We know pretty much exactly when and how lactase persistence evolved in Europe and in other pastoralist societies.

I wrote a whole chapter on this in A Brief History of Everyone Who Ever Lived. https://twitter.com/qikipedia/status/1309470204938911745
They were of course able to *drink* milk, just unable to digest milk in adulthood before the evolution of lactase persistence. Before that, they were eating soft cheeses and yoghurts, in which the sugar lactose is already broken down.
The mutation itself is not in the gene LCT itself, but around 13,000 base pairs upstream in a control region; this C>T change accounts for the majority of lactase persistence.
This as a classic example of how we have invoked shifts in our genome with our own practices – gene-culture co-evolution. The mutation occurred around 7000 years ago, and at different times in other pastoralist communities around the world.
White supremacists got hold of this phenomenon a few years ago, and milk chugging became a thing. Neo-Nazis downing gallons of milk to demonstrate their racial purity. Arch-racist hatefool Richard Spencer had a glass of milk emoji in his twitter handle.
The joke is of course on them, as ever. LP is common in many African populations and Middle Eastern camel herders. And racial purity is a myth.

This is all in my book #HowToArgueWithARacist, link in my bio.
You can follow @AdamRutherford.
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