Polyploidy is widely acknowledged as a major mechanism of adaptation and sp
eciation in plants. The stages in polyploid evolution include frequent fert
ility bottlenecks and infrequent events such as gametic nonreduction and in
terspecific hybridization, yet little is known about how these and other fa
ctors influence overall rates of polyploid formation. Here we review the li
terature regarding polyploid origins, and quantify parameter values for eac
h of the steps involved in the principal pathways. In contrast to the commo
n claim that triploids are sterile, our results indicate that the triploid
bridge pathway can contribute significantly to autopolyploid formation rega
rdless of the mating system, and to allopolyploid formation in outcrossing
taxa. We estimate that the total rate of autotetraploid formation is of the
same order as the genic mutation rate (10(-5)), and that a high frequency
of interspecific hybridization (0.2% for selfing taxa, 2.7% for outcrossing
taxa) is required for the rate of tetraploid formation via allopolyploidy
to equal that by autopolyploidy. We conclude that the rate of autopolyploid
formation may often be higher than the rate of allopolyploid formation. Fu
rther progress toward understanding polyploid origins requires studies in n
atural populations that quantify: (a) the frequency of unreduced gametes, (
b) the effectiveness of triploid bridge pathways, and (c) the rates of inte
rspecific hybridization.