Robustness of genetic diversity measures under spatial sampling and a new frequency-independent measure

The genetic diversity of a taxon has often been estimated by genetic diversity measures. However, they assume random sampling of individuals which is often inapplicable. Except when the distribution of the taxon is limited, researchers conventionally choose several sampling locations from the known distribution and then collect individuals from each location. Spatial sampling is a formalized version of the conventional sampling, which objectively provides geographically even sampling locations to cover genetic variation in a taxon assuming isolation by distance. To evaluate the validity of the spatial sampling in estimating genetic diversity, we conducted coalescent simulation experiments. The sampling locations were selected by spatial sampling and one sample was collected from each location for the sake of theoretical simplicity. We also devised a new measure of genetic diversity, ς, which assumes spatial sampling and is independent of allele frequency. This new measure places an emphasis on rare and phylogenetically distant alleles which have relatively small effect on nucleotide diversity. Therefore, it can complementarily serve for conservation studies although it cannot be used to estimate population mutation rate. We compared ς with the other diversity measures in the experiments. Nucleotide diversity, expected heterozygosity and ς showed within 3% relative biases on average while Watterson's theta was 31% overestimation on average. Thus, genetic diversities other than Watterson's theta held good robustness under the spatial sampling.