Any biological species of biparental organisms necessarily includes, and is fundamentally dependent on, sign processes between individuals. In this case, the natural category of the species is based on family resemblances, which is why a species is not a natural kind. We describe the mechanism that generates the family resemblance. An individual recognition window and biparental reproduction almost suffice as conditions to produce species naturally. This is due to assortativity of mating which is not based on certain individual traits, but (...) on the difference between individuals. The biosemiotic model described here explains what holds a species together. It also implies that boundaries of a species are fundamentally fuzzy, and that character displacement occurs in case of sympatry. Speciation is a special case of discretisation that is an inevitable result of any communication system in work. The biosemiotic mechanism provides the conditions and communicative restrictions for the origin and persistence of diversity in the realm of living systems. (shrink)