a male cardinals red flag is an example of a trait affected by natural selection. The females of the species choose mates based on 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 color of the male cardinals over time?

Decreased shade variation of red color because no trait form is now advantageous.

Explanation:

Earlier females choose mates based on vibrant colors of male feathers, therefore, there was a selection pressure on males to evolve the trait so that they get their mate and pass their genes to the next generation.

So when females switched to other criteria other than feather color to get their mate then the importance of color trait gets reduced and the trait becomes non-advantageous for male cardinal.  

Therefore due to this change, there is no longer necessity remained to evolve the color trait so the shade variation will decrease over time as now no trait form remained advantageous for this bird species.

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