Infinitesimal model

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The infinitesimal model, also known as the polygenic model, is a widely used statistical model in quantitative genetics and in genome-wide association studies. Originally developed in 1918 by Ronald Fisher, it is based on the idea that variation in a quantitative trait is influenced by an infinitely large number of genes, each of which makes an infinitely small (infinitesimal) contribution to the phenotype, as well as by environmental factors. [1] In "The Correlation between Relatives on the Supposition of Mendelian Inheritance", the original 1918 paper introducing the model, Fisher showed that if a trait is polygenic, "then the random sampling of alleles at each gene produces a continuous, normally distributed phenotype in the population". [2] However, the model does not necessarily imply that the trait must be normally distributed, only that its genetic component will be so around the average of that of the individual's parents. [3] The model served to reconcile Mendelian genetics with the continuous distribution of quantitative traits documented by Francis Galton. [4]

The model allows genetic variance to be assumed to remain constant even when natural selection is occurring, because each locus makes an infinitesimal contribution to the variance. [5] Consequently, all decline in genetic variance is assumed to be due to genetic drift. [6] It also relies on the fact that there must be a large enough number of loci for the distribution of loci to be normal, an assumption which breaks down if a trait is influenced by a small number of loci. According to one research group, the model "…is obviously not an exact representation of the genome of any species," as humans do not have an infinite number of genes, "but is a useful assumption to make in genetic evaluation," such as "explaining the underlying variation of a trait." [7] Some phenotypes undergo evolutionary adaptation such that they involve a modest number of loci of large effect. [8] Complex traits, however, have been shown to be largely explained by additive effects, with dominance being of negligible importance, though dominance and epistasis are still relevant for rare Mendelian disorders.[ improper synthesis? ] [9] [10] [11] [12] [13] [14] [15]

Related Research Articles

<span class="mw-page-title-main">Heredity</span> Passing of traits to offspring from the species parents or ancestor

Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction, the offspring cells or organisms acquire the genetic information of their parents. Through heredity, variations between individuals can accumulate and cause species to evolve by natural selection. The study of heredity in biology is genetics.

<span class="mw-page-title-main">Dominance (genetics)</span> 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 is called 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.

<span class="mw-page-title-main">Heritability</span> Estimation of effect of genetic variation on phenotypic variation of a trait

Heritability is a statistic used in the fields of breeding and genetics that estimates the degree of variation in a phenotypic trait in a population that is due to genetic variation between individuals in that population. The concept of heritability can be expressed in the form of the following question: "What is the proportion of the variation in a given trait within a population that is not explained by the environment or random chance?"

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

A quantitative trait locus (QTL) is a locus that correlates with variation of a quantitative trait in the phenotype of a population of organisms. QTLs are mapped by identifying which molecular markers correlate with an observed trait. This is often an early step in identifying the actual genes that cause the trait variation.

Genetic architecture is the underlying genetic basis of a phenotypic trait and its variational properties. Phenotypic variation for quantitative traits is, at the most basic level, the result of the segregation of alleles at quantitative trait loci (QTL). Environmental factors and other external influences can also play a role in phenotypic variation. Genetic architecture is a broad term that can be described for any given individual based on information regarding gene and allele number, the distribution of allelic and mutational effects, and patterns of pleiotropy, dominance, and epistasis.

A polygene is a member of a group of non-epistatic genes that interact additively to influence a phenotypic trait, thus contributing to multiple-gene inheritance, a type of non-Mendelian inheritance, as opposed to single-gene inheritance, which is the core notion of Mendelian inheritance. The term "monozygous" is usually used to refer to a hypothetical gene as it is often difficult to distinguish the effect of an individual gene from the effects of other genes and the environment on a particular phenotype. Advances in statistical methodology and high throughput sequencing are, however, allowing researchers to locate candidate genes for the trait. In the case that such a gene is identified, it is referred to as a quantitative trait locus (QTL). These genes are generally pleiotropic as well. The genes that contribute to type 2 diabetes are thought to be mostly polygenes. In July 2016, scientists reported identifying a set of 355 genes from the last universal common ancestor (LUCA) of all organisms living on Earth.

In multivariate quantitative genetics, a genetic correlation is the proportion of variance that two traits share due to genetic causes, the correlation between the genetic influences on a trait and the genetic influences on a different trait estimating the degree of pleiotropy or causal overlap. A genetic correlation of 0 implies that the genetic effects on one trait are independent of the other, while a correlation of 1 implies that all of the genetic influences on the two traits are identical. The bivariate genetic correlation can be generalized to inferring genetic latent variable factors across > 2 traits using factor analysis. Genetic correlation models were introduced into behavioral genetics in the 1970s–1980s.

<span class="mw-page-title-main">Additive genetic effects</span> Effect when genes source into a phenotype

Genetic effects are broadly divided into two categories: additive and non-additive. Additive genetic effects occur where expression of more than one gene contributes to phenotype, and the phenotypic expression of these gene(s) can be said to be the sum of these contributions.

