Quantitative genetics
Encyclopedia
Quantitative genetics is the study of continuous traits (such as height or weight) and their underlying mechanisms. It is effectively an extension of simple Mendelian inheritance
in that the combined effects of one or more genes and the environments in which they are expressed give rise to continuous distributions of phenotypic values.
ary terms, by the originators of the modern synthesis
, R.A. Fisher
, Sewall Wright
and J. B. S. Haldane
, and aimed to predict the response to selection given data on the phenotype
and relationships of individuals.
Analysis of Quantitative Trait Loci
, or QTL, is a more recent addition to the study of quantitative genetics. A QTL is a region in the genome that affects the trait or traits of interest. Quantitative trait loci approaches require accurate phenotypic, pedigree and genotypic data from a large number of individuals.
is the combined effect of the genotypic value (G) and the environmental deviation (E):
The genotypic value is the combined effect of all the genetic effects, including nuclear gene
s, mitochondrial
genes and interactions between the genes. It is worthwhile to note that the mathematics is related to the genetics: for which the brief following revision may be useful. In disomic (diploid) organisms, a nucleus gene is represented twice in the gene-set ("genotype"), one contribution being provided by each parent during sexual reproduction. Each "gene" is located at a particular place (a "locus" - the Latin word for place; plural "loci") on corresponding chromosomes (homologues), one from each parent. Any gene may have several functional forms in the species as a whole, and each of these may lead to outwardly different "effects" (= an average result in the phenotype considered over a large sample of gene-backgrounds and environments). These functional forms are "alleles" (or "allelomorphs", the original term). If both alleles at a gene have the same phenotypic effect (are the "same"), the gene is said to be "homozygous": if each allele at a gene is different in effect, the gene is "heterozygous". The average phenotypic outcome may also depend upon how alleles interact with their own homologous partner in the disomic genotype ("dominance"), and on how these alleles interact with those of other genes at other loci which also affect this phenotypic trait ("epistasis"). Notice that we have combined classical genetics ideas with those of statistics in this exposition. Terms such as "gene", "homologue", "allele", "homozygous" and "heterozygous" are genetical: but "effect" is statistical, and refers to the average observed over an infinity of backgrounds, both genetical and environmental. Thus, we have very sneakily defined the "genetic value" (or "genotypic" value) as the infinity mean of all the phenotypes it can ever produce in time and space! Before molecular genetics, there simply was no other way to do it! And after molecular genetics, this is still the most utilitarian way to tackle the idea of genetic value! Also notice that we have openly used fundamentals of reproductive biology behind the genetics. The founder of Quantitative Genetics - Sir Ronald Fisher - perceived all of this when he proposed the first mathematics of this branch of Genetics [Fisher R.A. (1930). The Genetical theory of Natural Selection. Oxford Clarendon Press.]. He sought to define a single statistical summary of all the variance arising from phenotypic change during the course of genetical assortment and segregation, which he called the "genetic" variance. His residual genotypic variance (which he called simply the "residual") represented that part of assortment which did not lead to phenotypic change, although the genes themselves had in fact been subject to meiosis and syngamy, of course. [A simplified exposition of this can be found in Falconer and Mackay (1966) - see References.] These partitions subsequently became the familiar subdivisions of the "additive" (A) and "dominance" (D) variances, respectively. These later names are utterly misleading and very unfortunate, and have led to much confusion as to what they mean genetically. [It would have been better for posterity had they been named "Assortative" (A), and "Stable" (S).] A more gene-focused partitioning was invented by Mather and Jinks in 1971, but they also were statisticians rather than geneticists, had their own rather opaque symbolism, and became somewhat overwhelmed by the Fisherian approach. Added to all of this was the problem that Fisher's underlying reproduction model (mating system) was unrealistically simplistic: whilst it facilitated solving the equations, it didn't describe many real-life scenarios. Fortunately, Wright (in the 1950s) did provide the means to overcome complex mating systems, but its own complexity minimised its popular adoption. Early in this millennium [Heredity (2003) 91: 85-89], a comprehensive linking together of all of these approaches reconciled their various meanings and relationships (as well as correcting an error), and suggested that new partitions reflecting real homozygosis [a] and heterozygosis [d] should replace the present "additive" [A] and "dominance" [D] subdivisions. This paper revealed, by the way, that the Additive Genetical variance consists of all the homozygote variance, plus part of the dominance variance, and a frequency-weighted covariance between homozygote and heterozygote gene effects. The so-called Dominance variance contains only the remainder of the overall dominance variance of the gene in question, being therefore very misleading indeed! It should be understood, however, that either method of partitioning still accounts for all of the genotypic variance in the model being used: it's the way it has been divided up which is being debated.
