Genetics: Mendel and Beyond

Much of the early study of biological inheritance was done with plants and animals of economic importance.

Records show that people were deliberately crossbreeding date palm trees and horses as early as 5,000years ago. By the early nineteenth century, plant breeding was widespread, especially with ornamental flowers such as tulips. Half a century later, Gregor Mendel used the existing kno wledge of plant reproduction to design and conduct experiments on inheritance. Although his published results were neglected by scientists for more than 30 years, they ultimately became the foundation for the science of genetics.

Plant breeders showed that both parents contribute equally to inheritance

Plants are good experimental subjects for the study of genetics. Many plants are easily grown in large quantities, produce large numbers of offspring (in the form of seeds) and have relatively short generation times. In most plant species, the same individuals have both male and female reproductive organs, permitting each plant to reproduce as a male, as a female or as both. Best of all, it is often easy to control which individuals mate. Some discoveries that Mendel found useful in his studies had been made in the late eighteenth century by a Germanbotanist, Josef Gottlieb Kölreuter. He had studied the offspring of reciprocal crosses, in which plants are crossed (mated with each other) in opposite directions. For example, in one cross, males that have white flowers are mated with females that have red flowers, while in a complementary cross, red-flowered males and white-flowered females are mated. In Kölreuter’s studies, such reciprocal crosses always gave identical results showing that both parents contributed equally to the offspring. Although the concept of equal parental contributions was an important discovery, the nature of what exactly the parents were contributing to their offspring—the units of inheritance—remained unknown. Laws of inheritance proposed at the time favored the concept of blending. If a plant that had one form of a characteristic (say, red flowers) was crossed with one that had a different form of that characteristic (blue flowers), the offspring would be a blended combination of the two parents (purple flowers). According to the blending theory, it was thought that once heritable elements were combined, they could not be separated again (like inks of different colors mixed together). The red and blue genetic determinants were thought to be forever blended into the new purple one. Then, about a century after Kölreuter completed his work, Mendel began his.

Mendel brought new methods to experiments on inheritance

Gregor Mendel was an Austrian monk, not an academic scientist, but he was qualified to undertake scientific investigations. Although in 1850 he had failed an examination for a teaching certificate in natural science, he later undertook in-tensive studies in physics, chemistry, mathematics, and various aspects of biology at the University of Vienna. His work in physics and mathematics probably led him to apply experimental and quantitative methods to the study of heredity, and these methods were the key ingredients in his success. Mendel worked out the basic principles of inheritance in plants over a period of about 9 years. His work culminated in a public lecture in 1865 and a detailed written publication in 1866. Mendel’s paper appeared in a journal that was received by 120 libraries and he sent reprinted copies (of which he had obtained 40) to several distinguished scholars. However, his theory was not accepted. In fact, it was ignored. The chief difficulty was that the most prominent biologists of Mendel’s time were not in the habit of thinking in mathematical terms, even the simple terms used by Mendel. Even Charles Darwin, whose theory of evolution by natural selection depended on genetic variation among individuals, failed to understand the significance of Mendel’s findings. In fact, Darwin performed breeding experiments on snapdragons similar to Mendel’s on peas and got data similar to Mendel’s but he missed the point, still relying on the concept of blending. Whatever the reasons, Mendel’s pioneering paper had no discernible influence on the scientific world for more than 30 years. Then, in 1900, after meiosis had been observed and described, Mendel’s discoveries burst into prominence as a result of independent experiments by three plant geneticists, Hugo DeVries, Carl Correns and Erich von Tschermak. Each carried out crossing experiments and obtained quantitative data about the progeny; each published his principal findings in 1900; each cited Mendel’s 1866 paper. They immediately realized that chromosomes and meiosis provided a physical explanation for the theory that Mendel had proposed to explain the data from his crosses. As we go through Mendel’s work, we will describe first his experiments and conclusions, and then the chromosomal explanation of his theories.

