Neutral theory of molecular evolution

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https://en.wikipedia.org/wiki/Neutral_theory_of_molecular_evolution 

The neutral theory of molecular evolution holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species, are due to random genetic drift of mutant alleles that are selectively neutral. The theory applies only for evolution at the molecular level, and is compatible with phenotypic evolution being shaped by natural selection as postulated by Charles Darwin. The neutral theory allows for the possibility that most mutations are deleterious, but holds that because these are rapidly removed by natural selection, they do not make significant contributions to variation within and between species at the molecular level. A neutral mutation is one that does not affect an organism's ability to survive and reproduce. The neutral theory assumes that most mutations that are not deleterious are neutral rather than beneficial. Because only a fraction of gametes are sampled in each generation of a species, the neutral theory suggests that a mutant allele can arise within a population and reach fixation by chance, rather than by selective advantage.

The theory was introduced by the Japanese biologist Motoo Kimura in 1968, and independently by two American biologists Jack Lester King and Thomas Hughes Jukes in 1969, and described in detail by Kimura in his 1983 monograph The Neutral Theory of Molecular Evolution. The proposal of the neutral theory was followed by an extensive "neutralist-selectionist" controversy over the interpretation of patterns of molecular divergence and gene polymorphism, peaking in the 1970s and 1980s.

Origins

While some scientists, such as Freese (1962) and Freese and Yoshida (1965), had suggested that neutral mutations were probably widespread, a coherent theory of neutral evolution was proposed by Motoo Kimura in 1968, and by King and Jukes independently in 1969. Kimura initially focused on differences among species, King and Jukes on differences within species.

Many molecular biologists and population geneticists also contributed to the development of the neutral theory. Principles of population genetics, established by J.B.S. Haldane, R.A. Fisher and Sewall Wright, created a mathematical approach to analyzing gene frequencies that contributed to the development of Kimura's theory.

Haldane's dilemma regarding the cost of selection was used as motivation by Kimura. Haldane estimated that it takes about 300 generations for a beneficial mutation to become fixed in a mammalian lineage, meaning that the number of substitutions (1.5 per year) in the evolution between humans and chimpanzees was too high to be explained by beneficial mutations.

Functional constraint

The neutral theory holds that as functional constraint diminishes, the probability that a mutation is neutral rises, and so should the rate of sequence divergence.

When comparing various proteins, extremely high evolutionary rates were observed in proteins such as fibrinopeptides and the C chain of the proinsulin molecule, which both have little to no functionality compared to their active molecules. Kimura and Ohta also estimated that the alpha and beta chains on the surface of a hemoglobin protein evolve at a rate almost ten times faster than the inside pockets, which would imply that the overall molecular structure of hemoglobin is less significant than the inside where the iron-containing heme groups reside.

There is evidence that rates of nucleotide substitution are particularly high in the third position of a codon, where there is little functional constraint. This view is based in part on the degenerate genetic code, in which sequences of three nucleotides (codons) may differ and yet encode the same amino acid (GCC and GCA both encode alanine, for example). Consequently, many potential single-nucleotide changes are in effect "silent" or "unexpressed". Such changes are presumed to have little or no biological effect.

Quantitative theory

Kimura also developed the infinite sites model (ISM) to provide insight into evolutionary rates of mutant alleles. If were to represent the rate of mutation of gametes per generation of individuals, each with two sets of chromosomes, the total number of new mutants in each generation is . Now let represent the evolution rate in terms of a mutant allele becoming fixed in a population.

According to ISM, selectively neutral mutations appear at rate in each of the copies of a gene, and fix with probability . Because any of the genes have the ability to become fixed in a population, is equal to , resulting in the rate of evolutionary rate equation:

This means that if all mutations were neutral, the rate at which fixed differences accumulate between divergent populations is predicted to be equal to the per-individual mutation rate, independent of population size. When the proportion of mutations that are neutral is constant, so is the divergence rate between populations. This provides a rationale for the molecular clock - which predated neutral theory. The ISM also demonstrates a constancy that is observed in molecular lineages.

This stochastic process is assumed to obey equations describing random genetic drift by means of accidents of sampling, rather than for example genetic hitchhiking of a neutral allele due to genetic linkage with non-neutral alleles. After appearing by mutation, a neutral allele may become more common within the population via genetic drift. Usually, it will be lost, or in rare cases it may become fixed, meaning that the new allele becomes standard in the population.

According to the neutral theory of molecular evolution, the amount of genetic variation within a species should be proportional to the effective population size.

