Abstract
Eusocial insects have higher diploid chromosome numbers than most of their closest phylogenetic relatives, and cockroaches (Blattidae) with gregarious offspring have higher 2N than do those with dispersed young. Increases in 2N may cause the within-brood distribution of sib-sib genetic relatedness to become continuous and reduce variance around the mean relationship. Convergence of actual genotypic similarities on the mean may reduce the likelihood that sterile workers will discriminate among sibs in need of assistance on the basis of their actual relatedness. Whereas offspring do not appear to gain or to lose from increases in the number of chromosomes, queens might benefit from such increases if those with cooperative broods outreproduce those with less cooperative, more discriminating offspring.