# Genetic drift

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In population genetics, genetic drift (or more precisely allelic drift) is the process of change in the gene frequencies of a population from one generation to the next due to statistical phenomena in which purely chance events determine which alleles (variants of a gene) within a reproductive population will be carried forward while others disappear. The statistical effect of random sampling of certain alleles from the overall population may result in an allele, and the biological traits that it confers, to become more common or rare over successive generations. The concept was first introduced by Sewall Wright in the 1920s, and is now held to be one of the primary mechanisms of biological evolution. It contrasts with natural selection, a non-random selection process in which the tendency of alleles to become more or less widespread in a population over time is due to the alleles' effects on adaptive and reproductive success.

Chance affects the commonality or rarity of an allele because an organism's survival and reproductive success is subject to other factors besides adaptive pressures. When chance events preserve the survival of randomly selected organisms of a given population, and the resulting allele frequency of the surviving group differs statistically from allele frequencies in that original population, the evolution occurs as a statistical phenomenon rather than selective phenomenon. When in such cases the frequency distribution in the survivors differs from the frequency distribution of the original population, the evolutionary result is due to the effect of sampling error and probability.

Genetic drift depends strongly on population size as a consequence of the law of large numbers. When many individuals carry a particular allele, and all face equal odds, the number of offspring they collectively produce will only slightly differ from the expected value, which is the expected average per individual times the number of individuals. But with a small effective breeding pool, a departure from the norm in even one individual can cause a disproportionately greater deviation from the expected result. Therefore small populations are more subject to genetic drift than large ones.[1] This is also the basis for the founder effect, a proposed mechanism of speciation.

By definition, genetic drift has no preferred direction. A neutral allele may be expected to increase or decrease in any given generation with equal probability. Given sufficiently long time, however, the mathematics of genetic drift (cf. Galton-Watson process) predict the allele will either die out or be present in 100% of the population, after which time there is no random variation in the associated gene. Thus genetic drift tends to sweep gene variants out of a population over time, such that all members of a species would eventually be homozygous for this gene. In this regard, genetic drift opposes genetic mutation which introduces novel variants into the population according to its own random processes.

## Allele frequencies

Simulations of genetic drift for 20 alleles with initial frequency 0.5, for populations of size N=10 and 100, respectively. In general, alleles drift to fixation (frequency of 0 or 1) significantly faster in smaller populations.

From the perspective of population genetics, drift is a "sampling effect." To illustrate: on average, coins turn up heads or tails with equal probability. Yet just a few tosses in a row are unlikely to produce heads and tails in equal number. The numbers are no more likely to be exactly equal for many tosses in a row, but the discrepancy in number can be very small (in percentage terms). As an example, ten tosses turn up at least 70% heads about once in every six tries, but the chance of a hundred tosses in a row producing at least 70% heads is only about one in 25,000.

Similarly, in a breeding population, if an allele has a frequency of p, probability theory dictates that (if natural selection is not acting) in the following generation, a fraction p of the population will inherit that particular allele. However, as with the coin toss above, allele frequencies in real populations are not probability distributions; rather, they are a random sample, and are thus subject to the same statistical fluctuations (sampling error).

When the alleles of a gene do not differ with regard to fitness, on average the number of carriers in one generation is proportional to the number of carriers in the previous generation. But the average is never tallied, because each generation parents the next one only once. Therefore the frequency of an allele among the offspring often differs from its frequency in the parent generation. In the offspring generation, the allele might therefore have a frequency p', slightly different from p. In this situation, the allele frequencies are said to have drifted. Note that the frequency of the allele in subsequent generations will now be determined by the new frequency p', meaning that drift is a memoryless process and may be modeled as a Markov process.

As in the coin toss example above, the size of the breeding population (the effective population size) governs the strength of the drift effect. When the effective population size is small, genetic drift will be stronger.

Drifting alleles usually have a finite lifetime. As the frequency of an allele drifts up and down over successive generations, eventually it drifts until fixation - that is, it either reaches a frequency of zero, and disappears from the population, or it reaches a frequency of 100% and becomes the only allele in the population. Subsequent to the latter event, the allele frequency can only change by the introduction of a new allele by a new mutation.

The lifetime of an allele is governed by the effective population size. In a very small population, only a few generations might be required for genetic drift to result in fixation. In a large population, it would take many more generations. On average, an allele will be fixed in ${\displaystyle 4N_{e}}$ generations, where ${\displaystyle N_{e}}$ is the effective population size.

According to the Hardy-Weinberg Principle, which holds that allele frequencies in a gene pool will not change over time, a population must be sufficiently large to prevent genetic drift from changing allele frequencies over time. This is why the law is unstable in a small population.

## Drift versus selection

Genetic drift and natural selection rarely occur in isolation from each other; both forces are always at play in a population. However, the degree to which alleles are affected by drift and selection varies according to circumstance.

In a large population, where genetic drift occurs very slowly, even weak selection on an allele will push its frequency upwards or downwards (depending on whether the allele is beneficial or harmful). However, if the population is very small, drift will predominate. In this case, weak selective effects may not be seen at all as the small changes in frequency they would produce are overshadowed by drift.

## Genetic drift in populations

Drift can have profound and often bizarre effects on the evolutionary history of a population. These effects may be at odds with the survival of the population.

In a population bottleneck, where the population suddenly contracts to a small size, genetic drift can result in sudden and dramatic changes in allele frequency that occur independently of selection. According to the Toba catastrophe theory this occurred in the history of human evolution. In such instances, many beneficial adaptations may be eliminated even if population later grows large again.

Similarly, migrating populations may see a founder effect, where a few individuals in the originating generation with a rare allele can produce a population that has allele frequencies that seem at odds with natural selection. Founder's effects are sometimes held to be responsible for high frequencies of some genetic diseases.

## References

• Hardy, G. H. (1908). "Mendelian proportions in a mixed population". Science 28: 49 – 50. ESP copy