The "neutralist–selectionist" debate

A heated debate arose when Kimura's theory was published, largely revolving around the relative percentages of polymorphic and fixed alleles that are "neutral" versus "non-neutral".

A genetic polymorphism means that different forms of particular genes, and hence of the proteins that they produce, are co-existing within a species. Selectionists claimed that such polymorphisms are maintained by balancing selection, while neutralists view the variation of a protein as a transient phase of molecular evolution. Studies by Richard K. Koehn and W. F. Eanes demonstrated a correlation between polymorphism and molecular weight of their molecular subunits. This is consistent with the neutral theory assumption that larger subunits should have higher rates of neutral mutation. Selectionists, on the other hand, contribute environmental conditions to be the major determinants of polymorphisms rather than structural and functional factors.

According to the neutral theory of molecular evolution, the amount of genetic variation within a species should be proportional to the effective population size. Levels of genetic diversity vary much less than census population sizes, giving rise to the "paradox of variation" . While high levels of genetic diversity were one of the original arguments in favor of neutral theory, the paradox of variation has been one of the strongest arguments against neutral theory.

There are a large number of statistical methods for testing whether neutral theory is a good description of evolution (e.g., McDonald-Kreitman test), and many authors claimed detection of selection (Fay et al. 2002, Begun et al. 2007, Shapiro et al. 2007, Hahn 2008, Akey 2009, Kern 2018). Some researchers have nevertheless argued that the neutral theory still stands, while expanding the definition of neutral theory to include background selection at linked sites.

Nearly neutral theory

Tomoko Ohta also emphasized the importance of nearly neutral mutations, in particularly slightly deleterious mutations. The population dynamics of nearly neutral mutations are only slightly different from those of neutral mutations unless the absolute magnitude of the selection coefficient is greater than 1/N, where N is the effective population size in respect of selection. The value of N may therefore affect how many mutations can be treated as neutral and how many as deleterious.

From Wikipedia, the free encyclopedia

Population bottleneck

Population bottleneck followed by recovery or extinction

A population bottleneck or genetic bottleneck is a sharp reduction in the size of a population due to environmental events such as famines, earthquakes, floods, fires, disease, and droughts or human activities such as specicide and human population planning. Such events can reduce the variation in the gene pool of a population; thereafter, a smaller population, with a smaller genetic diversity, remains to pass on genes to future generations of offspring through sexual reproduction. Genetic diversity remains lower, increasing only when gene flow from another population occurs or very slowly increasing with time as random mutations occur. This results in a reduction in the robustness of the population and in its ability to adapt to and survive selecting environmental changes, such as climate change or a shift in available resources. Alternatively, if survivors of the bottleneck are the individuals with the greatest genetic fitness, the frequency of the fitter genes within the gene pool is increased, while the pool itself is reduced.

The genetic drift caused by a population bottleneck can change the proportional random distribution of alleles and even lead to loss of alleles. The chances of inbreeding and genetic homogeneity can increase, possibly leading to inbreeding depression. Smaller population size can also cause deleterious mutations to accumulate.

Population bottlenecks play an important role in conservation biology) and in the context of agriculture (biological and pest control).

Scientists have witnessed population bottlenecks in American bison, greater prairie chickens, northern elephant seals, golden hamsters, and cheetahs. The New Zealand black robins experienced a bottleneck of five individuals, all descendants of a single female. Geneticists have found evidence for past bottlenecks in pandas, golden snub-nosed monkeys, and humans.

Minimum viable population size

In conservation biology, minimum viable population (MVP) size helps to determine the effective population size when a population is at risk for extinction. The effects of a population bottleneck often depend on the number of individuals remaining after the bottleneck and how that compares to the minimum viable population size.

Founder effects

A slightly different form of bottleneck can occur if a small group becomes reproductively (e.g. geographically) separated from the main population, such as through a founder event, e.g. if a few members of a species successfully colonize a new isolated island, or from small captive breeding programs such as animals at a zoo. Alternatively, invasive species can undergo population bottlenecks through founder events when introduced into their invaded range.

Examples

Humans

According to a 1999 model, a severe population bottleneck, or more specifically a full-fledged speciation, occurred among a group of Australopithecina as they transitioned into the species known as Homo erectus two million years ago. It is believed that additional bottlenecks must have occurred since Homo erectus started walking the Earth, but current archaeological, paleontological, and genetic data are inadequate to give much reliable information about such conjectured bottlenecks. That said, the possibility of a severe recent species-wide bottleneck cannot be ruled out.

A 2005 study from Rutgers University theorized that the pre-1492 native populations of the Americas are the descendants of only 70 individuals who crossed the land bridge between Asia and North America.

