With the development of colchicine treatment it has been relatively easy to produce novel autopolyploid and allopolyploid plants. These plants are usually reproductively isolated from their parents (crosses are typically sterile), and, if viable, fertile and true-breeding, qualify as biological species. However not all new polyploids meet these requirements. Some are generally inviable, due to incompatible combinations of genetic factors from the parents; some are of low fertility, generally because the parental genomes are too close, leading to multivalent formation at meiosis, and consquent disruption of gamete formation; and some have irregular mitosis, with consequent variability in chromosome complement.
Note that while two species A and B may be good species, it is not necessarily the cases that the same holds for their respective allopolyploids with a 3rd species C - AC and BC might not be reproductively isolated. For example, the C genome may compensate for post-zygotic isolating mechanisms separating A and B.
As cotton is the world's preminent vegetable fibre crop it has been extensively studied by agronomists, and consequently experimental polyploids have been frequently produced, both as objects of study in themselves, and as bridging populations for introducing wild germplasm to the cultivated species. In both cases whether a new species was produced was not a particular interest to the researchers, and it can be difficult to evaluate the status of a polyploid from the literature.
Autopolyploids of Gossypium arboreum are reported to have many quadrivalents at mitosis , and may be inferred to have low fertility.
The allopolylploid of G. stocksii × arboreum is reported by Beasley  to have "almost normal fertility".
Allopolyploids of Gossypium arboreum × bicksii (A2A2G1G1), Gossypium herbaceum × australe (A1A1G2G2) and Gossypium herbaceum × nelsonii (A1A1G3G3) have been produced.
These are allopolyploid hybrids between the cultivated Old World diploid cottons (A genome) and the New World tetraploid cottons (AD genome). Beasley  mentions that G. hirsutum × herbaceum is fertile, but doesn't indicate the degree of fertility.
These are allopolyploid hybrids between New World tetraploid cottons (AD genome), especially the cultivated Gossypium hirsutum, and New World diploid cottons (D genome). With 5 AD genome species and 12 D genome species this gives 60 theoretically possible combinations, but not all have been attempted. In general these appear to be of low fertility, probably as a result of disruption of meiosis due to formation of multivalents involving the D genomes of the two parents.
Gerstel  reports seed set in the range of (roughly) 1% to 10%, and low production of good pollen, for the crosses G. barbadense × raimondii, G. hirsutum × raimondii and G. hirsutum × thurberi. The cross G. hirsutum × davidsonii is inviable due to genic lethality factors, and the fertility of G. hirsutum × armourianum hexaploids was lower than the crosses mentioned previously.
Polyploids involving G. klotzschianumn might be expected to behave as G. davidsonii, and G. harknessii as G. armourianum. However Beasley  cites Harland as reporting "fully fertile" allohexaploids of G. hirsutum × harknessii.
The allopolylploid of G. stocksii × hirsutum is reported by Brown & Menzel  to be "exceedingly fertile".
The are allopolyploid hybrids between, and autopolyploids of New World tetraploid cottons, . Beasley  reports appreciably frequencies of quadrivalent formation in the octaploid G. barbadense and G. hirsutum, and in the allooctaploid G. barbadense × hirsutum. He doesn't mention the degree of fertility of these forms, but it may be assumed to be low.
© 2020 Stewart Robert Hinsley