these data with recentfindings from the epigenetic control of geneexpression, especially in embryonic stem cells,to develop and empirically support a mathe-matical model of epigenetic-based canalizationof sexual development. The model predictsthe evolution of homosexuality in both sexeswhen canalizing epi-marks carryover acrossgenerations with nonzero probability.

We will use the term epi-marks to denotechanges in chromatin structure that influ-ence the transcription rate of genes (codingand noncoding, such as miRNAs), includingnucleosome repositioning, DNA methylation,and/or modification of histone tails, but notincluding changes in DNA sequence. It is nowwell established that a parent’s epi-marks some-times carryover across generations and influ-ence the phenotypes of offspring (reviewed inMorgan and Whitelaw 2008). Epigenetics is arelatively new subdiscipline in genetics and itsimportance in evolution, especially as a majorcontributor to realized heritability, is currentlybeing developed and debated (e.g., Slatkin2009; Furrow et al. 2011). Nonetheless, there

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is now clear evidence that environmentallyinduced epigenetic modifications of genesexpressed in male mice (e.g., DNA methyl-ation; Franklin et al. 2010) that feminizetheir brains and behavior can be transgen-erationally inherited by their offspring (Mor-gan and Bale 2011). Our study examines theramifications of transgenerational epigene-tic inheritance to the phenomenon of hu-man homosexuality.

The first half of our analysis is general andapplied to all sexually dimorphic traits inmammals that are strongly influenced by fe-tal/neonatal androgen exposure. The sec-ond half focuses on homosexuality and itssimilarity with other common gonad-trait dis-cordances that have important medical sig-nificance. By homosexuality we mean anysame-sex partner preference, spanning allKinsey scores �0 (e.g., including bisexual-ity). Our model of homosexuality may alsoapply to transsexualism, but we do not de-velop this application here.

Classical View: Sex HormoneDifferences Fully Determine Sexual

DimorphismBeginning with Phoenix et al. (1959), a

long succession of studies have consistentlyand unambiguously demonstrated that sex-ual dimorphisms of the genitalia and brainof mammals are strongly influenced by an-drogen exposure during fetal development.The foundation for this conclusion is that XYfetuses experimentally exposed to androgenantagonists during gestation develop femi-nized genitalia, brains, and behavior, whereasXX fetuses exposed to elevated androgens de-velop masculinized phenotypes for these sametraits. Studies of untreated fetuses demon-strated that circulating androgen levels differbetween XX and XY genotypes, with signifi-cantly higher average androgen levels in XYfetuses at a time at or before the genitalia,brain, and behavior become sexually dimor-phic.

The logic of the “prenatal androgen par-adigm” (also known as the Jost paradigm) be-gins with the observation that only XY embryosexpress the Y-linked gene SRY (Figure 1A).This gene product induces development ofthe testes in XY embryos, which in turn pro-

duce androgens that influence later sexualdevelopment. The absence of elevated circu-lating androgens during fetal developmentleads to the female phenotype. Although manyaspects of sexual dimorphism are a response tothe “organizational” effects of sex-specific dif-ferences in circulating androgens during fetaland neonatal development, full manifestationof sexual dimorphism sometimes dependson the “activational” effects of androgensand estrogens at and after puberty. In hu-mans, the fact that XY individuals (with fullyformed testicles and normal levels of circu-lating androgens) that are homozygous for anull allele at the androgen receptor locus(and therefore cannot respond to circulat-ing androgens) develop fully female-typicalgenitalia and reproductive behavior (re-viewed in Wisniewski et al. 2008) providesstrong support for the prenatal androgenparadigm.

Sex Hormone Differences are notSufficient to Produce Sexual

DimorphismAlthough prenatal androgen levels play a

fundamental role in sexual development,there is also evidence that the prenatal andro-gen paradigm is at least partially incomplete(reviewed in Davies and Wilkinson 2006). Stud-ies in the mouse “four core” model system (inwhich a the male-determining Sry gene hasbeen translocated to an autosome, enablinggender and sex chromosome karyotype to beexperimentally manipulated independently)clearly demonstrate that some aspects of sexu-ally dimorphic behavior and brain anatomy arestrongly influenced by the sex chromosomekaryotype rather than the level of fetal andro-gen exposure alone (reviewed in Arnold andChen 2009). These studies are, however, con-sistent with the conclusion that androgen sig-naling is the predominant factor controllingsexual dimorphism in this model system.

Here we provide evidence that the prena-tal androgen paradigm is missing a majorcomponent. This conclusion is based on ourreanalysis of studies of circulating prenatalandrogens in human and rat fetuses. In hu-mans, the testes begin to secrete testosterone(T) in XY male fetuses beginning around theeighth week of gestation (Wilson et al. 1981).

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However, T is also present in XX femalefetuses in substantial amounts, originatingfrom the fetal adrenals and from placental/maternal sources. Secretion of T by the testesincreases its concentration in the blood ofXY fetuses. The maximum average differ-ence in T concentration between male (XY)and female (XX) fetuses occurs betweenweeks 11–17 (Reyes et al. 1974). After thistime, fetal secretion of T by the testes de-clines markedly, causing average T values inmales to become indistinguishable from lev-els in females (Reyes et al. 1974). Althoughmale fetuses have higher average T than fe-males starting around week 11, overlap in Tlevels between the sexes (i.e., some XXfetuses having higher T than some XY fe-tuses) was observed at all times except be-tween weeks 15–19 (Reyes et al. 1974). Thistransient lack of overlap (and hence an un-ambiguous signal of fetal gender) may begenuine or an artifact due to small samplesize. The latter explanation is supported by a

much larger study (166 female and 185 malefetuses) of amniotic fluid collected betweenweeks 15–19 (T diffuses from the fetal circu-lation into the amniotic fluid via the skin atthis stage of development), in which therewas about 5% overlap (i.e., 5% of XX fetuseshad higher T than some XY fetuses) in Tconcentration between male and female fe-tuses (Perera et al. 1987). In a large studyof rats, significantly higher circulating T inmale compared to female fetuses occurredonly between days 17–21 of gestation (Weiszand Ward 1980). Despite this window of sig-nificantly elevated T in male fetuses, T levelsoverlapped between the sexes throughout alltime points during gestation (Weisz andWard 1980). Collectively, these studies indi-cate that the level of circulating T alone isnot an unambiguous indicator of gonadalsex at any time during fetal developmentbecause T levels overlap between the sexes atnontrivial frequencies at all developmentaltime points.

Figure 1. The Sexual Dimorphism Signaling PathwayThe classical view of sexually dimorphic development (A) is that higher androgen levels in XY fetuses and

adults masculinize sexually dimorphic traits and lower androgen levels in XX fetuses and high estrogen inadults feminizes development. Our analysis (B) indicates that androgen signaling includes an additionalcomponent: it is canalized by epi-marks that are produced during the embryonic stem cell stage of develop-ment.

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Overlap in T concentrations between thesexes (despite highly significant differencesin average T between XX and XY fetuses)would make the prenatal androgen para-digm incomplete (i.e., missing an importantcomponent of androgen-induced sexual di-morphism) unless discordance between thegonad and sex-specific traits is observed to becorrespondingly common. This is, however,not the case. To illustrate this point, we canfocus on the ontogeny of the genitalia. Thehuman male phallus and female vulva areformed during weeks 9–15 of gestation, al-though the phallus requires T to continue togrow during later fetal development (summa-rized in Wilson et al. 1981). During this time ofgenital differentiation, data on fetal T collectedby Reyes et al. (1974) show high overlap in Tconcentrations between the sexes. The samerelationship is found in the rat, in which Tconcentrations strongly overlap between thesexes during the time (and all points previous)when the phallus and vulva are differentiating(Weisz and Ward 1980). Yet discordance be-tween the gonad and the genitalia (includingambiguous genitalia) is rare in both humans(Sax 2002) and rats (Ostby et al. 1999; Hotch-kiss et al. 2007). Therefore, the available datado not fully support the prenatal androgenparadigm because there is too much overlap incirculating androgens to be consistent with theobserved low discordance between the gonadand the genitalia observed in both humansand the rat model system.

Differential Sensitivity of XY andXX Fetuses to Androgens

One can fully rescue the prenatal andro-gen paradigm if XY fetuses have higher sen-sitivity to circulating androgens compared toXX fetuses. In this case, XX and XY fetuseswould respond differently even when T lev-els overlap to a limited degree between thesexes. Many lines of evidence indicate thatthis is the case.

First, in humans the expression of the 5-�-reductase-2 gene, which converts T into themore potent androgen dihydrotestosterone(DHT), is three times higher in XY fetusesthan XX fetuses within the urogenital swell-ings and tubercles (structures that developinto the phallus or vulva; Wilson et al. 1993).