Toba catastrophe theory

The controversial Toba catastrophe theory, presented in the late 1990s to early 2000s, suggested that a bottleneck of the human population occurred approximately 75,000 years ago, proposing that the human population was reduced to perhaps 10,000–30,000 individuals when the Toba supervolcano in Indonesia erupted and triggered a major environmental change. Parallel bottlenecks were proposed to exist among chimpanzees, gorillas, rhesus macaques, orangutans and tigers. The hypothesis was based on geological evidence of sudden climate change and on coalescence evidence of some genes (including mitochondrial DNA, Y-chromosome DNA and some nuclear genes) and the relatively low level of genetic variation in humans.

However, subsequent research, especially in the 2010s, appeared to refute both the climate argument and the genetic argument. Recent research shows the extent of climate change was much smaller than believed by proponents of the theory. Genetic material inherited exclusively from either father or mother can be traced back in time via either matrilineal or patrilineal ancestry.

In 2000, a Molecular Biology and Evolution paper suggested a transplanting model or a 'long bottleneck' to account for the limited genetic variation, rather than a catastrophic environmental change. This would be consistent with suggestions that in sub-Saharan Africa numbers could have dropped at times as low as 2,000, for perhaps as long as 100,000 years, before numbers began to expand again in the Late Stone Age.

Other animals

Year	American bison (est)
Before 1492	60,000,000
1890	750
2000	360,000

European bison, also called wisent (Bison bonasus), faced extinction in the early 20th century. The animals living today are all descended from 12 individuals and they have extremely low genetic variation, which may be beginning to affect the reproductive ability of bulls.

The population of American bison (Bison bison) fell due to overhunting, nearly leading to extinction around the year 1890, though it has since begun to recover (see table).

Overhunting pushed the northern elephant seal to the brink of extinction by the late 19th century. Though they have made a comeback, the genetic variation within the population remains very low.

A classic example of a population bottleneck is that of the northern elephant seal, whose population fell to about 30 in the 1890s. Although it now numbers in the hundreds of thousands, the potential for bottlenecks within colonies remains. Dominant bulls are able to mate with the largest number of females — sometimes as many as 100. With so much of a colony's offspring descended from just one dominant male, genetic diversity is limited, making the species more vulnerable to diseases and genetic mutations. The golden hamster is a similarly bottlenecked species, with the vast majority of domesticated hamsters descended from a single litter found in the Syrian desert around 1930, and very few wild golden hamsters remaining.

An extreme example of a population bottleneck is the New Zealand black robin, of which every specimen today is a descendant of a single female, called Old Blue. The Black Robin population is still recovering from its low point of only five individuals in 1980.

The genome of the giant panda shows evidence of a severe bottleneck about 43,000 years ago. There is also evidence of at least one primate species, the golden snub-nosed monkey, that also suffered from a bottleneck around this time. An unknown environmental event is suspected to have caused the bottlenecks observed in both of these species. The bottlenecks likely caused the low genetic diversity observed in both species.

Other facts can sometimes be inferred from an observed population bottleneck. Among the Galápagos Islands giant tortoises — themselves a prime example of a bottleneck — the comparatively large population on the slopes of the Alcedo volcano is significantly less diverse than four other tortoise populations on the same island. DNA analyses date the bottleneck to around 88,000 years before present (YBP). About 100,000 YBP the volcano erupted violently, deeply burying much of the tortoise habitat in pumice and ash.

Before Europeans arrived in North America, prairies served as habitats to greater prairie chickens. In Illinois alone, the number of greater prairie chickens plummeted from over 100 million in 1900 to about 50 in 1990. These declines in population were the result of hunting and habitat destruction, but the random consequences have also caused a great loss in species diversity. DNA analysis comparing the birds from 1990 and mid-century shows a steep genetic decline in recent decades. The greater prairie chicken is currently experiencing low reproductive success.

Population bottlenecking poses a major threat to the stability of species populations as well. Papilio homerus is the largest butterfly in the Americas and is endangered according to the IUCN. The disappearance of a central population poses a major threat of population bottleneck. The remaining two populations are now geographically isolated and the populations face an unstable future with limited remaining opportunity for gene flow.

Genetic bottlenecks exist in cheetahs.

Selective breeding

Bottlenecks also exist among pure-bred animals (e.g., dogs and cats: pugs, Persian) because breeders limit their gene pools by a few (show-winning) individuals for their looks and behaviors. The extensive use of desirable individual animals at the exclusion of others can result in a popular sire effect.

