How To Use A Punnett Square

Punnett Square

Referring to the Punnett square and the assumption that all alleles are uniformly distributed, Annett was able to charge the proportion of handedness.

From: Laterality in Sports , 2016

Punnett Square

J. Phelan , in Brenner's Encyclopedia of Genetics (Second Edition), 2013

Abstract

The Punnett square is a table in which all of the possible outcomes for a genetic cross between two individuals with known genotypes are given. In its simplest form, the Punnett square consists of a square divided into four quadrants. All possible genotypes for the haploid female gametes are listed across the top, one genotype at the head of each column; and down the left side of the square, all of the possible genotypes for the haploid male gametes are listed, one per row. With this information, it is then possible to fill in the squares of the table, which represent all of the possible outcomes of the cross. Each square contains the diploid genotype that would result from the combination of the male gamete for that row coming together at fertilization with the female gamete for that column.

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Human Genetic Analysis

Kelly M. Elkins , in Forensic DNA Biology, 2013

Part A: Paternity and Genotype Calculations

1.: Draw Punnett squares for each of the given STR loci in Table 18.2 using the parental alleles given.
2.: Compute the number of genotypes possible for the 13 CODIS loci using Table 18.4. Compare this to how many genotypes are possible using the profiles of the two parents. Comment on the numbers.
3.: Using the population database in Table 18.4, assign the allele frequencies for each of the child's alleles for the 13 CODIS loci in Table 18.2.
4.: Compute the CPE_P and LR for each of the child's 13 CODIS loci and the overall CPE_P and LR.
5.: Interpret the result of your analysis? Do the data support the conclusion that the child is the biological offspring of these parents based on Table 18.3? Report the result as included, inconclusive, or excluded. What do you think is the meaning of the "b" superscript notation in the table?

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Forensics and paternity

Frank H. Stephenson , in Calculations for Molecular Biology and Biotechnology (Second Edition), 2010

13.2 The Hardy–Weinberg Equation and Calculating Expected Genotype Frequencies

Gregor Mendel demonstrated by crossing pea plants with different characteristics that gametes combine randomly. He used a Punnett square to predict the outcome of any genetic cross. For example, if he crossed two plants both heterozygous for height, where T represents a dominant tall phenotype and t represents the recessive short phenotype, the Punnett square would have the following appearance:

From the Punnett square, Mendel predicted that the offspring of the cross would have a phenotypic ratio of tall to short plants of 3 : 1.

G.H. Hardy, a British mathematician, and W. Weinberg, a German physician, realized that they could apply a similar approach to predicting the outcome of random mating, not just for an individual cross but for crosses occurring within an entire population. After all, random combination of gametes, as studied by Mendel for individual crosses, is quite similar in concept to random mating of genotypes. In an individual cross, it is a matter of chance which sperm will combine with which egg. In an infinitely large, randomly mating population, it is a matter of chance which genotypes will combine. Determining the distribution of genotype frequencies in a randomly mating population can also be accomplished using a Punnett square. However, rather than a single cross between two parents, Hardy and Weinberg examined crosses between all mothers and all fathers in a population.

For a locus having two alleles, A and B, a Punnett square can be constructed such that an allele frequency of p is assigned to the A allele and an allele frequency of q is assigned to the B allele. The allele frequencies are multiplied as shown in the following Punnett square:

		Fathers
		pA	qB
Mothers	pA	pApA	pAqB
	qB	pAqB	qBqB

If AA represents the homozygous condition, then its frequency in the population is p ² (p × p = p ²). The frequency of the BB homozygous individuals is q ². Since heterozygous individuals can arise in two ways, by receiving alternate alleles from either parent, the frequency of the AB genotype in the population is 2pq since (p × q)+(p × q) = 2pq.

The sum of genotype frequencies is given by the expression

$p^{2} + 2 p q + q^{2} = 1.0$

This relationship is often referred to as the Hardy–Weinberg equation. It is used to determine expected genotype frequencies from allele frequencies.

Punnett squares can be used to examine any number of alleles. For example, a system having three alleles A, B, and C, with allele frequencies p, q, and r, respectively, will have the following Punnett square:

			Fathers
		pA	qB	rC
	pA	pApA	pAqB	pArC
Mothers	qB	pAqB	qBqB	qBrC
	rC	pArC	qBrC	rCrC

The sum of genotype frequencies for this three-allele system is

$p^{2} + q^{2} + r^{2} + 2 p q + 2 p r + 2 q r = 1.0$

This demonstrates, that no matter how many alleles are being examined, the frequency of the homozygous condition is always the square of the allele frequency (p ²), and the frequency of the heterozygous condition is always two times the allele frequency of one allele times the frequency of the other allele (2pq).

The Hardy–Weinberg equation was derived for a strict set of conditions. It assumes that the population is in equilibrium – that it experiences no net change in allele frequencies over time. To reach equilibrium, the following conditions must be met:

1.: Random mating,
2.: An infinitely large population,
3.: No mutation,
4.: No migration into or out of the population, and
5.: No selection for genotypes (all genotypes are equally viable and equally fertile).

In reality, of course, there are no populations that meet these requirements. Nevertheless, most reasonably large populations approximate these conditions to the extent that the Hardy–Weinberg equation can be applied to estimate genotype frequencies.

Problem 13.4

What are the expected genotype frequencies for the alleles described in Problem 13.3? (Assume the population is in Hardy–Weinberg equilibrium.)

