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The definition of a sex is that each sex produces a unique type of gamete. If it does not produce unique gametes then it is not a sex. A caregiver that does not contribute genes is a caste or morph, not a sex.

The advantage of being triploid and trisexual is that this reduces the risk of genetic bottlenecks and inbreeding depression.

The disadvantages are that three individuals are required to reproduce and, contrary to popular belief, reduce phenotypical diversity. Recessive alleles are fair less likely to display phenotypes because three copies would be required.

An environment where trisexual species outcompete dioecious species would need to place greater selection pressure on genetic redundancy over the costs of finding mates and reduced phenotypic diversity.

An example of a true trisexual species may be found @ sff.net/people/dragonwriter/worldbuilding/trisexual.html

EDIT: the ant genus Pogonomyrmex actually has four sexes on the demographic level. Each colony requires three individuals to reproduce: the female mates with males of her species and another. Males are spawned asexually by females. Same species mating produces only reproductive females. Different species mating produces sterile hybrid females that form the worker caste. Collectively all four sexes, two males and two females of different species, are required for both species to survive.

To put this by analogy with cells in one organism: reproductive cells require gametes from the other species to produce somatic cells.

This would not work the same way on the organism level. There the analogy would be the female produces a sterile hybrid offspring which she parasitizes similar to the anglerfish.

EDIT: species that engage in hybridogenesis may qualify as possessing multiple sexes on the demographic level. The Iberian minnow consists of triploid males, triploid females and diploid males. The diploid male is a sexual parasite whose offspring are always diploid males, and ultimately requires both triploid males and females to reproduce.

Trioecious reproduction

The definition of a sex is that each sex produces a unique type of gamete. If it does not produce unique gametes then it is not a sex. A caregiver that does not contribute genes is a caste or morph.

The advantage of being triploid and trioecious is that this reduces the risk of genetic bottlenecks and inbreeding depression.

The disadvantages are that three individuals are required to reproduce and, contrary to popular belief, reduce phenotypical diversity. Recessive alleles are fair less likely to display phenotypes because three copies would be required.

An environment where trioecious species outcompete dioecious species would need to place greater selection pressure on genetic redundancy over the costs of finding mates and reduced phenotypic diversity.

An example of a true trioecious species occurs in the speculative fiction novel Silent Runners (Source).

Hybridogenesis

Hybridogenesis is a form of sexual parasitism where one species is limited to a single sex and must parasitize the opposite sex of a closely related species in order to reproduce. The genes of the parasitized parent are discarded from the germline of their hybrid offspring, ensuring that the parasite species' purity is maintained.

Thus, species that engage in hybridogenesis may qualify as possessing multiple sexes on the demographic level. For example, the Iberian minnow consists of triploid males, triploid females and diploid males. The diploid male is a sexual parasite whose offspring are always diploid males, and ultimately requires both triploid males and females to reproduce.

Social Hybridogenesis

Social hybridogenesis is a form of hybridogenesis found in certain eusocial ants. (Source)

Symmetrical social hybridogenesis occurs when the parasitized species adopts the same strategy to parasitize the parasitize. The ant genus Pogonomyrmex, for example, has two species with four sexes on the demographic level. Each colony requires three individuals to reproduce: the female mates with males of her species and the other. Males are spawned asexually by females. Same species mating produces only reproductive females. Cross-species mating produces sterile hybrid females that form the worker caste. Collectively all four sexes, two males and two females of different species, are required for both species to survive.

To put this by analogy with cells in one organism: reproductive cells require gametes from the other species to produce somatic cells.

This would not work the same way on the organism level. There the analogy would be the female produces a sterile hybrid offspring which she parasitizes similar to the anglerfish. As far as I know this strategy does not occur in any known species.

The definition of a sex is that each sex produces a unique type of gamete. If it does not produce unique gametes then it is not a sex. A caregiver that does not contribute genes is a caste or morph, not a sex.

The advantage of being triploid and trisexual is that this reduces the risk of genetic bottlenecks and inbreeding depression.

The disadvantages are that three individuals are required to reproduce and, contrary to popular belief, reduce phenotypical diversity. Recessive alleles are fair less likely to display phenotypes because three copies would be required.

An environment where trisexual species outcompete dioecious species would need to place greater selection pressure on genetic redundancy over the costs of finding mates and reduced phenotypic diversity.