Boehmer et al. (2001) review evidence thatstrongly supports the conclusion that thissex-specific difference in gene expression isnot androgen-induced via a feed-forwardprocess (i.e., due to changes induced byhigher T in XY fetuses during earlier devel-opment). Higher conversion of T to DHTwould permit XY fetuses to develop maletraits even when T levels overlap (to a limiteddegree) with XX female fetuses, therebypromoting phallus development despite lowcirculating T. Similarly, lower 5-�-reductaseproduction in XX females would prevent orreduce masculinization of the vulva when Tlevels overlapped (to a limited degree) withthose of XY males.

Second, sex hormone binding globulin(SHBG) binds circulating T and makes itunavailable for uptake by cells. In humanfetuses in which T levels overlap betweengenetic males and females, SHBG is mark-edly higher (approximately 50%) in femalefetuses compared to male fetuses (Ham-mond et al. 1983). This elevated SHBG inXX fetuses would reduce sensitivity to circu-lating T when it overlaps with XY fetuses.

Third, in rhesus monkeys (but not hu-mans), levels of circulating progesterone aremarkedly higher (three times) in female fe-tuses compared to male fetuses (Hagemenasand Kittinger 1972). Progesterone acts as ananti-androgen because it has a high bindingaffinity for the androgen receptor (AR),which it inactivates. Its higher concentrationin female fetuses is expected to lower theirsensitivity to androgen levels that overlapwith males.

Fourth, human XX female fetuses homo-zygous for loss of function alleles at theCYP21 locus cannot produce the steroid hor-mone cortisol due to a block in its syntheticpathway (a form of Congenital Adrenal Hy-perplasia, CAH). Buildup of intermediateproducts leads to their conversion to T, andconsequently highly elevated circulating T inaffected XX CAH fetuses. This elevated levelof T begins in the seventh week of gestation(Speiser and White 2003; Trakakis et al.2009) and “the developing fetus is exposedto the excessive adrenal androgens, equiva-lent to the male fetal level, secreted by thehyperplastic adrenal cortex” (New 2004),

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including the period of maximal average Texcess in XY fetuses (Forest 1985). Despite amale-typical level of T throughout fetal devel-opment, the genitalia of XX newborns withCAH are usually only partially masculinized—about halfway between a typical male and fe-male genital (Hall et al. 2004), as is childhoodsexually dimorphic behavior (Hines 2011). Al-though rates of homosexuality and transsexu-ality are elevated in CAH patients, the vastmajority have female-typical sexual behavior(reviewed in Hines 2011). These data providestrong evidence that androgen-induced mascu-linization is blunted in the XX fetuses.

Fifth, human XY male fetuses with acute17�-HSD-3 deficiency are homozygous forloss-of-function alleles at the 17�-HSD-3 lo-cus and cannot produce T in the testes dueto a block in its synthetic pathway (reviewedin Rey and Grinspon 2011). Buildup of theprecursor androstenedione occurs in affectedindividuals, but this steroid is a much weakerandrogen than T (about a hundredfold lowerbinding affinity for the androgen receptor;Fang et al. 2003). These males experiencehighly reduced circulating T throughoutfetal development, although T is somewhatelevated later in fetal development due toallozymes expressed outside the testes thatconvert circulating androstenedione to T.Androgen-induced Wolffian duct structures(epididymis, vas deferens, seminal vesicles,ejaculatory ducts) that are in close proximity tothe testes developed normally despite the lowlevel of T they experience during their ontog-eny. The more distant genitals of affected indi-viduals, however, are highly feminized andmost affected newborns are reared as females.At puberty, these individuals experience asurge in T due to the nontesticular conversionof circulating androstenedione to T (via allo-zymes of 17�-HSD-3) and about one-half ofthese individuals, reared as girls, change theirsex to male (reviewed in Wisniewski et al.2008). This is the same rate of sex change asXY individuals with normal levels of T through-out life that were raised as girls because theywere born without a penis due to cloacal ex-strophy (Reiner and Gearhart 2004). Only afew reports on the sexual orientation of maleswith acute 17�-HSD-3 deficiency are avail-able, but they suggest a predominance of

male heterosexual orientation (Imperato-McGinley et al. 1979; Meyer-Bahlburg 1993).The high level of masculinization (of theWolffian duct structures, gender identity,and sexual orientation) indicate that, despitelow fetal levels of T, the XY genotype leads toincreased sensitivity of the fetuses to the ac-tion of T.

Sixth, as described in the previous section,the low prevalence of gonad/genital discor-dance in both XX and XY fetuses, despitesubstantial overlap in concentrations of cir-culating T when the genitals develop, indi-cates that the sex chromosome karyotypesomehow modulates sensitivity to T prior tothe onset of sex-specific androgen signaling.

The examples discussed above stronglysupport the conclusion that XX and XY fe-tuses have different sensitivities to circulatingandrogens. Because most of the genes re-sponsible for this asymmetric response to an-drogens are autosomal (see next section),they must be transregulated in response tothe XX versus XY sex chromosome karyo-type. Transregulation can occur in manyways, but recent studies demonstrate that thesex chromosome karyotype alone, indepen-dent of sex hormones, epigenetically regu-lates many autosomal genes (reviewed inWijchers and Festenstein 2011). Epigeneticmodification (i.e., methylation, histone tailmodifications, and nucleosome reposition-ing) is emerging as a pivotal factor control-ling gene expression. For example, variationin the level of a single histone modification(trimethylation of lysine residue-4 on his-tone-3; the H3K4me3 epi-mark) of gene pro-moters can account for almost 50% of thevariation in genome-wide gene expression lev-els in the early mouse embryo (Mikkelsen et al.2007). From these studies and others (see be-low), we conclude that XX- and XY-specificepi-marks almost certainly contribute to thedifferential sensitivity to androgens of XX andXY fetuses (Figure 1B). The remainder of thisarticle explores the potential for sex-specificepi-marks to contribute to the canalization ofsexually dimorphic phenotypes and, as a sideeffect of pleiotropy and transgenerational in-heritance, contribute to the evolution of ho-mosexuality and other gonad-trait discordance

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such as hypospadias, cryptorchidism, and idio-pathic hirsutism.

Mechanisms by which Sex-SpecificEpi-Marks can Canalize Androgen

SensitivityCanalization occurs when a developmen-

tal endpoint is reached despite environmen-tal interference that can potentially disrupt it(Waddington 1942). The androgen signal-ing pathway can be disrupted by natural vari-ation in androgen levels about their meanvalue as well as environmentally introducedandrogen agonists and antagonists. Studiesdemonstrating high natural variation in fetalT (e.g., Reyes et al. 1974; Weisz and Ward1980; Perera et al. 1987), as well as the com-mon occurrence of environmental androgenagonists and antagonists (Fang et al. 2003),demonstrate that there is strong selection tocanalize the androgen signaling pathway.

We can represent the androgen signalingpathway as flux (i.e., rate of flow) through aseries of steps, each capable of being aug-mented or depressed, ultimately leading toandrogen influence on a gene’s expression(Figure 2). There is a surprisingly large num-ber of mechanisms by which the androgensignal can be strengthened or weakened. Forexample, varying the SHBG concentration inthe blood, converting T to the more potentDHT, posttranslational modification of the AR(phosphorylation, ubiquitylation, and acetyla-tion) that change its activity, nucleosome place-ments that influence access to androgenresponse elements (AREs) in the DNA, andespecially the concentration of the numerous

and diverse array of AR cofactors. All of thesteps in Figure 2 could also be influenced bysex-specific regulation of miRNA levels that areknown to influence sexually dimorphism ofmRNA concentrations in the brains of mice,and to be influenced by epigenetic control thatis heritable across at least one generation (Mor-gan and Bale 2011). To canalize the impact ofnatural variation in T, the XY karyotype mustlead to one or more epigenetic modificationsthat boost signal transduction through thepathway, and XX karyotypes must do the re-verse.

To illustrate canalization of the androgensignaling pathway, suppose that the averagefetal concentration of circulating T � 10 inmales and T � 5 in females at a time when asexually dimorphic trait develops. Furthersuppose that boosting epi-marks by the XYkaryotype convert the actual T in the bloodto a doubled endpoint signal (TEndPoint � 20)affecting gene expression, and blunting epi-marks in XX fetuses lead to a halving of theendpoint value (TEndPoint � 2.5). If naturalvariation in T causes overlap between thesexes (e.g., T in males varies between 4–16and T in females between 2–8), then epige-netic modifications by the XX versus XY kar-yotype would cause the functional TEndPoint

values to be nonoverlapping (male T � 8–32and female T � 1–4).

