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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.[1][2] 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 (de novo) 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 (see Sex linkage). Since there is only one copy of the Y chromosome, Y-linked traits cannot be dominant nor 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.

Dominance is not inherent to an allele or its traits (phenotype). It is a strictly relative effect between two alleles of a given gene of any function; one allele can be dominant over a second allele of the same gene, recessive to a third and co-dominant with a fourth. Additionally, one allele may be dominant for one trait but not others.

Dominance is a key concept in Mendelian inheritance and classical genetics. Letters and Punnett squares are used to demonstrate the principles of dominance in teaching, and the use of upper case letters for dominant alleles and lower case letters for recessive alleles is a widely followed convention. A classic example of dominance is the inheritance of seed shape in peas. Peas may be round, associated with allele R, or wrinkled, associated with allele r. In this case, three combinations of alleles (genotypes) are possible: RR, Rr, and rr. The RR (homozygous) individuals have round peas, and the rr (homozygous) individuals have wrinkled peas. In Rr (heterozygous) individuals, the R allele masks the presence of the r allele, so these individuals also have round peas. Thus, allele R is dominant over allele r, and allele r is recessive to allele R.

Dominance differs from epistasis, the phenomenon of an allele of one gene masking the effect of alleles of a different gene.[3]

Background

Inheritance of dwarfing in maize. Demonstrating the heights of plants from the two parent variations and their F1 heterozygous hybrid (centre)

The concept of dominance was introduced by Gregor Johann Mendel. Though Mendel, "The Father of Genetics", first used the term in the 1860s, it was not widely known until the early twentieth century. Mendel observed that, for a variety of traits of garden peas having to do with the appearance of seeds, seed pods, and plants, there were two discrete phenotypes, such as round versus wrinkled seeds, yellow versus green seeds, red versus white flowers or tall versus short plants. When bred separately, the plants always produced the same phenotypes, generation after generation. However, when lines with different phenotypes were crossed (interbred), one and only one of the parental phenotypes showed up in the offspring (green, or round, or red, or tall). However, when these hybrid plants were crossed, the offspring plants showed the two original phenotypes, in a characteristic 3:1 ratio, the more common phenotype being that of the parental hybrid plants. Mendel reasoned that each parent in the first cross was a homozygote for different alleles (one parent AA and the other parent aa), that each contributed one allele to the offspring, with the result that all of these hybrids were heterozygotes (Aa), and that one of the two alleles in the hybrid cross dominated expression of the other: A masked a. The final cross between two heterozygotes (Aa X Aa) would produce AA, Aa, and aa offspring in a 1:2:1 genotype ratio with the first two classes showing the (A) phenotype, and the last showing the (a) phenotype, thereby producing the 3:1 phenotype ratio.

Mendel did not use the terms gene, allele, phenotype, genotype, homozygote, and heterozygote, all of which were introduced later. He did introduce the notation of capital and lowercase letters for dominant and recessive alleles, respectively, still in use today.

In 1928, British population geneticist Ronald Fisher proposed that dominance acted based on natural selection through the contribution of modifier genes. In 1929, American geneticist Sewall Wright responded by stating that dominance is simply a physiological consequence of metabolic pathways and the relative necessity of the gene involved. Wright's explanation became an established fact in genetics, and the debate was largely ended. Some traits may have their dominance influenced by evolutionary mechanisms, however.[4]phenotype). It is a strictly relative effect between two alleles of a given gene of any function; one allele can be dominant over a second allele of the same gene, recessive to a third and co-dominant with a fourth. Additionally, one allele may be dominant for one trait but not others.

Dominance is a key concept in Mendelian inheritance and classical genetics. Letters and Punnett squares are used to demonstrate the principles of dominance in teaching, and the use of upper case letters for dominant alleles and lower case letters for recessive alleles is a widely followed convention. A classic example of dominance is the inheritance of seed shape in peas. Peas may be round, associated with allele R, or wrinkled, associated with allele r. In this case, three combinations of alleles (genotypes) are possible: RR, Rr, and rr. The RR (homozygous) individuals have round peas, and the rr (homozygous) individuals have wrinkled peas. In Rr (heterozygous) individuals, the R allele masks the presence of the r allele, so these individuals also have round peas. Thus, allele R is dominant over allele r, and allele r is recessive to allele R.