Solution 13.4

From Problem 13.3, we have the following allele frequencies:

$p A = 0.230$

$q B = 0.295$

$r C = 0.475$

The Hardy–Weinberg equation gives the following values:

Genotype	Multiplication	Mathematics	Expected genotype frequency
AA	(freq. of A)²	(0.230)²	0.053
AB	2(freq. of A)(freq. of B)	2(0.230)(0.295) =	0.136
AC	2(freq. of A)(freq. of C)	2(0.230)(0.475) =	0.218
BB	(freq. of B)²	(0.295)² =	0.087
BC	2(freq. of B)(freq. of C)	2(0.295)(0.475) =	0.280
CC	(freq. of C)²	(0.475)² =	0.226

Note that the total of all genotype frequencies is equal to 1.000, as would be expected if the mathematics were performed correctly.

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Relationship Testing

John M. Butler , in Advanced Topics in Forensic DNA Typing: Interpretation, 2015

Figure caption: (a) A three-generation family pedigree with results from a single genetic locus (STR marker FGA). Squares represent males and circles females. (b) A Punnett square showing the possible allele combinations for offspring of individuals #1 and #2 in the pedigree. Individual #3 is 22,23.2 and inherited the 22 allele from his father and the 23.2 allele from his mother. (c) A Punnett square for one of the families in the second generation showing possible allele combinations for offspring of individuals #4 and #7.

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Laterality and Its Role in Talent Identification and Athlete Development

Jörg Schorer , ... Joseph Baker , in Laterality in Sports, 2016

Laterality and Genes

To understand the possible relationships between laterality and talent development, it is necessary to consider the influence of different genetic, biological, and environmental factors on laterality. Annett (1985) conducted one of the first studies concerning lateral development, establishing the right-shift theory . This theory explained the formation of asymmetries not through the direct influence of varying genes, but through an indirect influence, specifically the presence and absence of cerebral asymmetries which are induced by genes. The basis of this theory is a dominant allele (RS+) (right shift) that is responsible for the development of speech in the left hemisphere, which leads to a higher probability of being right-handed. The presence of a recessive allele (rs-) did not lead to this systematical drift, neither for speech nor for handedness. Referring to the Punnett square and the assumption that all alleles are uniformly distributed, Annett was able to charge the proportion of handedness. The result of the model is almost equal with the actual distribution. This theory influenced Geschwind and Galaburda (1985a, 1985b, 1985c) in their research. They refined Annett's model and assumed a cerebral asymmetry as a normal condition which could be suspended to symmetry by a left shift factor. Additionally, this factor might permit an asymmetry which prefers the right hemisphere. In conclusion the basis of this theory is a principal dominance of the left hemisphere. Geschwind and Galaburda (1985b) postulated that the left shift factor is influenced by genetic and nongenetic factors. Geschwind and Galaburda (1985b) discussed environmental influences on the development of handedness as well. They stated that cerebral asymmetries, which influence handedness, were characterized by the prenatal proportion of testosterone. The authors evolved a model which considered the greater involvement of the right hemisphere on the dominant hand in men with a higher proportion of prenatal testosterone. This theory was supported by different studies which found a higher amount of left-handers in men (Oldfield, 1971; Raymond, Pontier, Dufour, & Møller, 1996). Considering handedness and its association with talent development, it is unavoidable to take account of the brain development and structure.

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STR Population Data Analysis

John M. Butler , in Advanced Topics in Forensic DNA Typing: Interpretation, 2015

Hardy–Weinberg Equilibrium and Linkage Equilibrium

For a genetic marker with two alleles A and a in a random-mating population, the expected genotype frequencies of AA, Aa, and aa are given by p ², 2pq, and q ², where p and q are the allele frequencies of A and a, respectively, with p + q = 1 (Hartl & Jones 1998). Note that the use of p and q for allele frequencies should not be confused with the "p" and "q" labels used for chromosomal positions. While p and q are used in this book, a number of different symbols have been used for alleles and allele frequencies in the literature (D.N.A. Box 10.1).

D.N.A. BOX 10.1

AN ALLELE NOMENCLATURE ROSSETTA STONE

Sources: See chapter reference list.

One of the most confusing aspects of reading scientific publications describing theoretical population genetics involves the use of different symbols or letters to reflect quite-often straightforward concepts. To create a generic allele in order to perform algebraic functions, authors will usually draw from letters of the English alphabet beginning with P, Q, R, … or A, B, C, …. Sometimes a capital A with subscripts is used to denote alleles while a lower case p with subscripts is used to reflect specific allele frequencies.

Although each author typically introduces his or her specific variables for alleles, genotypes, and allele frequencies, looking across articles by different authors (and even different publications from the same authors) can lead to confusion unless this variation in nomenclature is recognized. The table below illustrates some of the allele, genotype, and allele frequency nomenclatures used in the literature.

Alleles	Genotype	Allele frequency	Reference
P, Q	PQ	p, q	This book
P, Q	PQ	p, q	SWGDAM (2010)
p , q	pq	p, q	Brenner (1997)
A_u, A_v	A_uA_v	p _u , p _v	Weir (2007)
A_i, A_j	A_iA_j	p_i, p_j	NRC II (1996)
A _i , A _j	A _i A _j	p _i , p _j	Fung & Hu (2008), Weir (2013)
A_1, A₂	A₁A₂	p ₁, p ₂	Evett & Weir (1998)
A, B	AB	Pr_A, Pr_B	Lucy (2005)
a, b	ab	p _a , p _b	Buckleton et al. (2005)
A, B	AB	p _A , p _B	Balding (2005); Buckleton et al. (2011)
a, b	ab	f _a , f _b	Evett (1992)

Having observed that subscripted i and j letters can sometimes be very challenging to differentiate in complex genetic equations, all of the examples used in this book follow a consistent nomenclature of P, Q, R, etc. for alleles and p, q, r, etc. (italicized lower case letters) for allele frequencies in order to avoid subscript characters. Examples in this book are worked using allele frequencies from U.S. Caucasians (one of four U.S. population groups included in Appendix 1).

