## Fraternal Birth Order and Fecundity

Two interesting research results about male homosexuality are intertwined. The first one shows that the probability of homosexuality in a man increases with the number of older brothers. That is, if a boy is the third son in a family, the probability of him being a homosexual is greater than the probability of a first son in a family being homosexual. The second research result shows that the probability of homosexuality increases with the number of children the mother has. So if a woman is fertile and has many children, the probability that each of her sons is a homosexual is greater than the probability that an only child is a homosexual.

Many people conclude from the first result that a woman undergoes hormonal or other changes while being pregnant with boys that influence the probability of future boys being homosexual. Looking at the second result, researchers conclude that homosexuality has a genetic component. Moreover, that component is tied up with the mother’s fecundity. The same genes are responsible for both the mother having many children and for her sons being homosexual. This assumption explains why homosexuality is not dying out in the evolution process.

In one of my previous essays I showed that the first results influences the second result. If each next son is homosexual with higher probability, then the more children a mother has the more probable it is that her sons are homosexuals. That means that the second result is a mathematical consequence of the first result. Therefore, the conclusion that the second result implies a genetic component might be wrong. The correlation between homosexuality and fecundity could be the consequence of hormonal changes.

Now let’s look at this from the opposite direction. I will show that the first result is the mathematical consequence of the second result: namely, if fertile women are more probable to give birth to homosexuals, then the probability that the second sons are is higher than the probability that the first sons are gay.

For simplicity let’s only consider mothers with one or two boys. Suppose the probability of a son of a one-son mother to be a homosexual is p1. Suppose the probability of a son of a two-sons mother to be a homosexual is p2. The data shows that p2 is greater than p1. What is the consequence? Suppose the number of mothers with one son is m1 and the number of mothers with two sons is m2. Then in the whole population the probability of a boy who is the first son to be gay is (p1m1+p2m2)/(m1+m2) and the probability of a boy who is the second son to be gay is p2. It is easy to see that the first probability is smaller than the second one.

Let me create an extreme hypothetical example. Suppose mothers of one son always have straight sons, and mothers of two sons always have gay sons. Now consider a random boy in this hypothetical setting. If he’s the second son, he is always gay, while if he is the first son he is not always gay.

We can conclude that if the probability of having homosexual sons depends on fecundity, then the higher numbered children would be gay with higher probability than the first-born. This means that if the genetics argument is true and being a homosexual depends on the mother’s fecundity gene, then it would follow mathematically that the probability of homosexuality increases with birth order. The conclusion that homosexuality depends on hormonal changes might not be valid.

So what is first, chicken or egg? Is homosexuality caused by fecundity, while birth order correlation is just the consequence? Or vice versa? Is homosexuality caused by the birth order, while correlation with fecundity is just the consequence?

What do we do when the research results are so interdependent? To untangle them we need to look at the data more carefully. And that is easy to do.

To show that homosexuality depends on the order of birth independently of the mother’s fertility, we need to take all the families with two boys (or the same number of boys) and show that in such families the second child is more probable to be homosexual than the first child.

To show the dependence on fertility, without the influence of the birth order, we need to take all first-born sons and show that they are more probable to be homosexuals if their mothers have more children.

It would be really interesting to look at this data.

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1. #### Theo:

One can rewrite the same data as variations on “Boys with lots of brothers are more likely to be gay than boys with no or few brothers”. But said that way, it suggests neither genetics relating male homosexuality with fecundity, nor biology relating male homosexuality with inter-womb hormonal changes. Rather, it suggests social effects of being raised in a home with lots of brothers.

Until adoption is less stigmatized (I posit that society’s conniptions around adoption will ruin most other effects), it will be hard to separate these possibilities. One way would be to look specifically at boys-who-are-adopted, and to compare those with many or few adopted brothers, and those with many or few genetic brothers. I don’t put high hopes on the availability of enough such data to draw good conclusions.

2. #### Quantum Mechanic:

@Theo: “Rather, it suggests social effects of being raised in a home with lots of brothers.” Strike “social”, and just say “effects”, which probably have multiple sources, with different weights depending on genetic factors for each individual.

3. #### Mark Velednitsky:

@Theo: There is work showing that homosexuality only depends on the number of biological older brothers and not adopted older brothers, even if those biological older brothers were raised apart from the younger brothers. See “Biological versus nonbiological older brothers and men’s sexual orientation.” Proceedings of the National Academy of Sciences 103.28 11 July, 2006: 10771-4. This research also covers the first experiment Tanya suggested.

@Tanya: You may be interested to read “Evidence for Maternally Inherited Factors Favouring Male Homosexuality and Promoting Female Fecundity.” Proceedings: Biological Sciences 271.1554 7 Nov. 2004: 2217-21. This research examines not only the fecundity of the mother of a homosexual male, but also of his maternal relatives versus his paternal relatives (because previous research determined that the genetic component of homosexuality, if it exists, is X-linked). The author also shows that first-born homosexuals come from larger families than first-born heterosexuals (exactly the second experiment you proposed), but the result is not statistically significant.

As far as I know, both hypotheses (genetic and birth order) are still being debated in the academic literature.