Dominance differs from epistasis, the phenomenon of an allele of one gene masking the effect of alleles of a different gene.[3]

The concept of dominance was introduced by Gregor Johann Mendel. Though Mendel, "The Father of Genetics", first used the term in the 1860s, it was not widely known until the early twentieth century. Mendel observed that, for a variety of traits of garden peas having to do with the appearance of seeds, seed pods, and plants, there were two discrete phenotypes, such as round versus wrinkled seeds, yellow versus green seeds, red versus white flowers or tall versus short plants. When bred separately, the plants always produced the same phenotypes, generation after generation. However, when lines with different phenotypes were crossed (interbred), one and only one of the parental phenotypes showed up in the offspring (green, or round, or red, or tall). However, when these hybrid plants were crossed, the offspring plants showed the two original phenotypes, in a characteristic 3:1 ratio, the more common phenotype being that of the parental hybrid plants. Mendel reasoned that each parent in the first cross was a homozygote for different alleles (one parent AA and the other parent aa), that each contributed one allele to the offspring, with the result that all of these hybrids were heterozygotes (Aa), and that one of the two alleles in the hybrid cross dominated expression of the other: A masked a. The final cross between two heterozygotes (Aa X Aa) would produce AA, Aa, and aa offspring in a 1:2:1 genotype ratio with the first two classes showing the (A) phenotype, and the last showing the (a) phenotype, thereby producing the 3:1 phenotype ratio.

Mendel did not use the terms gene, allele, phenotype, genotype, homozygote, and heterozygote, all of which were introduced later. He did introduce the notation of capital and lowercase letters for dominant and recessive alleles, respectively, still in use today.

In 1928, British population geneticist Ronald Fisher proposed that dominance acted based on natural selection through the contribution of modifier genes. In 1929, American geneticist Sewall Wright responded by stating that dominance is simply a physiological consequence of metabolic pathways and the relative necessity of the gene involved. Wright's explanation became an established fact in genetics, and the debate was largely ended. Some traits may have their dominance influenced by evolutionary mechanisms, however.[4][5][6]

Chromosomes, genes, and alleles

Most animals and some plants have paired chromosomes, and are described as diploid. They have two versions of each chromosome, one contributed by the mother's ovum, and the other by the father's sperm, known as gametes, described as haploid, and created through meiosis. These gametes then fuse during fertilization during sexual reproduction, into a new single cell zygote, which divides multiple times, resulting in a new organism with the same number of pairs of chromosomes in each (non-gamete) cell as its parents.

Each chromosome of a matching (homologous) pair is structurally similar to the other, and has a very similar DNA sequence (loci, singular locus). The DNA in each chromosome functions as a series of discrete genes that influence various traits. Thus, each gene also has a corresponding homologue, which may exist in different versions called alleles. The alleles at the same locus on the two homologous chromosomes may be identical or different.

The blood type of a human is determined by a gene that creates an A, B, AB or O blood type and is located in the long arm of chromosome nine. There are three different alleles that could be present at this locus, but only two can be present in any individual, one inherited from their mother and one from their father.[7]

If two alleles of a given gene are identical, the organism is called a homozygote and is said to be homozygous with respect to that gene; if instead the two alleles are different, the organism is a heterozygote and is heterozygous. The genetic makeup of an organism, either at a single locus or over all its genes collectively, is called its genotype. The genotype of an organism, directly and indirectly, affects its molecular, physical, and other traits, which individually or collectively are called its phenotype. At heterozygous gene loci, the two alleles interact to produce the phenotype.

Dominance

Complete dominance

In complete dominance, the effect of one allele in a heterozygous genotype completely masks the effect of the other. The allele that masks the other is said to be dominant to the latter, and the allele that is masked is said to be recessive to the former.Ronald Fisher proposed that dominance acted based on natural selection through the contribution of modifier genes. In 1929, American geneticist Sewall Wright responded by stating that dominance is simply a physiological consequence of metabolic pathways and the relative necessity of the gene involved. Wright's explanation became an established fact in genetics, and the debate was largely ended. Some traits may have their dominance influenced by evolutionary mechanisms, however.[4][5][6]

Most animals and some plants have paired chromosomes, and are described as diploid. They have two versions of each chromosome, one contributed by the mother's ovum, and the other by the father's sperm, known as gametes, described as haploid, and created through meiosis. These gametes then fuse during fertilization during sexual reproduction, into a new single cell zygote, which divides multiple times, resulting in a new organism with the same number of pairs of chromosomes in each (non-gamete) cell as its parents.

