Phylogenetic reconstructions are often plagued by difficulties in distinguishing 
phylogenetic signal (due to shared ancestry) from phylogenetic noise or 
homoplasy (due to character-state convergences or reversals). We use a new 
interpretive hypothesis, termed hemiplasy, to show how random lineage sorting 
might account for specific instances of seeming "phylogenetic discordance" among 
different chromosomal traits, or between karyotypic features and probable 
species phylogenies. We posit that hemiplasy is generally less likely for 
underdominant chromosomal polymorphisms (i.e., those with heterozygous 
disadvantage) than for neutral polymorphisms or especially for overdominant 
rearrangements (which should tend to be longer-lived), and we illustrate this 
concept by using examples from chiropterans and afrotherians. Chromosomal states 
are especially powerful in phylogenetic reconstructions because they offer 
strong signatures of common ancestry, but their evolutionary interpretations 
remain fully subject to the principles of cladistics and the potential 
complications of hemiplasy.