First, females may prefer mates that are similar to themselves. If you think about this, you may ask how a pigeon can figure out what color she is, since she doesn't have a mirror! Ecologists suggest that a female chooses a mate who is similar to her parents - and, of course, parents are likely to be similar to the female herself. Thus, if pairs in a flock are the same color and their offspring look just like them, then a "culture" might develop where pigeons always choose a mate of their parents' and their own color.
If pigeons of like color morphs always mate, then morphs that are genetically dominant will not "drown out" the other morphs over time. This hypothesis suggests that, all else being equal, color morphs will remain in fairly constant proportions over time. To test this hypothesis, we could examine the proportions of morphs in the same flocks over many years. If the proportions of colors remain constant, then some support for this idea exists. If, however, the proportions change over time, this doesn't mean that mate choice doesn't have an influence on pigeon-color variation.
A second suggestion is that females choose males that are unusualso-called "rare males." If females prefer rare males, then these males will always have mates, and thus they may have more offspring compared with males that are common. Unlike the first idea, this rare-male phenomenon will probably cause changes over time in the proportions of colors because the once-rare males will become common and females will choose the "new" rare color morphs.