Mendel and his Principles of Heredity

People have wondered how likes beget likes for thousands of years. Some ancients thought that blood was the key to the inheritance of traits. Others thought that traits were passed on by vapors from the parents’ bodies. It was not until 1865 that the beginnings of the modern gene theory were reported by a monk named Gregor Mendel before a small group of people at a meeting of the Brunn Natural History Society, of which he was one of the founders. After years of experiments, Mendel hypothesized that some sort of invisible “factors” affected visible plant traits. No one, apparently, understood what Mendel was talking about. But his paper was published the following year in the Proceedings of the Society, a journal which was circulated to libraries all over Europe. In addition, Mendel himself continued for a number of years to send copies of his paper to other biologists.

Mendel saw many forms of pea plants in the garden of his monastery. Some plants had short stems, others had tall ones; some plants had wrinkled, green peas, others had smooth, round ones. Of the many forms Mendel saw, he chose to study the seven traits shown below (Chart 2.2):

Chart 2.2

Pea trait Form Form

Seed shape Round Wrinkled

Seed color Yellow Green

Seed coat color Colored White

Pod shape Inflated Wrinkled

Pod color Green Yellow

Flower position Axial Terminal

Stem length Tall Short

Pea plants were a good choice for Mendel’s experiments. The petals of the pea plants tightly enclose the male and female flower parts. This flower shape keeps pollen grains inside the flower in which they are produced. Thus, new pea plants form from female sex cells that are fertilized by the pollen grains of the same flower. This kind of fertilization is called self -fertilization.

Mendel let the plants self-fertilize for many generations. He wanted to be sure that he had plants that were purebred for each trait he was studying. Purebred plants show the same form of a trait generation after generation. When Mendel was certain he had purebred plants for each of the seven traits he wanted to study, he began his experiments. He removed pollen grains from purebred plants with one form of each trait. He then placed these pollen grains in flowers of purebred plants with the opposite form of each trait.

After all the plants were crossed, he collected the seeds that formed. He called the seeds hybrids, meaning “half-breed”. In the other words, hybrid is offspring of two parents that differ in one or more heritable characters; offspring of two different varieties or of two different species.

Mendel planted these seeds and waited to see what traits would appear in the hybrid plants. In every case, the hybrid plants showed only one form of the trait; the opposite form of the trait seemed to disappear.

A cross involving one trait is called a monohybrid cross. A genetic cross between homozygous individuals results in identical genotypic and phenotypic ratios in the first generation. A cross involving a heterozygous individual and homozygous individual results in genotypic and phenotypic ratios of 1:1.

A cross involving two pairs of alleles is called a dihybrid cross. The study of this type of cross eventually caused Mendel to develop the principle of independent assortment. The same principles that govern monohybrid crosses also apply to alleles in dihybrid crosses.

According to the principle of independent assortment, each pair of alleles will segregate independently of the other pair.

Because of dominance, the nine genotypes produce just four phenotypes. The phenotypic ratio of the second generation can be expressed as 9:3:3:1.

The Principle of Dominance. Mendel’s next step was to cross the hybrid plants. The forms of the traits that disappeared in the hybrids reappeared in the offspring of the hybrids. Mendel called the form that was visible in the hybrids the dominant form, and the hidden form the recessive form.

Dominant gene: a gene that exerts its full phenotypic effect regardless of its allelic partner; a gene that masks the effect of its allele. Recessive gene: a gene whose phenotypic expression is masked by a dominant allele and so is manifest only in the homozygous condition. Heterozygotes involving recessives are phenotypically indistinguishable from dominant homozygotes.

Mendel noticed a pattern in the way that the forms of the traits appeared in the hybrid offspring. On the average, 75 percent of the plants showed the dominant form of a trait. Only 25 percent of the plants showed the recessive form of the trait. This kind of numerical pattern is called a ratio.

The principle of Segregation. Mendel’s experiments revealed that a parental trait, such as shortness, can disappear in the first generation. His experiments also showed that the same trait can reappear in the second generation in roughly a 3:1 ratio. To explain how traits can disappear and reappear in a certain pattern from generation to generation, Mendel proposed the principle of segregation. The principle of segregation states that the members of each pair of genes separate, or segregate, when gametes are formed.

The Principle of Independent Assortment. Mendel developed his two first principles through experiments involving the inheritance of a single pair of traits. He arrived at his third principle by crossing pea plants with two or more pairs of contrasting traits. He crossed a purebred plant with yellow, round seeds and a purebred plant with green, wrinkled seeds. Seeds produced from this cross were all yellow and round. This result illustrated the principle of dominance.

