This study reveals that the mitochondrial diversity of a given animal species does not reflect its population size: No correlation between mtDNA polymorphism and species abundance could be detected, despite the large body of data analyzed. Nuclear data, in contrast, are fairly consistent with intuitive expectations. We conclude that natural selection acting on mtDNA contributes to homogenization of the average diversity among groups, in agreement with the genetic draft theory. mtDNA appears to be anything but a neutral marker and probably undergoes frequent adaptive evolution, e.g., direct selection on the respiratory machinery, nucleo-cytoplasmic coadaptation, two-level selection, or adaptive introgression, perhaps hitchhiking with a maternally transmitted parasite. mtDNA diversity is essentially unpredictable and will, in many instances, reflect the time since the last event of selective sweep, rather than population history and demography. Low-diversity mitochondrial lineages, typically disregarded as important from a conservation standpoint, might sometimes correspond to recently selected, well-adapted haplotypes to be preserved (Bazin et al. 2006:571-572,).
Similar to but not the same as another study that concludes a similar thing. I’ve found quite a few items now that show this.