The dominance variance on a single locus

The dominance variance on a single locus

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I was reading the book "Genetics and Analysis of Quantitative Traits", by Lynch and Walsh. I how the covariance between two individuals with IBD $Theta$ gets divided into just the additive variance and dominance variance component, even in the simple $1$ locus case.

Here my understanding of the modelling (for the simple one allele case):

Given a genotypic value $G_{i,j}$ of mean $0$, $i,j in {0,1}$ we find numbers $alpha_0$ and $alpha_1$ minimising the least squares of the following form $mathbb{E}(G_{i,j}-alpha_i-alpha_j)^2$, where the expectation is over the population.

We next define the error terms in each case as $delta_{i,j}=G_{i,j}-alpha_i-alpha_j$. From the properties, viewed as functions of the population $alpha_i$ is independent of $delta_{i,j}$, and both have mean $0$.

The claim made in the book is that given two individuals, with IBD $Theta$ and probability that the genotype is equal $Delta$, the covariance of the genotypes $G_{i,j}$ and $G_{k,l}$ is given by,

$$ ext{cov}(G_{i,j},G_{k,l}) = 2Theta sigma_A^2 +Delta sigma_D^2,$$

where $sigma_A^2= ext{Var}(alpha_i)$, and $sigma_D^2 = ext{Var}(delta_{i,j})$.

Expanding the LHS of the expression, showing that $mathbb{E}[(alpha_i +alpha_j)(alpha_k+alpha_l)] =Theta sigma_A^2$ is quite easy. It also seems to follow from the that the the terms $mathbb{E}[(alpha_i +alpha_j)delta_{k,l}]=0$ from independence of errors from the $alpha$.

On analysing $mathbb{E}[delta_{i,j}delta_{k,l}]$, we see that if both genotypes are equal, which occurs with probability $Delta$, then this reduces to $sigma_D^2$. This gives us a term $Theta sigma_D^2$. Further, if both $i,j$ and $k,l$ are not IBD then the covariance is $0$. However when one of the two alleles are IBD, then it is not clear to me that this the covariance will still be $0$.

The book seems to claim that unless both alleles are IBD, $delta_{i,j}$ and $delta_{k,l}$ are independent. I do not see why this is the case. Am I missing anything here? I'd appreciate any help wrt this.

It looks like I could solve the question. My understanding is as follows.

Let $(X_1,Y_1)$, $(X_2,Y_2)$ (corresponds to $i,j$ and $k,l$ in the question) be the genotypes of two individuals at some location. We assume that neither individual is in-bred. In this case define, egin{align*} Delta_7&= ext{Pr}( ext{Both alleles ${X_1,Y_1}$ and ${X_2, Y_2}$ are IBD}), Delta_8&= ext{Pr}( ext{Exactly one allele pair of the four pairs is IBD}), Delta_9&= ext{Pr}( ext{ No IBD between the two individuals}). end{align*} $Delta_7$, $Delta_8$ and $Delta_9$ are calculated from the pedigrees. For example, for non-twin siblings, $Delta_7 = frac{1}{4}$, $Delta_8=frac{1}{2}$, $Delta_9 =frac{1}{4}$.

We note that the IBD coefficient (also called kinship coefficient) $Theta$ is egin{align*} Theta = frac{1}{2} Delta_7 + frac{1}{4} Delta_8. end{align*} Also the fraternity coefficient, $Delta =Delta_7$. Thus we have that the covariance between the genotypic value of two individuals is given by egin{align*} mathbb{E}[G(X_1,Y_1)G(X_2,Y_2)] =& Delta_7 mathbb{E}[G(X_1,Y_1)G(X_2,Y_2)| ext{both IBD}] + &Delta_8 mathbb{E}[G(X_1,Y_1)G(X_2,Y_2)| ext{one IBD}] + Delta_9 mathbb{E}[G(X_1,Y_1)G(X_2,Y_2)| ext{no IBD}]. end{align*}

