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Primarily because of the claims of H. J. Muller, many biologists have believed animal polyploids must be rare. Muller (1925) asserted that polyploidy could not have a relevant role in the evolution of sexual animals because chromosomal duplication would be incompatible with animal sex-determination mechanisms. This argument is flawed in at least four ways. First, as Westergaard (1940, 1958) and Stebbins (1950) pointed out, Muller's argument is based on the presumption that the sex-determining mechanism of fruit flies (Drosophila), which depends on the ratio of the number of X chromosomes to autosomes (i.e., chromosomes other than the X and Y), is typical for animals as a whole. Such is not the case. A Y-dominant system, where sex is determined by the presence or absence of a Y chromosome is more usual. But a variety of additional sex-determination systems exist among animals besides the two just mentioned. Even mammals do not always have standard X-Y sex determination. For example, Sharp and Hayman (1981) note that male swamp wallabies (Wallabia bicolor) have two Y chromosomes. Most turtles and all crocodiles have no sex chromosomes and sex is determined by egg incubation temperature, not chromosomes. Indeed, as Mable (2004: 454) points out, "In reality, little is known about the factors that control sex determination in the vast majority of dioecious organisms."
Second, in certain categories of animals sex chromosomes are not well differentiated. Such is the case, for example, among lizards, and many polyploid lizards of hybrid origin have been reported. Bogart (1980: 361) states that "of all the polyploids and possible ancestors [of those polyploids] in amphibians and reptiles, only Cnemidophorus tigris seems to have discernable sex chromosomes." White (1973a: 586) notes that sex chromosomes are lacking in the salamander families Cryptobranchidae and Hynobiidae, both of which are characterized by high chromosome numbers (which is consistent with the idea that the members of these families are polyploid).
Third, as Stebbins (1950: 367) points out, the tetraploid plant "Melandrium dioicum … has long been known to possess a typical X-Y sex-determination mechanism, with the male as the heterozygous sex." Muller (Muller 1925: 351) said his explanation predicted that such plants would not be found. It is now known that heteromorphic sex chromosomes are in fact found in a number of plant groups. Moreover, many animals do not reproduce sexually, particularly invertebrates. Even Muller (1925: 352) granted that "amongst groups of animals like earthworms and fresh-water snails, which are normally hermaphroditic, tetraploidy or even higher forms of polyploidy might occur as readily as amongst most plants." Judging from available reports, it seems that polyploids of hybrid origin are fairly common among invertebrates as well as in vertebrates, among fish, amphibians, and reptiles, but rare among birds and mammals.
Fourth, there have been many more studies of polyploidy in plants than in animals. Even sixteen years after Muller's paper Fankhauser (1941: 507) commented that
"Spontaneous deviations from the normal somatic chromosome number have been investigated extensively in populations of plants, partly because of the ease with which the chromosome number of each individual may be determined in root-tip preparations. Comparatively little information is available concerning the range and frequency of such aberrations among mammals."
Even in those cases where changes in chromosome number were in fact studied in animals, the interest was in connection with embryological and developmental effects, not evolution and breeding. Thus, it appears Muller presumed polyploidy was rare in animals because reports, especially ones bearing on the origin of new types of animals through polyploidization, were rare at the time he wrote. But reports could not possibly have been common in 1925 since adequate technology to carry out the necessary studies was not yet available. Given evidence now available, it appears polyploidization is far more important in animal evolution than Muller supposed.