In England based on Beddoe’s observations the frequency of light eyes among redheads is higher than the general population (~64%) but not as high as with blond hair. Distinctive red hair has to be fairly light and lighter hair and eyes are correlated. Darker eyes (brown to hazel) and red hair or even blond is still far from uncommon and you can see here:
In dark pigmented populations redheads may be much lighter eyed than the general population. Livi's Italian recruits with red hair were very significantly lighter than average. 50.2% of the recruits with red hair had light or intermediate eyes against 30.9% of the overall series. In Italy brown-black hair (Fischer-Saller U-Y) that is too dark to show a notable reddish tint is the strong majority. The red individuals would have to have at least medium brown hair. In Northern/Central Europe by contrast the most people are at least as light haired as dark auburn if not lighter auburn hair. The rule appears to be that the lighter haired a population the less difference in eye color from the overall population among is redheads and more obviously with blonds.
Italy:
This should make it clear that in a population as light haired as British redheads could not be so much lighter eyed as to make darker eyes especially uncommon.
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