Effective sizes and dynamics of uniparentally and diparentally inherited genes

Models to determine the temporal dynamics and spatial heterogeneity for maternally and paternally inherited genes were derived for populations that may or may not exhibit spatial subdivision. Results were compared to those for diparentally inherited genes. The models permit definition of parameters for mean and variance of litter sizes, breeding group (subpopulation) sizes, and numbers of female mates per male, dispersal rates, and multiple paternity. Exact solutions for asymptotic effective size and spatial divergence (FLS) for maternal and paternal genes are derived. It is shown that solutions for effective size and FLS are transformations of the same quadratic equation. When compared to values for diparentally inherited genes, it is shown that effective sizes for maternal genes may be considerably higher when female dispersal is low as in many mammalian taxa. Likewise, effective sizes for paternal genes may be higher than for diparentally inherited traits when male dispersal is relatively low, as in many species of birds. The traditional assumption that the effective size for maternal genes is approximately equal to the number of females is seldom realized. Spatial heterogeneity and temporal dynamics of genes are inextricably linked as is shown by the interdependency of effective size and spatial heterogeneity.