Each chromosome of a matching (homologous) pair is structurally similar to the other, and has a very similar DNA sequence (loci, singular locus). The DNA in each chromosome functions as a series of discrete genes that influence various traits. Thus, each gene also has a corresponding homologue, which may exist in different versions called alleles. The alleles at

Each chromosome of a matching (homologous) pair is structurally similar to the other, and has a very similar DNA sequence (loci, singular locus). The DNA in each chromosome functions as a series of discrete genes that influence various traits. Thus, each gene also has a corresponding homologue, which may exist in different versions called alleles. The alleles at the same locus on the two homologous chromosomes may be identical or different.

The blood type of a human is determined by a gene that creates an A, B, AB or O blood type and is located in the long arm of chromosome nine. There are three different alleles that could be present at this locus, but only two can be present in any individual, one inherited from their mother and one from their father.[7]

If two alleles of a given gene are identical, the organism is called a homozygote and is said to be homozygous with respect to that gene; if instead the two alleles are different, the organism is a heterozygote and is heterozygous. The genetic makeup of an organism, either at a single locus or over all its genes collectively, is called its genotype. The genotype of an organism, directly and indirectly, affects its molecular, physical, and other traits, which individually or collectively are called its phenotype. At heterozygous gene loci, the two alleles interact to produce the phenotype.

In complete dominance, the effect of one allele in a heterozygous genotype completely masks the effect of the other. The allele that masks the other is said to be dominant to the latter, and the allele that is masked is said to be recessive to the former.[8] Complete dominance, therefore, means that the phenotype of the heterozygote is indistinguishable from that of the dominant homozygote.

A classic example of dominance is the inheritance of seed shape (pea shape) in peas. Peas may be round (associated with allele R) or wrinkled (associated with allele r). In this case, three combinations of alleles (genotypes) are possible: RR and rr are homozygous and Rr is heterozygous. The RR individuals have round peas and the rr individuals have wrinkled peas. In Rr individuals the R allele masks the presence of the r allele, so these individuals also have round peas. Thus, allele R is completely

A classic example of dominance is the inheritance of seed shape (pea shape) in peas. Peas may be round (associated with allele R) or wrinkled (associated with allele r). In this case, three combinations of alleles (genotypes) are possible: RR and rr are homozygous and Rr is heterozygous. The RR individuals have round peas and the rr individuals have wrinkled peas. In Rr individuals the R allele masks the presence of the r allele, so these individuals also have round peas. Thus, allele R is completely dominant to allele r, and allele r is recessive to allele R.

Incomplete dominance (also called partial dominance, semi-dominance or intermediate inheritance) occurs when the phenotype of the heterozygous genotype is distinct from and often intermediate to the phenotypes of the homozygous genotypes. For example, the snapdragon flower color is homozygous for either red or white. When the red homozygous flower is paired with the white homozygous flower, the result yields a pink snapdragon flower. The pink snapdragon is the result of incomplete dominance. A similar type of incomplete dominance is found in the four o'clock plant wherein pink color is produced when true-bred parents of white and red flowers are crossed. In quantitative genetics, where phenotypes are measured and treated numerically, if a heterozygote's phenotype is exactly between (numerically) that of the two homozygotes, the phenotype is said to exhibit no dominance at all, i.e. dominance exists only when the heterozygote's phenotype measure lies closer to one homozygote than the other.

When plants of the F1 generation are self-pollinated, the phenotypic and genotypic ratio of the F2 generation will be 1:2:1 (Red:Pink:White).[9]

See partial dominance hypothesis.

Co-dominance

Co-dominance in a Camellia cultivar
[9]

See partial dominance hypothesis.

Co-dominance occurs when the contributions of both alleles are visible in the phenotype.

