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## Molecular population genetics and evolution - Masatoshi Nei

A Primer of Molecular Population Genetics. Fisher, Sewall Wright, and J. Haldane—who began to form, independently, its mathematical basis. During this classical phase, much progress was made in understanding allele frequency behavior, despite the fact that the structure of DNA was unknown, and molecular techniques that enabled the evaluation of genetic diversity at the nucleotide level were unavailable. When population geneticists began to employ molecular techniques in the s, the field shifted from a predominantly theoretical one to an empirical and applied one.

New data from molecular population genetics began to challenge many existing paradigms and provided biologists with a new lens to view the world.

Today, the scope of population genetics ranges from ecological modeling to medical genetics to speciation genomics. While population geneticists are still interested in understanding how genetic variation is formed, maintained, and transformed, they are employing an increasingly large arsenal of tools and resources, including sequences of entire genomes.

The references in this section provide foundational overviews important in understanding the development of the field of population genetics.

Provine serves a historical account of the early history of population genetics and presents a unique perspective of the problems that population geneticists first had to resolve. Dobzhansky provides a treatise that was instrumental in integrating both an empirical and a theoretical population genetics framework into our understanding of evolutionary change, initiating the Modern Evolutionary Synthesis. Three works published in the early to mids highlight different perspectives of the scope of population genetics theory: Kimura and Ohta focuses on neutral and nearly neutral trajectories of evolutionary change; Nei provides a theoretical basis that extends our understanding of evolutionary forces, particularly mutation, from the population level to between-species divergence; and Lewontin uses a population and quantitative genetics approach to understand what drives evolutionary change.

Lewontin provides an excellent overview of basic population and quantitative genetics. More-advanced readers should peruse the diverse collection of thirty-two chapters from Singh and Krimbas , an edited volume on evolutionary genetics. Dobzhansky, Theodosius. Genetics and the origin of species. New York: Columbia Univ. This edition, along with its first edition , is a historically important and influential account describing the relevance of basic population genetic principles to evolutionary change.

Although its examples are dated, it is very accessible and not formula heavy. Kimura, Motoo, and Tomoko Ohta. Theoretical aspects of population genetics. Princeton, NJ: Princeton Univ. Lewontin, Richard C. The genetic basis of evolutionary change. Note that in both generations, we consider gene frequencies at the zygotic stage; these may differ from the adult gene frequencies if there is differential survivorship. In the first generation, the genotypic frequencies at the zygotic stage are p 2 , 2 p q and q 2 for A 1 A 1 , A 1 A 2 , A 2 A 2 respectively, by the Hardy-Weinberg law.

### Anderson Felipe Teixeira da Silva

The three genotypes produce successful gametes in proportion to their fitnesses, i. Assuming there is no mutation, and that Mendel's law of segregation holds, then an A 1 A 1 organism will produce only A 1 gametes, an A 2 A 2 organism will produce only A 2 gametes, and an A 1 A 2 organism will produce A 1 and A 2 gametes in equal proportion.

Therefore, the proportion of A 1 gametes, and thus the frequency of the A 1 allele in the second generation at the zygotic stage, is:. The change in frequency between generations can then be written as:. It is possible for natural selection to occur but to have no effect on gene frequencies. Equations 1 and 2 show, in precise terms, how fitness differences between genotypes will lead to evolutionary change.

This enables us to explore the consequences of various different selective regimes.

## Population genetics - Wikipedia

So in each generation, the frequency of the A 1 allele will be greater than in the previous generation, until it eventually reaches fixation and the A 2 allele is eliminated from the population. Once the A 1 allele reaches fixation, i. This makes good sense inutitively: since the A 1 allele confers a fitness advantage on organisms that carry it, its relative frequency in the population will increase from generation to generation until it is fixed. A more interesting situation arises when the heterozygote is superior in fitness to both of the homozygotes, i.

Intuitively it is clear what should happen in this situation: an equilibrium situation should be reached in which both alleles are present in the population.