Selective breeding for dog breeds caused constricting breed-specific bottlenecks. These bottlenecks have led to dogs having an average of 2–3% more genetic loading than gray wolves. The strict breeding programs and population bottlenecks have led to the prevalence of diseases such as heart disease, blindness, cancers, hip dysplasia, cataracts, and more.

Selective breeding to produce high-yielding crops has caused genetic bottlenecks in these crops and has led to genetic homogeneity. This reduced genetic diversity in many crops could lead to broader susceptibility to new diseases or pests, which threatens global food security.

Plants

Research showed that there is incredibly low, nearly undetectable amounts of genetic diversity in the genome of the Wollemi pine (Wollemia nobilis). The IUCN found a population count of 80 mature individuals and about 300 seedlings and juveniles in 2011, and previously, the Wollemi pine had fewer than 50 individuals in the wild. The low population size and low genetic diversity indicates that the Wollemi pine went through a severe population bottleneck.

A population bottleneck was created in the 1970s through the conservation efforts of the endangered Mauna Kea silversword (Argyroxiphium sandwicense ssp. sandwicense). The small natural population of silversword was augmented through the 1970s with outplanted individuals. All of the outplanted silversword plants were found to be first or subsequent generation offspring of just two maternal founders. The low amount of polymorphic loci in the outplanted individuals led to the population bottleneck, causing the loss of the marker allele at eight of the loci.

Genetic drift

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Genetic_drift 

Evolutionary biology
Darwin's finches by John Gould

Genetic drift (allelic drift or the Sewall Wright effect) is the change in the frequency of an existing gene variant (allele) in a population due to random sampling of organisms. The alleles in the offspring are a sample of those in the parents, and chance has a role in determining whether a given individual survives and reproduces. A population's allele frequency is the fraction of the copies of one gene that share a particular form.

Genetic drift may cause gene variants to disappear completely and thereby reduce genetic variation. It can also cause initially rare alleles to become much more frequent and even fixed.

When there are few copies of an allele, the effect of genetic drift is larger, and when there are many copies the effect is smaller. In the middle of the 20th century, vigorous debates occurred over the relative importance of natural selection versus neutral processes, including genetic drift. Ronald Fisher, who explained natural selection using Mendelian genetics, held the view that genetic drift plays at the most a minor role in evolution, and this remained the dominant view for several decades. In 1968, population geneticist Motoo Kimura rekindled the debate with his neutral theory of molecular evolution, which claims that most instances where a genetic change spreads across a population (although not necessarily changes in phenotypes) are caused by genetic drift acting on neutral mutations.

Analogy with marbles in a jar

The process of genetic drift can be illustrated using 20 marbles in a jar to represent 20 organisms in a population. Consider this jar of marbles as the starting population. Half of the marbles in the jar are red and half are blue, with each colour corresponding to a different allele of one gene in the population. In each new generation the organisms reproduce at random. To represent this reproduction, randomly select a marble from the original jar and deposit a new marble with the same colour into a new jar. This is the "offspring" of the original marble, meaning that the original marble remains in its jar. Repeat this process until there are 20 new marbles in the second jar. The second jar will now contain 20 "offspring", or marbles of various colours. Unless the second jar contains exactly 10 red marbles and 10 blue marbles, a random shift has occurred in the allele frequencies.

If this process is repeated a number of times, the numbers of red and blue marbles picked each generation will fluctuate. Sometimes a jar will have more red marbles than its "parent" jar and sometimes more blue. This fluctuation is analogous to genetic drift – a change in the population's allele frequency resulting from a random variation in the distribution of alleles from one generation to the next.

It is even possible that in any one generation no marbles of a particular colour are chosen, meaning they have no offspring. In this example, if no red marbles are selected, the jar representing the new generation contains only blue offspring. If this happens, the red allele has been lost permanently in the population, while the remaining blue allele has become fixed: all future generations are entirely blue. In small populations, fixation can occur in just a few generations.

In this simulation each black dot on a marble signifies that it has been chosen for copying (reproduction) one time. There is fixation in the blue "allele" within five generations.

Probability and allele frequency

The mechanisms of genetic drift can be illustrated with a simplified example. Consider a very large colony of bacteria isolated in a drop of solution. The bacteria are genetically identical except for a single gene with two alleles labeled A and B. A and B are neutral alleles meaning that they do not affect the bacteria's ability to survive and reproduce; all bacteria in this colony are equally likely to survive and reproduce. Suppose that half the bacteria have allele A and the other half have allele B. Thus A and B each have allele frequency 1/2.

