Mean d(2) and divergence time: transformations and standardizations

The fitness consequences of inbreeding and outbreeding have intrigued biologists for a long time. Recently a measure of relatedness of parental haplotypes has been proposed called mean d(2). This measure is based on a stepwise mutational process and therefore is tailored to microsatellite genetic markers. Theoretical work suggests that mean d(2) typically is less suited for measuring fitness consequences due to close inbreeding rather than heterozygosity. However, mean d(2) may be more appropriate than heterozygosity for measuring divergence times over longer time scales and thus for detecting outbreeding depression. Here, simulations are used to (1). identify appropriate standardization coefficients and transformations for mean d(2), and (2). evaluate mean d(2) as a measure of divergence time of parental lineages over time scales up to 10000 generations. Results show that mean d(2) is a linear predictor of divergence time. The coefficient of variation of mean d(2) approaches a constant value with increasing divergence time and therefore logarithm transformation is appropriate to restore homoscedasticity. When mutation rates and sizes are known for each locus they can be incorporated into a standardization coefficient to increase the precision of mean d(2). As few as 10 loci can explain more than 70% of the variation in divergence time between lineages. While heterozygosity outperforms mean d(2) at detecting differences in divergence time over relative short time periods (or=1000 generations). However, gene flow of as little as 1% per generation can significantly reduce the ability of either mean d(2) or heterozygosity to estimate divergence time.