Why are there only two sexes?

Populations of most isogamous protists have gametes that belong to one of only two mating-types (alias sexes). That this should be so is paradoxical for, if there is any cost involved in the finding of a mate, then a gamete of a third mating-type would, at the point of invasion, be able to mate with the first gamete it encounters, hence suffering the minimum possible costs. The expectation is hence that the number of mating-types in most isogamous species should tend towards infinity. By the same logic, two mating-types is the least expected state. A demonstration of the evolution from three to two sexes, under the condition of costs to mate-finding, has yet to be provided. Here I show by a dynamic analysis that, if species with two mating-types coordinate uniparental inheritance of cytoplasmic genes more efficiently than do those with three, then, assuming the costs to mate finding are not too high, evolution from three to two sexes is expected as a response to the invasion of a costly selfish cytoplasmic factor that disrupts the normal pattern of inheritance. There exists also a limited domain in parameter space (in which costs to mate finding are moderate), in which collapse from four mating-types to three is possible, but the collapse from three to two is not. If costs to not finding a mate are high then it is expected that gametic fusion should be abandoned for a system in which nuclei are exchanged but cytoplasm is not.