Figure 10.2 illustrates these principles, which constitute HWE. This graphical representation of the cross between alleles A and a from both parents is referred to as a Punnett square . Godfrey Hardy (1877–1947) and Wilhelm Weinberg (1862–1937) both independently discovered the mathematics for independent assortment that is now associated with their names as the Hardy–Weinberg principle (Crow 1999). HWE proportions of genotype frequencies can be reached in a single generation of random mating. HWE is simply a way to relate allele frequencies to genotype frequencies.

Checking for HWE is performed by taking the observed allele frequencies and calculating the expected genotype frequencies based on the allele frequencies. If the observed genotype frequencies are close to the expected genotype frequencies calculated from the observed allele frequencies, then the population is in HWE and allele combinations are assumed to be independent of one another.

One of the principal implications of HWE is that the allele and genotype frequencies remain constant from generation to generation (Hartl & Jones 1998). Another implication is that when an allele is rare, the population contains more heterozygotes for the allele than it contains homozygotes for the same allele.

Genes (or genetic markers like STR loci) that are in random association are said to be in a state of linkage equilibrium, while those genes or segments of the genome that are not in random association (i.e. are inherited together as a block) are said to be in linkage disequilibrium. Computer programs are used to check for linkage equilibrium in order to verify that a genetic marker is independent of other genetic markers being examined.

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Basic Genetics

David P. Clark , Nanette J. Pazdernik , in Molecular Biology (Second Edition), 2013

Conceptual Questions

1.

a. Determine the potential phenotype(s) for the offspring of a mother with dominant red flowers (RR) and purple stem (PP) and a father with recessive white flowers (rr) and all green stems (pp). b. Using the checkerboard diagram or Punnett square, determine all the potential genotypes for the F2 generation if the F1 was to self-cross.

2.

Red-green color blindness in humans is caused by a recessive gene on the X-chromosome. The following pedigree was determined for a family in the United States. What is the probability that the daughter (III-1) will be a carrier? What is the probability that III-2 and III-3 will be color blind?

3.

Three precursor substances (X, Y, and Z) for an essential vitamin were added to minimal growth media for a wild-type and three different mutant strains of E. coli. Wild-type E. coli can synthesize this vitamin and all three precursor substances, but mutations in the biosynthetic enzymes for any of the three precursors cause a vitamin deficiency that is lethal. The growth was assessed and tabulated in the following table (+ means growth, − means no growth). Which of the strains is wild-type?

E. coli strain	Min. Media (no vitamin) (MM)	MM+X	MM+Y	MM+Z
HB101	−	−	+	+
BL21	+	+	+	+
EB898	−	−	+	−
CJ765	−	+	+	+

4.

In the plant Arabidopsis thaliana, there are three different genes on chromosome 4: CPK27 (ck), PUX3 (px), and IMMUTANS (im). To determine the order of the genes along the chromosome, the following parents were crossed and the following progeny recovered:

ck⁺	px im/ck px⁺	im⁺×ck px im/ck px im
ck⁺	px	im	207
ck	px⁺	im⁺	215
ck⁺	px	im⁺	167
ck	px⁺	im	188
ck⁺	px⁺	im	71
ck	px	im⁺	73
ck⁺	px⁺	im⁺	35
ck	px	im	44

What is the gene order for these three genes and what are the recombination frequencies between them? What genes are closer together on the chromosome?

5.

Researchers are trying to find a gene that is responsible for absolute pitch, which is the ability to identify tones with the correct musical note without any help from a reference note. Many people do not think absolute pitch is a genetic trait, and instead believe that absolute pitch is actually a learned skill. DNA samples were collected from 73 families with at least two people that have absolute pitch. Linkage analysis was performed for the various families and the LOD scores were analyzed to determine whether or not a particular haplotype was associated with absolute pitch. One haplotype on chromosome 8 was found to have a LOD score of 3.231. Does the linkage analysis support the hypothesis that absolute pitch is a genetic trait? Why or why not?

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Population Genetics and Medicine

Linda R. Adkison PhD , in Elsevier's Integrated Review Genetics (Second Edition), 2012

Hardy-Weinberg Equilibrium

Basic Algebraic Formula

Assume there are only two possible alleles, A and a, at a particular locus on an autosome. In addition, assume the frequency of the A allele in the population is designated "p," and "q" is the frequency of the a allele. Under these conditions, p + q = 1, since this is the totality of these alleles in an individual within a population. The probability of bringing two gametes bearing the A allele together is simply p × p = p². The chance of obtaining the aa genotype is q², and the chance of obtaining Aa is 2pq. The "2" in 2pq derives from the fact that there are two ways of forming the heterozygote, since each allele can be contributed to the zygote either through the egg or through the sperm.

The simplest case for understanding gene expression is the gene with only two alleles; however, as discussed in great detail in prior chapters, any change in DNA at a locus results in a new allele, making the possibilities seemingly endless. Though Hardy and Weinberg developed this formula prior to a proper appreciation of alleles, only two alleles are considered at a time and the formula still has applicability.

An important factor that influences the genetic composition of a population is the system of mating among individuals. The simplest scheme of breeding activity in a population is referred to as random mating (or panmixia), wherein any one individual has an equal chance of pairing with any other individual. Random mating does not imply promiscuity; it simply means that those who choose each other as mating partners do not do so on the basis of similarity or dissimilarity in a given trait or gene.

The absence of preferential mating in a population has interesting consequences. The gametes in a panmictic population are mixed at random. Each gamete carries either A or a . To predict the outcome of the random mixing of gametes, the "Punnett square" is used ( Fig. 12-1). This matrix essentially brings into play the multiplication rule of probability: the chance that two independent events will occur together is the product of their chances of occurring separately. The Punnett square checkerboard displayed in Figure 12-1 reveals the outcome of all possible combinations.

