Having the Rh- bloodtype makes reproduction difficult, because Rh- mothers paired with Rh+ fathers end up with a lot of miscarriages.*

The simplified version: Rh+ people have a specific antigen in their blood. Rh- people don’t have this antigen.

If a little bit of Rh+ blood gets into an Rh- person’s bloodstream, their immune system notices this new antibody they’ve never seen before and the immune response kicks into gear.

If a little bit of Rh- blood gets into an Rh+ person’s bloodstream, their immune system notices nothing because there’s nothing to notice.

During pregnancy, it is fairly normal for a small amount of the fetus’s blood to cross out of the placenta and get into the mother’s bloodstream. One of the effects of this is that years later, you can find little bits of their children’s DNA still hanging around in women’s bodies.

If the mother and father are both Rh- or Rh+, there’s no problem, and the mother’s body takes no note of the fetuses blood. Same for an Rh+ mother with an Rh- father. But when an Rh- mother and Rh+ father mate, the result is bloodtype incompatibility: the mother begins making antibodies that attack her own child’s blood.

The first fetus generally comes out fine, but a second Rh+ fetus is likely to miscarry. As a result, Female Rh- with Male Rh+ pairings tend not to have a lot of children. This seems really disadvantageous, so I’ve been trying to work out if Rh- bloodtype ought to disappear out over time.

Starting with a few simplifying assumptions and doing some quick back of the envelope calculations:

We’re in an optimal environment where everyone has 10 children unless Rh incompatibility gets in the way. Blood type is inherited via a simple Mendelian model. People who are ++, +-, and -+ all have Rh+ blood. People with — are Rh-. We start with a population that is 25% ++, +-, -+, and –, respectively.

So our 1st generation pairings are:

F++/M++ F++/M+- F++/M-+ F++/M–

F+-/M++ F+-/M+- F+-/M-+ F+-/M–

F-+/M++ F-+/M+- F-+/M-+ F-+/M–

F–/M++ F–/M+- F–/M-+ F–/M–

Which gives us:

10++, 5++, 5+- 5+-, 5++ 10+-

5++, 5-+ 2.5++, 2.5+-, 2.5-+, 2.5– 2.5+-, 2.5++, 2.5–, 2.5 -+ 5+-, 5–

5-+, 5++ 2.5-+, 2.5–, 2.5++, 2.5+- 2.5–, 2.5-+, 2.5+-, 2.5++ 5–, 5+-

1-+, It’s complicated It’s complicated 10–

or

50++, 40+-, 21-+, 30–, and some quantity of “It’s complicated.”

For the F–/M+- pairings, any — children will live and most -+ children will die. Since we’re assuming 10 children, we’re going to calculate the odds for ten kids. Dead kids in bold; live kids plain.

Kid 1: 50% -+, 50% —

Kid 2: 25% -+, 25% — 25% -+, 25% —

Kid 3: 25% -+, 25% — 12.5% -+, 12.5% — 12.5% -+, 12.5% —

Kid 4: 25% -+, 25% — 12.5% -+, 12.5% — 6.3% -+, 6.3% — 6.3% -+, 6.3% ––

Kid 5: 25% -+, 25% — 12.5% -+, 12.5% — 6.3% -+, 6.3% — 3.1% -+, 3.3% — 3.1% -+, 3.1% —

Obvious pattern is obvious: F–/M+- pairings lose 25% of their second kids, 37.5% of their third kids, 43.3% of their fourth kids, 46.4% of their fifth kids, etc, on to about 50% of their 10th kids.

Which I believe works out to an average of 5–, 1+-

The outcomes for F–/M-+ pairings are the same, of course: 5–, 1+-

So this gives us a total of:

50++, 41+-, 22-+, 40–, or 33% ++, 27% +-, 14% -+, 26% — (or, 54% of the alleles are + and 46% are -).

(This assumes, of course, that people cannot increase their number of pregnancies.)

Running the numbers through again (I will spare you my arithmetic), we get:

35% ++, 32% +-, 11.8%-+, 21.4% — (or, 57% of alleles are + and 43% are – ).

I’m going to be lazy and say that if this keeps up, it looks like the –s should become fewer and fewer over time.

But I’ve made a lot of simplifying assumptions to get here that might be affecting my outcome. For example, if people only have one kid, there’s no effect at all, because only second children on down get hit by the antibodies. Also, people can have additional pregnancies to make up for miscarriages. 20 pregnancies is obviously pushing the limits of what humans can actually get done, but let’s run with it.

So in the first generation, F–/M+- => 9–, 1+- ; F–/M-+ => 9–, 1-+ (that is, the extra pregnancies result in 8 extra — children.) The F–/M++ pairing still results in only one -+ child.

This gives us 50++, 41+-, 22-+, 48– children, or 31%++, 25%+-, 13.7%, 30%– (or 51% + vs 49% – alleles.)

At this point, the effect is tiny. However, as I noted before, having 20 pregnancies is a bit of a stretch for most people; I suspect the effect would still be generally felt under normal conditions. For example, I know an older couple who suffered Rh incompatibility; they wanted 4 children, but after many miscarriages, only had 3.

Which leads to the question of why Rh-s exist at all, which we’ll discuss tomorrow.

*Lest I worry anyone, take heart: modern medicine has a method to prevent the miscarriage of Rh+ fetuses of Rh- mothers. Unfortunately, it requires an injection of human blood serum, which I obviously find icky.