When these seeds grew into plants and self-pollinated, they produced 4 types of second generation seeds. The yellow, round seeds and the green, wrinkled seeds resembled the seeds of the parental generation. However, the second generation also included round, green seeds and yellow, wrinkled seeds. From this experiment, Mendel realized that two traits produced by recessive genes did not have to appear in the same offspring. For example, green color, a recessive trait, could appear with round seeds, a dominant trait. Mendel formulated the principle of independent assortment to explain this finding. The principle of independent assortment states that two or more pairs of genes segregate independently of one another during the formation of gametes. For instance, the segregation of the genes for seed color does not effect the segregation of genes for seed shape.

Today it is known that most gene pairs segregate independently only if they are located in different chromosomes. Traits determined by two genes of the same chromosomes tend to be inherited together. Mendel, however, was able to choose seven contrasting traits, each determined by a gene pair of a different pair of chromosomes.

The Punnett Square

To visualize the probable results of genetic crosses, geneticists use a grid, or chart, that shows the possible gene combinations for a cross. This grid is called a Punnett square (Chart 2.3). It is named for Reginald Punnett, the British geneticist who developed it in the early 1900s. In a Punnett square, symbols for all the possible gametes from the male parent appear across the top of the grid. Those from the female parent appear along the left side of the grid. By combining the symbol for each male gamete with the symbol for each female gamete, all the possible gamete combinations can be found.

Chart 2.3

Punnett square

Mendel’s Experiments and the Laws of Inheritance

That Mendel was able to make his discoveries before the discovery of meiosis was due in part to the methods of experimentation he used. Mendel’s work is a fine example of preparation, choice of experimental material, execution and interpretation. Let’s see how he approached each of these steps.

Mendel devised a careful research plan

Mendel chose the garden pea for his studies because of its ease of cultivation, the feasibility of controlled pollination and the availability of varieties with differing traits. He controlled pollination and thus fertilization of his parent plants by manually moving pollen from one plant to another. Thus he knew the parentage of the offspring in his experiments. The pea plants Mendel studied produce male and female sex organs and gametes in the same flower.

If untouched, they naturally self-pollinate—that is, the female organ of each flower receives pollen from the male organs of the same flower. Mendel made use of this natural phenomenon in some of his experiments. Mendel began by examining different varieties of peas in a search for heritable characters and traits suitable for study:

A character is an observable feature, such as flower color.

A trait is a particular form of a character, such as whiteflowers.

A heritable character trait is one that is passed from parentto offspring.

Mendel looked for characters that had well-defined, contrasting alternative traits, such as purple flowers versus white flowers. Furthermore, these traits had to be true-breeding, meaning that the observed trait was the only form present for many generations. In other words, peas with white flowers, when crossed with one another, would have to give rise only to progeny with white flowers for many generations; tall plants bred to tall plants would have to produce only tall progeny. Mendel isolated each of his true-breeding strains by repeated inbreeding (done by crossing of sibling plants that were seemingly identical or by allowing individuals to selfpollinate) and selection. In most of his work, Mendel concentrated on the seven pairs of contrasting traits. Before performing any experimental cross, he made sure that each potential parent was from a true-breeding strain— an essential point in his analysis of his experimental results. Mendel then collected pollen from one parental strain and placed it onto the stigma (female organ) of flowers of the other strain whose anthers were removed. The plants providing and receiving the pollen were the parental generation, designated P. In due course, seeds formed and were planted. The seeds and the resulting new plants constituted the first filial generation, or F1. Mendel and his assistants examined each F1 plant to see which traits it bore and then recorded the number of F1 plants expressing each trait. In some experiments the F1 plants were allowed to self-pollinate and produce a second filial generation, F2. Again, each F2 plant was characterized and counted. In summary, Mendel devised a well-organized plan of research, pursued it faithfully and carefully, recorded great amounts of quantitative data, and analyzed the numbers he recorded to explain the relative proportions of the different kinds of progeny. His results and the conclusions to which they led are the subject of the next several sections.