The distribution of genotypes in the next generation of a randomly breeding population is p²:AA 2pq:Aa q²:aa. The algebraic expansion of the binomial equation (p + q)² is reflected in this distribution, p²:2pq:q². The Hardy-Weinberg theorem states that the proportions of AA, Aa, and aa genotypes, as well as the proportions of A and a alleles, will remain constant from generation to generation, provided that the bearers of the three genotypes have equal opportunities of producing offspring in a large, randomly mating population. If blue-eyed persons are equally fertile as brown-eyed individuals and leave equal numbers of offspring each generation, then blue-eyed persons as well as brown-eyed individuals will persist in the population with the same frequency from one generation to the next.

Application of Hardy-Weinberg Theorem

It may seem ironic that the Hardy-Weinberg theorem is entirely theoretical. The following set of underlying assumptions can scarcely be fulfilled in any natural population. It is implicitly assumed that there is the absence of recurring mutations, any degree of preferential mating, differential mortality or fertility, immigration or emigration of individuals, and fluctuations in gene frequencies due to sheer chance. But therein lies the significance of the Hardy-Weinberg theorem. In revealing the conditions under which changes in gene frequencies cannot occur, it brings to light the possible forces that could cause a change in the genetic composition of a population: mutations, preferential matings, mortality, infertility, immigration and emigration, and chance fluctuations.

A population is a group of individuals living within a defined geographic area. Historically, it may have been easier to define a population because of the tendency for groups of individuals to remain in a location for long periods of time, represented by centuries in some cases. As groups within a population became segregated or separated from the larger population, subpopulations developed. Just as different populations may have developed unique mutations, subpopulations may have developed a specific genetic complement due to unique mutations that differ from other subpopulations or the population as a whole. In both cases, the gene pool is limited by the DNA variation contributed by individuals through mating. These differences among gene pools, which are directly affected by the DNA sequences available, develop through variations in meiotic reassortment and mutations (Box 12-1). These changes may confer a selective advantage or disadvantage to the gene and the individual or have a neutral effect. Of course, only those changes that are neutral or that confer a selective advantage are important for the survival of the population.

An understanding of Hardy-Weinberg equilibrium provides a basis for recognizing the forces that permit a change in gene frequencies. A few of the more obvious factors that prevent a natural population from attaining stationary equilibrium are (1) mutation, (2) natural selection, (3) chance events in a small population (genetic drift), and (4) migration. In any population, the more individuals contributing to the gene pool (i.e., the larger the population), the more stable the allele frequencies within the population and the more difficult it will be for frequencies to change. Conversely, small populations may have fluctuations in frequencies often; in some cases this can even occur between generations. The factors or forces affecting gene pools can profoundly modify the gene frequencies in natural populations. In essence, the Hardy-Weinberg theorem represents the cornerstone of population studies, since deviations from Hardy-Weinberg expectations direct attention to the forces that disturb, or upset, the theoretical equilibrium. The Hardy-Weinberg theorem is exceedingly useful for providing an estimate of (1) the frequencies of heterozygous carriers of deleterious recessive alleles and (2) the risk of bearing offspring with detrimental recessive disorders in various marriages (Table 12-1).

Estimating the Frequency of Heterozygotes

Contrary to popular opinion, heterozygotes of a rare recessive abnormality are rather common instead of comparatively rare. Recessive albinism may be used as an illustration. The frequency of albinos is about 1 in 20,000 in human populations. When the frequency of the homozygous recessive (q²) trait is known, the frequency of the recessive allele (q) can be calculated, as follows:

$q^{2} = \frac{1}{20, 000} = 0.00005$

$\begin{matrix} q = \sqrt{0.00005} = 0.007 \\ = about 1 / 140 or 1 in 140 (frequency of recessive allele) \end{matrix}$

The heterozygotes are represented by 2pq in the Hardy-Weinberg formula. Accordingly, the frequency of heterozygous carriers of albinism can be calculated as follows:

$q = 0.007$

$p + q = 1$

$p = 1 - 0.007 = 0.993$

Therefore:

$\begin{matrix} 2 pq = 2 0.993 \times 0.007 = 0.014 \\ = about 1 / 70 (frequency of heterozygous carriers) \end{matrix}$

Thus, although 1 person in 20,000 is an albino (recessive homozygote), about 1 person in 70 is a heterozygous carrier—or, there are 285 times as many carriers as affected individuals. The rarity of a recessive disorder does not signify a comparable rarity of heterozygous carriers. In fact, when the frequency of the recessive gene is extremely low, nearly all the recessive genes are in the heterozygous state.

Significance of the Heterozygote

When the frequency of a detrimental recessive allele becomes very low, most affected offspring (aa) will come from mating of two heterozygous carriers (Aa). For example, in the human population, the vast majority (>99%) of newly arising albino individuals (aa) in a given generation will come from normally pigmented heterozygous parents.

Detrimental recessive alleles in a population are unquestionably harbored mostly in the heterozygous state. As shown in Table 12-1, the frequency of heterozygous carriers is many times greater than the frequency of homozygous individuals afflicted with a trait. Thus, an extremely rare disorder such as alkaptonuria (blackening of urine) occurs in 1 in 1 million persons. One in 500 persons, however, carries this detrimental allele in the hidden state. There are 2000 times as many genetic carriers of alkaptonuria as there are individuals affected with this defect. For another recessive trait, cystic fibrosis, 1 in 2500 individuals is affected with this homozygous trait. One in 25 persons is a carrier of cystic fibrosis. In modern genetic counseling programs, an important consideration has been the development of simple, inexpensive means of detecting heterozygous carriers of inherited disorders. Molecular diagnostic techniques have increased the number of carrier screening programs available for at-risk populations.

