There is a massive difference. With that kind of mushroom one can expect that any random pair is very likely to match up. With humans you have tad less of 50% chance of being able to make kids with any random otherwise fertile human.

Err, that is an uncharitable reading of GP imo. If you pair males and females (rather than just "humans") then the anology holds quite well no?

I think the topic is getting a bit muddled here. Are we talking about couples who can't have children because one or the other is infertile/sterile, or couples who could have children with someone else but not one another?

I'm not familiar with this latter scenario. A man being sterile is nothing like this algae's situation, as it has nothing to do with "pairing," he's simply unable to produce children with anyone.

How often is the inability to have children naturally dependent on direct compatibility, rather than the ability of one or both partners to have children at all, regardless of partner?

This is an interesting idea because it seems like it could be true and we've just never noticed. I'm not sure how you'd go about designing a study but I guess it would be easy to find volunteers.

> but I guess it would be easy to find volunteers.

I don't know, in my experience people are sure picky about procreating with random strangers (and the ethical concerns regarding the output of the study are... significant).

From people I've known undergoing fertility treatments (and from my own limited research), the issue is frequently traceable to a specific cause in one or both partners (although it appears to be unexplained in about 20% of couples who seek treatment, which would be a small subset of the general population).