Mendel’s experiment 1 examined a monohybrid cross

“Experiment 1” in Mendel’s paper involved a monohybrid cross —one involving offspring of a cross in which each member of the P generation is true-breeding for a different trait. He took pollen from pea plants of a true-breeding strain with wrinkled seeds and placed it on the stigmas of flowers of a true-breeding strain with spherical seeds .

He also performed the reciprocal cross by placing pollen from the spherical-seeded strain on the stigmas of flowers of the wrinkled-seeded strain. In both cases, all the F1 seeds produced were spherical — it was as if the wrinkled seed trait had disappeared completely. The following spring, Mendel grew 253 F1 plants from these spherical seeds. Each of these plants was allowed to self-pollinate to produce F2 seeds. In all, there were 7,324 F2 seeds, of which 5,474 were spherical and 1,850 wrinkled Mendel observed that the wrinled seed trait was never expressed in the F1 generation, even though it reappeared in the F2 generation. He concluded that the spherical seed trait was dominant to the wrinkled seed trait, which he called recessive. In each of the other six pairs of traits Mendel studied, one proved to be dominant over the other. Of most importance, the ratio of the two traits in the F2 generation was always the same—approximately 3:1. That is, three-fourths of the F2 generation showed the dominant trait and one-fourth showed the recessive trait. In Mendel’s experiment 1, the ratio was 5,474:1,850 = 2.96:1. The reciprocal crosses in the parental generation both gave similar outcomes in the F2; it did not matter which parent contributed the pollen.

By themselves, the results from experiment 1 disproved the widely held belief that inheritance is always a blendingphenomenon. According to the blending theory, Mendel’s F1 seeds should have had an appearance intermediate between those of the two parents — in other words, they should have been slightly wrinkled. Furthermore, the blending theory offered no explanation for the reappearance of the wrinkled trait in the F2 seeds after its apparent absence in the F1 seeds. Mendel proposed that the units responsible for the inheritance of specific traits are present as discrete particles that occur in pairs and segregate (separate) from one another during the formation of gametes. According to this theory, the units of inheritance retain their integrity in the presence of other units. This particulate theory is in sharp contrast to the blending theory, in which the units of inheritance were believed to lose their identities when mixed together. As he worked mathematically with his data, Mendel reached the tentative conclusion that each pea plant has two units of inheritance for each character, one from each parent.

During the production of gametes, only one of these paired units is given to a gamete. Hence each gamete contains one unit, and the resulting zygote contains two, because it is produced by the fusion of two gametes. This conclusion is the core of Mendel’s model of inheritance. Mendel’s unit of inheritance is now called a gene. Mendel reasoned that in experiment 1, the two truebreeding parent plants had different forms of the gene affecting seed shape. The spherical-seeded parent had two genes of the same form, which we will call S, and the parent with wrinkled seeds ha two s genes. The SS parent produced gametes that each contained a single S gene, and the ss parent produced gametes each with a single s gene. Each member of the F1 generation had an S from one parent and an s from the other; an F1 could thus be described as Ss. We say that S is dominant over s because the trait specified by the s allele is not evident when both forms of the gene are present. The different forms of a gene (S and s in this case) are called alleles. Individuals that are true-breeding for a trait contain two copies of the same allele. For example, all the individuals in a population of a strain of true-breeding peas with wrinkled seeds must have the allele pair ss; if S were present, the plants would produce spherical seeds. We say that the individuals that produce wrinkled seeds are homozygous for the allele s, meaning that they have two copies of the same allele (ss). Some peas with spherical seeds—the ones with the genotype SS—are also homozygous. However, not all plants with spherical seeds have the SS genotype. Some spherical-seeded plants, like Mendel’s F1, are heterozygous: They have two different alleles of the genein question (in this case, Ss). To illustrate these terms with a more complex example, one in which there are three gene pairs, an individual with the genotype AABbcc is homozygous for the A and C genes, because it has two A alleles and two c alleles, but heterozygous for the B gene, because it contains the B and b alleles. An individual that is homozygous for a character is sometimes called a homozygote; a heterozygote is heterozygous for the character in question. The physical appearance of an organism is its phenotype. Mendel correctly supposed the phenotype to be the result of the genotype, or genetic constitution, of the organism showing the phenotype. In experiment 1 we are dealing with two phenotypes (spherical seeds and wrinkled seeds). The F2 generation contains these two phenotypes, but they are produced by three genotypes. The wrinkled seed phenotype is produced only by the genotype ss, whereas the spherical seed phenotype may be produced by the genotypes SS or Ss.