Biochemistry

Natural Selection for a Heterozygote: Sickle Cell Trait

Sickle cell trait is a heterozygous condition for a specific mutation in hemoglobin that is called hemoglobin S (Hb S). The occurrence of this mutation overlaps the distribution of malaria in Africa and is an example of a heterozygous condition that conveys a survival advantage in areas where malaria is endemic. Sickle trait cells, those with only one mutant allele, generally undergo little sickling at normal O₂ tension. Though some sickling will occur as O₂ tension lowers, it is not as much as in sickle cell anemia with two mutant alleles and twice as much mutant hemoglobin. Plasmodium falciparum requires normal intracellular K⁺ concentration. With lower O₂ tension in the cell, potassium diffuses out. P. falciparum grows poorly in the lower than normal O₂ tension occurring in Hb S cells and dies because of the inadequate O₂ and reduced K⁺.

X-Linked Loci

In the above discussions, the genes and alleles considered were autosomal genes with two possible alleles, A and a. For X chromosome loci, the principles are similar but the male gamete may or may not carry an X chromosome (Fig. 12-2). Since there is only one X chromosome in males, the genotype frequency of any allele on that X chromosome is equal to the allele frequency. In females, alleles may be distributed as p² AA: 2pqAa: q2aa, and thus a heterozygous carrier is determined just as with an autosomal trait. For example, if the frequencies of two X-linked alleles are 0.3 (A) and 0.7 (a), then for a female offspring, the probability of carrying both alleles (Aa) is

$2 pq = 2 0.3 \times 0.7 = 0.42$

whereas the probability that a male offspring will carry either allele is 0.3 or 0.7 for the A allele or a allele, respectively.

For recently arising mutations on the X chromosome, there may be a difference in allele frequencies between males and females. However, with each successive generation, differences in frequencies between males and females becomes less until equilibrium is approached. Allele frequencies will approach equilibrium or be in equilibrium for those alleles that have been in the gene pool for many generations. The expression of a recessive allele will occur at a higher frequency in males than in females just as implied above. In females, the frequency of expression is q². The X-linked form of color blindness affects 1 in 20 white males, so q = 0.05. The expected frequency in females is q² = (0.05)² = 0.0025 or 1 in 400 females.

Biochemistry

Lyonization of Ornithine Transcarbamylase (OTC) Deficiency in Females

Another example of X chromosome genes and the role of lyonization is ornithine transcarbamylase (OTC) deficiency, the most common disorder of the urea cycle. This enzyme, part of a mitochondrial matrix, catalyzes the conversion of ornithine and carbamyl phosphate to citrulline. It is the second step in the urea cycle.

As an X-linked disorder, OTC deficiency can be fatal in newborn males owing to hyperammonemia. In females, however, expression is variable because of lyonization. As might be surmised, penetrance is 100% in males (with a severity index of 50), whereas it is only 20% in females and the severity is low.

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The Basics of Heredity

Julia E. Richards , R. Scott Hawley , in The Human Genome (Third Edition), 2011

1.9 One Man's Disease Is Another Man's Trait

At a height of six feet tall, Julia is the short kid in her family. By the time she was in sixth grade, there were two people in the school who were taller than she – the vice principal and a fifth-grade teacher, both men. A lot of people who study genetics will tell you that height is complex, and that many genes and environmental factors affect height. They will say that extremes of height tend to move back towards average height as mixtures of multiple genes combine and get passed from one generation to the next. Yet in Julia's rather small family, height above six feet tall can be seen in nine people among four straight generations, among both men and women. Apparently, there is some difference in her genetic blueprint that makes her relatives and herself unusually tall. If she has a difference in her blueprint, does that mean she has a genetic disease? No. Her height is actually a minor thing and clearly not a disease. It is helpful when she wants to reach the top shelf and a pain when she can't buy pants that are long enough. Even the simple asking of that question raises a troubling issue. Is something caused by a change in the genetic blueprint necessarily a disease? Who gets to decide whether something is a disease and not just a trait on the continuum of human diversity? Although we would like to think that you would immediately declare, "The person who has the trait decides, of course," it is surprising how complicated the issues can become. Too often the world ends up judging us from the outside, rendering judgments about us that they would never render about themselves, often while claiming they have our best interests at heart. One person with the apparent best of intentions asked whether Julia's height had made her feel like a freak when she was growing up. Until that moment, such a thought had never entered her head. If Julia's height can elicit a reaction like that from someone who is actually a very civil and kind person, imagine the "helpful" remarks that must assail people struggling with more complex problems than whether they can buy pants that fit.

So what have we been talking about so far, genetic diseases or genetic traits? Clearly, there appears to be a change in the genetic blueprint involved in all three traits we have discussed so far – albinism, dominant deafness, and nail–patella syndrome. This comes back to the question we raised about Julia's height: does it have to be a genetic disease just because it is caused by a change in the genetic blueprint? Frankly, the answer is no.

That answer throws us onto shaky ground as we face the question of what does constitute a genetic disease. If finding out that something is caused by a change in the genetic blueprint doesn't tell us whether it is a genetic disease, what can?

Here we come to an incredibly important concept – the distinction between a trait and a disease. The term genetic disease may be applied if the trait results in medical problems. If the effects are simply cosmetic, we may end up referring to it as a genetic trait instead. However, we find that this actually leaves us with many traits that occupy some middle ground, perceived differently by different people.