XY epi-marks that boost androgen signal-ing, and XX epi-marks that blunt androgensignaling, can also protect against androgenantagonists. For example, rats fed daily on anaturally occurring anti-androgen found inlicorice root (that blocks the action of 17�-

Figure 2. Androgen Signal TransductionSteps in the androgen signaling pathway that can boost or blunt signal transduction. T � testosterone; AR �

androgen receptor; ARE � androgen response element (DNA); CoFacts � androgen receptor cofactors.

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HSD in the T synthesis pathway) developedsignificantly reduced circulating T (Zaman-soltani et al. 2009). Epi-marks that boost an-drogen signaling in XY fetuses (such ashigher conversion of T to DHT or lowerSHBG concentrations) would protect themfrom the action of anti-androgens in thesame way that they protect them from en-dogenous variation in T, as described in theabove paragraph. In the same way, epi-marksthat blunt androgen signaling in XX femalefetuses would protect them from environ-mental agents that elevate the level of circu-lating androgens.

An androgen mimic (e.g., as found in theIndian medicinal herb Tinospora cordifolia;Kapur et al. 2009) can be canalized in adifferent manner. It is well established that Tis modified by the enzyme 5-�-reductase-2 tothe more potent DHT in some tissues and thismodification is necessary to achievesufficient androgen signal to induce a male-specific phenotype, e.g., in the external geni-tals and the internal prostate. Work on theprostate indicates that T and DHT are inter-changeable (qualitatively identical) in promot-ing prostate growth, but DHT is two-and-a-halftimes more potent (Wright et al. 1996). Theconversion of T to the more potent DHT willcanalize androgen signaling in the presenceof an androgen mimic whenever the 5-�-reductase-2 enzyme does not catalyze the con-version of the androgen mimic to DHT. Forexample, again suppose that the normal con-centration of circulating T � 10 in males andT � 5 in females at a time when a sexuallydimorphic trait differentiates. Next supposethat a T-mimic (TMimic) is present in the fetalblood at a concentration emulating T � 5. Inmales, the androgen mimic poses no problemwith respect to feminization, but in females themimic would produce TSignal � T � TMimic �5 � 5 � 10 and a female fetus would beexpected to incorrectly develop the male-specific trait. However, if the target tissueconverted T to DHT, with a threshold ofTEndPoint � 25 (i.e., two-and-a-half times av-erage T in males) to induce the male trait,then the female would be “canalized”against the androgen mimic assuming theandrogen mimic was not converted to the

more potent DHT (because in femalesTEndPoint � 2.5 * 5 � 1 * 5 � 17.5 � 25).

Interestingly, this last mode of canaliza-tion may provide an explanation for theenigmatic within-cell conversion of T to es-tradiol (E) by the enzyme aromatase in theandrogen signaling that occurs in the brainof rodents. Our review of many publishedstudies of levels of circulating T and E indi-cates that, at its peak during the estrus cycle,unbound E is at least tenfold less commonthan peak unbound T in males (e.g., Bao etal. 2003; Travison et al. 2007). E is thereforea steroid hormone that is at least tenfoldmore potent than T (i.e., it functions at aconcentration tenfold lower). By convertingT to E, and assuming aromatase does notconvert the androgen mimic to E, canaliza-tion will occur by the same logic as the con-version of T to the more potent DHT. Amore formal model of canalized androgensignaling is provided in Appendix 1.

Timing of XX/XY-Induced Epi-Marksthat Canalize Sexual DevelopmentEpi-marks that boost androgen signaling

in XY male fetuses and blunt it in XX femalefetuses could, in principle, be produced anytime prior to the onset of androgen signaling(when the fetal testes begins to secrete T).However, it is already established that epi-marks that are dimorphic between XX andXY embryos are produced during the nearlygenome-wide episode of epigenetic repro-gramming that occurs at the embryonic stemcell stage of early development (reviewed inBermejo-Alvarez et al. 2011). Epi-marks pro-duced during this early embryonic stage areknown to strongly influence gene expressionlater in development (Mikkelsen et al. 2007).In addition, epi-marks produced so early indevelopment would be transmitted to celllineages leading to both the soma and thegermline and would therefore have the po-tential to be heritable across generations. Be-low we develop these recent findings in moredetail.

During early development, there is a nearlyglobal erasure of epi-marks (DNA methylationand histone tail modification) that originatedin the sperm and egg stages. As reviewed inHemberger et al. (2009), the erasures occur:

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when protamines are replaced by histones onthe paternal genome prior to fusion of pronu-clei; and during the first few cell divisions ofembryonic development due to low availabilityof enzymes that methylate DNA (erasure onboth the maternally and paternally inheritedDNA). Although the majority of genes losetheir gameticly inherited epi-marks at this time,some—such as imprinted genes and activetransposons—somehow escape epi-mark era-sure (Hemberger et al. 2009). The expansiveepigenetic erasure that occurs over the first fewcell divisions is immediately followed by nearlygenome-wide de novo epi-marking (gene pro-moters remodeled by histone modificationand DNA methylation; reviewed in Hembergeret al. 2009). Genes essential to stem cell func-tioning (including housekeeping genes) aremarked by an activating epi-mark on their pro-moters (trimethylation of the lysine-4 residueof histone H3, H3K4me3). There is a stronggenome-wide correlation (0.67) between thelevel of this histone modification and thelevel of gene expression (Mikkelsen et al.2007). Genes used only in later developmentare marked by a silencing epi-mark on theirpromoter’s histones (trimethylation of thelysine-27 residue of histone H3, hereafterH3K27me3; Mikkelsen et al. 2007), or viamethylation of their promoter’s DNA (Fouseet al. 2008). Interestingly, thousands of re-pressed genes (that are expressed later indevelopment) are bivalently marked withboth a repressing (H3K27me3) and an acti-vating (H3K4me3) epi-mark (Mikkelsen etal. 2007).

The nearly genome-wide epi-marking thatoccurs in early development provides a poten-tially simple and efficient way for epi-marksthat influence androgen signaling to bemanifest across all androgen-sensitive tissues.Consider the abundant bivalent epi-marks—containing both a silencing (H3K27me3) andan activating (H3K4me3) epi-mark—discov-ered by Mikkelsen et al. (2007). The overridingrepressive effect of the silencing epi-mark turnsoff these genes early on in development whilethe activating epi-marks enable immediatestrong gene expression when the silencing partof the epi-mark is removed later in develop-ment. By increasing the size of the activatingepi-mark (e.g., more CpGs of the promoter

histones methylated) in genes that boost an-drogen signaling (e.g., those whose gene prod-ucts acetylate the AR) and decreasing the sizeof these same epi-marks in genes that bluntandrogen signaling (e.g., those coding forSHBG and/or its up-regulators), XY fetuseswould be protected (canalized) from low cir-culating T in the fetus. The reverse patternwould protect (canalize) XX fetuses when Twas atypically high.

There is clear evidence that XX and XY em-bryos differ epigenetically at the earliest stagesof mammalian development, i.e., in the preim-plantation embryo (blastocyst stage). At thistime, XY embryos are physiologically distinctfrom XX embryos, having a higher metab-olic rate, faster growth rate, and increasedresistance to some stress agents (reviewed inGardner et al. 2010). Correspondingly, by thepreimplantation blastula stage, the two sexesare reported to have widespread differencesin gene expression levels at many hundredsof genes, most of which are autosomal (seeBermejo-Alvarez et al. 2010 and referencetherein). Regulation of gene expression incomplex eukaryotes is usually accomplishedvia epigenetic modifications (methylation ofCpGs on the DNA or modification of histonetails; see Gordon et al. 2011). Recent studieshave demonstrated that, at this early embry-onic stage, there are also sex-specific differ-ences in DNA methylation on the promotersof specific loci (reviewed in Bermejo-Alvarezet al. 2011). It has also been established thatthe Y-linked transcription-regulating genesSRY and ZFY are expressed in the preimplan-tation human embryo (Fiddler et al. 1995).

There is also evidence for XX/XY-induceddifferences in gene expression later in devel-opment, but prior to secretion of T by the fetaltestes in XY males. At this time in the mousemodel system there is differential expressionof 51 genes in the brains of XX versus XYembryos, most of which are autosomal (Dew-ing et al. 2003). These data indicate that theXX/XY karyotype somehow influences (intrans) the expression of many genes duringlater embryo development (but before thetestes start secreting T) in a manner that isindependent of androgen signaling. SuchXX/XY karyotype-specific transregulation isknown to occur in adult humans (Wijchers

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and Festenstein 2011). For example, a gene onthe human Y chromosome (TSPY) transregu-lates the level of expression of the X-linkedandrogen receptor in the adult germline(Akimoto et al. 2010).