The drop of solution then shrinks until it has only enough food to sustain four bacteria. All other bacteria die without reproducing. Among the four who survive, there are sixteen possible combinations for the A and B alleles:

(A-A-A-A), (B-A-A-A), (A-B-A-A), (B-B-A-A),
(A-A-B-A), (B-A-B-A), (A-B-B-A), (B-B-B-A),
(A-A-A-B), (B-A-A-B), (A-B-A-B), (B-B-A-B),
(A-A-B-B), (B-A-B-B), (A-B-B-B), (B-B-B-B).

Since all bacteria in the original solution are equally likely to survive when the solution shrinks, the four survivors are a random sample from the original colony. The probability that each of the four survivors has a given allele is 1/2, and so the probability that any particular allele combination occurs when the solution shrinks is

${\displaystyle {\frac {1}{2}}\cdot {\frac {1}{2}}\cdot {\frac {1}{2}}\cdot {\frac {1}{2}}={\frac {1}{16}}.}$

(The original population size is so large that the sampling effectively happens with replacement). In other words, each of the sixteen possible allele combinations is equally likely to occur, with probability 1/16.

Counting the combinations with the same number of A and B, we get the following table.

A	B	Combinations	Probability
4	0	1	1/16
3	1	4	4/16
2	2	6	6/16
1	3	4	4/16
0	4	1	1/16

As shown in the table, the total number of combinations that have the same number of A alleles as of B alleles is six, and the probability of this combination is 6/16. The total number of other combinations is ten, so the probability of unequal number of A and B alleles is 10/16. Thus, although the original colony began with an equal number of A and B alleles, it is very possible that the number of alleles in the remaining population of four members will not be equal. Equal numbers is actually less likely than unequal numbers. In the latter case, genetic drift has occurred because the population's allele frequencies have changed due to random sampling. In this example the population contracted to just four random survivors, a phenomenon known as population bottleneck.

The probabilities for the number of copies of allele A (or B) that survive (given in the last column of the above table) can be calculated directly from the binomial distribution where the "success" probability (probability of a given allele being present) is 1/2 (i.e., the probability that there are k copies of A (or B) alleles in the combination) is given by

${\displaystyle {n \choose k}\left({\frac {1}{2}}\right)^{k}\left(1-{\frac {1}{2}}\right)^{n-k}={n \choose k}\left({\frac {1}{2}}\right)^{n}\!}$

where n=4 is the number of surviving bacteria.

Mathematical models

Mathematical models of genetic drift can be designed using either branching processes or a diffusion equation describing changes in allele frequency in an idealised population.

Wright–Fisher model

Consider a gene with two alleles, A or B. In diploid populations consisting of N individuals there are 2N copies of each gene. An individual can have two copies of the same allele or two different alleles. We can call the frequency of one allele p and the frequency of the other q. The Wright–Fisher model (named after Sewall Wright and Ronald Fisher) assumes that generations do not overlap (for example, annual plants have exactly one generation per year) and that each copy of the gene found in the new generation is drawn independently at random from all copies of the gene in the old generation. The formula to calculate the probability of obtaining k copies of an allele that had frequency p in the last generation is then

${\displaystyle {\frac {(2N)!}{k!(2N-k)!}}p^{k}q^{2N-k}}$

where the symbol "!" signifies the factorial function. This expression can also be formulated using the binomial coefficient,

${\displaystyle {2N \choose k}p^{k}q^{2N-k}}$

Moran model

The Moran model assumes overlapping generations. At each time step, one individual is chosen to reproduce and one individual is chosen to die. So in each timestep, the number of copies of a given allele can go up by one, go down by one, or can stay the same. This means that the transition matrix is tridiagonal, which means that mathematical solutions are easier for the Moran model than for the Wright–Fisher model. On the other hand, computer simulations are usually easier to perform using the Wright–Fisher model, because fewer time steps need to be calculated. In the Moran model, it takes N timesteps to get through one generation, where N is the effective population size. In the Wright–Fisher model, it takes just one.

In practice, the Moran and Wright–Fisher models give qualitatively similar results, but genetic drift runs twice as fast in the Moran model.

Other models of drift

If the variance in the number of offspring is much greater than that given by the binomial distribution assumed by the Wright–Fisher model, then given the same overall speed of genetic drift (the variance effective population size), genetic drift is a less powerful force compared to selection. Even for the same variance, if higher moments of the offspring number distribution exceed those of the binomial distribution then again the force of genetic drift is substantially weakened.

Random effects other than sampling error

Random changes in allele frequencies can also be caused by effects other than sampling error, for example random changes in selection pressure.