Whether nail–patella syndrome is a trait or a disease varies from one person to the next. For some people, the only effects are cosmetic; for others, the effects can be crippling or even lethal. We tend to talk about nail–patella syndrome as if it were a disease because the potential for the medical complications is there for all of the affected individuals, and in some cases we won't know until late in life whether someone with an apparently cosmetic case of nail–patella syndrome has missed the serious medical consequences that could have arisen. Is the use of the term "disease" fair to the many people with unusual thumbnails and kneecaps who have no medical problems?

In the case of albinism, coloration seems like something cosmetic that should be considered a trait. However, vision problems are normally a part of albinism, and a true lack of pigment actually has medical implications in terms of susceptibility to damage from sunlight that is serious enough to make it a genetic disease. If you have a form of albinism that isn't one of the rare forms of syndromic albinism that causes other major medical problems, if you manage your vision problems and if you don't develop skin cancer, do you have a disease? If you have a trait that merely has the potential for medical problems, but those medical problems have not occurred, how might you be affected if people around you told you (or each other) that you have a disease? What if you started out from early childhood surrounded by people referring to you as someone with a disease when you had few if any health problems?

One parent of a child with albinism recently offered the vehement argument that albinism is not a disease. In many ways, this argument is valid. Even though there are some inconveniences associated with the vision problems that can be part of albinism, they can be managed so that these are people who live normal, healthy lives, and many of them might be surprised that anyone might think that they are ill. If people with the albinism trait do not consider themselves ill, the rest of us should accept this self-insight and notice how much like the rest of us they are.

In the case of deafness, which you might think would be classified as a disease because of the functional repercussions; there is an alternative perspective (Box 1.13). Some people consider deafness a genetic disease, but others consider it simply a trait. In fact, the news that a newborn child is deaf may be greeted with anguish by some families and calmness by others. The thing that determines whether the news is distressing is often, but not always, the "hearing" status of the parents.

Box 1.13

Deafness – An Illness, A Trait, or an Ethnic Group?

According to the American Association of Pediatrics, 1 in every 300 infants is born with hearing loss. There are more than 50 distinct genetic causes of deafness known so far, and hearing loss can result from a variety of nongenetic causes, including as one of the consequences of some types of infectious disease. Even as doctors work to restore hearing and researchers work to develop new technologies for those doctors to use, there are those who don't think the need for those efforts is so obvious. The deaf community has a large and thriving culture that includes its own separate language and is quite distinct from the culture of the hearing society in which this culture is embedded. Mannerisms, patterns of communication and interaction, even art forms have all emerged in unique ways that make them not just copies of the cultural patterns in the hearing world. When a deaf child is born, there can be very different reactions depending on whether the child is born into a deaf family or a hearing family. Some within the deaf community want their children to have the choice of whether to hear or not, and hearing parents usually wish there was a way to give their children the gift of sound. For all of them, the continued development of new technologies and the availability of medical assistance are incredibly important. There are some within the deaf culture who regard medical efforts to eliminate deafness as a threat of cultural genocide – an effort to eliminate an entire separate culture and people by forcing their assimilation into a different mainstream culture for which they hold great distaste. Many others in the deaf community hold much more mild views in this era in which moderate help is available to those who seek it and not required for those who don't. With technological aids available, such as cochlear implants, it is interesting to find that some who have received these implants and gained the ability to carry on aural communication with those of us who don't speak sign language have then decided to return to the world of silence they were born into. Advances in the quality of the technological results have others who resisted cochlear implants in the past taking another look at them. If you ever find yourself saying, "Of course they should all just have their hearing restored," first spend some time reading about deaf culture and exploring the idea that in silence they may have found some things that the hearing world lacks. You may or may not end up agreeing with them, but many who hear what they have to say come away changed by it.

Some families believe that their deaf child has a disease and they want someone to come forward with a cure. Other families think that their child has a trait, and they have no interest in altering that trait. Individuals who wish they could hear view advances such as the cochlear implant as a gift that can restore a missing sense. However, there are those within the deaf community who see the cochlear implant as a tool for carrying out cultural genocide. They see it as a technology that causes a deaf child to grow up as a marginalized individual on the fringes of a cruel "hearing" society instead of growing up safe and esteemed as a full peer within the deaf community. What a complex ethical problem to weigh and measure the gain or loss of hearing against the gain or loss of esteem and acceptance. We find ourselves wondering if there is such a thing as a right answer.

This complex set of ethical issues mirrors so many situations that we encounter in human genetics, where the answers are often terribly complex but often become at least a bit simpler if we fall back on the principle of self-determination. Julia can't tell someone deaf whether their deafness is a trait or a disease, and that deaf person can't tell Julia whether her height is a trait or a disease. Each of us knows which call constitutes the truth for our own situations. There are others who would make a different judgment call.

In this chapter, we have deliberately selected traits that are usually not seen as diseases by the people who have the trait but that sometimes are labeled as diseases by others or by rare individuals whose cases are especially severe. We have done this expressly for the purpose of making the point that one man's disease may be another man's trait. Is the trait actually causing a problem? Sometimes yes; often not. But sometimes something that is not a problem can become a problem based on how outside people treat the situation. There can be many consequences to an individual who is perfectly healthy if people around them start telling them that they have something wrong with them. This is especially true if someone is treated as if they are ill starting in infancy so that they grow up internalizing a self image that they would not have developed on their own.

As we will discuss in the final chapter of this book, some of the gravest ethical errors in genetics in the past have been made when society or medicine removed the rights of individuals to judge this for themselves. Is it broken, and should we fix it? If we look beyond the tricky issue of whether or not we can fix it, we find that the real answer to whether we should even try to fix it lies in the heart of the individual with the trait. One man's trait is another man's disease. Only the individual with the trait can judge for himself or herself whether the trait is severe enough to be considered a problem, and different individuals with the same trait may arrive at very different perspectives on the question.