Mendel’s first law says that alleles segregate

How does Mendel’s model of inheritance explain the composition of the F2 generation in experiment 1? Consider first the F1 which has the spherical seed phenotype and the Ss genotype. According to Mendel’s model, when any individual produces gametes, the two alleles separate, so that each gamete receives only one member of the pair of alleles. This is Mendel’s first law, the law of segregation. In experiment 1, half the gametes produced by the F1 generation contained the S allele and half the s allele. In the F2 generation, since both SS and Ss plants produce spherical seeds while ss produces wrinkled seeds, there are three ways to get a spherical-seeded plant but only one way to get a wrinkled-seeded plant (s from both parents)—predicting a 3:1 ratio remarkably close to the values Mendel found experimentally for all six of the traits he compared. While this simple example is easy to work out in your head, determination of expected allelic combinations for more complicated inheritance patterns can be aided by use of a Punnett square, devised in 1905 by the British geneticist Reginald Crundall Punnett. This device reminds us to consider all possible combinations of gametes when calculating expected genotype frequencies. APunnett square looks like this: It is a simple grid with all possible male gamete genotypes shown along one side and all possible female gamete genotypes along another side. To complete the grid, we fill in each square with the corresponding pollen genotype and egg genotype, giving the diploid genotype of a member of the F2 generation. For example, to fill the rightmost square, we put in the S from the egg (female gamete) and the s from thepollen (male gamete), yielding Ss (Figure ). Mendel did not live to see his theory placed on a sound physical footing based on chromosomes and DNA. Genes are now known to be regions of the DNA molecules in chromosomes.

More specifically, a gene is a portion of the DNA that resides at a particular site on a chromosome, called a locus (plural, loci), and encodes a particular character. Genes are expressed in the phenotype mostly as proteins with particular functions, such as enzymes. So a dominant gene can be thought of as a region of DNA that is expressed as a functional enzyme, while a recessive gene typically expresses a nonfunctional enzyme. Mendel arrived at his law of segregation with no knowledge of chromosomes or meiosis, but today we can picture the different alleles of a gene segregating as chromosomes separate in meiosis I.

Mendel verified his hypothesis by performing a test cross

Mendel set out to test his hypothesis that there were two possible allelic combinations (SS and Ss) in the spherical-seeded F1 generation. He did so by performing a test cross, which is a way of finding out whether an individual showing a dom-inant trait is homozygous or heterozygous. In a test cross, the individual in question is crossed with an individual known to be homozygous for the recessive trait—an easy individual to identify, because in order to have the recessive phenotype, it must be homozygous for the recessive trait. For the seed shape gene that we have been considering, the recessive homozygote used for the test cross is ss. The individual being tested may be described initially as S–because we do not yet know the identity of the second allele. We can predict two possible results:

If the individual being tested is homozygous dominant (SS), all offspring of the test cross will be Ss and show the dominant trait (spherical seeds).

If the individual being tested is heterozygous (Ss), then approximately half of the offspring of the test cross will be heterozygous and show the dominant trait (Ss), but the other half will be homozygous for, and will show, the recessive trait (ss). The second prediction closely matches the results that Mendel obtained; thus Mendel’s hypothesis accurately predicted the results of his test cross. With his first hypothesis confirmed, Mendel went on to ask another question: How do different pairs of genes behave in crosses when considered together?