One important alternative source of stochasticity, perhaps more important than genetic drift, is genetic draft. Genetic draft is the effect on a locus by selection on linked loci. The mathematical properties of genetic draft are different from those of genetic drift. The direction of the random change in allele frequency is autocorrelated across generations.

Drift and fixation

The Hardy–Weinberg principle states that within sufficiently large populations, the allele frequencies remain constant from one generation to the next unless the equilibrium is disturbed by migration, genetic mutations, or selection.

However, in finite populations, no new alleles are gained from the random sampling of alleles passed to the next generation, but the sampling can cause an existing allele to disappear. Because random sampling can remove, but not replace, an allele, and because random declines or increases in allele frequency influence expected allele distributions for the next generation, genetic drift drives a population towards genetic uniformity over time. When an allele reaches a frequency of 1 (100%) it is said to be "fixed" in the population and when an allele reaches a frequency of 0 (0%) it is lost. Smaller populations achieve fixation faster, whereas in the limit of an infinite population, fixation is not achieved. Once an allele becomes fixed, genetic drift comes to a halt, and the allele frequency cannot change unless a new allele is introduced in the population via mutation or gene flow. Thus even while genetic drift is a random, directionless process, it acts to eliminate genetic variation over time.

Rate of allele frequency change due to drift

Ten simulations of random genetic drift of a single given allele with an initial frequency distribution 0.5 measured over the course of 50 generations, repeated in three reproductively synchronous populations of different sizes. In these simulations, alleles drift to loss or fixation (frequency of 0.0 or 1.0) only in the smallest population.

Assuming genetic drift is the only evolutionary force acting on an allele, after t generations in many replicated populations, starting with allele frequencies of p and q, the variance in allele frequency across those populations is

${\displaystyle V_{t}\approx pq\left(1-\exp \left(-{\frac {t}{2N_{e}}}\right)\right)}$

Time to fixation or loss

Assuming genetic drift is the only evolutionary force acting on an allele, at any given time the probability that an allele will eventually become fixed in the population is simply its frequency in the population at that time. For example, if the frequency p for allele A is 75% and the frequency q for allele B is 25%, then given unlimited time the probability A will ultimately become fixed in the population is 75% and the probability that B will become fixed is 25%.

The expected number of generations for fixation to occur is proportional to the population size, such that fixation is predicted to occur much more rapidly in smaller populations. Normally the effective population size, which is smaller than the total population, is used to determine these probabilities. The effective population (N_e) takes into account factors such as the level of inbreeding, the stage of the lifecycle in which the population is the smallest, and the fact that some neutral genes are genetically linked to others that are under selection. The effective population size may not be the same for every gene in the same population.

One forward-looking formula used for approximating the expected time before a neutral allele becomes fixed through genetic drift, according to the Wright–Fisher model, is

${\displaystyle {\bar {T}}_{\text{fixed}}={\frac {-4N_{e}(1-p)\ln(1-p)}{p}}}$

where T is the number of generations, N_e is the effective population size, and p is the initial frequency for the given allele. The result is the number of generations expected to pass before fixation occurs for a given allele in a population with given size (N_e) and allele frequency (p).

The expected time for the neutral allele to be lost through genetic drift can be calculated as

${\displaystyle {\bar {T}}_{\text{lost}}={\frac {-4N_{e}p}{1-p}}\ln p.}$

When a mutation appears only once in a population large enough for the initial frequency to be negligible, the formulas can be simplified to

${\displaystyle {\bar {T}}_{\text{fixed}}=4N_{e}}$

for average number of generations expected before fixation of a neutral mutation, and

${\displaystyle {\bar {T}}_{\text{lost}}=2\left({\frac {N_{e}}{N}}\right)\ln(2N)}$

for the average number of generations expected before the loss of a neutral mutation.

Time to loss with both drift and mutation

The formulae above apply to an allele that is already present in a population, and which is subject to neither mutation nor natural selection. If an allele is lost by mutation much more often than it is gained by mutation, then mutation, as well as drift, may influence the time to loss. If the allele prone to mutational loss begins as fixed in the population, and is lost by mutation at rate m per replication, then the expected time in generations until its loss in a haploid population is given by

${\displaystyle {\bar {T}}_{\text{lost}}\approx {\begin{cases}{\dfrac {1}{m}},{\text{ if }}mN_{e}\ll 1\\[8pt]{\dfrac {\ln {(mN_{e})}+\gamma }{m}}{\text{ if }}mN_{e}\gg 1\end{cases}}}$

where ${\displaystyle \gamma }$ is Euler's constant. The first approximation represents the waiting time until the first mutant destined for loss, with loss then occurring relatively rapidly by genetic drift, taking time N_e ≪ 1/m. The second approximation represents the time needed for deterministic loss by mutation accumulation. In both cases, the time to fixation is dominated by mutation via the term 1/m, and is less affected by the effective population size.

