## Tuesday, September 05, 2006

### pr(child 2=boy|child 1 = boy) - pr(child 2 = boy|child 1=girl) = ?

Okay, so shout-outs to this blog have previously proven extremely useful for when I've needed, say, obscure mp3s or emergency HTML advice. Let's try something more difficult and even work related: I am trying to figure out (preferably for a contemporary population in a developed country like the United States) whether/how much the probability of one's second child being a boy/girl is affected by whether one's first child is a boy/girl. Basically, is the second child more likely to be of the same sex as the first child, and, if so, how large is the effect? I've been surprisingly flummoxed in my efforts, leading to this post. Does anyone have any ideas for tracking this down?

(I know, I am an affiliate in a demography center, so you'd think I could just send an e-mail to one of them. Which I might. But, given the interests of the ones I know well, they're usually more helpful for questions about death statistics than birth statistics.)

Anonymous said...

Not trying to be simple, so please excuse if advanced statistics prove me wrong but...

From what I know of science and birthing babies, isn't it a 50/50 proposition (boy/girl) each time regardless of earlier births?

Think of flipping a coin. Even if it came up heads the first 10, so long as the coin isn't flawed, you still have a 50/50 chance on flip 11... right?

Anonymous said...

ps.
So the probability wouldn't be affected at all (unless you are calculating deliberate abortions based on predicted sonograms of the second child's sex, which hopefully doesn't occur too often.)

jeremy said...

That's exactly what I'm trying to figure out. I understand full well the independence of coin flips, but the degree of independence of successive childbirths is a biological matter, and I'm trying to find out empirically if successive births are independent and if not how close to independent they are.

Anonymous said...

I don't think successive births are entirely independent. In 1996, James (1,2) hypothesized that secondary sex ratio depends on parental hormones around the time of conception (i.e., high concentrations of testosterone and estrogen increase the probability of a son; and high concentrations of gonadotropins and progesterone increase the probability of a daughter). Subsequently, two papers by Bernstein et al. showed that levels of estradiol (a type of estrogen) decrease with each successive pregnancy (3,4). If James's "parental hormone status" hypothesis is correct, we would expect the odds of having a male birth to DECREASE with each successive birth (holding all other predictors of sex ratio constant). Thus, if the parents conceived a girl in a previous birth, and this is a reflection of lower levels of estrogen, then I think there is a higher probability that the next birth will be female...

I don't think this has been tested empirically, but the theory is out there...

1. James WH. Evidence that mammalian sex ratios at birth are partially controlled by parental hormone levels at the time of conception. J Theor Biol 1996;180:271-86.
2. James WH. Further evidence that mammalian sex ratios at birth are partially controlled by parental hormone levels around the time of conception. Hum Reprod 2004;19:1250-6.
3. Bernstein L, Depue RH, Ross RK, et al. Higher maternal levels of free estradiol in first compared to second pregnancy: early gestational differences. J Natl Cancer Inst 1986;76:1035-9.
4. Bernstein L, Lipworth L, Ross RK, Trichopoulos D. Correlation of estrogen levels between successive pregnancies. American Journal of Epidemiology 1995;142:625-8.

Anonymous said...

Oops. I should clarify that the Bernstein papers came out BEFORE the James papers.

Anonymous said...

I believe that the probablities are not equal. The overall, unconditional probability of having a boy is .5, but it is higher than .5 when there is a younger brother.

Kieran said...

This seems like a tricky problem because -- apart from any low-level sex selection stuff in the biology -- the decision to have another child may often not be independent of the sex of the child/children you already have. If people really want a girl, they may keep trying until they get one or run out of time (or energy). So disentangling the effects of a social desire to have a boy or a girl from the effects of biological stuff like hormonal variation or sperm competition will be hard.

Anonymous said...

So THIS is what sociologists do?

Teddy Love said...

I just wanted to reiterate what Kieran said and to add that you'd have to say more about what you're trying to tease out here because yeah culturally, there is at least anecdotal evidence that sex of child 1 has an effect on sex of child 2. Also, I don't know if this helps at all, but it's well known within the infertility community (for lack of a better word) that sex selection can be influenced by timing intercourse in certain ways, e.g., because Y sperm are more fragile (but faster), you can increase your chance of conceiving a boy by having intercourse closer to ovulation (so that the faster Y sperm get to the egg first ... if you time intercourse 3-5 days before ovulation the weaker Y sperm die off and the stronger X sperm are left to fertilize the egg when it is finally released). But how many people really do that, I don't know. I'd look on Medline for articles on sex selection. I'd love to hear more about where you're going with this. I would just say that given what we know about cultural notions regarding sex selection (e.g., "one of each"; preference for at least one male), we might expect something besides a 50/50 split (in addition to any "purely" biological effect ... do you really think such a thing exists?).
-TL

Winston said...

If #1 is male, all subsequent children will be male.
If #1 is female, all subsequent children will be female.

If a family appears to have a mix, they are either adopted, had genders manipulated in vitro, borrowed, stolen, switched at birth, or they are just flat out lying.

Tonya said...

If what Winston says is true, then I'm relieved that my older sibling is female.

Anonymous said...

Re the claim that timing of intercourse relative to ovulation may influence sex of offspring, Wilcox et al's seminal (no pun intended) 1995 NEJM paper refutes this theory.

molly said...

Also, consider 2 demographic phenomena: (1) the secondary sex ratio at birth (# boys/ # girls) is usually around 1.05 (i.e., more boys are born than girls). But there's also greater infant mortality for boys, such that at age 1 the secondary sex ratio is lower, and closer to 1.0. (2) the secondary sex ratio is lower in populations exposed to exogenous stressors (i.e., fewer boys are actually born). There's a recent paper by R. Catalano et al in Human Reproduction (Aug 26, 2006) investigating whether this is due to reduced conception of males or greater fetal loss of males. Answer (in this paper): greater fetal loss of males.