There are two ways eukaryotes double number of chromosomes: (1) whole genome duplication (polyploidy), in which all nuclear DNA is replicated, and (2) karyotypic fission (pseudopolyploidy), in which all chromosomes are physically bifurcated. We contrast polyploidy with pseudopolyploidy, highlighting when it is crucial to look at genetic vs. genomic levels. We review history of pseudopolyploidy, including recent mechanisms by which chromosomal bifurcation may occur and outline methods for detecting such genomic changes. We then delve into the evolutionary implications, with particular focus on adaptive potential, of these two forms of doubling chromosome numbers. We address the common assertion that polyploidy induces adaptive radiations, which contains three fallacies. First, while polyploidy causes quantum speciation, evolutionary theory implies that these radiations should be non-adaptive. Polyploidy causes reproductive isolation, minute effective population sizes, and increased mutation rates, which all imply a diminished role for selection. Second, due to lack of karyotyping in recent decades and lack of distinction between genomic and genetic effects, it is usually impossible to detect pseudopolyploids. Third, pseudopolyploids lack minority cytotype exclusion because they readily backcross with their progenitors, which thereby means no reproductive isolation for newly formed pseudopolyploids. Pseudopolyploidy will thereby not result in radiations until pseudopolyploid descendants undergo subsequent chromosome rearrangements or grow new centromeres. Pseudopolyploids may have a modest selective advantage over their progenitors due to diminished linkage disequilibrium. Thus, pseudopolyploidy may induce adaptive non-radiations. We encourage a renaissance of karyotyping to distinguish between these two mechanisms and a renaissance in genomic perspectives in evolution. J. Exp. Zool. (Mol. Dev. Evol.) 320B:286–294, 2013. © 2013 Wiley Periodicals, Inc.