In statistical genetics, inclusive composite interval mapping (ICIM) has been proposed as an approach to QTL mapping for populations derived from bi-parental crosses. QTL mapping is based on genetic linkage map and phenotypic data to attempt to locate individual genetic factors on chromosomes and to estimate their genetic effects.

A recombinant inbred strain or recombinant inbred line (RIL) is an organism with chromosomes that incorporate an essentially permanent set of recombination events between chromosomes inherited from two or more inbred strains. F1 and F2 generations are produced by intercrossing the inbred strains; pairs of the F2 progeny are then mated to establish inbred strains through long-term inbreeding.

Quasi-linkage equilibrium (QLE) is a mathematical approximation used in solving population genetics problems. Motoo Kimura introduced the notion to simplify a model of Fisher's fundamental theorem. QLE greatly simplifies population genetic equations whilst making the assumption of weak selection and weak epistasis. Selection under these conditions rapidly changes allele frequencies to a state where they evolve as if in linkage equilibrium. Kimura originally provided the sufficient conditions for QLE in two-locus systems, but recently several researchers have shown how QLE occurs in general multilocus systems. QLE allows theorists to approximate linkage disequilibria by simple expressions, often simple functions of allele or genotype frequencies, thereby providing solutions to highly complex problems involving selection on multiple loci or polygenic traits. QLE also plays an important role in justifying approximations in the derivation of quantitative genetic equations from mendelian principles.

The missing heritability problem arises from the difference between heritability estimates from genetic data and heritability estimates from twin and family data across many physical and mental traits, including diseases, behaviors, and other phenotypes. This is a problem that has significant implications for medicine, since a person's susceptibility to disease may depend more on the combined effect of all the genes in the background than on the disease genes in the foreground, or the role of genes may have been severely overestimated.

<span class="mw-page-title-main">Genetic variance</span> Biological concept

Genetic variance is a concept outlined by the English biologist and statistician Ronald Fisher in his fundamental theorem of natural selection. In his 1930 book The Genetical Theory of Natural Selection, Fisher postulates that the rate of change of biological fitness can be calculated by the genetic variance of the fitness itself. Fisher tried to give a statistical formula about how the change of fitness in a population can be attributed to changes in the allele frequency. Fisher made no restrictive assumptions in his formula concerning fitness parameters, mate choices or the number of alleles and loci involved.

Genome-wide complex trait analysis (GCTA) Genome-based restricted maximum likelihood (GREML) is a statistical method for heritability estimation in genetics, which quantifies the total additive contribution of a set of genetic variants to a trait. GCTA is typically applied to common single nucleotide polymorphisms (SNPs) on a genotyping array and thus termed "chip" or "SNP" heritability.

A human disease modifier gene is a modifier gene that alters expression of a human gene at another locus that in turn causes a genetic disease. Whereas medical genetics has tended to distinguish between monogenic traits, governed by simple, Mendelian inheritance, and quantitative traits, with cumulative, multifactorial causes, increasing evidence suggests that human diseases exist on a continuous spectrum between the two.

<span class="mw-page-title-main">Epistasis</span> Dependence of a gene mutations phenotype on mutations in other genes

Epistasis is a phenomenon in genetics in which the effect of a gene mutation is dependent on the presence or absence of mutations in one or more other genes, respectively termed modifier genes. In other words, the effect of the mutation is dependent on the genetic background in which it appears. Epistatic mutations therefore have different effects on their own than when they occur together. Originally, the term epistasis specifically meant that the effect of a gene variant is masked by that of different gene.

<span class="mw-page-title-main">Polygenic score</span> Numerical score aimed at predicting a trait based on variation in multiple genetic loci

In genetics, a polygenic score (PGS) is a number that summarizes the estimated effect of many genetic variants on an individual's phenotype. The PGS is also called the polygenic index (PGI) or genome-wide score; in the context of disease risk, it is called a polygenic risk score or genetic risk score. The score reflects an individual's estimated genetic predisposition for a given trait and can be used as a predictor for that trait. It gives an estimate of how likely an individual is to have a given trait based only on genetics, without taking environmental factors into account; and it is typically calculated as a weighted sum of trait-associated alleles.

Polygenic adaptation describes a process in which a population adapts through small changes in allele frequencies at hundreds or thousands of loci.

<span class="mw-page-title-main">Complex traits</span>

Complex traits are phenotypes that are controlled by two or more genes and do not follow Mendel's Law of Dominance. They may have a range of expression which is typically continuous. Both environmental and genetic factors often impact the variation in expression. Human height is a continuous trait meaning that there is a wide range of heights. There are an estimated 50 genes that affect the height of a human. Environmental factors, like nutrition, also play a role in a human's height. Other examples of complex traits include: crop yield, plant color, and many diseases including diabetes and Parkinson's disease. One major goal of genetic research today is to better understand the molecular mechanisms through which genetic variants act to influence complex traits. Complex traits are also known as polygenic traits and multigenic traits.

References

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