Further note that, egin{align*} mathbb{E}[G(X_1,Y_1)G(X_2,Y_2)| ext{both IBD}] &= mathbb{E}[G^2(X_1,Y_1)], &= sigma_A^2 +sigma_D^2. end{align*}

egin{align*} mathbb{E}[G(X_1,Y_1)G(X_2,Y_2)| ext{no IBD}] &= mathbb{E}[G(X_1,Y_1)] mathbb{E}[G(X_2,Y_2)], &=0. end{align*}

egin{align*} mathbb{E}[G(X_1,Y_1)G(X_2,Y_2)| ext{one IBD}] &= mathbb{E}[(alpha(X)+alpha(Y_1)+delta(X,Y_1))(alpha(X)+alpha(Y_2)+delta(X,Y_2))], &=mathbb{E}[alpha^2(X)] + 2 mathbb{E}(alpha(X) delta(X,Y_1)) + mathbb{E} [delta(X,Y_1)delta(X,Y_2)], &= frac{1}{2} sigma_A^2 + 2 mathbb{E} [ alpha(X) mathbb{E}[delta(X,Y_1) | X] ] + mathbb{E} [mathbb{E}[delta(X,Y_1)|X]mathbb{E}[delta(X,Y_2)|X]], &= frac{1}{2} sigma_A^2. end{align*}

Thus we have that, egin{align*} mathbb{E}[G(X_1,Y_1)G(X_2,Y_2)] =& left(frac{1}{2}Delta_7 + frac{1}{4}Delta_8 ight) 2 sigma_A^2 + Delta_7 sigma_D^2, &= 2Theta sigma_A^2 + Delta sigma_D^2, end{align*} which is as claimed.

Single-locus heterotic effects and dominance by dominance interactions can adequately explain the genetic basis of heterosis in an elite rice hybrid

The genetic basis of heterosis of an elite rice hybrid was investigated by using an "immortalized F(2)" population produced by randomly permutated intermating of 240 recombinant inbred lines from a cross between the parents of Shanyou 63, the most widely cultivated hybrid in China. Measurements of heterosis for crosses in the immortalized F(2) population were obtained from replicated field trials over 2 years by inter-planting the hybrids with the parental recombinant inbred lines. The analyses were conducted making use of a linkage map comprising 231 segregating molecular marker loci covering the entire rice genome. Heterotic effects were detected at 33 loci for the four traits with modified composite interval mapping. The heterotic loci showed little overlap with quantitative trait loci for trait performance, suggesting that heterosis and trait performance may be conditioned by different sets of loci. Large numbers of digenic interactions were resolved by using two-way ANOVA and confirmed by randomization tests. All kinds of genetic effects, including partial-, full-, and overdominance at single-locus level and all three forms of digenic interactions (additive by additive, additive by dominance, and dominance by dominance), contributed to heterosis in the immortalized F(2) population, indicating that these genetic components were not mutually exclusive in the genetic basis of heterosis. Heterotic effects at the single-locus level, in combination with the marginal advantages of double heterozygotes caused by dominance by dominance interaction at the two-locus level could adequately explain the genetic basis of heterosis in Shanyou 63. These results may help reconcile the century-long debate concerning the genetic basis of heterosis.

Dominance genetic variance and inbreeding in natural populations

It is assumed that dominance genetic variance contributes little to the prediction of evolutionary change in polygenic traits. This is based on the assumption that populations are large, panmictic, and randomly mating. However, the ecological contexts of most wild populations studied to date violate one, if not several, of these assumptions, and the widespread occurrence of inbreeding and inbreeding depression of phenotypic traits and fitness suggests dominance genetic effects are ubiquitous. This chapter reviews what genetic dominance represents at the level of a single locus and how this contributes to phenotypic variation and discusses how to estimate dominance variance with emphasis on the complications arising in wild populations and with inbreeding. Next, empirical estimates of dominance variance are reviewed. Since no estimates exist of dominance variance in the wild (except for humans), laboratory and agricultural populations are examined, and it is shown that dominance variance is a major contributor to phenotypic variation and in some cases contributes as much as additive genetic variance. This chapter also discusses how inbreeding and dominance affect predictions of evolutionary change, and ends with a review of some of the empirical questions for which genetic dominance is an important quantity in its own right. In this chapter, it is argued that dominance variance has been ignored for too long, may hamper the ability to predict evolutionary change, can be a major contributor to phenotypic variance, is interesting to study in its own right, and provides many avenues of research to be addressed by empirical study.

