Parent-offspring regression has often been used for the estimation of breeding value and narrow-sense heritability in experimental populations, particularly for diploid species with regular disomic inheritance. With polysomic inheritance, estimates of heritability based on parent-offspring regression are expected to be systematically biased, particularly when intra- and inter-generation ploidy polymorphisms occur as a result of unusual megasporogenesis. Measuring the discrepancy between true and estimated heritability has important theoretical and practical implications for the genetic improvement of plantain and bananas. In this regard, formulas were developed to describe the relationships between parental and filial generations with different ploidy states and this information was used to estimate heritability for several traits of plantains and bananas. This approach may be extended to other polysomic species with similar meiotic behaviour and ploidy polymorphism. © 2012 Elsevier B.V.