Green-beard effects are genes that:
- Produce an effect that can be detected
- Produce preference to others with the same effect
Are there any examples of this in humans?
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Your examples are way too broad. A green-beard effect only applies to the effects of a single gene or group of linked genes, not to just any trait. Racism and your Mongol war example are too complex to be explained by this effect. In reality examples will mostly be found in single-celled organisms where expression of a single protein can have whole-organism effects such as causing aggregation, or in larger organisms where some highly visible effect is possible such as a colour change.
There are very few real known examples of the green-beard effect, but four are listed on the Wikipedia page: