Estimated international population of gay men

I recently learned about the "fraternal birth order effect," where apparently for every older brother a man has, his probability of being gay as an adult increases. Here's a wikipedia entry.

Now, apparently there's some debate over how real or how strong this effect really is, so I'm almost certainly taking some numerical result a little too seriously. But, it occurred to me that data such as total fertility rate, and birth sex ratios are attainable international statistics. If this fraternal birth order effect is pretty strong and reliable, you should be able to estimate what percent of the male population of a country is gay.

So, I grabbed some data on international total fertility rate from here, and data on birth sex ratios here. Now, I have to make some assumptions. First, all of these calculations take the average total fertility rate as a country level descriptor, but there's almost certainly a unique probability distribution for different fertility rates for every country. Second, I have to treat the probability of having a male baby as being independent from the sex of the prior babies a woman has had. Third, and most importantly, I'm treating fraternal birth order as the only determinant of sexual orientation.

These are all pretty drastic assumptions. For instance, there's some evidence that my second assumption (birth sex of babies from the same mother are independent processes) is false. From the UN data I have, here's the total fertility rate of the country by the sex ratio:

This seems to suggest that as women have more babies, they're more likely to have girls. Note: I've left out data from four countries with highly skewed birth sex ratios, since these countries apparently have high rates of abortion of female fetuses.

So, I'm thinking about this as a very rough back of the envelope estimate, not to be taken too seriously, but maybe some sort of indicator of the shape of the world.

Here's the math:

• babies = 1, 2, ... total.fertility.rate
• boy.probability = male.ratio/2
• boy.babies = boy.probability^(babies)
• prob.gay.first.born = 0.12 (more on this below)
• prob.gay.n.born = prob.gay.n-1.born * 1.3 (from wikipedia)
• prob.gay = sum(prob.gay.1-to-n.born * boy.babies)

I hope that makes some sense. I grabbed 1.3 from wikipedia, which says "each older brother increases a man's odds of developing a homosexual orientation by 28–48%." I basically made up the probability that a first born son is gay. This was the one number that I couldn't seem to find, so I adjusted and played with it until the predicted percent of gay men in the United States was about 10%.

Here are my results for the top 10 countries for percent of gay men.

1. Afghanistan (19%)
2. Niger (18%)
3. Liberia (18%)
4. Mali (18%)
5. Nigeria (18%)
6. Burkina Faso (17%)
7. Guinea (17%)
8. Yemen (17%)
9. Iraq (17%)
10. Uganda (17%)

Unsurprisingly, the percent of gay men in a country is highly correlated with total fertility rate. I think this top 10 list highlights the importance of gay rights activism in Africa, especially in Uganda, which is considering making homosexuality a capital offense. 

And for the self obsessed, the United States looked like this:

• Smaller percent than 100 countries > tied with 17 countries > larger percent than 43.