Genetic drift occurs as a result of chance events causing changes in the allele frequency of a population. It doesn't favor the most fit individuals, but occurs at random.

Mutations can contribute to genetic drift, however, genetic drift is a more specific answer and more relevant to the question at hand.

Genetic drift is the random process of alleles being passed from parents to offspring. Increasing genetic diversity in a population requires introducing a greater number of alleles, which can only occur through mutations or addition of unrelated members to the population. Genetic drift only affects how already-existing alleles are passed down.

If an allele has a high frequency at baseline, the chance of it being passed down to subsequent generations is higher than alleles of a lower frequency. Through random chance, a high-frequency allele can eventually have a frequency of 100%, becoming fixed in the population. Conversely, a low-frequency allele can eventually disappear from the population if none of the few parents who possess that allele happen to pass it onto their offspring.

Genetic drift describes the random selection of alleles that are passed from one generation to the next due to independent assortment in gametogenesis. Genetic drift cannot create new alleles, so it cannot increase genetic diversity (the number of alleles in a population). It can, however, decrease genetic diversity if an allele of a low frequency is not passed down to subsequent generations due to pure chance.

There is no hard and fast rule for whether genetic drift or natural selection have had a greater effect on shaping populations. Both have greatly shaped the populations present on Earth today, but their relative importance varies between species and has also varied over time. The conditions of Hardy-Weinberg equilibrium require that both natural selection and genetic drift be negligible. If genetic drift is occurring, then the population cannot be in Hardy-Weinberg equilibrium.

Small populations tend to have less genetic variation to begin with. Introducing a bottleneck effect further reduces variation and population size, amplifying the effect of genetic drift. This leaves them susceptible to changes in the environment that they may not be capable of adapting to due to limited differences among individuals.

A bottleneck effect is the term used to describe the loss of genetic variation that occurs after outside forces destroy most of a population. The few individuals left to reproduce pass their traits on to all of their offspring, which then may thrive without the competition of a large population. Eventually, there may be a large, very genetically similar population based on the traits of the few original survivors.

The founder effect describes the low genetic variation of a population derived from a small group of individuals in a new geographic location. Genetic drift is the random change of allele frequency in a population.

The bottleneck effect describes the phenomenon when a population has a sudden reduction in the gene pool due to natural environmental events, natural disasters, disease, or human involvement. This reduction in the gene pool will likely cause a bias that did not exist in the original population. For example, suppose a population of birds has a small number with a mutation making them unable to fly. If a disease reaches this population that kills all birds when they reach an altitude above 50m, then the gene pool of the population will suddenly shift to favor the flightless birds.

The bottleneck effect, after a long time, could potentially lead to speciation, but this is not a defining factor of the effect. Introducing a new species can increase the pressures of natural selection, but does not directly relate to the bottleneck effect. A decrease in genetic variety due to a small number of individuals from a larger population establishing a new population more aptly describes the founder effect.

The bottleneck effect describes the sudden, sharp decrease in the size of a population. After a bottleneck event, a population could either recover or go extinct depending on the fitness of the individuals remaining in the population.

Depending on the type of event that created the bottleneck, it is possible that the surviving members are the most fit, but this is not always the case. The new smaller population likely has less genetic diversity, which typically makes successful adaption more difficult and less likely, but if the surviving members of the population are highly fit, their ability to adapt may not be hindered.

While man-made events certainly are a source of bottleneck effects in the world today, there are still natural bottleneck events and no concrete evidence to say that man-made bottleneck events are more frequent or have more of an effect on genetic drift than natural events.

The founder effect describes the phenomenon when a smaller group that originally came from a part of a larger population forms their own population. This new population will likely have a biased gene pool that will not be identical to the parent population. For example, if a certain species of bird gains a mutation such that some members are capable of flying farther, these birds may eventually separate to a different location and form their own unique population with a higher predominance of the "sustained flight" mutation than the original population.

The founder effect, after a long time, can lead to speciation, but this is not an essential part of the founder effect. Introducing a new species to native populations may influence the balance of the ecosystem and change genetic frequencies, but is not linked to the founder effect. A decrease in genetic variety due to fluctuation of certain traits would more aptly describe the bottleneck effect.

The founder effect describes a scenario in which a new population is started by a small group from a larger population. This smaller population is most likely not representative of the larger group and displays certain genetic bias. The high rate of Huntington's disease is most likely a result of the fact that the small group of European colonists had a high rate of the gene that produces the disease.

Natural selection and sympatric speciation do not apply in this situation. The bottleneck effect occurs when a large population is thinned, and a non-representative group of the original population is all that remains; this does not describe the situation presented above. 

A smaller group being separated permanently from a larger population is a classic example of the founder effect. These 500 members likely have far less genetic diversity than the larger population, so the subsequent population that develops will only contain alleles found in these 500 members.

The founder effect is a particular example of the bottleneck effect, wherein the number of individuals in a population is reduced very quickly from a non-selective pressure, such as a natural disaster or geographic barrier. Though the rest of the larger population is presumably still alive, these 500 people have gone from living in a large population to living in a relatively small one. The result is a decrease in genetic diversity when the smaller portion of the population is compared to the previously-existing larger group.

In the immediate future, this group could experience genetic drift wherein the relative frequencies of their alleles shift due to random chance. Genetic drift is more prominent in smaller groups, and would therefore help to understand what could happen in the population's immediate future. Since the group is relatively small, we could expect to see the results of genetic drift as early as fifty years after the separation event.

Natural selection occurs over many generations and longer time periods. It would not help us to understand the immediate future of this new population.