On the Mathematics of the Fraternal Birth Order Effect and the Genetics of Homosexuality

On the Mathematics of the Fraternal Birth Order Effect and the Genetics of Homosexuality. Tanya Khovanova. Archives of Sexual Behavior, November 5 2019. https://link.springer.com/article/10.1007/s10508-019-01573-1

Abstract: Mathematicians have always been attracted to the field of genetics. The mathematical aspects of research on homosexuality are especially interesting. Certain studies show that male homosexuality may have a genetic component that is correlated with female fertility. Other studies show the existence of the fraternal birth order effect, that is, the correlation of homosexuality with the number of older brothers. This article is devoted to the mathematical aspects of how these two phenomena are interconnected. In particular, we show that the fraternal birth order effect implies a correlation between homosexuality and maternal fecundity. Vice versa, we show that the correlation between homosexuality and female fecundity implies the increase in the probability of the younger brothers being homosexual.

Keywords: Fraternal birth order effect Male homosexuality Fecundity Genetics Sexual orientation

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Introduction

According to the study by Blanchard and Bogaert (1996): “[E]ach additional older brother increased the odds of [male] homosexuality by 34% ” (see also Blanchard [2004], Bogaert [2006], Bogaert  et al. [2018], and a recent survey by Blan-chard [2018]). The current explanation is that carrying a boy to term changes their mother’s uterine environment. Male fetuses produce H–Y antigens which may be responsible for this environmental change for future fetuses.

The research into a genetic component of male gayness shows that there might be some genes in the X chromosome that influence male homosexuality. It also shows that the same genes might be responsible for increased fertility in females (see Ciani, Cermelli, & Zanzotto [2008] and Iemmola & Ciani [2009]).

In this article, we compare two mathematical models. In these mathematical models, we disregard girls for the sake of clarity and simplicity.

The first mathematical model of the Fraternal Birth Order Effect (FBOE), which we denote FBOE-model, assumes that each next-born son becomes homosexual with increased probability. This probability is independent of any other factor.

The second mathematical model of Female Fecundity (FF), which we denote FF-model, assumes that a son becomes homosexual with probability depending on the total number of chil-dren and nothing else.

We show mathematically how FBOE-model implies correlation with family size and FF-model implies correlation with birth order. That means these two models are math-ematically intertwined.We also propose the Brother Effect. Brothers share a lot of the same genes. It is not surprising that brothers are more probable to share traits. With respect to homosexuality, we call the correlation that homosexuals are more probable to have a homosexual brother than a non-homosexual the Brother Effect. The existence of genes that increase predisposition to homo-sexuality implies the Brother Effect. The connection between the FBOE-model and the Brother Effect is more complicated.

We also discuss how to separate FBOE and FF in the data.

The “Extreme Examples” section contains  extreme mathematical examples that amplify the results of this article. The “FBOE-model and the family size” section shows how FBOE-model implies the correlation with family size. The “FF-model implies birth order correlation” section shows how FF-model implies the correlation with birth order. In the “Brothers” section, we discuss the connection between FBOE-model and the Brother Effect. In the “Separating Birth Order and Female Fecundity” section, we discuss how to separate the birth order from the family size.