Versus natural selection

In natural populations, genetic drift and natural selection do not act in isolation; both phenomena are always at play, together with mutation and migration. Neutral evolution is the product of both mutation and drift, not of drift alone. Similarly, even when selection overwhelms genetic drift, it can only act on variation that mutation provides.

While natural selection has a direction, guiding evolution towards heritable adaptations to the current environment, genetic drift has no direction and is guided only by the mathematics of chance. As a result, drift acts upon the genotypic frequencies within a population without regard to their phenotypic effects. In contrast, selection favors the spread of alleles whose phenotypic effects increase survival and/or reproduction of their carriers, lowers the frequencies of alleles that cause unfavorable traits, and ignores those that are neutral.

The law of large numbers predicts that when the absolute number of copies of the allele is small (e.g., in small populations), the magnitude of drift on allele frequencies per generation is larger. The magnitude of drift is large enough to overwhelm selection at any allele frequency when the selection coefficient is less than 1 divided by the effective population size. Non-adaptive evolution resulting from the product of mutation and genetic drift is therefore considered to be a consequential mechanism of evolutionary change primarily within small, isolated populations. The mathematics of genetic drift depend on the effective population size, but it is not clear how this is related to the actual number of individuals in a population. Genetic linkage to other genes that are under selection can reduce the effective population size experienced by a neutral allele. With a higher recombination rate, linkage decreases and with it this local effect on effective population size. This effect is visible in molecular data as a correlation between local recombination rate and genetic diversity, and negative correlation between gene density and diversity at noncoding DNA regions. Stochasticity associated with linkage to other genes that are under selection is not the same as sampling error, and is sometimes known as genetic draft in order to distinguish it from genetic drift.

When the allele frequency is very small, drift can also overpower selection even in large populations. For example, while disadvantageous mutations are usually eliminated quickly in large populations, new advantageous mutations are almost as vulnerable to loss through genetic drift as are neutral mutations. Not until the allele frequency for the advantageous mutation reaches a certain threshold will genetic drift have no effect.

Population bottleneck

Changes in a population's allele frequency following a population bottleneck: the rapid and radical decline in population size has reduced the population's genetic variation.

A population bottleneck is when a population contracts to a significantly smaller size over a short period of time due to some random environmental event. In a true population bottleneck, the odds for survival of any member of the population are purely random, and are not improved by any particular inherent genetic advantage. The bottleneck can result in radical changes in allele frequencies, completely independent of selection.

The impact of a population bottleneck can be sustained, even when the bottleneck is caused by a one-time event such as a natural catastrophe. An interesting example of a bottleneck causing unusual genetic distribution is the relatively high proportion of individuals with total rod cell color blindness (achromatopsia) on Pingelap atoll in Micronesia. After a bottleneck, inbreeding increases. This increases the damage done by recessive deleterious mutations, in a process known as inbreeding depression. The worst of these mutations are selected against, leading to the loss of other alleles that are genetically linked to them, in a process of background selection. For recessive harmful mutations, this selection can be enhanced as a consequence of the bottleneck, due to genetic purging. This leads to a further loss of genetic diversity. In addition, a sustained reduction in population size increases the likelihood of further allele fluctuations from drift in generations to come.

A population's genetic variation can be greatly reduced by a bottleneck, and even beneficial adaptations may be permanently eliminated. The loss of variation leaves the surviving population vulnerable to any new selection pressures such as disease, climatic change or shift in the available food source, because adapting in response to environmental changes requires sufficient genetic variation in the population for natural selection to take place.

There have been many known cases of population bottleneck in the recent past. Prior to the arrival of Europeans, North American prairies were habitat for millions of greater prairie chickens. In Illinois alone, their numbers plummeted from about 100 million birds in 1900 to about 50 birds in the 1990s. The declines in population resulted from hunting and habitat destruction, but a consequence has been a loss of most of the species' genetic diversity. DNA analysis comparing birds from the mid century to birds in the 1990s documents a steep decline in the genetic variation in just the latter few decades. Currently the greater prairie chicken is experiencing low reproductive success.

However, the genetic loss caused by bottleneck and genetic drift can increase fitness, as in Ehrlichia.

Over-hunting also caused a severe population bottleneck in the northern elephant seal in the 19th century. Their resulting decline in genetic variation can be deduced by comparing it to that of the southern elephant seal, which were not so aggressively hunted.