For example, in the ABO blood group system, chemical modifications to a glycoprotein (the H antigen) on the surfaces of blood cells are controlled by three alleles, two of which are co-dominant to each other (IA, IB) and dominant over the recessive i at the ABO locus. The IA and IB alleles produce different modifications. The enzyme coded for by IA adds an N-acetylgalactosamine to a membrane-bound H antigen. The IB enzyme adds a galactose. The i allele produces no modification. Thus the IA and IB alleles are each dominant to i (IAIA and IAi individuals both have type A blood, and IBIB and IBi individuals both have type B blood), but IAIB individuals have both modifications on their blood cells and thus have type AB blood, so the IA and IB alleles are said to be co-dominant.

Another example occurs at the locus for the beta-globin component of hemoglobin, where the three molecular phenotypes of HbA/HbA, HbA/HbS, and HbS/HbS are all distinguishable by protein electrophoresis. (The medical condition produced by the heterozygous genotype is called sickle-cell trait and is a milder condition distinguishable from sickle-cell anemia, thus the alleles show incomplete dominance with respect to anemia, see above). For most gene loci at the molecular level, both alleles are expressed co-dominantly, because both are transcribed into RNA.

Co-dominance, where allelic products co-exist in the phenotype, is different from incomplete dominance, where the quantitative interaction of allele products produces an intermediate phenotype. For example, in co-dominance, a red homozygous flower and a white homozygous flower will produce offspring that have red and white spots. When plants of the F1 generation are self-pollinated, the phenotypic and genotypic ratio of the F2 generation will be 1:2:1 (Red:Spotted:White). These ratios are the same as those for incomplete dominance. Again, this classical terminology is inappropriate – in reality such cases should not be said to exhibit dominance at all. For example, in the ABO blood group system, chemical modifications to a glycoprotein (the H antigen) on the surfaces of blood cells are controlled by three alleles, two of which are co-dominant to each other (IA, IB) and dominant over the recessive i at the ABO locus. The IA and IB alleles produce different modifications. The enzyme coded for by IA adds an N-acetylgalactosamine to a membrane-bound H antigen. The IB enzyme adds a galactose. The i allele produces no modification. Thus the IA and IB alleles are each dominant to i (IAIA and IAi individuals both have type A blood, and IBIB and IBi individuals both have type B blood), but IAIB individuals have both modifications on their blood cells and thus have type AB blood, so the IA and IB alleles are said to be co-dominant.

Another example occurs at the locus for the beta-globin component of hemoglobin, where the three molecular phenotypes of HbA/HbA, HbA/HbS, and HbS/HbS are all distinguishable by protein electrophoresis. (The medical condition produced by the heterozygous genotype is called sickle-cell trait and is a milder condition distinguishable from sickle-cell anemia, thus the alleles show incomplete dominance with respect to anemia, see above). For most gene loci at the molecular level, both alleles are expressed co-dominantly, because both are transcribed into RNA.

Co-dominance, where allelic products co-exist in the phenotype, is different from incomplete dominance, where the quantitative interaction of allele products produces an intermediate phenotype. For example, in co-dominance, a red homozygous flower and a white homozygous flower will produce offspring that have red and white spots. When plants of the F1 generation are self-pollinated, the phenotypic and genotypic ratio of the F2 generation will be 1:2:1 (Red:Spotted:White). These ratios are the same as those for incomplete dominance. Again, this classical terminology is inappropriate – in reality such cases should not be said to exhibit dominance at all.

While it is often convenient to talk about a recessive allele or a dominant trait, dominance is not inherent to either an allele or its phenotype. Dominance is a relationship between two alleles of a gene and their associated phenotypes. A "dominant" allele is dominant to a particular allele of the same gene that can be inferred from the context, but it may be recessive to a third allele, and codominant to a fourth. Similarly, a "recessive" trait is a trait associated with a particular recessive allele implied by the context, but that same trait may occur in a different context where it is due to some other gene and a dominant allele.

Dominance is unrelated to the nature of the phenotype itself, that is, whether it is regarded as "normal" or "abnormal," "standard" or "nonstandard," "healthy" or "diseased," "stronger" or "weaker," or more or less extreme. A dominant or recessive allele may account for any of these trait types.

