Dark-eyed Europeans were more likely to leave for the colonies (data)
The Europeans who left for America, Canada, and Australia were obviously not a representative sample of their home populations. Since they were not plucked at random by a Martian lab scientist, there must have been something different about them that made them want to leave. We can imagine all sorts of socioeconomic factors influencing this decision, but let's not forget that some people just have a greater sense of wanderlust than others.
In populations where eye and hair color vary a decent amount, like Northern Europe, correlational studies show that children with lighter eyes or hair tend to be more socially nervous, less exploratory in social situations. When we humans domesticated animals, their coat and eye colors lightened up (even if only partially, like large patches of white). Something similar probably happened when Europeans domesticated themselves, as they had to settle down in order to farm well. Looking at it the other way, the darker-colored ones like Christopher Marlowe must have had wilder personalities compared to their countrymen.
It's not very hard to see that Americans and Australians are a lot more sprawling and rambunctious than the British, and even Canadians are closer to the former than the latter. I've always wondered why there is such a disconnect between North Americans and the British on the topic of dark Irish or Scottish beauties. We seem to have a lot of them here, while those in Scotland and Ireland swear there's no such thing, that we Americans must be delusional. (It seems like there's more agreement on the presence of handsome, darker-looking Irish and Scottish men in the UK.)
Maybe, I thought, the colonies drew away the Europeans with darker eyes and hair? It would fit with the picture of lighter hair and eyes being associated with a less roaming social nature. Fortunately GameFAQs ran a poll on the eye color of its users. These are mostly 20-something males who are into video games. I collapsed blue, gray, and green into a single "light" category. Nation-level data were available for some parts of the world, including three Northwestern European countries and three former Anglo colonies. Here is the percent who have light eyes within each:
The clear and big split is between the homeland populations and their colonial offshoots. Notice how little variation there is within each of the two clusters -- mid-50s for Northwestern Europe, upper 30s for the former colonies. The lower numbers outside of Europe are not due to the greater presence of Southern Europeans, Africans, Asians, etc. If that were true, it would imply that the Northern European populations of all three former colonies were only about 2/3 of the entire country. In the US, it's somewhere in the 70-80% range, in Canada in the 80-90% range, and in Australia about 90%. (The US may look so similar to Canada and Australia in this poll, despite having more dark-eyed people, if the American users of GameFAQs are mostly white. The website has never run a poll on race or ethnicity.)
So little data is collected on eye color that I'm sure this is the first demonstration that the colonists who set off from Northwestern Europe were darker-eyed than those they were leaving behind. It fits with the tiny number of studies done on eye / hair color and personality. And it also helps explain why Americans and Britons can disagree so much on the prevalence of dark Celtic beauties -- looks like we have a lot more of 'em outside of the UK.