Children receive one copy of each paired chromosome from each parent. It follows that if one parent has two copies of a dominant gene, every one of their children will receive at least one copy, regardless of what the other parent has. All children of this mother and father will have brown eyes, if even one parent has two brown eye alleles, and even if the other parent has two blue eye alleles.
If both parents have one brown and one blue allele, then for any particular child, there’s a 1 in 4 chance of receiving two brown alleles, a 1 in 4 chance of receiving two blue alleles (the only case that will result in blue eyes), and a 2 in 4 chance of receiving one brown and one blue allele (hence brown eyes). If one parent has blue eyes, and the other has both a brown and a blue allele, then the odds are 50/50 for each of their children to have either brown or blue eyes. So if one or both parents have brown eyes, it’s possible for them to have blue-eyed children. But when both parents have blue eyes, so all of their alleles are for blue eyes, all of their children will have blue eyes. In that case, if any child has brown eyes, it must be the case that one parent – most likely the male – is not the biological parent. Oops.
So a blue-eyed man has an interesting advantage over men with brown eyes – a very dependable way of knowing that he is not the father of a particular child, provided he mates with a blue-eyed woman. Further, a blue-eyed man who regards blue-eyed women as more attractive than women of other eye colors is more likely to mate with blue-eyed women. And so such a blue-eyed man has a selective advantage over other blue-eyed men who have no such preference (or a preference for brown-eyed women).
This would be advantageous, at least in prehistoric times, if in addition such a man was less inclined to provide for a child without blue eyes – even if there was no conscious recognition that the child could not be his own. Some recent research has indicated that blue-eyed men sometimes actually, if unconsciously, do have a tendency to regard blue-eyed women as more “attractive”, and hence (presumably) are more likely to choose them as mates:
Both blue-eyed and brown-eyed women showed no difference in their preferences for male models of either eye color. Similarly, brown-eyed men showed no preference for either blue-eyed or brown-eyed female models. However, blue-eyed men rated blue-eyed female models as more attractive than brown-eyed models.