Infinite alleles model

Last updated

The infinite alleles model is a mathematical model for calculating genetic mutations. The Japanese geneticist Motoo Kimura and American geneticist James F. Crow (1964) introduced the infinite alleles model, an attempt to determine for a finite diploid population what proportion of loci would be homozygous. This was, in part, motivated by assertions by other geneticists that more than 50 percent of Drosophila loci were heterozygous, a claim they initially doubted. In order to answer this question they assumed first, that there were a large enough number of alleles so that any mutation would lead to a different allele (that is the probability of back mutation to the original allele would be low enough to be negligible); and second, that the mutations would result in a number of different outcomes from neutral to deleterious.

They determined that in the neutral case, the probability that an individual would be homozygous, F, was:

where u is the mutation rate, and Ne is the effective population size. The effective number of alleles n maintained in a population is defined as the inverse of the homozygosity, that is

which is a lower bound for the actual number of alleles in the population.

If the effective population is large, then a large number of alleles can be maintained. However, this result only holds for the neutral case, and is not necessarily true for the case when some alleles are subject to selection, i.e. more or less fit than others, for example when the fittest genotype is a heterozygote (a situation often referred to as overdominance or heterosis).

In the case of overdominance, because Mendel's second law (the law of segregation) necessarily results in the production of homozygotes (which are by definition in this case, less fit), this means that population will always harbor a number of less fit individuals, which leads to a decrease in the average fitness of the population. This is sometimes referred to as genetic load , in this case it is a special kind of load known as segregational load. Crow and Kimura showed that at equilibrium conditions, for a given strength of selection (s), that there would be an upper limit to the number of fitter alleles (polymorphisms) that a population could harbor for a particular locus. Beyond this number of alleles, the selective advantage of presence of those alleles in heterozygous genotypes would be cancelled out by continual generation of less fit homozygous genotypes.

These results became important in the formation of the neutral theory, because neutral (or nearly neutral) alleles create no such segregational load, and allow for the accumulation of a great deal of polymorphism. When Richard Lewontin and J. Hubby published their groundbreaking results in 1966 which showed high levels of genetic variation in Drosophila via protein electrophoresis, the theoretical results from the infinite alleles model were used by Kimura and others to support the idea that this variation would have to be neutral (or result in excess segregational load).

Related Research Articles

Dominance (genetics) One gene variant masking the effect of another in the other copy of the gene

In genetics, dominance is the phenomenon of one variant (allele) of a gene on a chromosome masking or overriding the effect of a different variant of the same gene on the other copy of the chromosome. The first variant is termed dominant and the second recessive. This state of having two different variants of the same gene on each chromosome is originally caused by a mutation in one of the genes, either new or inherited. The terms autosomal dominant or autosomal recessive are used to describe gene variants on non-sex chromosomes (autosomes) and their associated traits, while those on sex chromosomes (allosomes) are termed X-linked dominant, X-linked recessive or Y-linked; these have an inheritance and presentation pattern that depends on the sex of both the parent and the child. Since there is only one copy of the Y chromosome, Y-linked traits cannot be dominant or recessive. Additionally, there are other forms of dominance such as incomplete dominance, in which a gene variant has a partial effect compared to when it is present on both chromosomes, and co-dominance, in which different variants on each chromosome both show their associated traits.

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.

Fitness (biology) Expected reproductive success

Fitness is the quantitative representation of individual reproductive success. It is also equal to the average contribution to the gene pool of the next generation, made by the same individuals of the specified genotype or phenotype. Fitness can be defined either with respect to a genotype or to a phenotype in a given environment. The fitness of a genotype is manifested through its phenotype, which is also affected by the developmental environment. The fitness of a given phenotype can also be different in different selective environments.

Population genetics Subfield of genetics

Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and population structure.

Allele frequency, or gene frequency, is the relative frequency of an allele at a particular locus in a population, expressed as a fraction or percentage. Specifically, it is the fraction of all chromosomes in the population that carry that allele over the total population or sample size. Microevolution is the change in allele frequencies that occurs over time within a population.

Richard Charles Lewontin was an American evolutionary biologist, mathematician, geneticist, and social commentator. A leader in developing the mathematical basis of population genetics and evolutionary theory, he pioneered the application of techniques from molecular biology, such as gel electrophoresis, to questions of genetic variation and evolution.

Motoo Kimura Japanese biologist

Motoo Kimura was a Japanese biologist best known for introducing the neutral theory of molecular evolution in 1968. He became one of the most influential theoretical population geneticists. He is remembered in genetics for his innovative use of diffusion equations to calculate the probability of fixation of beneficial, deleterious, or neutral alleles. Combining theoretical population genetics with molecular evolution data, he also developed the neutral theory of molecular evolution in which genetic drift is the main force changing allele frequencies. James F. Crow, himself a renowned population geneticist, considered Kimura to be one of the two greatest evolutionary geneticists, along with Gustave Malécot, after the great trio of the modern synthesis, Ronald Fisher, J. B. S. Haldane, and Sewall Wright.