Dominance does not determine whether an allele is deleterious, neutral or advantageous. However, selection must operate on genes indirectly through phenotypes, and dominance affects the exposure of alleles in phenotypes, and hence the rate of change in allele frequencies under selection. Deleterious recessive alleles may persist in a population at low frequencies, with most copies carried in heterozygotes, at no cost to those individuals. These rare recessives are the basis for many hereditary genetic disorders.

Dominance is also unrelated to the distribution of alleles in the population. Both dominant and recessive alleles can be extremely common or extremely rare.

Nomenclature

In genetics, symbols began as algebraic placeholders. When one allele is dominant to another, the oldest convention is to symbolize the dominant allele with a capital letter. The recessive allele is assigned the same letter in lower case. In the pea example, once the dominance relationship between the two alleles is known, it is possible to designate the dominant allele that produces a round shape by a capital-letter symbol R, and the recessive allele that produces a wrinkled shape by a lower-case symbol r. The homozygous dominant, heterozygous, and homozygous recessive genotypes are then written RR, Rr, and rr, respectively. It would also be possible to designate the two alleles as W and w, and the three genotypes WW, Ww, and ww, the first two of which produced round peas and the third wrinkled peas. The choice of "R" or "W" as the symbol for the dominant allele does not pre-judge whether the allele causing the "round" or "wrinkled" phenotype when homozygous is the dominant one.

A gene may have several alleles. Each allele is symbolized by the locus symbol followed by a unique superscript. In many species, the most common allele in the wild population is designated the wild type allele. It is symbolized with a + character as a superscript. Other alleles are dominant or recessive to the wild type allele. For recessive alleles, the locu

Dominance is unrelated to the nature of the phenotype itself, that is, whether it is regarded as "normal" or "abnormal," "standard" or "nonstandard," "healthy" or "diseased," "stronger" or "weaker," or more or less extreme. A dominant or recessive allele may account for any of these trait types.

Dominance does not determine whether an allele is deleterious, neutral or advantageous. However, selection must operate on genes indirectly through phenotypes, and dominance affects the exposure of alleles in phenotypes, and hence the rate of change in allele frequencies under selection. Deleterious recessive alleles may persist in a population at low frequencies, with most copies carried in heterozygotes, at no cost to those individuals. These rare recessives are the basis for many hereditary genetic disorders.

Dominance is also unrelated to the distribution of alleles in the population. Both dominant and recessive alleles can be extremely common or extremely rare.

In genetics, symbols began as algebraic placeholders. When one allele is dominant to another, the oldest convention is to symbolize the dominant allele with a capital letter. The recessive allele is assigned the same letter in lower case. In the pea example, once the dominance relationship between the two alleles is known, it is possible to designate the dominant allele that produces a round shape by a capital-letter symbol R, and the recessive allele that produces a wrinkled shape by a lower-case symbol r. The homozygous dominant, heterozygous, and homozygous recessive genotypes are then written RR, Rr, and rr, respectively. It would also be possible to designate the two alleles as W and w, and the three genotypes WW, Ww, and ww, the first two of which produced round peas and the third wrinkled peas. The choice of "R" or "W" as the symbol for the dominant allele does not pre-judge whether the allele causing the "round" or "wrinkled" phenotype when homozygous is the dominant one.

A gene may have several alleles. Each allele is symbolized by the locus symbol followed by a unique superscript. In many species, the most common allele in the wild population is designated the wild type allele. It is symbolized with a + character as a superscript. Other alleles are dominant or recessive to the wild type allele. For recessive alleles, the locus symbol is in lower case letters. For alleles with any degree of dominance to the wild type allele, the first letter of the locus symbol is in upper case. For example, here are some of the alleles at the

A gene may have several alleles. Each allele is symbolized by the locus symbol followed by a unique superscript. In many species, the most common allele in the wild population is designated the wild type allele. It is symbolized with a + character as a superscript. Other alleles are dominant or recessive to the wild type allele. For recessive alleles, the locus symbol is in lower case letters. For alleles with any degree of dominance to the wild type allele, the first letter of the locus symbol is in upper case. For example, here are some of the alleles at the a locus of the laboratory mouse, Mus musculus: Ay, dominant yellow; a+, wild type; and abt, black and tan. The abt allele is recessive to the wild type allele, and the Ay allele is codominant to the wild type allele. The Ay allele is also codominant to the abt allele, but showing that relationship is beyond the limits of the rules for mouse genetic nomenclature.

