5.4: Apomixis and Triangular Numbers
(Continued from the previous page)
Any form of life capable of apomixis would have an easier time getting established than would a purely sexual form. Stebbins (1969: 29) correctly noted that the deleterious effect of hybridization on fertility would prevent many natural hybrids from getting established as new forms of life:
In many hybrids, the complete sterility of the F1 individuals effectively negates any possible influence of hybridization, and in many others a high degree of sterility is a serious barrier to its later influence.
He also notes that
most of the [genetic types derived] from wide crosses will be less adaptive than the parental genotypes, particularly in the original parental environments.
But when they are capable of vegetative reproduction (or agamospermous reproduction), even extremely sterile hybrids can get established as new forms. In fact, the possession of such alternative reproductive capacities would with time often permit the production by sexual means of a variety of later-generation hybrids, some of which might have an enhanced level of fertility. Such fertile types would be favored by natural selection and therefore would likely get established as new forms.
As Asker and Jerling (1992: 113–114) note, certain agamosperms of hybrid origin
would be unable to reproduce sexually. Some are male sterile, even if the sterility might depend on other factors than hybridity. To acquire the capacity for apomictic seed formation, in a sterile hybrid capable only of vegetative reproduction, would mean an enormous increase in fitness.
Moreover, as has already been shown, it is not important that hybrids from most crosses will be maladaptive. The number of combinations that can be made from a set of n types is a triangular number, n(n-1)/2 (to review the section on triangular numbers, click here). So the number of potential hybrid pairings that can be produced from a given set of related forms is usually far in excess of the number of forms in that set. Thus, in the example given earlier, 100 different forms could be paired in 100(99)/2 = 4,950 different ways. And, in point of fact, the number of hybrids known for a given taxonomic category often does exceed the number of forms in the category.
For example, there are about 130 types of waterfowl treated as species. But there are about 500 different known types of waterfowl hybrids. About 18,000 orchids are treated as species. More than 35,000 types of orchid hybrids are on record, and the number is ever increasing. Rienikka notes that by 1960, "hundreds of new orchid crosses were being registered each month." Obviously, then, it makes little difference if the vast majority of hybrid pairings fail; for if even a small percentage of the total possible combinations are successful, then it will be possible for many types of hybrids to get established as new forms of life. For example, in the case of orchids there are 18,000(17,999)/2 = 161,991,000 combinations. If only one in a thousand of these combinations were successful, 161,991 new viable forms would come into being.
In addition, there are many reasons to suppose that natural hybridization is more common than available reports suggest. This underreporting of hybridization is the result of several different factors (for a discussion of underreporting, click here). NEXT PAGE >>
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