Collectively, these studies indicate that XXand XY embryos are epigenetically differenti-ated by the stem cell stage of the blastocyst—farin advance of androgen production by the tes-tes. Epi-marks produced at this time are there-fore strong candidates for the causative agentsunderlying the canalization of sexually dimor-phic development later in development in re-sponse to circulating androgens. The recentfinding that environmentally induced epi-marks that reverse sexually dimorphic braindevelopment (i.e., feminize male develop-ment) can carryover and produce the samereversal in the following generation (Frank-lin et al. 2010; Morgan and Bale 2011) dem-onstrates the potential for epi-marks laiddown during very early development to in-fluence androgen signaling later in develop-ment.

Heritable Epi-MarksA consequence of epi-marks being laid

down at the stem cell stage of development,before the division between soma and germ-line, is that such epi-marks have the potentialto be transmitted across generations, but onlywhen the cycle of epi-mark erasure and re-newal, within and between generations, issomehow circumvented. Studies in both miceand humans clearly demonstrate that trans-generational inheritance of epi-marks occursat nontrivial rates (reviewed in Morgan andWhitelaw 2008). When the epi-marks aresexually dimorphic, their transgenerationalinheritance would be expected to influencethe sexual development of opposite-sex off-spring, as described in the next section.

A Model for Heritable SexuallyAntagonistic Epi-Marks

Any physiological mechanism that protectsXX fetuses from atypically high T and/or en-vironmental androgen agonists during devel-opment would be favored by natural selection,assuming no counterbalancing harmful sideeffects. The same logic applies to mechanisms

that protect XY fetus from atypically low T andor environmental androgen antagonists. Asdescribed above, sex-specific epi-marks (i.e.,XX- or XY-specific) laid down during early em-bryonic development represent one mecha-nism to achieve such adaptations. However,such epi-marks would be sexually antagonisticif they sometimes carryover to the next gener-ation and redirect development in a gonad-discordant direction. We will refer to thesesexually antagonistic epi-marks as SA-epi-ma-rks.

SA-epi-marks can be favored by natural se-lection. In the autosomal case, an XX- andXY-dependent epi-mark always increase thefitness of the individual in which it is formed,and when there is carryover across genera-tions, it has only a 50% chance of decreasingfitness by being expressed in the oppositesex. The situation is somewhat more com-plex on the sex chromosomes but, as weshow more formally below, sexually antago-nistic epi-marks can be favored across theentire genome under feasible selective pa-rameters.

autosomal mutationWe next more formally solve for the param-

eter space that supports the evolution of muta-tions that produce SA-epi-marks. Throughout,we assume that the mutation has some expres-sion in the heterozygous state and our selec-tion coefficients apply to heterozygotes. Firstconsider an autosomal mutation that producesan XX- or XY-dependent epi-mark (in cis, at itsown location) that increases fitness of one sex(say, females) by an increment s, but with prob-ability q it carries over to the next generationand decreases the fitness of the opposite sex(sons) by a decrement �. Because of the trans-generational effects, we need to consider thenumber of grandchildren of a mutant. Theexpected number of copies (w) of a mutantallele in the grandchildren’s generation is (seeAppendix 2):

w � 1⁄2 * 1 * �1/2 * 1 � 1/2 * �1 � s))

� 1⁄2 * �1 � s) * [q/2 * �1 � ��

� ��1 � q)/2� * 1

� 1/2 * �1 � s)],

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where the first term on the right side repre-sents the number of grandchildren when themutation originates in a male and the sec-ond term when it originates in a female. Theallele invades if w � 1, which for small s andq is equivalent to

s � q * �/4,

or

cost/benefit � �/s � 4/q.

Even when the rate of transgenerational car-ryover is 100% (q � 1), the mutation invadeswhen the costs are fourfold larger than ben-efits. When transgenerational carryover ismuch smaller, there is essentially no con-straint on the invasion. The above inequalityis compatible with a two-generation general-ization of Hamilton’s rule: the benefit b goesto the carrier (r � 1) and its same sex off-spring (r � 1/2), while the cost c goes to theopposite-sex offspring (r � 1/2).

x-linked mutationWhen the mutation is X-linked, it occurs

in a female with probability 2/3 and in amale with probability 1/3. First assume thatthe mutation is dominant and canalizes de-velopment toward the female phenotypeand is expressed in XX fetuses. The ex-pected number of copies of a mutant allelein the grandchildren’s generation is (see Ap-pendix 2):

w � 1/3 * 1 * ��1 � s� * 1� � 2/3

* �1 � s� * q/2 * �1 � ��

� �1 � q�/2 * 1 � 1/2 * �1 � s�,

where the first term on the right side repre-sents grandchildren when the mutation origi-nates in a male and the second term when itoriginates in a female. The allele invades ifw � 1, which for small s and q is equivalent to:

s � q * �/4

or

cost/benefit � �/s � 4/q.

This is the same constraint that was found forautosomal linkage.

Next assume that the X-linked mutation isexpressed in XY embryos and canalizes de-velopment toward the male phenotype. Theexpected number of copies of a mutant al-lele in the grandchildren’s generation is (seeAppendix 2):

w � 1/3 * �1 � s)(q * �1 � ��

� �1 � q� * 1� � 2/3 * 1 * �1/2

* �1 � s) � 1/2 * 1�,

where the first term on the right side repre-sents grandchildren when the mutation orig-inates in a male and the second term whenit originates in a female. The allele invadesif w � 1, which for small s and q is equival-ent to:

s � q * �/2

or

cost/benefit � �/s � 2/q.

In this case, the cost/benefit ratio must be halfas large as the autosomal case for the mutationto invade. Nonetheless, the mutation can in-vade under a broad and feasible range of pa-rameter space. For example, if transmissionacross generations (q) is 0.25, the mutation willinvade when costs are eight-times larger thanbenefits. Our X-linked analysis has assumeddominance of the epi-mark producing muta-tion. For partial dominance, the selection co-efficients s (female canalization) or � (malecanalization) must be multiplied by a domi-nance scaler h (0 � h 1).

x-linked trans-effectOur model has assumed that an X- or

autosome-linked mutation producing an SA-epi-mark makes the epigenetic modificationin cis at its own location (i.e., it epi-marksitself). When the mutation produces an SA-epi-mark in trans anywhere else in the ge-nome, the same equations as describedabove can be applied by replacing the param-eter q with q/2, since the mutation cosegre-gates with its SA-epi-mark with probability 1/2.When the SA-epi-mark is produced at anotherlocus on the same chromosome, the parame-ter q must be replaced with q * (1 � r), wherer is the recombinational distance between the

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mutation and the SA-epi-mark it produces, and(1 � r) is the probability that the mutation andits epi-mark cosegregate.

y-linked mutationLastly, when the mutation is Y-linked and

canalizes development toward the male phe-notype, the allele invades when s � 0 irre-spective of the value of � and irrespective ofwhere the epi-mark is produced.

generalizationsThese calculations demonstrate that mu-

tations causing sexually antagonistic epi-marks can invade even when the cost to theharmed sex far exceeds the benefit to thefavored sex. This conclusion holds irrespec-tive of linkage to the sex chromosomes orautosomes. Such invasions are expected tolead to the eventual fixation of mutationsproducing SA-epi-marks, unless there weresome additional factors such as frequency-dependent fitness.

Although our model predicts that muta-tions causing SA-epi-marks will go to fixation,the androgen-induced phenotypes they af-fect may nonetheless be highly variable. Thisis expected because epi-marks can be highlyvariable despite genetic monomorphism. Asdescribed in the next section, monozygotictwins at birth show strong differences inmethylation levels of individual promotersand large differences in gene expression lev-els at as many as hundreds of gene loci.These data indicate that epi-marks are intrin-sically variable and that the same fixed mu-tation can produce variable epi-marks. Moreextreme epi-marks (e.g., with denser or lon-ger tracts of histone modification and/orDNA methylation) would span more chro-matin locations and hence have a higherprobability of serendipitously achieving atleast partial transgenerational inheritance.

Homosexuality and SA-Epi-MarksAlthough pedigree studies indicate a fa-

milial association of homosexuality in bothmales (e.g., Hamer et al. 1993) and females(e.g., Pattatucci and Hamer 1995), morethan a decade of molecular genetic studieshave produced no consistent evidence for a

major gene, or other genetic marker, con-tributing to male homosexuality (reviewedin Ngun et al. 2011). Moreover, the mostrecent genome-wide association study usingexceptionally high marker density found nosignificant association between homosexual-ity in males and any SNPs (Ramagopalan etal. 2010). These negative/inconsistent re-sults may reflect insufficient statistical power,but they also support another agent causingthe familial association of homosexuality: ep-igenetic inheritance.

