First, the study replicates the common finding of some differences in perceived dominance between blue vs. brown-eyed males. But, they observed that when the eye colors were digitally manipulated the dominance ranking did not change. In other words the eye colors seem to have correlated with other traits of masculinity, rather than been a causal signal. The authors offer up a model whereby socialization of blue eyed individuals for longer periods as children (because the trait is neotenous) produces less facial masculinization. But I don’t buy the idea that this couldn’t be genetically mediated by variation on the HERC2/OCA2 locus (where most blue vs. non-blue eye color variation is controlled). In particular, I believe there’s a body of literature that melanin and testosterone production pathways affect each other so that there is a positive correlation, though the exact causal connections are still to be worked out. Note that all this only applies within populations; between population complexion differences don’t necessarily predict dominance differences because the genetic variates are not controlled as they are within populations.