An example of a true trisexual species may be found @ sff.net/people/dragonwriter/worldbuilding/trisexual.html

EDIT: the ant genus Pogonomyrmex actually has four sexes on the demographic level. Each colony requires three individuals to reproduce: the female mates with males of her species and another. Males are spawned asexually by females. Same species mating produces only reproductive females. Different species mating produces sterile hybrid females that form the worker caste. Collectively all four sexes, two males and two females of different species, are required for both species to survive.

To put this by analogy with cells in one organism: reproductive cells require gametes from the other species to produce somatic cells.

This would not work the same way on the organism level. There the analogy would be the female produces a sterile hybrid offspring which she parasitizes similar to the anglerfish.

The definition of a sex is that each sex produces a unique type of gamete. If it does not produce unique gametes then it is not a sex. A caregiver that does not contribute genes is a caste or morph, not a sex.

The advantage of being triploid and trisexual is that this reduces the risk of genetic bottlenecks and inbreeding depression.

The disadvantages are that three individuals are required to reproduce and, contrary to popular belief, reduce phenotypical diversity. Recessive alleles are fair less likely to display phenotypes because three copies would be required.

An environment where trisexual species outcompete dioecious species would need to place greater selection pressure on genetic redundancy over the costs of finding mates and reduced phenotypic diversity.

An example of a true trisexual species may be found @ sff.net/people/dragonwriter/worldbuilding/trisexual.html

EDIT: the ant genus Pogonomyrmex actually has four sexes on the demographic level. Each colony requires three individuals to reproduce: the female mates with males of her species and another. Males are spawned asexually by females. Same species mating produces only reproductive females. Different species mating produces sterile hybrid females that form the worker caste. Collectively all four sexes, two males and two females of different species, are required for both species to survive.

To put this by analogy with cells in one organism: reproductive cells require gametes from the other species to produce somatic cells.

This would not work the same way on the organism level. There the analogy would be the female produces a sterile hybrid offspring which she parasitizes similar to the anglerfish.

EDIT: species that engage in hybridogenesis may qualify as possessing multiple sexes on the demographic level. The Iberian minnow consists of triploid males, triploid females and diploid males. The diploid male is a sexual parasite whose offspring are always diploid males, and ultimately requires both triploid males and females to reproduce.

The definition of a sex is that each sex produces a unique type of gamete. If it does not produce unique gametes then it is not a sex. A caregiver that does not contribute genes is a caste or morph, not a sex.

The advantage of being triploid and trisexual is that this reduces the risk of genetic bottlenecks and inbreeding depression.

The disadvantages are that three individuals are required to reproduce and, contrary to popular belief, reduce phenotypical diversity. Recessive alleles are fair less likely to display phenotypes because three copies would be required.

An environment where trisexual species outcompete dioecious species would need to place greater selection pressure on genetic redundancy over the costs of finding mates and reduced phenotypic diversity.

An example of a true trisexual species may be found @ sff.net/people/dragonwriter/worldbuilding/trisexual.html

The definition of a sex is that each sex produces a unique type of gamete. If it does not produce unique gametes then it is not a sex. A caregiver that does not contribute genes is a caste or morph, not a sex.

The advantage of being triploid and trisexual is that this reduces the risk of genetic bottlenecks and inbreeding depression.

The disadvantages are that three individuals are required to reproduce and, contrary to popular belief, reduce phenotypical diversity. Recessive alleles are fair less likely to display phenotypes because three copies would be required.

An environment where trisexual species outcompete dioecious species would need to place greater selection pressure on genetic redundancy over the costs of finding mates and reduced phenotypic diversity.

An example of a true trisexual species may be found @ sff.net/people/dragonwriter/worldbuilding/trisexual.html

EDIT: the ant genus Pogonomyrmex actually has four sexes on the demographic level. Each colony requires three individuals to reproduce: the female mates with males of her species and another. Males are spawned asexually by females. Same species mating produces only reproductive females. Different species mating produces sterile hybrid females that form the worker caste. Collectively all four sexes, two males and two females of different species, are required for both species to survive.

To put this by analogy with cells in one organism: reproductive cells require gametes from the other species to produce somatic cells.

This would not work the same way on the organism level. There the analogy would be the female produces a sterile hybrid offspring which she parasitizes similar to the anglerfish.