Eye colour is determined by a single factor – melanin. This is the same pigment that determines human skin and hair colour.
Eyes colour does not come in discrete categories like “blue”, “green, or “brown”, but in a spectrum ranging from pale blue* to dark brown. What we call green is in the middle.
Several genes contribute to eye colour, all by affecting melanin pathways and the regulation of other genes.
So I would guess that “green” eyes are relatively rare because there is a narrow range of melanin concentrations that give that effect, and a small combination of alleles that underlying that.
*Or albino if you lack melanin at all.
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Sturm RA, Larsson M. Genetics of human iris colour and patterns. Pigment Cell Melanoma Res. 2009 Oct;22(5):544-62. doi: 10.1111/j.1755-148X.2009.00606.x. Epub 2009 Jul 8. Review. PubMed: 19619260.
White D, Rabago-Smith M. Genotype-phenotype associations and human eye color. J Hum Genet. 2011 Jan;56(1):5-7. doi: 10.1038/jhg.2010.126. Epub 2010 Oct 14. Review. PubMed: 20944644
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