Founder effect

When very few members of a population migrate to form a separate new population, the founder effect occurs. For a period after the foundation, the small population experiences intensive drift. In the figure this results in fixation of the red allele.

The founder effect is a special case of a population bottleneck, occurring when a small group in a population splinters off from the original population and forms a new one. The random sample of alleles in the just formed new colony is expected to grossly misrepresent the original population in at least some respects. It is even possible that the number of alleles for some genes in the original population is larger than the number of gene copies in the founders, making complete representation impossible. When a newly formed colony is small, its founders can strongly affect the population's genetic make-up far into the future.

A well-documented example is found in the Amish migration to Pennsylvania in 1744. Two members of the new colony shared the recessive allele for Ellis–Van Creveld syndrome. Members of the colony and their descendants tend to be religious isolates and remain relatively insular. As a result of many generations of inbreeding, Ellis–Van Creveld syndrome is now much more prevalent among the Amish than in the general population.

The difference in gene frequencies between the original population and colony may also trigger the two groups to diverge significantly over the course of many generations. As the difference, or genetic distance, increases, the two separated populations may become distinct, both genetically and phenetically, although not only genetic drift but also natural selection, gene flow, and mutation contribute to this divergence. This potential for relatively rapid changes in the colony's gene frequency led most scientists to consider the founder effect (and by extension, genetic drift) a significant driving force in the evolution of new species. Sewall Wright was the first to attach this significance to random drift and small, newly isolated populations with his shifting balance theory of speciation. Following after Wright, Ernst Mayr created many persuasive models to show that the decline in genetic variation and small population size following the founder effect were critically important for new species to develop. However, there is much less support for this view today since the hypothesis has been tested repeatedly through experimental research and the results have been equivocal at best.

History

The role of random chance in evolution was first outlined by Arend L. Hagedoorn and A. C. Hagedoorn-Vorstheuvel La Brand in 1921. They highlighted that random survival plays a key role in the loss of variation from populations. Fisher (1922) responded to this with the first, albeit marginally incorrect, mathematical treatment of the 'Hagedoorn effect'. Notably, he expected that many natural populations were too large (an N ~10,000) for the effects of drift to be substantial and thought drift would have an insignificant effect on the evolutionary process. The corrected mathematical treatment and term "genetic drift" was later coined by a founder of population genetics, Sewall Wright. His first use of the term "drift" was in 1929, though at the time he was using it in the sense of a directed process of change, or natural selection. Random drift by means of sampling error came to be known as the "Sewall–Wright effect," though he was never entirely comfortable to see his name given to it. Wright referred to all changes in allele frequency as either "steady drift" (e.g., selection) or "random drift" (e.g., sampling error). "Drift" came to be adopted as a technical term in the stochastic sense exclusively. Today it is usually defined still more narrowly, in terms of sampling error, although this narrow definition is not universal. Wright wrote that the "restriction of "random drift" or even "drift" to only one component, the effects of accidents of sampling, tends to lead to confusion." Sewall Wright considered the process of random genetic drift by means of sampling error equivalent to that by means of inbreeding, but later work has shown them to be distinct.

In the early days of the modern evolutionary synthesis, scientists were beginning to blend the new science of population genetics with Charles Darwin's theory of natural selection. Within this framework, Wright focused on the effects of inbreeding on small relatively isolated populations. He introduced the concept of an adaptive landscape in which phenomena such as cross breeding and genetic drift in small populations could push them away from adaptive peaks, which in turn allow natural selection to push them towards new adaptive peaks. Wright thought smaller populations were more suited for natural selection because "inbreeding was sufficiently intense to create new interaction systems through random drift but not intense enough to cause random nonadaptive fixation of genes."

Wright's views on the role of genetic drift in the evolutionary scheme were controversial almost from the very beginning. One of the most vociferous and influential critics was colleague Ronald Fisher. Fisher conceded genetic drift played some role in evolution, but an insignificant one. Fisher has been accused of misunderstanding Wright's views because in his criticisms Fisher seemed to argue Wright had rejected selection almost entirely. To Fisher, viewing the process of evolution as a long, steady, adaptive progression was the only way to explain the ever-increasing complexity from simpler forms. But the debates have continued between the "gradualists" and those who lean more toward the Wright model of evolution where selection and drift together play an important role.

In 1968, Motoo Kimura rekindled the debate with his neutral theory of molecular evolution, which claims that most of the genetic changes are caused by genetic drift acting on neutral mutations.

The role of genetic drift by means of sampling error in evolution has been criticized by John H. Gillespie and William B. Provine, who argue that selection on linked sites is a more important stochastic force.