Mendel’s second law says that alleles of different genes assort independently

Consider an organism that is heterozygous for two genes (SsYy), in which the S and Y alleles came from its mother and s and y came from its father. When this organism produces gametes, do the alleles of maternal origin (S and Y) go together to one gamete and those of paternal origin (s and y) to another gamete? Or can a single gamete receive one maternal and one paternal allele, S and y (or s and Y)? To answer these questions, Mendel performed another series of experiments. He began with peas that differed in two seed characters: seed shape and seed color. One true-breeding parental strain produced only spherical, yellow seeds (SSYY), and the other produced only wrinkled, green ones (ssyy). A cross between these two strains produced an F1 generation in which all the plants were SsYy. Because the S and Y alleles are dominant, the F1 seeds were all spherical and yellow. Mendel continued this experiment to the F2 generation by performing a dihybrid cross, which is a cross made between individuals that are identical double heterozygotes. There are two possible ways in which such doubly heterozygous plants might produce gametes, as Mendel saw it. (Remember that he had never heard of chromosomes or meiosis.) First, if the alleles maintain the associations they had in the parental generation (that is, if they are linked), then the F1 plants should produce two types of gametes (SY and sy) and the F2 progeny resulting from self-pollination of the F1 plants should consist of three times as many plants bearing spherical, yellow seeds as ones with wrinkled, green seeds. Were such results to be obtained, there might be no reason to suppose that seed shape and seed color were regulated by two different genes, because spherical seeds would always be yellow and wrinkled ones always green. The second possibility is that the segregation of S from s is independent of the segregation of Y from y (that is, that the two genes are not linked). In this case, four kinds of gametes should be produced by the F1 in equal numbers: SY, Sy, sY, and sy. When these gametes combine at random, they should produce an F2 of nine different genotypes. The F2 progeny could have any of three possible genotypes for shape (SS, Ss, or ss) and any of three possible genotypes for color (YY, Yy, or yy). The combined nine genotypes should produce just four phenotypes (spherical yellow, spherical green, wrinkled yellow, wrinkled green). By using a Punnett square, we can show that these four phenotypes would be expected to occur in a ratio of 9:3:3:1 (Figure ). The results of Mendel’s dihybrid crosses matched the second prediction: Four different phenotypes appeared in the F2 in a ratio of about 9:3:3:1. The parental traits appeared in new combinations (spherical green and wrinkled yellow). Such new combinations are called recombinant phenotypes. These results led Mendel to the formulation of what is now known as Mendel’s second law: Alleles of different genes assort independently of one another during gamete formation. That is, the segregation of the alleles of gene Ais independent of the segregation of the alleles of gene B. We now know that this law of independent assortment is not as universal as the law of segregation, because it applies to genes located on separate chromosomes but not necessarily to those located on the same chromosome, as we will see below. However, it is correct to say that chromosomes segregate independently during the formation of gametes, and so do any two genes on separate homologous chromosome pairs (Figure ). One of Mendel’s major contributions to the science of genetics was his use of the rules of statistics and probability to analyze his masses of data from hundreds of crosses producing thousands of plants. His mathematical analyses led to clear patterns in the data, and then to his hypotheses. Ever since Mendel, geneticists have used simple mathematics in the same ways that Mendel did.

Punnett squares or probability calculations: A choice of methods

Punnett squares provide one way of solving problems in genetics, and probability calculations provide another. Many people find it easiest to use the principles of probability, perhaps because they are so familiar. When we flip a coin, the law of probability states that it has an equal probability of landing “heads” or “tails.” For any given toss of a fair coin, the probability of heads is independent of what happened in all the previous tosses. A run of ten straight heads implies nothing about the next toss. No “law of averages” increases the likelihood that the next toss will come up tails, and no “momentum” makes an eleventh occurrence of heads any more likely. On the eleventh toss, the odds of getting heads are still 50/50. The basic conventions of probability are simple:

If an event is absolutely certain to happen, its probabilityis 1.

If it cannot possibly happen, its probability is 0.

Otherwise, its probability lies between 0 and 1.

A coin toss results in heads approximately half the time, so the probability of heads is 1⁄2 — as is the probability of tails.

Multiplying probabilities

How can we determine the probability of two independent events happening together? If two coins (a penny and a dime, say) are tossed, each acts independently of the other. What, then, is the probability of both coins coming up heads? Half the time, the penny comes up heads; of that fraction, half the time the dime also comes up heads. Therefore, the joint probability of both coins coming up heads is half of one-half, or 1⁄2 x 1⁄2 = 1⁄4. To find the joint probability of independent events, then, we multiply the probabilities of the individual events. How does this method apply to genetics?