Rules of genetic nomenclature have evolved as genetics has become more complex. Committees have standardized the rules for some species, but not for all. Rules for one species may differ somewhat from the rules for a different species.[10][11]

Although any individual of a diploid organism has at most two different alleles at any one locus (barring aneuploidies), most genes exist in a large number of allelic versions in the population as a whole. If the alleles have different effects on the phenotype, sometimes their dominance relationships can be described as a series.

For example, coat color in domestic cats is affected by a series of alleles of the TYR gene (which encodes the enzyme tyrosinase). The alleles C, cb, cs, and ca (full colour, Burmese, Siamese, and albino, respectively) produce different levels of pigment and hence different levels of colour dilution. The C allele (full colour) is completely dominant over the last three and the ca allele (albino) is completely recessive to the first three.[12]tyrosinase). The alleles C, cb, cs, and ca (full colour, Burmese, Siamese, and albino, respectively) produce different levels of pigment and hence different levels of colour dilution. The C allele (full colour) is completely dominant over the last three and the ca allele (albino) is completely recessive to the first three.[12][13][14]

In humans and other mammal species, sex is determined by two sex chromosomes called the X chromosome and the Y chromosome. Human females are typically XX; males are typically XY. The remaining pairs of chromosome are found in both sexes and are called autosomes; genetic traits due to loci on these chromosomes are described as autosomal, and may be dominant or recessive. Genetic traits on the X and Y chromosomes are called sex-linked, because they are linked to sex chromosomes, not because they are characteristic of one sex or the other. In practice, the term almost always refers to X-linked traits and a great many such traits (such as red-green colour vision deficiency) are not affected by sex. Females have two copies of every gene locus found on the X chromosome, just as for the autosomes, and the same dominance relationships apply. Males, however, have only one copy of each X chromosome gene locus, and are described as hemizygous for these genes. The Y chromosome is much smaller than the X, and contains a much smaller set of genes, including, but not limited to, those that influence 'maleness', such as the SRY gene for testis determining factor. Dominance rules for sex-linked gene loci are determined by their behavior in the female: because the male has only one allele (except in the case of certain types of Y chromosome aneuploidy), that allele is always expressed regardless of whether it is dominant or recessive. Birds have oppositely sex chromosomes: male birds have ZZ and female birds ZW chromosomes. However, inheritance of traits reminds XY-system otherwise; male zebra finches may carry white colouring gene in their one of two Z chromosome, but females develop white colouring always. Grasshoppers have XO-system. Females have XX, but males only X. There is no Y chromosome at all.

Epistasis

Epistasis ["epi + stasis = to sit on top"] is an interaction between alleles at two different gene loci that affect a single trait, which may sometimes resemble a dominance interaction between two different alleles at the same locus. Epistasis modifies the characteristic 9:3:3:1 ratio expected for two non-epistatic genes. For two loci, 14 classes of epistatic interactions are recognized. As an example of recessive epistasis, one gene locus may determine whether a flower pigment is yellow (AA or Aa) or green (aa), while another locus determines whether the pigment is produced (BB or Bb) or not (bb). In a bb plant, the flowers will be white, irrespective of the genotype of the other locus as AA, Aa, or aa. The bb combination is not dominant to the A allele: rather, the B gene shows recessive epistasis to the A gene, because the B locus when homozygous for the recessive allele (bb) suppresses phenotypic expression of the A locus. In a cross between two AaBb plants, this produces a characteristic 9:3:4 ratio, in this case of yellow : green : white flowers.

In dominant epistasis, one gene locus may determine yellow or green pigment as in the previous example: AA and Aa are yellow, and aa are green. A second locus determines whether a pigment precursor is produced (dd) or not (DD or Dd). Here, in a DD or Dd plant, the flowers will be colorless irrespective of the genotype at the A locus, because of the epistatic effect of the dominant D allele. Thus, in a cross between two AaDd plants, 3/4 of the plants will be colorless, and the yellow and green phenotypes are expressed only in dd plants. This produces a characteristic 12:3:1 ratio of white : yellow : green plants.