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Accession codes

Primary accessions

European Nucleotide Archive

Data deposits

Details of the SNPs used in the study have been deposited in dbSNP ( under accession numbers ss1867919552–ss1868858426, and re-sequencing data have been deposited in EMBL Nucleotide Sequence Database (European Nucleotide Archive) under accession number PRJEB10744. SNP genotype and phenotype data and detailed DNA sequence information of the main candidate gene regions are available in Dryad (

Materials and methods

Plant material

In the cultivated octoploid F.×ananassa, a pseudo full-sibling F1 population obtained from a cross between the Capitola variety and the CF1116 (CireF_1116) genotype described previously by Lerceteau-Köhler et al. (2003) was used. The two parents Capitola and CF1116 display PF and SF behaviours, respectively ( Fig. 1A). The segregating population plus the parental lines were observed from 2002 to 2007 under tunnel production ( Table 1).

Analyses of the pseudo full-sibling F1 population segregating for the PF and RU traits. Phenotypic data were obtained from 2002 to 2007, except for 2006. According to the year, one to four plants per genotype were studied. In 2003, notations were performed twice, on the first planting of the segregating population (named 2003) and on the second planting in 2003 (named 2003b).

Year of observation . 2002 . 2003 . 2003b . 2004 . 2005 . 2007 .
Studied trait:
Perpetual flowering (PF) PF-2002 PF-2003 PF-2003b PF-2004 PF-2005 PF-2007
Runnering (RU) RU-2002 RU-2003 RU-2005
No. plants per genotype 1 1 4 4 3 3
Year of observation . 2002 . 2003 . 2003b . 2004 . 2005 . 2007 .
Studied trait:
Perpetual flowering (PF) PF-2002 PF-2003 PF-2003b PF-2004 PF-2005 PF-2007
Runnering (RU) RU-2002 RU-2003 RU-2005
No. plants per genotype 1 1 4 4 3 3

Analyses of the pseudo full-sibling F1 population segregating for the PF and RU traits. Phenotypic data were obtained from 2002 to 2007, except for 2006. According to the year, one to four plants per genotype were studied. In 2003, notations were performed twice, on the first planting of the segregating population (named 2003) and on the second planting in 2003 (named 2003b).

Year of observation . 2002 . 2003 . 2003b . 2004 . 2005 . 2007 .
Studied trait:
Perpetual flowering (PF) PF-2002 PF-2003 PF-2003b PF-2004 PF-2005 PF-2007
Runnering (RU) RU-2002 RU-2003 RU-2005
No. plants per genotype 1 1 4 4 3 3
Year of observation . 2002 . 2003 . 2003b . 2004 . 2005 . 2007 .
Studied trait:
Perpetual flowering (PF) PF-2002 PF-2003 PF-2003b PF-2004 PF-2005 PF-2007
Runnering (RU) RU-2002 RU-2003 RU-2005
No. plants per genotype 1 1 4 4 3 3


Inflorescence and primary stolon emergence was evaluated on Capitola and CF1116 parents during one production season (April to October) by counting the newly emerged organs every 2 or 3 weeks. For the segregating population and their parents, the PF trait was evaluated as the number of newly emerged inflorescences from the end of May to the beginning of August, whilst RU was evaluated as the total number of primary stolons counted in summer. These measures were performed over 6 and 3 years, respectively ( Table 1).