There is a consensus among studies com-paring homosexuality in monozygotic versusdizygotic twins that one or more coinheritedelements (assumed to be genes, but whichcould just as well be heritable epi-marks) con-tribute substantially to this trait—accountingfor an estimated 20–50% of the phenotypicvariation in sexual orientation in both sexes(Kirk et al. 2000; Alanko et al. 2010; Lang-strom et al. 2010; Burri et al. 2011). How-ever, estimates of proband concordanceamong monozygotic twins (i.e., the probabil-ity that a twin is homosexual given that theother twin is homosexual) are surprisinglylow in both sexes (about 20%) for a traitpredominantly influenced by genetic factors(Bailey et al. 2000; Langstrom et al. 2010).Correspondingly, studies of twins consistentlyreport a high “nonshared environment” con-tribution to homosexuality, typically account-ing for at least 50% of the phenotypic variationin both sexes (Kirk et al. 2000; Alanko et al.2010; Langstrom et al. 2010; Burri et al. 2011).The substantial estimated heritability of homo-sexuality, low proband concordance betweenmonozygotic twins, and negative results fromnumerous molecular genetic association stud-ies are collectively consistent with an epigeneticcausation for homosexuality that contains twoindependent components: monozygotic twinsshare inherited (transgenerational) gonad-discordant SA-epi-marks influencing androgensignaling (contributing to the observed sub-stantial heritability estimates and negative re-sults from genetic association studies), but donot share one or more de novo gonad-concordant epi-marks (including erasure of acoinherited SA-epi-mark) that are laid downduring fetal development (independently ineach twin) that also influence androgen signal-

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ing (contributing to the observed low concor-dance between monozygotic twins).

To understand how the homosexual pat-tern of substantial estimated heritability andlow concordance between identical twins canbe feasibly caused by epigenetic inheritance,we summarize results from studies of twins.In the remainder of this section, we first focuson arbitrary phenotypic traits and how epige-netics can contribute to both phenotypic simi-larity and dissimilarity between monozygotictwins. Next we focus on twin studies of traitsother than homosexuality that are stronglyinfluenced by fetal androgen signaling andwell characterized at birth by numerous stud-ies. Finally, we extend these studies to homo-sexuality.

arbitrary traitsEmpirical studies indicate that epigenetics

can contribute substantially to the similarityof identical twins. For example, Gartner andBaunack (1981) used an isogenic mouse lineto created monozygotic and dizygotic “iden-tical” twins and compared them for a varietydevelopmental traits. They consistently foundhigher phenotypic similarity between monozy-gotic compared to dizygotic identical twins, de-spite the fact that all mice were isogenic anddeveloped (in utero and postnatally) in surro-gate mothers. This finding, and others sum-marized in Wong et al. (2005), supports theconclusion that there is a substantial contribu-tion of shared epi-marks to the phenotypic sim-ilarity of twins.

Empirical studies also indicate that epige-netics can contribute substantially to the dis-similarity of identical twins. Bouchard et al.(1990) compared a large sample of humanidentical twins who were reared together orapart since birth. They found that pheno-typic dissimilarity for a wide diversity of traits(with a substantial “environmental” compo-nent of variation) was commonly no higherwhen twins were reared apart. This findingindicates that many phenotypic differencesbetween monozygotic twins developed prena-tally, i.e., at a time of extensive de novo epige-netic programming. This finding also indicatesthat nonshared epi-marks laid down indepen-dently in each individual twin (or other typesof relatives) during fetal development may

contribute importantly to the “environmentalvariance” that causes heritability to be less thanone for most traits. This conclusion is sup-ported by a study that compared methylationlevels at the promoters of four genes in new-born monozygotic human twins (Ollikainen etal. 2010). Median differences in methylationlevels were only about 3–4% (about half thevalue for dizygotic twins), but values as high as54% were seen when looking at individualCpG units. At the level of genome-wide geneexpression, Gordon et al. (2011) found thatsome newborn monozygotic twins had over600 genes at which expression differed by atleast twofold. They also found that newbornidentical twins that separated earlier in devel-opment (1–3 days compared to 4–9 days post-fertilization) had larger differences in theirgene expression profiles, indicating that “thisshort period, very early in development, repre-sents an important window for epigenetic vari-ability” (Gordon et al. 2011).

twin studies of androgen-influencedtraits other than homosexualityEvidence that epigenetics contributes to

high levels of phenotypic variation for traitsinfluenced by fetal androgen exposure comesfrom studies on two phenotypes in humans:hypospadias (subterminal opening of the ure-thra on the phallus) and cryptorchidism (oneor both testes fail to descend into the scrotumby birth). Like homosexuality, in which thegenitals are concordant with the gonad butsexual preference (and brain anatomy; e.g.,Savic and Lindstrom 2008) is not, both traitsrepresent a gonad-trait discordance in whichone aspect of androgen signaling matchesthe gonad while the other does not. Inhypospadias, the phallus is generally male-typical in size, shape, and internal com-position, but the length of the urethra isfeminized (shortened). In cryptorchidism,the phallus is usually normal in all respects,but the position of the gonad is feminized(nondescended).

The prevalence of cryptorchidism is sub-stantial and similar to that of human homo-sexuality (2–9%; Bay et al. 2011), while thatof hypospadias is substantial but somewhatlower (prevalence of about .3–4%; Ahmed etal. 2004; Boisen et al. 2005). Animal models

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indicate that exposure to androgen antago-nists during a short period when the genitalsdifferentiate (but not later in development)leads to highly elevated levels of both hypo-spadias and cryptorchidism, confirming thatboth traits are strongly influenced by fetal an-drogen signaling. In humans, however, the si-multaneous expression of naturally occurringhypospadias and cryptorchidism is rare (i.e.,they usually occur in isolation; Weidner et al.1999). This pattern indicates that the two traitsare caused, in large part, by different disrup-tions to androgen signaling. Like homosexual-ity, both traits display a familial association:when one brother in a family is affected, theprevalence is elevated in other brothers byabout tenfold for hypospadias and threefoldfor cryptorchidism (Weidner et al. 1999). Sim-ilar to homosexuality, both traits are usuallynot shared among monozygotic twins (approx-imately 25% concordance for each trait; Fre-dell et al. 2002; Jensen et al. 2010). Also likehomosexuality being elevated in individualswith loss of function at the CYP21 gene (butthis gene not being a major cause of femalehomosexuality), extensive genetic studies havefound that while loss of function at some can-didate genes can lead to both hypospadias andcryptorchidism, the majority of cases are notassociated with any known mutations (re-viewed in Bay et al. 2011; Kalfa et al. 2011).Further evidence for a substantial nongeneticcontribution in the case of cryptorchidism is:higher concordance (twofold) between dizy-gotic twins than that between singletonbrothers (Jensen et al. 2010); and the highincidence of cryptorchidism (up to 70%) ob-served in some isolated wildlife populationsdespite no genetic evidence for inbreedingor a founder effect—presumably due to anenvironmental hormone-signaling disruptor(Latch et al. 2008).

The familial association observed in bothandrogen-influenced traits (cryptorchidismand hypospadias) indicates a substantial con-tribution of some coinherited factor (geneor epi-mark), while the low concordance forboth traits observed in monozygotic twinsindicates a substantial contribution of a“nonshared environment.” Since the traitsare measured in newborns, the nonsharedenvironment must occur during gestation.

But since monozygotic twins would be ex-pected to share nearly all environmentaleffects during gestation (like exposure to an-drogen antagonists), something other thantraditional environmental variation is almostcertainly responsible for their observed lowconcordance. Epi-marks influencing andro-gen signaling that are laid down indepen-dently between monozygotic twins are themost feasible candidate to account for thestrong “nonshared environment” componentof both androgen-influenced traits. If theseepi-marks sometimes escaped transgenera-tional erasure, they could also account for thefamilial association of both traits.

homosexualityAs described above, there is compelling

evidence that epi-marks contribute to boththe similarity and dissimilarity of familymembers, and can therefore feasibly contrib-ute to the observed familial inheritance ofhomosexuality and its low concordance be-tween monozygotic twins. We also showedthat two other androgen-sensitive pheno-types, cryptorchidism and hypospadias, showthe same pattern of high prevalence, strongfamilial associations, low monozygotic twinconcordance, and discordance between thegonad and the trait (i.e., testes paired withundescended gonad(s) or testes paired withshort urethral length). Just as epigenetics is aprobable etiological agent contributing tocryptorchidism and hypospadias, so too is it aprobable agent contributing to homosexuality.In this case, epi-marks that sometimes carry-over across generations would contribute tothe causation of homosexuality and its obser-ved heritability while de novo epi-marks pro-duced independently in each monozygotictwin would account for the low observed con-cordance for homosexuality between monozy-gotic twins.