Study Questions

1.: Which of Mendel's findings helped to rule out the vital spark theory of inheritance?
2.: Which of Mendel's findings helped to rule out the homunculus theory of inheritance?
3.: What are the standard symbols used to represent a male and a female in a pedigree drawing?
4.: In a standard pedigree drawing, how is a deceased individual marked?
5.: What is a heterozygote?
6.: What is a homozygote?
7.: What is the difference between genotype and phenotype, and how are they related?
8.: How many alleles of a gene come from each parent, and how many are passed along to the offspring?
9.: Define the term allele.
10.: What is a dominant allele?
11.: What is a recessive allele?
12.: What are the modes of inheritance of deafness?
13.: Could albinism be considered a syndrome? Why or why not?
14.: What is the difference between monozygotic twins and fraternal twins?
15.: What is pleiotropy and why can a defect in a single gene have pleiotropic effects?
16.: Kate and Dan, two individuals who do not have cystic fibrosis, are both carriers of a defect in the cystic fibrosis gene and decide to have children together. Draw a Punnett square that shows the genotypes of the sperm and eggs they can produce and the genotypes that we would predict for their children. What fraction of their children will be carriers and how many will not have cystic fibrosis?
17.: Is the proband of a family always someone with the trait? Explain.
18.: What do identical twins and fraternal twins have in common that is important to researchers doing twin studies?
19.: Draw a three generation pedigree showing inheritance of a dominant form of epilepsy where the grandfather is affected, the grandmother is deceased, and a granddaughter is the proband. Use standard pedigree symbols.
20.: What determines whether a genetic trait is a genetic disease?

Short Essays

1.: How might our experimental outcomes be influenced by the way we think about the question and the extent to which we stop looking for further answers when we see an answer that fits our expectations? Why do we believe in what Mendel did even if his data were "too pretty?" As you consider your answer, read the article "Mud sticks: On the alleged falsification of Mendel's data" by Daniel L. Hartl and Daniel J. Fairbanks in Genetics, 2007;175:975–9.
2.: Like Albert Einstein, Gregor Mendel lacked the stellar academic credentials that seem to be essential for anyone striving to make a mark in scientific history these days. What alternative environment allowed Mendel to pursue his questions and develop his theories outside of a university academic setting? What alternative environments currently exist for someone with talent and a shortage of official credentials to advance the examination of a question that interests them? As you consider your answer, read pages 3 through 49 of The Impact of the Gene: From Mendel's Peas to Designer Babies by Colin Tudge (2001, Hill and Wang).
3.: How could society be structured to avoid the marginalization of deaf individuals that leads some members of the deaf community to seek a separate society outside of the hearing world? Given the increasing fraction of elderly people in our population, how might such altered social structure benefit most of us? As you consider your answer read Everyone Here Spoke Sign Language by Nora Ellen Groce (1985, Harvard University Press).
4.: How can art be used to combat genetic ignorance and prejudice and maybe even make people safer? As you consider your answer, visit Rick Guidotti's Positive Exposure website http://www.positiveexposure.org/home.html to learn about his publications, gallery showings, and educational programs aimed at reducing prejudice and protecting people with albinism from violence.
5.: Belyaev showed that it was possible to domesticate a kind of animal for which domestication had long been thought to be impossible. Why was Belyaev able to bring about this domestication in a few decades when he started with an animal that had existed for many thousands of years without showing any sign of domestication? As you consider your answer read the article "Destabilizing selection as a factor in domestication" by Dmitri Belyaev in Journal of Heredity, 1979;70:301–8.

Resource Project

Mendelweb.org presents original and translated versions of Mendel's paper plus supplementary information to assist students of Mendel's work at http://www.mendelweb.org/. Go to Mendelweb and look at the translated version of Mendel's paper. Write a one paragraph report on one of the pea plant traits that he studied other than pod color, and discuss the characteristic and the mode of inheritance.

Gene-Gene Interactions: An Essential Component to Modeling Complexity for Precision Medicine

Molly A. Hall , ... Jason H. Moore , in Encyclopedia of Bioinformatics and Computational Biology, 2019

Historical Perspectives on Analysis and Interpretation of Gene–Gene Interactions

The analysis of gene-gene interactions long predated the elucidation of the structure of DNA. After the rediscovery of Mendel's pioneering experiments of pea crosses that spawned the field of genetics, an explosive period of genetic discovery, driven by experiments in model systems and mathematical analysis at the population level, dominated the first two decades of the twentieth century (Sturtevant, 2001). It was during this gilded age of genetics that pioneering analysis of model systems extended and refined Mendel's laws into a cohesive theory of genetics that formed the basis of our modern understanding. During this period, epistasis was discovered by William Bateson, the biologist who coined the term "genetics" to name the nascent field of the study of heritable variation (Bateson, 1909).

Bateson used the term "epistasis" to describe a cross between two strains in which the phenotypic distribution of the resulting offspring departs from the ratios expected by Mendel's laws (Cordell, 2002). Specifically, Bateson used the term epistasis to describe one mutation blocking or masking the effects of another, hence the use of term "epistasis" which may be translated as "resting upon." Bateson's usage of the term epistasis described an interaction between two genetic variants in which one variant negates the effects of another (Phillips, 2008 ). This type of genetic interaction, sometimes called modification, was the first form of gene-gene interactions to be observed in experimental crosses. Working together with Reginald Punnett, Bateson developed a two-locus Punnett square to describe the phenotypic ratios of F ₂ progeny from crosses of two strains of the flowering sweet pea Lathyrus odoratus which displayed a flower coloration trait only when two separate dominant alleles were present at separate loci (Sturtevant, 2001). This two-locus epistasis model extended Mendel's original postulations of a two-locus model to incorporate an interaction between genetic variants, without which the phenotypic ratios of Bateson's and Punnett's sweet peas did not conform to Mendel's laws.