At least the Environmental variance is much more straight-forward. This can be subdivided into a pure environmental component (E) and an interaction component (I) describing the gene-environment interaction. The overall "single gene" model can be written as:
Expansion of the model to multiple genes (loci) is still not resolved satisfactorily, and until that is solved it is not possible to account for epistasis. The problem is being tackled currently.
The contribution of those components cannot be determined in a single individual, but they can be estimated for whole populations by estimating the variance
s for those components, denoted as:
The heritability
of a trait is the proportion of the total (i.e. phenotypic) variance (VP) that is explained by the total genotypic variance (VG). This is known also as the "broad sense" heritability (H2). If only Additive genetic variance (VA) is used in the numerator, the heritability is "narrow sense" (h2). Unfortunately, this is often simply called "heritability", with little reflection about its true meaning. The broadsense heritability indicates the genotypic determination of the phenotype: while the latter estimates the degree of assortative disequlibrium in the trait. Fisher proposed that this narrow-sense heritability might be appropriate in considering the results of natural selection, focusing as it does on disequilibrium: and it has been used also for predicting the results of artificial selection. This latter usage seems to be inappropriate, however, as breeders are interested in steering attributes towards new phenotypes (that is in utilising all the gene effects), rather than simply exploiting disequilibrium.
s, and the phenotypic covariance (CovP) between two traits can be partitioned in the same way as the variances described above. The genetic correlation
is calculated by dividing the covariance between the additive genetic effects of two traits by the square root of the product of the variances for the additive genetic effects of the two traits:
Mendelian inheritance
Mendelian inheritance is a scientific description of how hereditary characteristics are passed from parent organisms to their offspring; it underlies much of genetics...
in that the combined effects of one or more genes and the environments in which they are expressed give rise to continuous distributions of phenotypic values.
History
The field was founded, in evolutionEvolution
Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...
ary terms, by the originators of the modern synthesis
Modern evolutionary synthesis
The modern evolutionary synthesis is a union of ideas from several biological specialties which provides a widely accepted account of evolution...
, R.A. Fisher
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
, Sewall Wright
Sewall Wright
Sewall Green Wright was an American geneticist known for his influential work on evolutionary theory and also for his work on path analysis. With R. A. Fisher and J.B.S. Haldane, he was a founder of theoretical population genetics. He is the discoverer of the inbreeding coefficient and of...
and J. B. S. Haldane
J. B. S. Haldane
John Burdon Sanderson Haldane FRS , known as Jack , was a British-born geneticist and evolutionary biologist. A staunch Marxist, he was critical of Britain's role in the Suez Crisis, and chose to leave Oxford and moved to India and became an Indian citizen...
, and aimed to predict the response to selection given data on the phenotype
Phenotype
A phenotype is an organism's observable characteristics or traits: such as its morphology, development, biochemical or physiological properties, behavior, and products of behavior...
and relationships of individuals.
Analysis of Quantitative Trait Loci
Quantitative trait locus
Quantitative traits refer to phenotypes that vary in degree and can be attributed to polygenic effects, i.e., product of two or more genes, and their environment. Quantitative trait loci are stretches of DNA containing or linked to the genes that underlie a quantitative trait...
, or QTL, is a more recent addition to the study of quantitative genetics. A QTL is a region in the genome that affects the trait or traits of interest. Quantitative trait loci approaches require accurate phenotypic, pedigree and genotypic data from a large number of individuals.
Basic principles
The phenotypic value (P) of an individualIndividual
An individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...
is the combined effect of the genotypic value (G) and the environmental deviation (E):
- P = G + E
The genotypic value is the combined effect of all the genetic effects, including nuclear gene
Nuclear gene
A Nuclear gene is a gene located in the cell nucleus of a eukaryote. The term is used to distinguish nuclear genes from the genes in the mitochondrion, and in case of plants, also the chloroplast, which host their own genetic system and can produce proteins from scratch...
s, mitochondrial
Mitochondrion
In cell biology, a mitochondrion is a membrane-enclosed organelle found in most eukaryotic cells. These organelles range from 0.5 to 1.0 micrometers in diameter...