An inherited gonad-discordant epi-markcausing homosexuality must not be maskedby any gonad-concordant epi-marks pro-duced during the recipient’s ontogeny. Thiswould occur most simply when an inheritedepi-mark is stronger than average and is com-bined with a relatively weak de novo epi-mark(s) produced in the recipient. Thesetwo processes (i.e., transgenerational inheri-

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tance of an epi-mark and its penetrance onceinherited) are collectively subsumed in ourmodel parameter q � probability that anSA-epi-mark carries over to the next genera-tion and decreases the fitness of the oppositesex (see above modeling section).

An epi-mark producing homosexuality mustalso have a highly restricted effect, i.e., causediscordance between the gonad and sexualpreference, but no discordance for other traitssuch as the genitalia and sexual identity. Asdescribed above, most cases of cryptorchid-ism and hypospadias are not associated withgonad-trait discordance for other androgen-influenced traits. This observation demon-strates that gonad-trait discordances can occurindependently for different traits in the sameindividual. The most feasible explanation forthis independence is the exceptionally widediversity of AR cofactors that are known to oc-cur and their high tissue specificity (Heemersand Tindall 2007)—each of which may be epi-genetically regulated independently.

Although we cannot provide definitiveevidence that homosexuality has a strongepigenetic underpinning, we do think thatavailable evidence is fully consistent with thisconclusion. For example, we now have clearevidence that epigenetic changes to gene pro-moters that influence their expression (e.g.,levels of CpG methylation) can be transmittedacross generations (Franklin et al. 2010) andthat such heritable epigenetic changes canstrongly influence, in the next generation,both sex-specific behavior and gene expressionin the brain (Morgan and Bale 2011). As aconsequence, we next apply our model of sex-ually antagonistic epi-marks to the human ho-mosexual phenotype (as described in Table 1and Figure 3).

DiscussionSexually antagonistic selection is now well

appreciated as a powerful factor in biologicalevolution (Parker 1979; Haig 1993; Rice andHolland 1997; Partridge and Hurst 1998;Chapman et al. 2003; Arnqvist and Rowe 2005;Bonduriansky and Chenoweth 2009). It hasbeen shown to significantly affect or drive anumber of biological phenomena and pro-cesses, including survival and fertility (Rice1996), mate choice (Gavrilets et al. 2001), ge-

netic differentiation (Hayashi et al. 2007),reproductive isolation (Gavrilets 2000) andspeciation (Parker and Partridge 1998; Gavri-lets and Waxman 2002; Gavrilets and Hayashi2005), sex chromosome evolution (Rice et al.2008), sib competition (Rice et al. 2009), ma-ternal selection (Miller et al. 2006), and grand-parental care (Rice et al. 2010). This paperargues that sexually antagonistic selection canalso be involved in epigenetic effects and ex-plain the enigmatic high prevalence of severalfitness-reducing human characters. As de-scribed below, our model and its predictionsare consistent will the major empirical patternsassociated with male and female homosexual-ity, and other common gonad-trait discor-dances.

Homosexuality is frequently considered tobe an unusual phenotype because it repre-sents an evolutionary enigma—a trait that isexpected to reduce Darwinian fitness, yet itpersists at substantial frequency across manydifferent (possibly all) human populations.However, from the perspective of other traitsinfluenced by fetal androgen signaling, andin which there is gonad-trait discordance, thehigh prevalence of homosexuality is not un-usual. For example, the prevalence of hypos-padias (gonad-trait discordance for urethrallength) varies from 0.4% to 1% in newborns,and when including milder cases (ascertainedin three years postpartum), its prevalence canbe as high as 4% (Boisen et al. 2005). Thisphenotype is expected to interfere with sp-erm transfer during copulation, but despitethis fitness cost, it persists at substantial fre-quency. Cryptorchidism (gonad-trait discor-dance for the position—abdominal versusdescended—of the gonads) is associated withreduced fertility and increased rates of testicu-lar cancer. The prevalence of this androgen-influenced trait is 2-9% (Bay et al. 2011).Examples of other androgen-influenced phe-notypes with a high prevalence of gonad-traitdiscordance, but less obvious fitness effects, aremale childhood cross-gender behavior (3.2%;van Beijsterveldt et al. 2006), female childhoodcross-gender behavior (5.2%; van Beijsterveldtet al. 2006), and female idiopathic hirsutism(i.e., male-like pattern of body hair in the ab-sence of both atypical menstrual cycles andelevated circulating androgens, 6%; Carmina

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1998). From these examples it is clear that thesubstantial prevalence of homosexuality (agonad-trait discordance) is not unusual for aphenotype strongly influenced by fetal andro-gen exposure.

Why should phenotypes associated with fe-tal androgen signaling commonly have highfrequencies of gonad-trait discordance? Wedo not know. The simplest hypothesis is thatenvironmental stress and androgen agonistsand antagonists are sufficiently common thatthey generate constant selection for new,more effective epi-marks that protect (cana-lize) each sex from their effects. Some ofthese newly evolved epi-marks escape the

normal generational cycle of erasure/re-programming and thereby carryover acrossgenerations (by happenstance and with mod-erate to low probability) and lead to gonad-traitdiscordance. Since it is now well establishedthat environmentally induced epi-marks, likethose from prenatal/perinatal stress, are com-mon and can be heritable with sex-specific ef-fects on the brain and behavior (Franklin et al.2010; Morgan and Bale 2011), it seems inevi-table that some epi-marks produced by newmutations (coding for epi-marks that cana-lize sex-specific development) will also some-times carryover across generations and formSA-epi-marks. Our modeling analysis clearly

TABLE 1Sexually antagonistic epi-mark hypothesis of homosexuality

We describe our hypothesis for an epigenetic cause of homosexuality as a series of statements (see Figure 3 for a graphicalsummary):

a) Empirical studies demonstrate that XX fetuses are canalized to blunt androgen signaling (lower sensitivity to T) and XYfetuses are canalized to boost androgen signaling (higher sensitivity to T).

b) Empirical studies demonstrate the production of XX- and XY-induced epi-marks in embryonic stem cells and extensivesex-specific differences in gene expression at this time. Epi-marks laid down during the embryonic stem cell stage arealso established to influence gene expression later in development. This stem cell period is the most plausible candidatetime point for the production of epi-marks influencing sensitivity to androgens later in development (canalization offetal androgen signaling).

c) Epi-marks produced in embryonic stem cells are mitotically transmitted to cell lineages leading to both the soma andthe germline, and hence can contribute to pseudo-heritability when they escape erasure across generations (nonerasurein the primordial germ cells and in the zygote and first few cell divisions of the next generation). Animal models as wellas human data unambiguously demonstrate that such a multistep escape from erasure does occur at nontrivialfrequency.

d) Epi-marks blunting (in XX fetuses) or boosting (in XY fetuses) androgen signaling will be sexually antagonistic(SA-epi-marks) when they have a nonzero probability of carryover across generations and are expressed in oppose sexdescendants. Such carryover will contribute to discordance between the gonad and one or more sexually dimorphictraits.

e) Our modeling work shows that SA-epi-marks are favored by natural selection over a broad span of parameter spacebecause there is a net benefit to the carrier (due to canalization of sexually dimorphic development) that is not offsetsufficiently by transmission (and fitness reduction) to opposite sex descendants.

f) Genetic mutations causing SA-epi-marks are expected to fix in populations and are therefore not expected to bepolymorphic except transiently during their initial spread within a population. Therefore, no association betweengenotype and homosexuality is predicted.

g) Because the androgen signaling pathways differ among organs and tissues (e.g., use of different AR cofactors), the sameinherited SA-epi-mark can affect only a subset of sexually dimorphic traits, e.g., no effect on the genitalia, but a largeeffect on a sexually dimorphic region of the brain.

h) Shared, gonad-discordant SA-epi-marks that carryover across generations would contribute to the observed realizedheritability of homosexuality, e.g., monozygotic twins share the same SA-epi-marks coinherited from a parent.

i) Unshared, gonad-concordant SA-epi-marks, produced during fetal development, would contribute to the low probandconcordance of homosexuality observed between monozygotic twins, i.e., they need not share SA-epi-marks generatedduring development that occurs after the twins have separated.

j) Homosexuality occurs when an individual inherits one or more gonad-discordant SA-epi-marks that are not masked norerased by the production of de novo gonad-concordant SA-epi-marks that accrue during ontogeny. The SA-epi-mark(s)influence androgen signaling in the part of the brain controlling sexual orientation, but not the genitalia nor the brainregion(s) controlling gender identity.