Bateson and Punnett's description of epistasis is the result of crosses between self-fertilizing strains of plants, which are essentially controlled for genetic background, allowing the analysis of the effects of one or a small number of genetic variants on visible phenotypes such as morphological traits. Natural populations of organisms, including humans and wild populations of other organisms which are used as model systems in experimental genetics, contain genetic variation across the genome, eliminating the ability to analyze the effects of one or a small number of genetic variants against a controlled background (Moore and Williams, 2005). The statistical geneticist R. A. Fisher extended the description of epistasis to populations which are not controlled for genomic background by defining "epistasy" as deviations from additivity in a linear model (Fisher, 1919). This definition of gene-gene interactions allows for the statistical detection of epistasis in a population which contains a large number of polymorphic sites in the genome by defining epistasis as a statistical deviation from additivity, a definition which incorporates the mean effect of two or more genetic variants in a given population of organisms (Doust et al., 2014.). Importantly, Bateson's definition of epistasis involved organisms which share almost all of their genome (inbred strains) and Fisher's definition involved organisms which contain polymorphisms across the genome (wild populations). Modern scientists have synthesized these concepts into biological and statistical epistasis (Moore and Williams, 2005). Biological epistasis refers to experimental crosses in which the distribution of phenotypes in offspring deviate from Mendelian ratios (as described by Bateson and Punnett), and statistical epistasis indicates genetic effects which deviate significantly from additivity in highly polymorphic populations (as described by Fisher). As a hypothetical example to demonstrate statistical epistasis consider two loci: LocusA and LocusB. If the relationship between the two loci is additive, we would expect the combined effect of the two on a phenotype to be the addition of the main effect of LocusA and the main effect of LocusB. For example, if there is a 2-fold and 3-fold risk associated with the risk alleles for LocusA and LocusB, respectively, the additive result from both loci is a 5-fold increase risk. If the relationship is epistatic, however, the effect of the two loci together will significantly differ from the combined main effects of the two loci. In the scenario described, the presence of both risk alleles under an epistatic relationship could be a 15-fold risk increase; alternately, risk could decrease to 1.1-fold. In other words, when statistical epistasis occurs, there is a non-linear relationship between the effects of two or more loci when combined. While these two forms of epistasis are experimentally distinct, the underlying theory is identical: epistasis, defined broadly, is the interaction between distinct genetic variants (Phillips, 1998, 2008). This definition encompasses both statistical epistasis which might be detectable in population-scale studies and biological epistasis which might be observable in controlled crosses.

Epistasis research has continued to play a central role in genetics since the early work of Bateson, Punnett, Fisher, and others at the dawn of the twentieth century. An important application of epistasis to biological discovery came in the form of pathway ordering, in which multiple strains of a model organism are crossed together and phenotypes observed such that the ordering of a biological pathway becomes evident (Avery and Wasserman, 1992). This important genetic tool can be used to discover which gene products are upstream or downstream of other gene products, providing evidence of gene product function without molecular or biochemical analysis. This can be achieved by crossing together separate mutant strains of a model organism which display different phenotypes (Beadle, 1945). If a double mutant displays the same phenotype as one of the mutants does individually, one mutation likely occurs in a gene whose product functions downstream in a biochemical pathway. While this is certainly not always the case, epistasis as a tool for pathway ordering elucidated the ordering of mutations (and thereby their gene products, even if the molecular functions were only later established) in the biological pathways which control cell cycle in yeast, sex determination in C. elegans, embryonic development in D. melanogaster, and other pathways (Phillips, 2008).

As described by Moore (2003), epistasis is thought to be ubiquitous in biology (Moore, 2003; Templeton, 2000). Examples of epistasis have been observed in many model organisms (Mackay, 2014), including yeast (Wagner, 2000; Boone et al., 2007; Tong et al., 2004; Szappanos et al., 2011; Moore, 2005; Baryshnikova et al., 2013), C. elegans (Lehner et al., 2006; Gaertner et al., 2012; Byrne et al., 2007), D. melanogaster (Horn et al., 2011; Huang et al., 2012; Lloyd et al., 1998), M. musculus (Cheng et al., 2011; Hanlon et al., 2006; Gale et al., 2009), and A. thaliana (Rowe et al., 2008; Kroymann and Mitchell-Olds, 2005). While examples of epistasis have accrued in model organisms over the years, epistasis is not confined to Mendelian traits, for which a small set of highly penetrant mutations explain much of the variance in observed phenotypes. Epistatic interactions between genetic loci have been discovered in human traits ranging from blood types and eye coloration to complex, polygenic, and multifactorial traits such as disease susceptibility (Moore, 2005). Nelson et al. (2001) identified interactions between ApoB and ApoE in females as well as between the low-density lipoprotein receptor and the ApoAI/CIII/AIV complex in males for triglyceride levels (Nelson et al., 2001). Interactions between SNPs in three estrogen metabolism genes, COMT, CYP1B1, and CYP1A1, were identified by Ritchie et al. (2001) that were predictive of sporadic breast cancer (Ritchie et al., 2001). Further, a study by Hemani et al. (2014) identified and replicated a large number of genetic interactions involved in gene expression regulation (Hemani et al., 2014).

Epistasis research was spawned shortly after the rediscovery of Mendel's foundational work that gave rise to the field of genetics and has found application in the understanding of how genetic variants interact to determine phenotypic outcomes. While genetic interactions have provided insight into traits which cannot be adequately explained by additive models or Mendelian ratios, epistasis research remains an active application of genetics in the modern scientific research enterprise. Particularly, detection of epistasis in studies of complex traits in humans presents methodological and computational challenges that remain an active area of development.

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