Data analysis

For the two parents and the progeny, the mean and standard deviation of newly emerged inflorescences and the primary stolon numbers were calculated for each year of observation. Pairwise comparisons among parents were done using Student’s t-test (P <0.05) for the mean number of inflorescences and primary stolons. For the two traits PF and RU, and for each year of observation, genotypic effect within progeny, broad sense heritability, and identification of transgressive trait were evaluated as described previously by Lerceteau-Köhler et al. (2012). Spearman correlation coefficients were calculated for the different trait values, both between and within years (PROC CORR SAS).

Evaluation of PF as a Mendelian trait was done by grouping the number of newly emerged inflorescences into two classes, PF and SF ( Fig. 2A). A segregation ratio of 1:1 (PF:SF) of the segregating population was tested for goodness of fit to the theoretical ratio for the hypothesis that one dominant locus controls the PF trait (χ 2 test).

Frequency distribution of newly emerged inflorescences (A) and primary stolons (B) in the Capitola×CF1116 segregating population. Values are the adjusted means. The phenotypic values of the parents, Capitola and CF1116, are indicated by arrows. Each genotype presenting fewer than three or more than four newly emerged inflorescences was considered as SF or PF, respectively.

Frequency distribution of newly emerged inflorescences (A) and primary stolons (B) in the Capitola×CF1116 segregating population. Values are the adjusted means. The phenotypic values of the parents, Capitola and CF1116, are indicated by arrows. Each genotype presenting fewer than three or more than four newly emerged inflorescences was considered as SF or PF, respectively.

Genetic maps and QTL detection

For the octoploid population, the female and male genetic maps were developed previously using data obtained from the cross Capitola×CF1116 ( Rousseau-Gueutin et al., 2008 Lerceteau-Köhler et al., 2012). The PF trait was mapped as a Mendelian marker named FaPF. QTL detection was performed by composite-interval mapping using QTL Cartographer software ( Basten et al., 1997) as described by Lerceteau-Köhler et al. (2012) except that the logarithm of odds (LOD) thresholds corresponded to a genome-wide significance level of α=0.05.

The dominance variance on a single locus - Biology

For human complex traits, non-additive genetic variation has been invoked to explain “missing heritability,” but its discovery is often neglected in genome-wide association studies. Here we propose a method of using SNP data to partition and estimate the proportion of phenotypic variance attributed to additive and dominance genetic variation at all SNPs ( h S N P 2 and δ S N P 2 ) in unrelated individuals based on an orthogonal model where the estimate of h S N P 2 is independent of that of δ S N P 2 . With this method, we analyzed 79 quantitative traits in 6,715 unrelated European Americans. The estimate of δ S N P 2 averaged across all the 79 quantitative traits was 0.03, approximately a fifth of that for additive variation (average h S N P 2 = 0.15). There were a few traits that showed substantial estimates of δ S N P 2 , none of which were replicated in a larger sample of 11,965 individuals. We further performed genome-wide association analyses of the 79 quantitative traits and detected SNPs with genome-wide significant dominance effects only at the ABO locus for factor VIII and von Willebrand factor. All these results suggest that dominance variation at common SNPs explains only a small fraction of phenotypic variation for human complex traits and contributes little to the missing narrow-sense heritability problem.

End of Chapter Review Questions

When the product of the lacZ gene, beta-galactosidase, interacts with the substrate X-Gal on LB agar, colonies turn blue.

-genetic maps indicate the relative position of genes as they are aligned along the chromosome, but does not give information about the space between the genes
-physical maps are based on the sequence of the chromosome and give information on all the base pairs but may not give information on which base pairs are genes

Which trait would best respond to artificial selection by the farmer? A: Shell color (59/112= .53)

-Template DNA is incubated with primers, nucleotides, and a thermostable polymerase in a buffer with Mg2+Mg2+ ions (required for polymerase activity).

-PCR reaction:
-There is an initial denaturation step at 95 °C and then the following steps are cycled 25-30 times.