Supplementary epistasis occurs when two loci affect the same phenotype. For example, if pigment color is produced by CC or Cc but not cc, and by DD or Dd but not dd, then pigment is not produced in any genotypic combination with either cc or dd. That is, both loci must have at least one dominant allele to produce the phenotype. This produces a characteristic 9:7 ratio of pigmented to unpigmented plants. Complementary epistasis in contrast produces an unpigmented plant if and only if the genotype is cc and dd,

Epistasis ["epi + stasis = to sit on top"] is an interaction between alleles at two different gene loci that affect a single trait, which may sometimes resemble a dominance interaction between two different alleles at the same locus. Epistasis modifies the characteristic 9:3:3:1 ratio expected for two non-epistatic genes. For two loci, 14 classes of epistatic interactions are recognized. As an example of recessive epistasis, one gene locus may determine whether a flower pigment is yellow (AA or Aa) or green (aa), while another locus determines whether the pigment is produced (BB or Bb) or not (bb). In a bb plant, the flowers will be white, irrespective of the genotype of the other locus as AA, Aa, or aa. The bb combination is not dominant to the A allele: rather, the B gene shows recessive epistasis to the A gene, because the B locus when homozygous for the recessive allele (bb) suppresses phenotypic expression of the A locus. In a cross between two AaBb plants, this produces a characteristic 9:3:4 ratio, in this case of yellow : green : white flowers.

In dominant epistasis, one gene locus may determine yellow or green pigment as in the previous example: AA and Aa are yellow, and aa are green. A second locus determines whether a pigment precursor is produced (dd) or not (DD or Dd). Here, in a DD or Dd plant, the flowers will be colorless irrespective of the genotype at the A locus, because of the epistatic effe

In dominant epistasis, one gene locus may determine yellow or green pigment as in the previous example: AA and Aa are yellow, and aa are green. A second locus determines whether a pigment precursor is produced (dd) or not (DD or Dd). Here, in a DD or Dd plant, the flowers will be colorless irrespective of the genotype at the A locus, because of the epistatic effect of the dominant D allele. Thus, in a cross between two AaDd plants, 3/4 of the plants will be colorless, and the yellow and green phenotypes are expressed only in dd plants. This produces a characteristic 12:3:1 ratio of white : yellow : green plants.

Supplementary epistasis occurs when two loci affect the same phenotype. For example, if pigment color is produced by CC or Cc but not cc, and by DD or Dd but not dd, then pigment is not produced in any genotypic combination with either cc or dd. That is, both loci must have at least one dominant allele to produce the phenotype. This produces a characteristic 9:7 ratio of pigmented to unpigmented plants. Complementary epistasis in contrast produces an unpigmented plant if and only if the genotype is cc and dd, and the characteristic ratio is 15:1 between pigmented and unpigmented plants.[15]

Classical genetics considered epistatic interactions between two genes at a time. It is now evident from molecular genetics that all gene loci are involved in complex interactions with many other genes (e.g., metabolic pathways may involve scores of genes), and that this creates epistatic interactions that are much more complex than the classic two-locus models.

The frequency of the heterozygous state (which is the carrier state for a recessive trait) can be estimated using the Hardy–Weinberg formula:

This formula applies to a gene with exactly two alleles and relates the frequencies of those alleles in a large population to the frequencies of their three genotypes in that population.

For example, if p is the frequency of allele A, and q is the frequency of allele a then the terms p2, 2pq, and q2 are the frequencies of the genotypes AA, Aa and aa respectively. Since the gene has only two alleles, all alleles must be either A or a and p + q = 1. Now, if A is completely dominant to a then the frequency of the carrier genotype Aa cannot be directly observed (since it has the same traits as the homozygous genotype AA), however it can be estimated from the frequency of the recessive trait in the population, since this is the same as that of the homozygous genotype aa. i.e. the individual allele frequencies can be estimated: q = f(aa), p = 1 − q, and from those the frequency of the carrier genotype can be derived: f(Aa) = 2pq.

This formula relies on a number of assumptions and an accurate estimate of the frequency of the recessive trait. In general, any real-world situation will deviate from these assumptions to some degree, introducing corresponding inaccuracies into the estimate. If the recessive trait is rare, then it will be hard to estimate its frequency accurately, as a very large sample size will be needed.

Dominant versus advantageous