Biologic parsimony, I'd imagine. Ie: the KISS principle (keep it simple, stupid).
I agree. Two sexes probably balances genetic diversity with simplicity in a way that no other method has displaced due to being better.
It's hard to imagine what advantage further sexual complexity would confer, or how it would evolve. What would be the function of a third sex? Meiosis only produces two types of gametes, after all
I'd hesitate to underestimate the extravagance of Nature, though. Some of the reproductive strategies of certain parasites would put Rube Goldberg to shame, for example.
I can imagine some advantages.
Partner Mating Percentages:
-If there is one sex that is a hermaphrodite (but that is sexual, not asexual), then any individual could mate with 100% of the other individuals of that species. Any two individuals could pair up.
-If there are three sexes, and any combination of two works for reproduction, then any individual could mate with 66.67% of other individuals of that species.
-If there are four sexes, and any combination of two works for reproduction, then any individual could mate with 75% of other individuals in that species.
-Currently with only two sexes, approximately 50% of individuals represent viable mating partners.
Specialization:
-Two sexes means two opportunities to specialize. Male and female humans are optimized for slightly different things. Male and female lions are optimized for slightly different things.
-More sexes means more opportunities to specialize. In one of the Isaac Asimov novels, 'The Gods Themselves', there is an alien race that has three sexes that has to form a 3-member bond to mate. One sex is rational, one is emotional, and one is parental.
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Most of those scenarios I guess don't offer enough survival benefits to offset the additional complexity. The hermaphrodite scenario where all members have both sexes and can mate with one another may actually be the simplest and most optimal but probably for a good reason or another is not how it developed for most complex species.