1) 95 °C - Denaturation Time - to generate ssDNA
2) 55 °C - Annealing Time - primers bind to complementary regions of the template DNA
3) 68 °C - Extension Time - the polymerase extends the primers to form dsDNA.

-The incubation times depend on the size of the DNA being copied.

-After 25-30 cycles, there is a final extension step at 68 °C to ensure the polymerase completes the extension of all DNA strands.


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 Edit

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.

Complete dominance Edit

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 dominant to allele r, and allele r is recessive to allele R.

Incomplete dominance Edit

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]

Co-dominance Edit

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 (I A , I B ) and dominant over the recessive i at the ABO locus. The I A and I B alleles produce different modifications. The enzyme coded for by I A adds an N-acetylgalactosamine to a membrane-bound H antigen. The I B enzyme adds a galactose. The i allele produces no modification. Thus the I A and I B alleles are each dominant to i (I A I A and I A i individuals both have type A blood, and I B I B and I B i individuals both have type B blood), but I A I B individuals have both modifications on their blood cells and thus have type AB blood, so the I A and I B 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 Hb A /Hb A , Hb A /Hb S , and Hb S /Hb S 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.

Addressing common misconceptions Edit

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.

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 locus of the laboratory mouse, Mus musculus: A y , dominant yellow a + , wild type and a bt , black and tan. The a bt allele is recessive to the wild type allele, and the A y allele is codominant to the wild type allele. The A y allele is also codominant to the a bt 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]

Multiple alleles Edit

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, c b , c s , and c a (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 c a allele (albino) is completely recessive to the first three. [12] [13] [14]

Autosomal versus sex-linked dominance Edit

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 opposite 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 Edit

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, 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.

Hardy–Weinberg principle (estimation of carrier frequency) Edit

The frequency of the heterozygous state (which is the carrier state for a recessive trait) can be estimated using the Hardy–Weinberg formula: p 2 + 2 p q + q 2 = 1 +2pq+q^<2>=1>

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 p 2 , 2pq, and q 2 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 Edit

The property of "dominant" is sometimes confused with the concept of advantageous and the property of "recessive" is sometimes confused with the concept of deleterious, but the phenomena are distinct. Dominance describes the phenotype of heterozygotes with regard to the phenotypes of the homozygotes and without respect to the degree to which different phenotypes may be beneficial or deleterious. Since many genetic disease alleles are recessive and because the word dominance has a positive connotation, the assumption that the dominant phenotype is superior with respect to fitness is often made. This is not assured however as discussed below while most genetic disease alleles are deleterious and recessive, not all genetic diseases are recessive.

Nevertheless, this confusion has been pervasive throughout the history of genetics and persists to this day. Addressing this confusion was one of the prime motivations for the publication of the Hardy–Weinberg principle.

The molecular basis of dominance was unknown to Mendel. It is now understood that a gene locus includes a long series (hundreds to thousands) of bases or nucleotides of deoxyribonucleic acid (DNA) at a particular point on a chromosome. The central dogma of molecular biology states that "DNA makes RNA makes protein", that is, that DNA is transcribed to make an RNA copy, and RNA is translated to make a protein. In this process, different alleles at a locus may or may not be transcribed, and if transcribed may be translated to slightly different versions of the same protein (called isoforms). Proteins often function as enzymes that catalyze chemical reactions in the cell, which directly or indirectly produce phenotypes. In any diploid organism, the DNA sequences of the two alleles present at any gene locus may be identical (homozygous) or different (heterozygous). Even if the gene locus is heterozygous at the level of the DNA sequence, the proteins made by each allele may be identical. In the absence of any difference between the protein products, neither allele can be said to be dominant (see co-dominance, above). Even if the two protein products are slightly different (allozymes), it is likely that they produce the same phenotype with respect to enzyme action, and again neither allele can be said to be dominant.