Heterosis, hybrid vigor, or outbreeding enhancement is the improved or increased function of any biological quality in a hybrid offspring. An offspring is heterotic if its traits are enhanced as a result of mixing the genetic contributions of its parents. These effects can be due to Mendelian or non-Mendelian inheritance.

Balancing selection refers to a number of selective processes by which multiple alleles are actively maintained in the gene pool of a population at frequencies larger than expected from genetic drift alone. This can happen by various mechanisms, in particular, when the heterozygotes for the alleles under consideration have a higher fitness than the homozygote. In this way genetic polymorphism is conserved.

A heterozygote advantage describes the case in which the heterozygous genotype has a higher relative fitness than either the homozygous dominant or homozygous recessive genotype. The specific case of heterozygote advantage due to a single locus is known as overdominance. Overdominance is a condition in genetics where the phenotype of the heterozygote lies outside of the phenotypical range of both homozygote parents, and heterozygous individuals have a higher fitness than homozygous individuals.

Genetics, a discipline of biology, is the science of heredity and variation in living organisms.

Genetic load is the difference between the fitness of an average genotype in a population and the fitness of some reference genotype, which may be either the best present in a population, or may be the theoretically optimal genotype. The average individual taken from a population with a low genetic load will generally, when grown in the same conditions, have more surviving offspring than the average individual from a population with a high genetic load. Genetic load can also be seen as reduced fitness at the population level compared to what the population would have if all individuals had the reference high-fitness genotype. High genetic load may put a population in danger of extinction.

Inbreeding depression is the reduced biological fitness in a given population as a result of inbreeding. Population biological fitness refers to an organism's ability to survive and perpetuate its genetic material. Inbreeding depression is often the result of a population bottleneck. In general, the higher the genetic variation or gene pool within a breeding population, the less likely it is to suffer from inbreeding depression.

Test cross

Under the law of dominance in genetics, an individual expressing a dominant phenotype could contain either two copies of the dominant allele or one copy of each dominant and recessive allele. By performing a test cross, one can determine whether the individual is heterozygous or homozygous dominant.

Mitotic recombination is a type of genetic recombination that may occur in somatic cells during their preparation for mitosis in both sexual and asexual organisms. In asexual organisms, the study of mitotic recombination is one way to understand genetic linkage because it is the only source of recombination within an individual. Additionally, mitotic recombination can result in the expression of recessive genes in an otherwise heterozygous individual. This expression has important implications for the study of tumorigenesis and lethal recessive genes. Mitotic homologous recombination occurs mainly between sister chromatids subsequent to replication. Inter-sister homologous recombination is ordinarily genetically silent. During mitosis the incidence of recombination between non-sister homologous chromatids is only about 1% of that between sister chromatids.

Neutral mutations are changes in DNA sequence that are neither beneficial nor detrimental to the ability of an organism to survive and reproduce. In population genetics, mutations in which natural selection does not affect the spread of the mutation in a species are termed neutral mutations. Neutral mutations that are inheritable and not linked to any genes under selection will either be lost or will replace all other alleles of the gene. This loss or fixation of the gene proceeds based on random sampling known as genetic drift. A neutral mutation that is in linkage disequilibrium with other alleles that are under selection may proceed to loss or fixation via genetic hitchhiking and/or background selection.

In population genetics, fixation is the change in a gene pool from a situation where there exists at least two variants of a particular gene (allele) in a given population to a situation where only one of the alleles remains. In the absence of mutation or heterozygote advantage, any allele must eventually be lost completely from the population or fixed. Whether a gene will ultimately be lost or fixed is dependent on selection coefficients and chance fluctuations in allelic proportions. Fixation can refer to a gene in general or particular nucleotide position in the DNA chain (locus).

History of molecular evolution History of the field of study of molecular evolution

The history of molecular evolution starts in the early 20th century with "comparative biochemistry", but the field of molecular evolution came into its own in the 1960s and 1970s, following the rise of molecular biology. The advent of protein sequencing allowed molecular biologists to create phylogenies based on sequence comparison, and to use the differences between homologous sequences as a molecular clock to estimate the time since the last common ancestor. In the late 1960s, the neutral theory of molecular evolution provided a theoretical basis for the molecular clock, though both the clock and the neutral theory were controversial, since most evolutionary biologists held strongly to panselectionism, with natural selection as the only important cause of evolutionary change. After the 1970s, nucleic acid sequencing allowed molecular evolution to reach beyond proteins to highly conserved ribosomal RNA sequences, the foundation of a reconceptualization of the early history of life.

Zygosity Degree of similarity of the alleles in an organism

Zygosity is the degree to which both copies of a chromosome or gene have the same genetic sequence. In other words, it is the degree of similarity of the alleles in an organism.

Genetic purging is the reduction of the frequency of a deleterious allele, caused by an increased efficiency of natural selection prompted by inbreeding.

References

    See also