The monohybrid cross

To apply the principles of probability to genetics problems, we need only deal with gamete formation and random fertilization instead of coin tosses. A homozygote can produce only one type of gamete, so, for example, the probability of an SS individual producing gametes with the genotype S is 1. The heterozygote Ss produces S gametes with a probability of 1⁄2, and s gametes with a probability of 1⁄2. Consider the F2 progeny of the cross in. They are obtained by self-pollination of F1 plants of genotype Ss. The probability that an F2 plant will have the genotype SS must be 1⁄2 x 1⁄2 = 1⁄4 because there is a 50:50 chance that the sperm will have the genotype S, and that chance is independent of the 50:50 chance that the egg will have the genotype S. Similarly, the probability of ss offspring is 1⁄2 x 1⁄2 = 1⁄4.

Adding probabilities

How are probabilities calculated when an event can happen in different ways? The probability of an F2 plant getting an S allele from the sperm and an s allele from the egg is 1⁄4, but remember that the same on the same chromosome, as we will see below. However, it is correct to say that chromosomes segregate independently during the formation of gametes, and so do any two genes on separate homologous chromosome pairs. One of Mendel’s major contributions to the science of genetics was his use of the rules of statistics and probability to analyze his masses of data from hundreds of crosses producing thousands of plants. His mathematical analyses led to clear patterns in the data, and then to his hypotheses. Ever since Mendel, geneticists have used simple mathematics in the same ways that Mendel did.

The dihybrid cross

If F1 plants heterozygous for two independent characters self-pollinate, the resulting F2 plants express four different phenotypes. The proportions of these phenotypes are easily determined by probability calculations. Let’s see how this works for the experiment shown in Figure . Using the principle described above, we can calculate that the probability that an F2 seed will be spherical is 3⁄4: the probability of an Ss heterozygote (1⁄2) plus the probability of an SS homozygote (1⁄4) = 3⁄4. By the same reasoning, the probability that a seed will be yellow is also 3⁄4. The two characters are determined by separate genes and are independent of each other, so the joint probability that a seed will be both spherical and yellow is 3⁄4 x 3⁄4 = 9⁄16. What is the probability of F2 seeds being both wrinkled and yellow? The probability of being yellow is again 3⁄4; the probability of being wrinkled is 1⁄2 x 1⁄2 = 1⁄4. The joint probability that a seed will be both wrinkled and yellow, then, is 1⁄4 x 3⁄4 = 3⁄16. The same probability applies, for similar reasons, to spherical, green F2 seeds. Finally, the probability that F2 seeds will be both wrinkled and green is 1⁄4 x 1⁄4 = 1⁄16. Looking at all four phenotypes, we see they are expected in the ratio of 9:3:3:1.

Probability calculations and Punnett squares give the same results. Learn to do genetics problems both ways and then decide which method you prefer.

Mendel’s laws can be observed in human pedigrees

After Mendel’s work was uncovered by plant breeders, Mendelian inheritance was observed in humans. Currently, the patterns of over 2,500 inherited human characteristics have been described. How can Mendel’s laws of inheritance be applied to humans? Mendel worked out his laws by performing many planned crosses and counting many offspring. Neither of these approaches is possible with humans. So human geneticists rely on pedigrees, family trees that show the occurrence of phenotypes (and alleles) in several generations of related individuals. Because humans have such small numbers of offspring, human pedigrees do not show the clear proportions of offspring phenotypes that Mendel saw in his pea plants. For example, when two people who are both heterozygous for a recessive allele (say, Aa) marry, there will be, for each of their children, a 25 percent probability that the child will be a recessive homozygote (aa). Thus, over many such marriages, one-fourth of all the children will be recessive homozygotes (aa). But the offspring of a single marriage are likely to be too few to show the exact one-fourth proportion. In a family with only two children, for example, both could easily be aa (or Aa, or AA). To deal with this ambiguity, human geneticists assume that any allele that causes an abnormal phenotype is rare in the human population. This means that if some members of a given family have a rare allele, it is highly unlikely that an outsider marrying into that family will have that same rare allele.