Loss of function and haplosufficiency Edit

Dominance typically occurs when one of the two alleles is non-functional at the molecular level, that is, it is not transcribed or else does not produce a functional protein product. This can be the result of a mutation that alters the DNA sequence of the allele. [ citation needed ] An organism homozygous for the non-functional allele will generally show a distinctive phenotype, due to the absence of the protein product. For example, in humans and other organisms, the unpigmented skin of the albino phenotype [16] results when an individual is homozygous for an allele that encodes a non-functional version of an enzyme needed to produce the skin pigment melanin. It is important to understand that it is not the lack of function that allows the allele to be described as recessive: this is the interaction with the alternative allele in the heterozygote. Three general types of interaction are possible:

  1. In the typical case, the single functional allele makes sufficient protein to produce a phenotype identical to that of the homozygote: this is called haplosufficiency. For example, suppose the standard amount of enzyme produced in the functional homozygote is 100%, with the two functional alleles contributing 50% each. The single functional allele in the heterozygote produces 50% of the standard amount of enzyme, which is sufficient to produce the standard phenotype. If the heterozygote and the functional-allele homozygote have identical phenotypes, the functional allele is dominant to the non-functional allele. This occurs at the albino gene locus: the heterozygote produces sufficient enzyme to convert the pigment precursor to melanin, and the individual has standard pigmentation.
  2. Less commonly, the presence of a single functional allele gives a phenotype that is not normal but less severe than that of the non-functional homozygote. This occurs when the functional allele is not haplo-sufficient. The terms haplo-insufficiency and incomplete dominance are typically applied to these cases. The intermediate interaction occurs where the heterozygous genotype produces a phenotype intermediate between the two homozygotes. Depending on which of the two homozygotes the heterozygote most resembles, one allele is said to show incomplete dominance over the other. For example, in humans the Hb gene locus is responsible for the Beta-chain protein (HBB) that is one of the two globin proteins that make up the blood pigment hemoglobin. [16] Many people are homozygous for an allele called Hb A some persons carry an alternative allele called Hb S , either as homozygotes or heterozygotes. The hemoglobin molecules of Hb S /Hb S homozygotes undergo a change in shape that distorts the morphology of the red blood cells, and causes a severe, life-threatening form of anemia called sickle-cell anemia. Persons heterozygous Hb A /Hb S for this allele have a much less severe form of anemia called sickle-cell trait. Because the disease phenotype of Hb A /Hb S heterozygotes is more similar to but not identical to the Hb A /Hb A homozygote, the Hb A allele is said to be incompletely dominant to the Hb S allele.
  3. Rarely, a single functional allele in the heterozygote may produce insufficient gene product for any function of the gene, and the phenotype resembles that of the homozygote for the non-functional allele. This complete haploinsufficiency is very unusual. In these cases, the non-functional allele would be said to be dominant to the functional allele. This situation may occur when the non-functional allele produces a defective protein that interferes with the proper function of the protein produced by the standard allele. The presence of the defective protein "dominates" the standard protein, and the disease phenotype of the heterozygote more closely resembles that of the homozygote for two defective alleles. The term "dominant" is often incorrectly applied to defective alleles whose homozygous phenotype has not been examined, but which cause a distinct phenotype when heterozygous with the normal allele. This phenomenon occurs in a number of trinucleotide repeat diseases, one example being Huntington's disease. [17]

Dominant-negative mutations Edit

Many proteins are normally active in the form of a multimer, an aggregate of multiple copies of the same protein, otherwise known as a homomultimeric protein or homooligomeric protein. In fact, a majority of the 83,000 different enzymes from 9800 different organisms in the BRENDA Enzyme Database [18] represent homooligomers. [19] When the wild-type version of the protein is present along with a mutant version, a mixed multimer can be formed. A mutation that leads to a mutant protein that disrupts the activity of the wild-type protein in the multimer is a dominant-negative mutation.