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demonstrates that mutations that cause epi-marks that blunt androgen signaling in XXfetuses, or boost it in XY fetuses, can have aselective advantage even when they carryoveracross generations at nontrivial frequencyand reduce fitness by feminizing or mascu-linizing opposite-sex descendants. Modifiersthat restrict androgen blunting/boostingepi-marks to the appropriate sex would beexpected to eventually evolve and producenearly invariant canalization, but new muta-tions creating new epi-marks may continueto evolve (requiring new modifiers) if andro-gen agonists and antagonists are sufficientlyvariable across time and/or space.

Another possibility leading to persistentlyhigh levels of gonad-trait discordance is anarms race between male- and female-benefit

SA-epi-marks that blunt/boost androgen sig-naling during fetal development. The accumu-lation of such SA-epi-marks favoring one sexgenerates selection in the other sex to evolvenew epi-marks that protect them from oppo-site-sex SA-epi-marks that sometimes carryoveracross generations. Such an arms race could, inprinciple, lead to protracted periods of highlevels of gonad-trait discordance.

Levels of gonad-trait discordance amongandrogen sensitive traits are highly vari-able. The genitalia (phallus or vulva) andcore sexual identity (masculine or femi-nine) are highly canalized, with gonad-traitdiscordance levels of 1/10,000 or less (Sax2002; Swaab 2007). However, prevalence ofgonad-trait discordance for components of thegenitalia and sexual identity can be orders of

Figure 3. SA-Epi-Marks and HomosexualityOur SA-epi-mark model predicts that homosexuality is produced by transgenerational epigenetic inheri-

tance. As in nature, epi-marks are assumed to sometimes carryover across generations (depicted by the “*”superscript) and epi-mark strengths are assumed to be variable, irrespective of genetic polymorphism (depictedby the intensity of their letter symbols). Masculinizing (superscript “M”) epimarks are produced in response tothe XY genotype in the early embryo stage (stem cells) and canalize male development by increasing sensitivityto fetal T. Feminizing (superscript “F”) epi-marks similarly canalize female development by reducing sensitivityto fetal T. Homosexuality occurs when one or more stronger than average epi-marks—bold, that canalizesexual preference (Sp), but not the genitals (Ge) nor sexual identity (Si)—carryover across generations intoan opposite-sex descendent and cause gonad-trait discordance when combined with weaker than average(light) de novo sexually concordant epi-mark(s).

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magnitude higher, as we previously describedfor homosexuality, cross-gender behavior, hy-pospadias, cryptorchidism, and idiopathic hir-sutism. The developmental switch to form aphallus or a vulva (or the switch to form amasculine or feminine gender identity) in re-sponse to high or low fetal T concentrationsdates back to at least the origin of mammals(over 200 million years ago). This long timeperiod would have provided substantial oppor-tunity to evolve modifiers that reliably canalizethese sex-specific developmental dichotomies.

Although major dichotomies of the genitalia(phallus/vulva) and sexual identity (male/fe-male) have been invariant over long periods ofevolutionary time, the phenotypes of the gen-italia and sexual behavior evolve rapidly in allspecies, including mammals (reviewed inEberhard 1996). Such continual and rapidevolutionary modification of the structuralattributes of genitalia and sexual behaviorwould be expected to provide far less timefor the evolution of reliable canalization, andhence the observed higher gonad-trait dis-cordance for components of the genitaliaand sexual behavior. Although we know ofno reported data, we suspect that few if anyof the sexual signals used by chimps (ourclosest relative, from which we have evolvedindependently for only six to eight millionyears) are sexually attractive to humans, andhence that most of the neurological net-works underlying human sexual attractionare relatively newly evolved. This recent evo-lution may explain the observed lower canal-ization of human sexual orientation, andhence the higher prevalence of homosexu-ality (compared to the very low prevalence ofgender dysphoria). The rapid and surpris-ingly extensive divergence of the male geni-talia between humans and chimps (see Coldand McGrath 1999) may similarly be causallyassociated with the high prevalence of crypt-orchidism and hypospadias. Similarly, therapid divergence in body hair between hu-mans and chimps may explain the high prev-alence of idiopathic hirsutism in females.

Unlike past genetic models of homosexu-ality based on kin selection, overdominance,or sexually antagonistic alleles (Camperio-Ciani et al. 2004, 2008; Gavrilets and Rice2006; Iemmola and Camperio-Ciani 2009),

our model of homosexuality via SA-epi-marks predicts no genetic polymorphisms willbe associated with homosexuality. Polymor-phic phenotypes but monomorphic genotypesare predicted to occur because of the nonzeroprobability of cross-generation transmission ofheritable SA-epi-marks coded by mutationsthat are fixed except during brief and transientperiods of the recruitment of new mutations. Ifthis epi-inheritance were the sole cause of ho-mosexuality, then we would expect high con-cordance between monozygotic twins—whichis not observed. Low concordance of monozy-gotic twins indicates that homosexuality (andother common gonad-trait discordances) re-quire the combination of an inherited stron-ger-than-average sexually discordant epi-markand a weaker-than-average sexually concordantepi-mark produced during early fetal develop-ment (that does not mask or erase the inher-ited sexually discordant epi-mark; Figure 3).

The point estimates of an approximately8% prevalence of homosexuality in bothsexes (Bailey et al. 2000) and an approxi-mately 20% proband concordance for ho-mosexuality for both sexes among identicaltwins (Bailey et al. 2000; Langstrom et al.2010) can be combined to estimate the trans-mission rate of an SA-epi-mark that causeshomosexuality. We start with the general re-lationship,

PrevMHS � Pstrong(F) * Punerased * (1 � Pstrong(M)),

where PrevMHS is the prevalence of male homo-sexuality, Pstrong(F) is the probability of a stron-ger-than-average feminizing epi-mark in themother, Punerased is the probability that this epi-mark is not erased when it is passed to the son,and (1 � Pstrong(M)) is the probability that thereis no stronger-than-average masculinizing epi-mark produced in the son that masks the in-herited strong transgenerational feminizingepi-mark. In our modeling section, the scaler qequals the joint probability of nonerasure of anSA-epi-mark and its being paired with a rela-tively weak de novo epi-mark in the recipient—i.e., q � Punerased * (1 � Pstrong(M)). If we assumethat strong masculinizing and feminizingepi-marks are equally common (i.e.,Pstrong(M) � Pstrong(F)), then the probability ofproband concordance (Cproband) betweenmonozygotic twins is then Cproband � 1 �

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Pstrong(M). Note that PrevMHS � Cproband(1 � Cpro-

band)Punerased, from which Punerased � PrevMHS/[Cproband(1 � Cproband)].

Proband concordance of monozygotic twinsestimates the probability that there is no strongmasculinizing epi-mark in the son that over-rides the inherited feminizing epi-mark, soCproband is estimated to be 0.2. The prevalenceof homosexuality estimates its rate of occur-rence in the general population (PrevMHS �0.08). Substitution of these values and solvingfor a homosexual-inducing SA-epi-mark’stransmission rate gives a value of Punerased �.08/[.2(1 � .2)] � 0.5. Therefore, the lowconcordance for homosexuality among mono-zygotic twins (20%) when coupled with lowprevalence in the general population (8%) in-dicates that a causative SA-epi-mark has a hightransgenerational transmission rate (50%).This value may or may not be unusually high.Transgenerational epi-marks canalizing se-xually dimorphic traits lead to conspicuousgonad-trait discordances in opposite sex off-spring. In contrast, transgenerational epi-marks influencing most other traits wouldlikely go unnoticed because they lead to in-creased parent-offspring similarity and wouldtherefore be confounded with genetic herita-bility.

Although the studies are somewhat contra-dictory, there is evidence that relatives of malehomosexuals have higher fecundity on one orboth sides of their family pedigree (reviewed inSchwartz et al. 2010). Homosexuality via SA-epi-marks would predict higher fecundity ofopposite-sex relatives if these epi-marks in-creased the level of sexual attraction to theopposite sex in the father or mother of femaleand male homosexuals, respectively. The find-ing in an Italian population of higher thanaverage fecundity in the maternal female rela-tives of homosexual males (replicated in twoindependent studies: Camperio-Ciani et al.2004; Iemmola and Camperio-Ciani 2009) isconsistent with this prediction. Another studyfound the same pattern for aunts in a sampleof white men in England—but the pattern wasreversed in nonwhites and extended to morecategories of relatives and in both sexes (Rah-man et al. 2008). A second study in Englandfound more relatives for homosexual com-pared to heterosexual men on the paternal

side of the family lineage and the same butnearly significant pattern (P � 0.058) on thematernal side of the family (King et al. 2005).Another study found that homosexual menhave more siblings (of both sexes) comparedto a sample of heterosexual men (Blanchardand Lippa 2007). In aggregate, these studiesare consistent with an SA-epi-mark causation ofhomosexuality because they indicate that ho-mosexual men have more fecund mothersand/or female relatives on the maternal, pater-nal, or both sides of the family. The heteroge-neity in these studies could arise if differentethnic groups are fixed for mutations produc-ing different SA-epi-marks that are inheritedprimarily through only the matriline, the patri-line, or through both lineages.

