Quantitative genetics

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Quantitative genetics is the study of continuously measured traits (such as height or weight) and their mechanisms. It can be 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.

History

The field was founded, in evolutionary 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.

Basic principles

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The phenotypic value (P) of an individual 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 genes, 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 diploid organisms, a nucleus gene is represented twice in the genotype, one provided by each parent during sexual reproduction. Each gene is located at a particular place (a locus) on homologous chromosomes, one from each parent. Functional forms are called alleles. If both alleles at a gene have the same phenotypic effect, the gene is homozygous: if each allele at a gene is different, the gene is heterozygous. The average phenotypic outcome may be affected by dominance and by how genes interact with genes at other loci ("epistasis"). 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 Genetic 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 genetic assortment and segregation, which he called genetic variance. His residual genotypic variance ("residual") represented assortment which did not lead to phenotypic change. These specifications became the subdivisions of the additive (A) and dominance (D) variances.

The Environmental variance is much more straightforward. 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 variances for those components, denoted as:

V_P = V_a + V_d + V_E + V_I

The heritability of a trait is the proportion of the total (i.e. phenotypic) variance (V_P) that is explained by the total genotypic variance (V_G). This is known also as the "broad sense" heritability (H²). If only Additive genetic variance (V_A) is used in the numerator, the heritability is "narrow sense" (h²). 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.

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 (V_P) is explained by the above-mentioned components.

The principle of relationship (R) is central to understanding the resemblances within families and can be useful when calculating inbreeding. Relationship has two definitions that can be applied: -The probable portion of genes that are the same for two individuals due to common ancestry exceeding that of the base population -Additive/numerator relationship: the relationship coefficient (Rxy¬) = twice the probability of two genes at loci in different individuals being identical by descent. Rxy values can range from 0 to 2. Relationship can be calculated in several ways; from the known relationships of the individual, from bracket pedigrees, and from pedigree path diagrams.

Calculating relationship from known relationships

• Note: if the common ancestor is inbred, multiply the relationship by (1+inbreeding coefficient)

Calculating relationship from bracket pedigrees

Bracket pedigree

The number of common alleles is halved with each generation. See the attached pedigree for an example.

RXA = .5

RXC = .25

RBE = .5

RAB = 0 (no common ancestors in this pedigree)

Calculating relationship from pathway diagrams

Pathway diagram

RXY = Σ(.5)n(1+FCA)

n = number of segregations between X and Y through their common ancestor FCA = the inbreeding coefficient of the common ancestor

Example: calculating RAE and RBE Note: valid pathways only go through ancestors (only go against the direction of the arrow). For example, to calculate the relationship of A and B, the pathway A-D-B would be acceptable, whereas the pathway A-X-B would be not. The reason behind this is that having progeny together does not make two individuals related.

RAB: there are two possible pathways from A to E. A-D-F-E = (1/2)3 = .125 A-D-E = (1/2)2 = .25 Total: .375

RBE: there are four possible pathways from B to E. B-D-E = (1/2)2 = .25 B-D-F-E = (1/2)3 = .125 B-C-D-E = (1/2)3 = .125 B-C-D-F-E = (1/2)4 = .0625 Total: .5625

Allele frequency

Calculating allele frequency using the Hardy-Weinberg equation

The frequency of a genotype is the proportion of the population with that genotype. There are a few conditions for using the Hardy-Weinberg Equation: the population must be large, mating must be random, and the gene frequency must be the same whether male or female. If these conditions are met, the Hardy-Weinberg equation can be used to calculate exact frequency.

As an example, let “A” represent the dominant allele and “a” represent the recessive allele. The frequency of “A” is “p”, and the frequency of “a” is “q.” Put these into the Hardy-Weinberg equation to calculate.

Genotype: AA, Aa, aa

Frequency: p^2 + 2pq + q^2 = 1

The equation can be expanded to include more than two alleles by expanding (p+q+…+z)^2

Calculating allele frequency of a sex-linked trait

Population allele frequencies can be calculated from either the heterogametic or homogametic sex. Calculating from the homogametic sex requires use of the Hardy-Weinberg equation. In heterogametic cases, the frequencies are as follows (where E/e represents the gene linked on the X chromosome: f(X^EY) = p f(X^eY) = q

Forces that change gene frequency

In the field of animal production, allele frequency can be modified using selection. While artificial selection is not practiced in humans, it is an extremely influential factor in the growing field of production, and as such, has been included in this article. A common misconception in animal breeding states that inbreeding will change allele frequency; allele frequency does not change, but heterozygosity decreases, leading to more homozygous recessive genotypes and therefore more expression of the recessive phenotype.

