An example of natural selection is the red color of a male cardinal. The females of the species choose mates based on the vibrant colors of the males' feathers. If females begin using different criteria than feather color when they choose mates, what would most likely happen to the tails of peacocks over time?

Decreased variation in the shades of red because no form of the trait is advantageous.

Explanation:

Natural selection may be defined as the differential reproduction and survival of the individual due to their differences in the phenotype. Natural selection acts as the main driving force for evolution.

The male cardinal red color gets change or may show variation as it is no longer used by them to attract the females. The red shade variation get decreases and may get changed over time. The red color trait is non advantageous and get extinct with time.

If female's species would chose their mates using different criteria other than feather, it may lead to decrease in variation in tail feather color because the only reason for the variation was selection pressure.

Explanation:

The opposite gender for mating are chosen based on specific criteria like color of feathers, eye color etc ... The selection of opposite gender is the natural selection considering the red color of the male cardinal. This red color male cardinal which depends only on the sexual selection pressure will now reduce. As this was now neutralized it may lead to decreased variation.