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Equation 2 confirms this intuition. The asterisk indicates that this is an equilibrium condition. Since p must be non-negative, this condition can only be satisfied if there is heterozygote superiority or heterozygote inferiority; it represents an equilibrium state of the population in which both alleles are present. This equilibrium is known as polymorphic , by contrast with the monomorphic equilibria that arise when either of the alleles has gone to fixation. The possibility of polymorphic equilibrium is quite significant.

## Population genetics

It teaches us that natural selection will not always produce genetic homogeneity; in some cases, selection preserves the genetic variation found in a population. Numerous further questions about natural selection can be addressed using a simple population-genetic model. For example, by incorporating a parameter which measures the fitness differences between genotypes, we can study the rate of evolutionary change, permitting us to ask questions such as: how many generations are needed for selection to increase the frequency of the A 1 allele from 0.

If a given deleterious allele is recessive, how much longer will it take to eliminate it from the population than if it were dominant? By permitting questions such as these to be formulated and answered, population geneticists have brought mathematical rigour to the theory of evolution, to an extent that would have seemed unimaginable in Darwin's day.

Of course, the one-locus model discussed above is too simple to apply to many real-life populations, for it incorporates simplifying assumptions that are unlikely to hold true. Selection is rarely the only evolutionary force in operation, genotypic fitnesses are unlikely to be constant across generations, Mendelian segregation does not always hold exactly, and so-on. Much research in population genetics consists in devising more realistic evolutionary models, which rely on fewer simplifying assumptions and are thus more complicated.

But the one-locus model illustrates the essence of population-genetic reasoning, and the attendant clarification of the evolutionary process that it brings. Mutation is the ultimate source of genetic variation, preventing populations from becoming genetically homogeneous in situations where they otherwise would. Once mutation is taken into account, the conclusions drawn in the previous section need to be modified. Even if one allele is selectively superior to all others at a given locus, it will not become fixed in the population; recurrent mutation will ensure that other alleles are present at low frequency, thus maintaining a degree of polymorphism.

Population geneticists have long been interested in exploring what happens when selection and mutation act simultaneously. Continuing with our one-locus, two allele model, let us suppose that the A 1 allele is selectively superior to A 2 , but recurrent mutation from A 1 to A 2 prevents A 1 from spreading to fixation. The rate of mutation from A 1 to A 2 per generation, i. Empirical estimates of mutation rates are typically in the region of 10 Back mutation from A 2 to A 1 can be ignored, because we are assuming that the A 2 allele is at a very low frequency in the population, thanks to natural selection.

What happens to the gene frequency dynamics under these assumptions? Recall equation 1 above, which expresses the frequency of the A 1 allele in terms of its frequency in the previous generation. Since a certain fraction u of the A 1 alleles will have mutated to A 2 , this recurrence equation must be modified to:. The condition for equilibrium is therefore:. A useful simplification of equation 3 can be achieved by making some assumptions about the genotype fitnesses, and adopting a new notation.

Let us suppose that the A 2 allele is completely recessive as is often the case for deleterious mutants. This means that the A 1 A 1 and A 1 A 2 genotypes have identical fitness. Substituting these genotype fitnesses in equation 3 yields:. Equation 4 gives the equilibrium frequency of the A 2 allele, under the assumption that it is completely recessive.

This is highly intuitive: the greater the mutation rate from A 1 to A 2 , the greater the frequency of A 2 that can be maintained at equilibrium, for a given value of s. This is also intuitive: the stronger the selection against the A 2 A 2 homozygote, the lower the equilibrium frequency of A 2 , for a given value of u.

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It is easy to see why equation 4 is said to describe selection-mutation balance—natural selection is continually removing A 2 alleles from the population, while mutation is continually re-creating them. Equation 4 tells us the equilibrium frequency of A 2 that will be maintained, as a function of the rate of mutation from A 1 to A 2 and the magnitude of the selective disadvantage suffered by the A 2 A 2 homozygote.

Importantly, equation 4 was derived under the assumption that the A 2 allele is completely recessive, i. However, it is straightforward to derive similar equations for the cases where the A 2 allele is dominant, or partially dominant. If A 2 is dominant, or partially dominant, its equilibrium frequency will be lower than if it is completely recessive; for selection is more efficient at removing it from the population.