Natural selection was originally proposed by Darwin, and means that some genotypes have a higher probability of survival and reproducing due to being adapted to their particular environment. Artificial selection is used to set breed standards and is seen both in selective breeding and in migration (acquiring genetic material from outside the population, such as by using artificial insemination). Occasionally, mutations can modify genes, but many mutations are either silent or lethal.

Testing for carriers of recessive alleles

In animal production, progeny testing is frequently used to determine whether a sire is a recessive carrier or not. The sire can be mated to known homozygous recessives, known carriers, a population with a known frequency, or his own daughters. The accuracy depends on the number of matings; the following table illustrates the accuracy with one mating (q represents the frequency of the recessive allele).

As the number of progeny increases, the accuracy does as well. Breeding to homozygous recessives has the highest accuracy with the lowest amount of progeny (ten versus 25 for heterozygotes and more than 35 for daughters).

Heritability and repeatability

Heritability in the broad sense (H^2) measures the total genetic influence on phenotype. It takes into account additive genetics, dominance, and epistatic genetic effects. The more specific measure of heritability (h^2) is generally more useful in production because only additive effects are passed from one generation to the next, and h^2 represents the average proportion of differences due to additive genetics. The square root of h^2 equals the correlation between additive genotype and expressed phenotype. Low heritability leads to higher environmental influence, while high heritability can lead to more rapid genetic progress. Typically, heritability of reproductive traits is low, disease resistance and production are moderately low to moderate, and conformation is high.

Heritability can be calculated by taking the variance of additive genetics and dividing it by the variance of the phenotype.

h^2 = σ^2a/σ^2p

σ^2p is the sum of the variances of additive genetics, dominance, epistasis, and environmental effects, and can also be written as σ^2g.

Repeatability (r) is the average proportion of differences likely to be repeated in later records. This value can only be determined for traits that manifest multiple times in an animal’s lifetime; birth weight, et cetera would not have a repeatability value. Generally, repeatability indicates the upper level of the heritability. Repeatability is calculated by taking the sum of genetic variance (σ^2g) and permanent environment variance, and dividing by the phenotypic variance.

r = (σ^2g + σ^2pe)/σ^2p

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 covariances, and the phenotypic covariance (Cov_P) 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:

See also

• Artificial selection
• Behavioral genetics
• Diallel cross
• Ewens's sampling formula
• Experimental evolution
• Genetic distance
• Heritability
• Population genetics, built on some of the same principles as quantitative genetics
• Selective breeding

References

• Seykora, Tony. Animal Science 3221 Animal Breeding. Tech. Minneapolis: University of Minnesota, 2011. Print.
• Falconer, D. S. & Mackay TFC (1996). Introduction to Quantitative Genetics. Fourth edition. Addison Wesley Longman, Harlow, Essex, UK.
• Roff DA (1997). Evolutionary Quantitative Genetics. Chapman & Hall, New York.
• Lynch M & Walsh B (1998). Genetics and Analysis of Quantitative Traits. Sinauer, Sunderland, MA.
• Gordon I.L. (2003). Refinements to the partitioning of the inbred genotypic variance. Heredity 91: 85-89.
• Fisher R.A. (1930). The Genetical Theory of Natural Selection. Clarendon Press, Oxford, UK.
• Mather K. & Jinks J.L. (1971). Biometrical Genetics. Chapman & Hall, London.
• Wright S. (1951). The genetical structure of populations. Annals of Eugenics 15: 323-354.

External links

• Quantitative Genetics Resources by Michael Lynch 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 Barton et al. from the textbook, Evolution.

v t e Genetics: Quantitative genetics Concepts in Quantitative Genetics Heritability · Quantitative trait locus · Candidate gene · Effective population size Related Topics Population genetics · Genomics · Evolutionary biology · Heredity