Ours is not the first nongenetic hypothesisfor the evolution of human homosexuality.One highly intuitive, nongenetic hypothesis forhomosexuality is that it is due to reduced an-drogen signaling that occurs after the first tri-mester of gestation (Swaab 2007), i.e., after thegenitalia have formed. Many environmentalagents can potentially reduce androgen signal-ing and these could episodically affect someperiods of fetal development and not others.Studies with rhesus monkeys clearly demon-strate that sex-specific behavior and the gen-itals can be masculinized/feminized duringdifferent gestational time periods (reviewedin Thornton et al. 2009). Therefore, discor-dance between the gonad/genitals and sex-ual orientation could be feasibly producedby fluctuating exposure to environmentalandrogen agonists and antagonists. Despiteits intuitive appeal, we do not think that this“timing” hypothesis is consistent with avail-able data. The micropenis phenotype is pro-duced in humans when there is sufficient Tduring the first trimester of development toinduce normal phallus formation, but toolittle T is produced during the second andthird trimesters to stimulate its continuedgrowth (for example, due to gonadal dysgen-esis after the first trimester). These individu-als are usually reared as males and they showno elevation in gender dysphoria and only asmall increase in same-sex partner prefer-ence (reviewed in Wisniewski et al. 2008).This pattern indicates that low androgen sig-naling during the second two trimesters of

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fetal development is not associated with sub-stantially elevated levels of same-sex partnerpreference in XY males.

Another nongenetic model for homosex-uality is based on birth-order effect, in whichmales with more older brothers are morelikely to be homosexual (reviewed in Bogaertand Skorska 2011). Because available evi-dence indicates that birth order can at mostaccount for only one in seven homosexualmen (Cantor et al. 2002), and because thishypothesis does not apply to female homo-sexuality, we think that most of the phenom-enon of human homosexuality cannot beattributed to this nongenetic mechanism.

Although we think that the low concor-dance for monozygotic twins argues againstmost extant genetic hypotheses as a majorcause of human homosexuality, we want toclearly state that our epigenetic hypothesis isnot mutually exclusive with some influenceof genetic polymorphisms contributing tohomosexuality (or an important role for abirth-order influence). Future genome-wideassociation studies should eventually find suchgenetic polymorphisms if they exist and con-tribute substantially to human homosexuality.

PredictionsA major strength of our epigenetic model

of homosexuality is that it makes two unam-biguous predictions that are testable withcurrent technology. Therefore, if our modelis wrong, it can be rapidly falsified and dis-carded.

First, future, larger-scale genetic associa-tion studies will fail to identify geneticmarkers associated with most homosexual-

ity. Our model does not preclude somemutations being associated with homosex-uality because it is already established thatsome mutations affecting androgen signal-ing (e.g., those contributing to CAH orCAI) can strongly influence the level ofgonad-trait discordance for sexual orienta-tion. Our model does predict, however,that any genetic associations discovered inthe future will be weak and account forlittle of the phenotype variation in sexualorientation.

Second, future genome-wide epigeneticprofiles will find differences between homo-sexuals and nonhomosexuals, but only atgenes associated with androgen signaling inthe later parts of the pathway (e.g., AR co-factors or miRNAs that regulate them) or berestricted to brain regions controlling sexualorientation, i.e., not affecting sexually dimor-phic traits like genitalia or sexual identity.

It may be feasible to readily test the secondprediction with current technology in thecase of female homosexuality. Our hypothe-sis predicts that differences will be foundwhen comparing the genome-wide epige-netic profiles of sperm from fathers with andwithout homosexual daughters.

acknowledgments

This work was conducted as a part of the Intrag-enomic Conflict Working Group at the National In-stitute for Mathematical and Biological Synthesis,sponsored by the National Science Foundation, theU.S. Department of Homeland Security, and the U.S.Department of Agriculture through NSF Award #EF-0832858, with additional support from the Universityof Tennessee, Knoxville. Support was also provided bythe Swedish Foundation for Strategic Research.

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APPENDIX 1A Formal Model for Epigenetic Canalization of Androgen Signaling

The androgen signaling pathway can be represented as a series of n steps at each of which the signalcan be augmented (in males) or depressed (in females) by the effects of epi-marks. For example, letT0 be the level of androgen in serum. Then the signal at the end of the pathway can be written as

TEndPoint � T0 �1 � �1�1� �1 � �2�2� · · · �1 � �n�n)

� T0�(1 � �i�i),

where �i is the effect of the epi-mark controlling the ith step and �i scales the relative importanceof the ith step in the pathway. When the values of �i are positive for male fetuses and negative forfemale fetuses, androgen signaling will be boosted in males and blunted in females.

Epi-marks can cause substantially elevated androgen signal in males compared to females at the endof the pathway (TEndPoint) even when the levels of androgen in serum (T0) overlap between the sexes toa limited degree (as appears to occur at nontrivial rate in humans and the rat model system).

As described above, additional canalization occurs when T is converted to a more potent metabolite(like DHT or E) but the androgen mimic is not recognized by the enzyme responsible for thisconversion. To incorporate canalization against androgen mimics we can add a second term (� TM(e))to our previous equation,

TEndPoint � T0 �1 � �1�1� �1 � �2�2� · · · �1 � �n�n� � TM(e)

� T0�(1 � �i�i) � TM(e),

where TM(e) represents the effective concentration of the androgen mimic (its concentration multiplied byits relative ability to functionally substitute for T). If the androgen mimic is not converted to the more potentmetabolite of T, and this conversion is required to achieve sufficient androgen signaling (TEndPoint) in males,then XX fetuses will be protected from inappropriately expressing the male form of a trait, i.e., (T �TM(e))Female � TMale but (TEndPoint)Female �� (TEndPoint)Male.

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APPENDIX 2Invasion of Genetic Mutations that Code for Epi-Marks that Canalize Sexual Development

Autosomal mutant. Consider a genetic mutation that, exclusively in one sex (say females), inducesan epi-mark that increase fitness (w) by s. The induced epi-mark escapes erasure between gener-ations with probability q. If the epi-mark is transmitted to offspring of the opposite sex of the parent (here,sons) it decreases fitness by �. Due to the transgenerational effects we need to consider the number ofgrandchildren of a mutant, when calculating the invasion criteria. The expected number of copies of amutant allele in the grandchildren generation is:

From fathers From mothers

fraction 1/2 1/2w 1 1 � s

Sons Daughters Sons DaughtersEpi-mark present no no (but carriers of gene) Yes no irrelevantfraction 1/2 1/2 q/2 (1 � q)/2 1/2w 1 1 � s 1 � � 1 1 � s

w � 1/ 2 1 1/ 2 1 � 1/ 2 �1 � s� � 1/ 2 �1 � s�

q/ 2 �1 � �� � �1 � q�/ 2 1 � 1/ 2 �1 � s�

� 1 � s � q �/4

To invade:

1 � 1 � s � q �/4

s � q �/4.

X-linked mutant. Such mutant finds itself in a female with probability 2/3 and in a male withprobability 1/3. We first consider the case with a feminizing effect:

From fathers From mothers

Fraction 1/3 2/3W 1 1 � s

Daughters Sons DaughtersEpi-mark present no (but carriers of gene) yes no irrelevantFraction 1 q/2 (1 � q)/2 1⁄2W 1 � s 1 � � 1 1 � s

w � 1/3 1 1 �1 � s� � 2/3 �1 � s� q/ 2 �1 � ��

� �1 � q�/2 1 � 1/2 �1 � s�

� 1 � 4/3 s � 1/3 q �

To invade:

1 � 1 � 4/3 s � 1/3 q �

s � q �/4.

And next the case with a masculinizing effect:

From fathers From mothers

fraction 1/3 2/3w 1 � s 1

Daughters Sons DaughtersEpi-mark present yes no no (but carriers of gene) nofraction q (1 � q) 1/2 1/2w 1 � � 1 1 � s 1

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w � 1/3 �1 � s� q �1 � �� � �1 � q� 1 � 2/3 1 1/2 �1 � s� � 1/2 1

� 1 � 2/3 s � 1/3 q �

To invade:

1 � 1 � 2/3 s � 1/3 q �

S � q �/ 2.

Handling Editor: Hanna Kokko

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