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Eye color comes from a pigment known as melanin, a brownish pigment, present in the iris of a person. It is the amount of melanin present in the iris that confers the color to a particular eye. The genetics of eye color is quite complex and not completely understood.
In this article the genetics behind blue eyes will be explained based on a simplified model of two different genes. It is a basic and convenient model to explain blue eye genetics (and also the genetics behind green and brown eyes). In reality several genes are responsible for eye color.
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Blue Eye Genetics
There are two genes located at different loci. One gene, called B for simplicity, confers brown eye color, and it is dominant over the b allele (recessive) which gives rise to the blue eye color. The other gene, named G, also has two alleles: G (dominant for green) and g (recessive) for lighter greenish colored eyes.
Considering these two genes (B and G), and the fact that people have two copies of a gene (one from mom and one from dad) and that B is dominant over b, G dominant over g, and that the gene B is dominant over G, the genotype for true blue eyes must be bbgg.
To evaluate the possibilities of eye colors based on this simple two gene model we can build up a matrix (called Punnett Square) for a cross between parents who have the dominant and recessive alleles of both genes. It is also assumed that these two genes segregate independently, that is, that each one behaves independently of the other (this assumption is valid if they are located on different chromosomes for example). This model gives rise to sixteen possibilities of alleles at the two loci combined and segregated independently.
According to this model the presence of a B allele will give brown eyes because of its dominance. There are 12 possible genotypes for brown eyes (see Punnett square), 2 for green eyes (bbGG, bbGg), and one for blue eyes (bbgg).
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The Model is not Perfect
Although this is a very simple model that helps explain what lies behind blue eye genetics, it is not complete. For example, there are brown-eyed children who descend from blue-eyed parents (mistaken fatherhood has been genetically ruled out).
According to this model brown-eyed children would require the presence of a B allele which is not possible because none of the parents has it in their genotype (blue eyes: bbgg)
One explanation may be that that the parents in this case are of the bbGg genotype and that this genotype is manifested as a light blue eye instead of green eyes. Then, a child could have a bbGG genotype where the presence of the two G alleles will give rise to brown eye color instead of green.
Sulem et al. 2007. Genetic determinants of hair, eye and skin pigmentation in Europeans Nature Genetics 39, 1443 - 1452.