How does natural selection relate to differentiated reproductive success?

If individuals exhibiting variation A of a trait are demonstrated to reach reproductive age more often and produce more offspring than individuals with variation B of the same trait, the differential reproductive success rate allows you to infer that natural selection is at work and that variation A is advantageous—at least for conditions at the time. Those individuals with variation A will deliver more genetic material for that trait to the next generation, making it more likely to persist and carry on to future generations. Variation B, meanwhile, is likely to gradually vanish.

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