ABSTRACT
Several methods have been proposed to test for introgression across genomes. One method tests for a genome-wide excess of shared derived alleles between taxa using Patterson’s D statistic, but does not establish which loci show such an excess or whether the excess is due to introgression or ancestral population structure. Several recent studies have extended the use of D by applying the statistic to small genomic regions, rather than genome-wide. Here, we use simulations and whole genome data from Heliconius butterflies to investigate the behavior of D in small genomic regions. We find that D is unreliable in this situation as it gives inflated values when effective population size is low, causing D outliers to cluster in genomic regions of reduced diversity. As an alternative, we propose a related statistic 
a modified version of a statistic originally developed to estimate the genome-wide fraction of admixture. 
is not subject to the same biases as D, and is better at identifying introgressed loci. Finally, we show that both D and 
outliers tend to cluster in regions of low absolute divergence (dXY), which can confound a recently proposed test for differentiating introgression from shared ancestral variation at individual loci.