genes and interactions between the genes. It is worthwhile to note that the mathematics is related to the genetics: for which the brief following revision may be useful. In disomic (diploid) organisms, a nucleus gene is represented twice in the gene-set ("genotype"), one contribution being provided by each parent during sexual reproduction. Each "gene" is located at a particular place (a "locus" - the Latin word for place; plural "loci") on corresponding chromosomes (homologues), one from each parent. Any gene may have several functional forms in the species as a whole, and each of these may lead to outwardly different "effects" (= an average result in the phenotype considered over a large sample of gene-backgrounds and environments). These functional forms are "alleles" (or "allelomorphs", the original term). If both alleles at a gene have the same phenotypic effect (are the "same"), the gene is said to be "homozygous": if each allele at a gene is different in effect, the gene is "heterozygous". The average phenotypic outcome may also depend upon how alleles interact with their own homologous partner in the disomic genotype ("dominance"), and on how these alleles interact with those of other genes at other loci which also affect this phenotypic trait ("epistasis"). Notice that we have combined classical genetics ideas with those of statistics in this exposition. Terms such as "gene", "homologue", "allele", "homozygous" and "heterozygous" are genetical: but "effect" is statistical, and refers to the average observed over an infinity of backgrounds, both genetical and environmental. Thus, we have very sneakily defined the "genetic value" (or "genotypic" value) as the infinity mean of all the phenotypes it can ever produce in time and space! Before molecular genetics, there simply was no other way to do it! And after molecular genetics, this is still the most utilitarian way to tackle the idea of genetic value! Also notice that we have openly used fundamentals of reproductive biology behind the genetics. The founder of Quantitative Genetics - Sir Ronald Fisher - perceived all of this when he proposed the first mathematics of this branch of Genetics [Fisher R.A. (1930). The Genetical theory of Natural Selection. Oxford Clarendon Press.]. He sought to define a single statistical summary of all the variance arising from phenotypic change during the course of genetical assortment and segregation, which he called the "genetic" variance. His residual genotypic variance (which he called simply the "residual") represented that part of assortment which did not lead to phenotypic change, although the genes themselves had in fact been subject to meiosis and syngamy, of course. [A simplified exposition of this can be found in Falconer and Mackay (1966) - see References.] These partitions subsequently became the familiar subdivisions of the "additive" (A) and "dominance" (D) variances, respectively. These later names are utterly misleading and very unfortunate, and have led to much confusion as to what they mean genetically. [It would have been better for posterity had they been named "Assortative" (A), and "Stable" (S).] A more gene-focused partitioning was invented by Mather and Jinks in 1971, but they also were statisticians rather than geneticists, had their own rather opaque symbolism, and became somewhat overwhelmed by the Fisherian approach. Added to all of this was the problem that Fisher's underlying reproduction model (mating system) was unrealistically simplistic: whilst it facilitated solving the equations, it didn't describe many real-life scenarios. Fortunately, Wright (in the 1950s) did provide the means to overcome complex mating systems, but its own complexity minimised its popular adoption. Early in this millennium [Heredity (2003) 91: 85-89], a comprehensive linking together of all of these approaches reconciled their various meanings and relationships (as well as correcting an error), and suggested that new partitions reflecting real homozygosis [a] and heterozygosis [d] should replace the present "additive" [A] and "dominance" [D] subdivisions. This paper revealed, by the way, that the Additive Genetical variance consists of all the homozygote variance, plus part of the dominance variance, and a frequency-weighted covariance between homozygote and heterozygote gene effects. The so-called Dominance variance contains only the remainder of the overall dominance variance of the gene in question, being therefore very misleading indeed! It should be understood, however, that either method of partitioning still accounts for all of the genotypic variance in the model being used: it's the way it has been divided up which is being debated.
At least the Environmental variance is much more straight-forward. This can be subdivided into a pure environmental component (E) and an interaction component (I) describing the gene-environment interaction. The overall "single gene" model can be written as:
- P = a + d + E + I.
Expansion of the model to multiple genes (loci) is still not resolved satisfactorily, and until that is solved it is not possible to account for epistasis. The problem is being tackled currently.