A dominant-negative mutation may arise in a human somatic cell and provide a proliferative advantage to the mutant cell, leading to its clonal expansion. For instance, a dominant-negative mutation in a gene necessary for the normal process of programmed cell death (Apoptosis) in response to DNA damage can make the cell resistant to apoptosis. This will allow proliferation of the clone even when excessive DNA damage is present. Such dominant-negative mutations occur in the tumor suppressor gene p53. [20] [21] The P53 wild-type protein is normally present as a four-protein multimer (oligotetramer). Dominant-negative p53 mutations occur in a number of different types of cancer and pre-cancerous lesions (e.g. brain tumors, breast cancer, oral pre-cancerous lesions and oral cancer). [20]

Dominant-negative mutations also occur in other tumor suppressor genes. For instance two dominant-negative germ line mutations were identified in the Ataxia telangiectasia mutated (ATM) gene which increases susceptibility to breast cancer. [22] Dominant negative mutations of the transcription factor C/EBPα can cause acute myeloid leukemia. [23] Inherited dominant negative mutations can also increase the risk of diseases other than cancer. Dominant-negative mutations in Peroxisome proliferator-activated receptor gamma (PPARγ) are associated with severe insulin resistance, diabetes mellitus and hypertension. [24]

Dominant-negative mutations have also been described in organisms other than humans. In fact, the first study reporting a mutant protein inhibiting the normal function of a wild-type protein in a mixed multimer was with the bacteriophage T4 tail fiber protein GP37. [25] Mutations that produce a truncated protein rather than a full-length mutant protein seem to have the strongest dominant-negative effect in the studies of P53, ATM, C/EBPα, and bacteriophage T4 GP37.

In humans, many genetic traits or diseases are classified simply as "dominant" or "recessive". Especially with so-called recessive diseases, which are indeed a factor of recessive genes, but can oversimplify the underlying molecular basis and lead to misunderstanding of the nature of dominance. For example, the recessive genetic disease phenylketonuria (PKU) [26] results from any of a large number (>60) of alleles at the gene locus for the enzyme phenylalanine hydroxylase (PAH). [27] Many of these alleles produce little or no PAH, as a result of which the substrate phenylalanine (Phe) and its metabolic byproducts accumulate in the central nervous system and can cause severe intellectual disability if untreated.

To illustrate these nuances, the genotypes and phenotypic consequences of interactions among three hypothetical PAH alleles are shown in the following table: [28]

In unaffected persons homozygous for a standard functional allele (AA), PAH activity is standard (100%), and the concentration of phenylalanine in the blood [Phe] is about 60 μM (= μmol/L). In untreated persons homozygous for one of the PKU alleles (BB), PAH activity is close to zero, [Phe] ten to forty times standard, and the individual manifests PKU.

In the AB heterozygote, PAH activity is only 30% (not 50%) of standard, blood [Phe] is elevated two-fold, and the person does not manifest PKU. Thus, the A allele is dominant to the B allele with respect to PKU, but the B allele is incompletely dominant to the A allele with respect to its molecular effect, determination of PAH activity level (0.3% < 30% << 100%). Finally, the A allele is an incomplete dominant to B with respect to [Phe], as 60 μM < 120 μM << 600 μM. Note once more that it is irrelevant to the question of dominance that the recessive allele produces a more extreme [Phe] phenotype.

For a third allele C, a CC homozygote produces a very small amount of PAH enzyme, which results in a somewhat elevated level of [Phe] in the blood, a condition called hyperphenylalaninemia, which does not result in intellectual disability.

That is, the dominance relationships of any two alleles may vary according to which aspect of the phenotype is under consideration. It is typically more useful to talk about the phenotypic consequences of the allelic interactions involved in any genotype, rather than to try to force them into dominant and recessive categories.

