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1995, 1997). Outcrossing rates in the two cytotypes were very similar; values (after correcting for inbreeding depression in the diploid) are 0.45 and 0.43 for diploids and tetraploids, respectively. However, the tetraploids have substantially lower inbreeding depression (0.95 for diploids versus 0.67 for tetraploids), as expected from population genetic theory.

Outcrossing rates also have been estimated in diploid and allotetraploid species of Tragopogon (Cook and Soltis, 1999, 2000). Outcrossing rates in the allotetraploid T. mirus (0.381 and 0.456 for two populations) were higher than those found in the diploid parent Tragopogon dubius (0.068 and 0.242), although significantly higher than only one of the two populations; the other parent, Tragopogon porrifolius (Ownbey, 1950; Soltis et al., 1995), lacked segregating allozyme variation from which to estimate outcrossing rates. This pattern is exactly the opposite of that predicted by population genetic theory, and one explanation offered to explain it is that rates of outcrossing were underestimated, particularly in T. dubius, because of limited polymorphic loci in all populations. To account for this possibility, outcrossing rates were estimated in T. mirus and T. dubius from artificial arrays constructed to maximize the chances of detecting an outcrossing event if one had occurred. Outcrossing rates ranged from 0 to >1 for diploid and tetraploid families, and the mean values were quite similar (0.696 and 0.633, respectively, for T. mirus and T. dubius) and higher than those estimated for natural populations, suggesting that some outcrossing events in both species, and especially the diploid T. dubius, had gone undetected (Cook and Soltis, 2000). If the outcrossing rates estimated from the artificial arrays are more accurate than are those from natural populations, the discrepancy between predictions and results may be attributable to the recent ancestry of T. mirus (most likely post-1928; Ownbey, 1950; Soltis et al., 1995) and to the limited time for the mating systems to have diverged.

THE GENETIC IMPLICATIONS OF RECURRENT POLYPLOID FORMATION

The application of isozyme analysis and DNA techniques to the study of polyploid ancestry dramatically altered our view of polyploid origins. Although morphological or cytological differences among populations of a few polyploid species suggested evidence of repeated polyploid formation (see example in Ownbey, 1950), most polyploid species, until recently, were considered to have had a unique origin. Nearly all polyploid species of plants that have been examined with molecular markers have been shown to be polyphyletic, having arisen multiple times from the same diploid species (reviewed in Soltis and Soltis, 1993, 1999; Soltis et al., 1992). Polyphyletic polyploid species have been reported for mosses



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