There are two main ways in which polyploidy arises in a natural setting: (1) somatic chromosome multiplication; and (2) unreduced gametes. Evidence suggests that the latter of these two modes is the commoner in both animals and plants.
The production of polyploidy via somatic multiplication requires a doubling of the chromosome number to occur in some part of the parent organism. So it requires the production of a polyploid shoot, bud, or fragment that can in some way (i.e., via sexual reproduction, agamospermy, vegetative reproduction, or some combination thereof) go on to maintain itself as a new form of life. This doubling must initially occur in a single cell of the organism. That cell must then initiate new growth and proliferate to become a distinct multicellular polyploid portion of the parent organism. Individual polyploid cells commonly occur in plants otherwise composed of diploid cells, but the frequency with which such cells initiate new growth and give rise to polyploidy in offspring forms is poorly known.
Somatic multiplication was once thought to be the most common way of producing polyploidy in plants. More recent literature, however, suggests unreduced gametes are the most common source of plant polyploidy, as has long been assumed for animals. A wide variety of organisms produce unreduced gametes, which are usually either diploid or triploid. For example, Franke (1975) lists 31 plant families for which they have been reported. It is often suggested that the union of two unreduced gametes must be a very rare event, but this claim appears to have been made only in considering such unions as a percentage of all gametic unions. If, however, one considers the fact that gametes are produced in vast numbers and that the expected rate at which unreduced eggs will be fertilized by unreduced male gametes is equal to the fraction of all male gametes that are unreduced, then it becomes apparent such unions must be very numerous indeed.
For example, suppose a very small fraction of the eggs produced by a particular population were diploid, say one egg in a million, and that a similarly low fraction of all male gametes produced by that population were diploid. If the population contained one million females each producing one million gametes, then they would produce a total of one trillion gametes, one million of which would be diploid. Among these million diploid gametes, one would be expected to be fertilized by a diploid male gamete giving rise to a tetraploid offspring. Thus, even with the assumption of this unrealistically low rate of diploid gamete production, a tetraploid would be produced by such a population in every generation. In the case of a tetraploid capable of self-fertilization or of vegetative reproduction, the production of even one individual could result in a new form getting established.
However, actual rates at which diploid gametes occur are far higher than assumed in the example. In a broad survey of plants, Ramsey and Schemske (1998) found the mean frequency of diploid gametes produced by non-hybrid individuals was 0.56 percent (about one gamete in 200). Applying this rate in the example just given would give 0.0056 × 1012 = 5.6 × 109 = 5,600,000,000 diploid eggs. Under the assumption that 0.56 percent of the male gametes were also diploid, 0.56 percent of these 5,600,000,000 diploid eggs would be fertilized by a diploid male gamete. That is, 0.0056 ×5,600,000,000 = 31,360,000 tetraploid offspring would be produced in every generation. This is a very large number indeed.
Moreover, hybridization greatly promotes the formation of diploid gametes. Ramsey and Schemske (1998) say that in studies of hybrids the mean reported rate of diploid gamete production was 50-fold greater (27.52%) than in non-hybrids. In fact, unreduced gametes are often the only functional ones in hybrids produced by interbreeding between distinct chromosets. We have already seen two examples of this phenomenon, Tripsacum dactyloides × Zea mays; Brassica oleracea × Raphanus sativus (see cross-references in the e-book version). In hybrid populations the union of unreduced gametes must therefore be rampant and the production of polyploids by the union of such gametes must surely be accordingly amplified. In some hybrid zones polyploids are, no doubt, produced en masse on an ongoing basis. Indeed, in recent years it has been empirically verified that many polyploids are derived from their progenitors repeatedly via separate polyploidization events producing separate polyploid individuals. For example, in the border region between Washington and Idaho, over a 50-year period, two types of tetraploid goatsbeard, Tragonopagon mirus and T. miscellus, probably formed, respectively, on 12 and 20 separate occasions. Hedrén et al. (2001: 1868) say this appears to be a general pattern.
Many polyploids produced by the union of unreduced gametes would get established as new forms even if they were obligate outcrossers (i.e., organisms capable of reproducing by sex, but incapable of self-fertilization, agamospermy, or vegetative reproduction). Consider the example of the hypothetical tetraploid just given. Such tetraploids are normally quite fertile since they have fully paired karyotypes. In that example we saw many such tetraploids were produced. These could interbreed to produce a line of descendants. Moreover, new tetraploid individuals of this sort, and their karyotypically identical tetraploid descendants, normally produce hybrids of low fertility when they backcross with either of their diploid parents. They would thus have no tendency to be swamped out of existence by interbreeding with their initially more numerous parents. Only when fertilized by others of their own kind would they produce significant numbers of fertile offspring. In this way they could maintain themselves as a new stable chromotype and, presumably, as a new somatype as well.