Homosexuality has been documented throughout history and is found in almost all human cultures (Kirkpatrick, 2000). The oldest depictions of homosexuality come from Mesolithic rock art (Nash, 2001), although generally it is accepted that the prevalence of homosexuality in human societies is low (Diamond, 1993; Grulich, Visser, Smith, Rissel, & Richters, 2003; Sell, Wells, & Wypij, 1995). Homosexual males on average have less reproductive success than heterosexuals (Iemmola & Ciani, 2009; Rieger, Blanchard, Schwartz, Bailey, & Sanders, 2012; Van de Ven, Rodden, Crawford, & Kippax, 1997). Consequently, from an evolutionary perspective, homosexuality is a paradox: How can a phenomenon associated with low reproductive success be maintained at relatively stable frequencies (Hutchinson, 1959; Wilson, 1975)?

Research suggests that sexual orientation is influenced by genetic factors. Specifically, monozygotic (MZ) twins, who share all of their genes, are more likely to be concordant in their sexual orientation than are dizygotic (DZ) twins or simple siblings, who only share, on average, half of their genes (Kendler, Thornton, Gilman, & Kessler, 2000; Kirk, Bailey, Dunne, & Martin, 2000). In an effort to identify the gene or genes that influence sexual orientation, Hamer, Hu, Magnuson, Hu, and Pattatucci (1993) conducted a genetic study in a group of 40 families in which there were two gay brothers. Their data indicated a linkage between the Xq28 markers and sexual orientation. More recently, a genome-wide study replicated results showing linkage of homosexuality not only to Xq28, but also to elements on chromosome 8 (Sanders et al., 2014).

It is, however, also demonstrable that homosexual men, compared to heterosexual men, tend to come from larger families (Ciani, Corna, & Capiluppi, 2004; Ciani & Pellizzari, 2012; Iemmola & Ciani, 2009; King et al., 2005). Greater fecundity in relatives of homosexual men could potentially explain the counterintuitive persistence of homosexuality through sexually antagonistic selection—genes predisposing homosexuality in men increase fecundity in females who carry them (Ciani & Pellizzari, 2012; Iemmola & Ciani, 2009; Zietsch et al., 2008).

However, the positive fecundity increment accruing to mothers of homosexual men is not large: 1.16 times higher per Ciani et al. (2004), 1.31 times higher per Iemmola and Ciani (2009), and 1.38 times higher per Vasey and VanderLaan (2007), and it is not clear if this associated increased fecundity is sufficient to compensate for the reduced fecundity of homosexual men. Several studies attempted to address this question from a theoretical population genetics perspective. MacIntyre and Estep (1993) studied a model of overdominance, in which they suggest that homosexuality can persist in a population if heterozygous individuals have a reproductive advantage. Getz (1993) assumed that reduced mating success of homosexual men was compensated by increased rearing success of females, or increased joint fecundity and cooperation of couples. Later, Gavrilets and Rice (2006) developed a number of genetic models for overdominance, maternal effects, and sexual antagonism considering a single diallelic locus, either autosomal or X-linked. They showed by deterministic models that genes which predispose a carrier to homosexuality can persist in a polymorphic population across a wide range of conditions. Ciani, Cermelli, and Zanzotto (2008) expanded these models and tested them, along with two-locus genetic models; they concluded that only the two-locus genetic model, with at least one locus on the X chromosome, and incorporating sexually antagonistic gene expression, was able to explain the persistence of homosexuality. All other models yielded either extinction or fixation of alleles favoring homosexuality in the modeled populations.

Traditional mathematical models, which were used in the above listed studies, describe populations as an entire system, usually using differential equations. The basic principle of such genetic models is to find stable equilibrium between allele frequencies under which polymorphism can be maintained. Sex-linked locus equilibrium models are discussed in detail in Haldane and Jayakar (1964). An alternative, more recent approach uses individual-based modeling (IBM), wherein each individual is represented as an independent unit. IBMs allow for the possibility to include individual variation and to design more experiment-like scenarios (Borrill & Tesfatsion, 2011; Grimm & Railsback, 2013; Roughgarden, 2012). IBMs have not been used to address homosexuality, although they have been used to model sex chromosome dynamics in populations (Taylor & Jaenike, 2002, 2003). Published models (Ciani et al., 2008; Gavrilets & Rice, 2006; Getz, 1993) have thus provided significant contributions to theoretical genetic studies of homosexuality and laid the foundation for further research. However, they do not specifically treat separately homosexual and non-homosexual carriers of genes predisposing to homosexuality.

Not all MZ twin pairs who share the same genes are concordant for homosexuality. Population sample-based studies suggest that, on average, 20 % of twins are concordant for homosexuality: Bailey, Dunne, and Martin (2000): 23.1 %, Kendler et al. (2000): 31.6 %, Långström, Rahman, Carlström, and Lichtenstein (2010): 9.9 %. Older, self-selection studies suggest higher rates, about 50 % concordance: Kallmann (1952): 100 %, Heston and Shields (1968): 42.9 %, Bailey and Pillard (1991): 51.8 %, Whitam, Diamond, and Martin (1993): 64.7 %. In line with the underlying influence of genetic factors, these reports also indicate the existence of carrier males. This means that, on average, 50–80 % of males who have genes predisposing them to homosexuality are heterosexual, and there are no data to suggest that they have reduced fecundity. Zietsch et al. (2008) showed that heterosexuals who have a homosexual twin have, on average, the same number of female sex partners as heterosexuals who have a heterosexual twin.

Here I report individual-based modeling results of single locus X-linked, sexually antagonistic model of homosexuality.