Answer:
Over Production Of Offspring
Overpopulation doesn't necessarily have to occur in order for Natural Selection to happen within a population, but it must be a possibility in order for the environment to put selective pressure on the population and some adaptations to become desirable over others.
Variation
Increased variation of traits in a population actually increases the likelihood of survival of a species as a whole. Even if part of a population is wiped out due to various environmental factors (disease, natural disaster, climate change, etc.), it is more likely that some individuals would possess traits that would help them survive and repopulate the species after the dangerous situation has passed.
Selection
This is one of the factors that can actually change during the lifespan of an individual in a species. Sudden changes in the environment may happen and therefore which adaptation is actually the best one would also change. Individuals that were once thriving and considered the "fittest" may now be in trouble if they are no longer suited as well to the environment after it changes.
Reproduction of Adaptations
Individuals that possess those favorable traits will live long enough to reproduce and pass down those traits to their offspring. On the other side of the coin, those individuals that lack the advantageous adaptations will not live to see their reproductive periods in their lives and their less desirable characteristics will not be passed down.
This changes the allele frequency in the population's gene pool. There will eventually be less of the undesirable traits seen as those poorly suited individuals do not reproduce. The "fittest" of the population will pass down those traits during reproduction to their offspring and the species as a whole will become "stronger" and more likely to survive in their environments.
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