Natural selection occurs given heritability, variation, significant population growth and individual differences in survival and reproduction. Despite its common definition as survival of the fittest, natural selection has more to do with reproductive success than survival.
Not all traits depend strongly on inheritance from one generation to the next, but rather on environmental factors. For natural selection to occur in a population, factors that are strongly heritable from parents to offspring must exist, as these are the traits that natural selection acts upon. Natural selection also requires that a population show variation in its traits. For example, a population of animals with no individual differences in fur length is not conducive to natural selection.
The growth of the population in question must be high for the occurrence of natural selection; in order for there to be a reproductive or survival advantage, there must be a high enough population to require competition for resources. Finally, natural selection occurs when some individuals in a population have a higher chance of reproducing or surviving.
Organisms need not have higher rates of survival to be favorable in natural selection; they must only be better at reproduction. For example, perhaps a certain population of birds contains bright blue males and dull blue males. Both color variations could survive equally well, but if bright blue males have a higher chance of attracting mates and reproducing, natural selection favors the bright blue trait.