Homosexuality is a common occurrence in humans and other species, yet its genetic and evolutionary basis is poorly understood. Here, we formulate and study a series of simple mathematical models for the purpose of predicting empirical patterns that can be used to determine the form of selection that leads to polymorphism of genes influencing homosexuality. Specifically, we develop theory to make contrasting predictions about the genetic characteristics of genes influencing homosexuality including: We conclude that the measurement of the genetic characteristics of quantitative trait loci QTLs found in genomic screens for genes influencing homosexuality can be highly informative in resolving the form of natural selection maintaining their polymorphism.
There are several reasons for the long-standing interest among evolutionary biologists e. Second, there are two lines of evidence that homosexuality is influenced by polymorphic genes: Third, even if one assumes only a small fitness cost to the expression of homosexuality, it appears to be more common in both males and females than can be plausibly Genetica homosexual relationship by mutation—selection balance Kinsey et al.
Maternal effects may contribute Genetica homosexual relationship the homosexual phenotype. For example, there is a curious relationship between birth order and the incidence of male homosexuality. There have been a few attempts to Genetica homosexual relationship the specific genes that influence male homosexuality.
The complex nature of the occurrence of male homosexuality in human pedigrees indicates that its inheritance is not a simple Mendelian trait Pillard et al. Recently, a genome-wide QTL screen for male homosexuality Mustanski et al.
These initial results are only preliminary and require confirmation from additional genetic studies. Two mechanisms for the maintenance of polymorphism in genes that cause homosexuality have been most frequently mentioned in evolutionary biology literature: The potential importance of this mechanism is highlighted by recent data which indicate that female maternal relatives of homosexuals Camperio-Ciani et al. The topic of homosexuality has so far received only very "Genetica homosexual relationship" attention in theoretical evolutionary genetics and we are aware of only two previous papers that Genetica homosexual relationship attempted to model it.
The second paper was by Getzwho assumed that reduced mating success of homosexual men was compensated by increased rearing success of females or increased joint fecundity and cooperation of couples. Both these papers studied the case of a single autosomal, diallelic locus, and they concentrated on the conditions for invasion of Genetica homosexual relationship allele promoting homosexuality.
Our goal is to formulate a series of simple mathematical models for the purpose of predicting empirical patterns that can be used to guide future genetic analysis of homosexuality. We specifically wanted to generate testable predictions that will provide a foundation for the generation of empirical evidence for or against alternative evolutionary hypotheses for the maintenance of polymorphic genes that influence homosexuality. Accordingly, we develop theory to make predictions about: Because homosexuality has previously received very little attention in the context of sexually antagonistic alleles, our main focus will be on this model, but we will also extend the previous work on overdominance.
Lastly, our approach uses as a foundation extant simple models of sexually antagonistic genes Rice and of maternal and parental selections Gavrilets ; Spencer ; Miller et al.
We will assume throughout that males are the heterogametic sex, but all our results can be applied reciprocally to the case of female heterogamety. We do not attempt to analyse the altruism towards kin model.
Because neither any existing data nor any mathematical models known to us support its plausibility, we consider it premature to include the kin-altruism mechanism in our analysis. We consider a one-locus, two-allele diploid population with genotypes AAAa and aa. Generations are discrete and non-overlapping. The population size effectively infinite.
Fitness is understood as viability i. Mating is random among the individuals who enter the mating pool.
Throughout the manuscript, A is an allele that has little or no influence on sexual orientation, and allele a masculinizes or feminizes both sexes, and thereby increases the probability of homosexuality in the discordant sex. A feminizing allele a would be one that canalized development towards the female sex-determination pathway.
Such an allele would be favoured in females because it protects them when exposed to masculinizing environmental conditions, but this same allele, when expressed in males, would feminize them and could thereby lead to homosexuality.
Below, our main focus is on the conditions required for the maintenance of genetic variation. The dynamic equations describing specific models are given in appendix A. First, we analyse the case when fitness and sexual orientation in both sexes are influenced solely by the direct Genetica homosexual relationship effects of genes residing in a zygote. In later sections, we will consider the cases, where maternal effects influence these characters. Assume that the locus under consideration is autosomal.
Let female Genetica homosexual relationship be f 1f 2 and f 3 and male fitnesses be m 1Genetica homosexual relationship 2 and m 3 in genotypes AAAa and aarespectively. In this system, the polymorphism is protected i. Note that inequality 3. We consider three different cases. If heterozygotes have the highest fitness in both sexes i. Although overdominance in both sexes is possible, the more plausible scenario for overdominance of a feminizing or masculinizing allele would be overdominance in one sex and directional selection in the other sex, as described subsequently.
However, the same conclusions are reached if the roles of the two sexes are reversed. Here and throughout, primed and unprimed symbols denote fitness effects in opposite sexes. Genetica homosexual relationship left-hand side of inequality 3. Overall, overdominance need not be strong to maintain polymorphism. Increasing the degree of dominance h of allele a in females promotes the maintenance of genetic variation; if allele a is dominant in females i.
For illustration, we assume that a feminizing allele a increases the fitness "Genetica homosexual relationship" females but decreases the fitness of males.
However, the conclusions are not changed, if the roles of the two sexes are reversed. Then, allele a increases in frequency when rare if. Allele a does not go to fixation if. These conditions are illustrated in figure 1.
Note that if G is small, the conditions for the maintenance of genetic variation are very strict. Also note that conditions 3. Conditions for the maintenance of genetic variation by sexually antagonistic selection in an autosomal locus. Variation is maintained for parameter values between the two lines. In the above example, we assumed that Genetica homosexual relationship degree of dominance is equal in both sexes.
If this is not so, then the most favourable scenario for the maintenance of variation is when allele a is dominant in the sex, where it is advantageous and is recessive in the sex where it is deleterious. Assume that the locus under consideration is X-linked.