Variation in the SERPINA6/SERPINA1 locus alters morning plasma cortisol, hepatic corticosteroid binding globulin expression, gene expression in peripheral tissues, and risk of cardiovascular disease

The stress hormone cortisol modulates fuel metabolism, cardiovascular homoeostasis, mood, inflammation and cognition. The CORtisol NETwork (CORNET) consortium previously identified a single locus associated with morning plasma cortisol. Identifying additional genetic variants that explain more of the variance in cortisol could provide new insights into cortisol biology and provide statistical power to test the causative role of cortisol in common diseases. The CORNET consortium extended its genome-wide association meta-analysis for morning plasma cortisol from 12,597 to 25,314 subjects and from

7 M SNPs, in 17 population-based cohorts of European ancestries. We confirmed the genetic association with SERPINA6/SERPINA1. This locus contains genes encoding corticosteroid binding globulin (CBG) and α1-antitrypsin. Expression quantitative trait loci (eQTL) analyses undertaken in the STARNET cohort of 600 individuals showed that specific genetic variants within the SERPINA6/SERPINA1 locus influence expression of SERPINA6 rather than SERPINA1 in the liver. Moreover, trans-eQTL analysis demonstrated effects on adipose tissue gene expression, suggesting that variations in CBG levels have an effect on delivery of cortisol to peripheral tissues. Two-sample Mendelian randomisation analyses provided evidence that each genetically-determined standard deviation (SD) increase in morning plasma cortisol was associated with increased odds of chronic ischaemic heart disease (0.32, 95% CI 0.06-0.59) and myocardial infarction (0.21, 95% CI 0.00-0.43) in UK Biobank and similarly in CARDIoGRAMplusC4D. These findings reveal a causative pathway for CBG in determining cortisol action in peripheral tissues and thereby contributing to the aetiology of cardiovascular disease.


The quantities needed to obtain the expression for FST and QST are the gene diversity within populations HS, the overall HT, the variance among populations VB, and the additive variance within populations VAW.

With these quantities, FST is defined as (H artl and C lark 1997), while QST is defined as

(B onnin et al. 1996), where VB is the among population component of variance for the trait, and VAW is the additive genetic variance within populations. The factor 2 associated with VAW is due to the fact that for quantitative traits genotypes are compared, while genes are compared when computing FST (L ynch and S pitze 1994).

Consider a locus with two alleles, A and B, with respective frequencies pi and qi = 1 − pi in population i. We use the notation of Falconer (F alconer and M ac K ay 1996) for genotypic value. Under regular inbreeding, genotypic values and frequencies of the different genotypes are given in Table 1 .


Genotypes, their genotypic values, and frequencies in a population with inbreeding coefficient f due to regular inbreeding

Gene diversity within population HS depends only on allelic frequencies. It writes as

Overall diversity HT writes as

where is the average frequency of the recessive allele A.

The variance among populations of trait means, VB is defined as

After replacement and simplifications, VB becomes

While under pure additivity, VB is proportional to (and therefore to the first and second moments of allele frequencies), in the presence of dominance VB becomes a complex function of higher moments of allele frequencies. The effect of dominance depends on allelic frequencies and gene diversity. When the recessive allele is frequent (), the covariance term is negative and VB increases compared to the case without dominance. When the recessive allele is rare (), VB increases provided that , where β(p, HS) is the slope of the regression of the frequency of the recessive allele on HS.

Finally, we seek within-population additive variance. For nl loci, additive variance is quantified as (L ynch and W alsh 1998), where eij represents the average excess of allele i at locus j and αij is the average effect of allele i at locus j. For one locus, following T empleton (1987), we obtain

Expression for the additive variance within population i is then

which, after replacement and simplifications gives

For a number n of populations, the expression becomes

From this expression we see that dominance decreases the additive variance within populations when the recessive allele is rare (p < 0.5), while it increases it when the recessive allele is frequent. This is easily understood since when the recessive allele is rare, it will be found mainly in heterozygotes that do not differ much in phenotype from the dominant homozygote.

From Equations 3 and 5, we see that inbreeding diminishes the contribution of dominance to both VB and VAW. Thus, as inbreeding increases, the effect of dominance on QST diminishes, and, unless , dominance will have little effect on QST under strong inbreeding.

The expression of QST for specific cases is listed below:

No dominance, ∀f: In the absence of dominance (d = 0), VAW reduces to

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