The contribution of those components cannot be determined in a single individual, but they can be estimated for whole populations by estimating the variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
s for those components, denoted as:
- VP = Va + Vd + VE + VI
The heritability
Heritability
The Heritability of a population is the proportion of observable differences between individuals that is due to genetic differences. Factors including genetics, environment and random chance can all contribute to the variation between individuals in their observable characteristics...
of a trait is the proportion of the total (i.e. phenotypic) variance (VP) that is explained by the total genotypic variance (VG). This is known also as the "broad sense" heritability (H2). If only Additive genetic variance (VA) is used in the numerator, the heritability is "narrow sense" (h2). Unfortunately, this is often simply called "heritability", with little reflection about its true meaning. The broadsense heritability indicates the genotypic determination of the phenotype: while the latter estimates the degree of assortative disequlibrium in the trait. Fisher proposed that this narrow-sense heritability might be appropriate in considering the results of natural selection, focusing as it does on disequilibrium: and it has been used also for predicting the results of artificial selection. This latter usage seems to be inappropriate, however, as breeders are interested in steering attributes towards new phenotypes (that is in utilising all the gene effects), rather than simply exploiting disequilibrium.
Resemblance between relatives
Central in estimating the variances for the various components is the principle of relatedness. A child has a father and a mother. Consequently, the child and father share 50% of their alleles, as do the child and the mother. However, the mother and father normally do not share alleles as a result of shared ancestors. Similarly, two full siblings share also on average 50% of the alleles with each other, while half siblings share only 25% of their alleles. This variation in relatedness can be used to estimate which proportion of the total phenotypic variance (VP) is explained by the above-mentioned components.Correlated traits
Although some genes have only an effect on a single trait, many genes have an effect on various traits. Because of this, a change in a single gene will have an effect on all those traits. This is calculated using covarianceCovariance
In probability theory and statistics, covariance is a measure of how much two variables change together. Variance is a special case of the covariance when the two variables are identical.- Definition :...
s, and the phenotypic covariance (CovP) between two traits can be partitioned in the same way as the variances described above. The genetic correlation
Genetic correlation
Genetic correlation is the proportion of variance that two traits share due to genetic causes. Outside the theoretical boundary case of traits with zero heritability, the genetic correlation of traits is independent of their heritability: i.e., two traits can have a very high genetic correlation...
is calculated by dividing the covariance between the additive genetic effects of two traits by the square root of the product of the variances for the additive genetic effects of the two traits:
See also
- Artificial selectionArtificial selectionArtificial selection describes intentional breeding for certain traits, or combination of traits. The term was utilized by Charles Darwin in contrast to natural selection, in which the differential reproduction of organisms with certain traits is attributed to improved survival or reproductive...
- Diallel cross
- Ewens's sampling formulaEwens's sampling formulaIn population genetics, Ewens' sampling formula, describes the probabilities associated with counts of how many different alleles are observed a given number of times in the sample.-Definition:...
- Experimental evolutionExperimental evolutionIn evolutionary and experimental biology, the field of experimental evolution is concerned with testing hypotheses and theories of evolution by use of controlled experiments. Evolution may be observed in the laboratory as populations adapt to new environmental conditions and/or change by such...
- Genetic distanceGenetic distanceGenetic distance refers to the genetic divergence between species or between populations within a species. It is measured by a variety of parameters. Smaller genetic distances indicate a close genetic relationship whereas large genetic distances indicate a more distant genetic relationship...
- HeritabilityHeritabilityThe Heritability of a population is the proportion of observable differences between individuals that is due to genetic differences. Factors including genetics, environment and random chance can all contribute to the variation between individuals in their observable characteristics...
- Population geneticsPopulation geneticsPopulation genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population...
, built on some of the same principles as quantitative genetics - Selective breedingSelective breedingSelective breeding is the process of breeding plants and animals for particular genetic traits. Typically, strains that are selectively bred are domesticated, and the breeding is sometimes done by a professional breeder. Bred animals are known as breeds, while bred plants are known as varieties,...
External links
- Quantitative Genetics Resources by Michael LynchMichael Lynch (geneticist)Michael Lynch is Distinguished Professor of Evolution, Population Genetics and Genomics at Indiana University, Bloomington, Indiana, USA. Besides many highly acclaimed papers, especially in population genetics, he has written a two volume textbook with Bruce Walsh, widely considered the "Bible" of...
and Bruce Walsh, including the two volumes of their textbook, Genetics and Analysis of Quantitative Traits and Evolution and Selection of Quantitative Traits. - Resources by Nick BartonNick BartonProfessor Nicholas Hamilton Barton FRS FRSE is a British evolutionary biologist.He was educated at Peterhouse, Cambridge where he graduated with a first-class degree in Natural Sciences in 1976 and gained his PhD under Godfrey Hewitt at the University of East Anglia in 1979...
et al. from the textbook, Evolution.