Human geneticists may wish to know whether a particular rare allele is dominant or recessive. Figure 10.10 depicts a pedigree showing the pattern of inheritance of a rare domi-nant allele. The following are the key features to look for in such a pedigree:

Every affected person has an affected parent.

About half of the offspring of an affected parent are also affected.

The phenotype occurs equally in both sexes. The pattern of inheritance of a rare recessive allele:

Affected people usually have two parents who are not affected.

In affected families, about one-fourth of the children of unaffected parents can be affected.

The phenotype occurs equally in both sexes.

In pedigrees showing inheritance of a recessive phenotype, it is not uncommon to find a marriage of two relatives. This pattern is a result of the rarity of recessive alleles that give rise to abnormal phenotypes. For two phenotypically normal parents to have an affected child (aa), the parents must both be heterozygous (Aa). If a particular recessive allele is rare in the general population, the chance of two people marrying who are both carrying that allele is quite low. On the other hand, if that allele is present in a family, two cousins might share it. This is why studies on populations isolated either culturally (by religion, as with the Amish in the United States) or geographically (as on islands) have been so valuable to human geneticists. People in these groups tend to have large families, or to marry among themselves or both. Because the major use of pedigree analysis is in the clinical evaluation and counseling of patients with inherited abnormalities, a single pair of alleles is usually followed. However, just as pedigree analysis shows the segregation of alleles, it also can show independent assortment if two different allele pairs are considered.

Alleles and Their Interactions

In many cases, alleles do not show the simple relationships between dominance and recessiveness that we have described. In others, a single allele may have multiple phenotypic effects. Existing alleles can give rise to new alleles by mutation, so there can be many alleles for a single character.

New alleles arise by mutation

Different alleles of a gene exist because genes are subject to mutations, which are rare, stable and inherited changes in the genetic material. In other words, an allele can mutate to become a different allele. Mutation is a random process; different copies of the same allele may be changed in different ways. One particular allele of a gene may be defined as the wild type because it is present in most individuals in nature (“the wild”) and gives rise to an expected trait or phenotype. Other alleles of that gene, often called mutant alleles, may produce a different phenotype. The wild-type and mutant alleles reside at the same locus and are inherited according to the rules set forth by Mendel. A genetic locus with a wild-type allele that is present less than 99 percent of the time (the rest of the alleles being mutant) is said to be polymorphic (from the Greek poly “many” and morph “form”).

Many genes have multiple alleles

Because of random mutations, a group of individuals may have more than two alleles of a given gene. (Any one individual has only two alleles, of course — one from its mother genes have alleles that are not dominant or recessive to one another. Instead, the heterozygotes show an intermediate phenotype — at first glance, like that predicted by the old blending theory of inheritance. For example, if a true-breeding red snapdragon is crossed with a true-breeding white one, all the F1 flowers are pink. That this phenomenon can still be explained in terms of Mendelian genetics, rather than blending, is readily demonstrated by a further cross. The blending theory predicts that if one of the pink F1 snapdragons is crossed with a true-breeding white one, all the offspring should be a still lighter pink. In fact, approximately 1⁄2 of the offspring are white, and 1⁄2 are the same shade of pink as the F1 parent. When the F1 pink snapdragons are allowed to self-pollinate, the resulting F2 plants are distributed in a ratio of 1 red : 2 pink : 1 white. Clearly the hereditary particles — the genes — have not blended; they are readily sorted out in the F2.

We can understand these results in terms of the Mendelian laws of inheritance. All we need to do is recognize that the heterozygotes show a phenotype intermediate between those of the two homozygotes. In such cases, the gene is said to be governed by incomplete dominance. Incomplete dominance is common in nature. In fact, Mendel’s paper was unusual in that all seven of the examples he described are characterized by complete dominance.

In codominance, both alleles are expressed

Sometimes the two alleles at a locus produce two different phenotypes that both appear in heterozygotes. An example of this phenomenon, called codominance, is seen in the ABO blood group system in humans. Early attempts at blood transfusion frequently killed the patient. Around 1900, the Austrian scientist Karl Landsteiner mixed blood cells and serum (blood from which cells have been removed) from different individuals. He found that only certain combinations of blood are compatible. In other combinations, the red blood cells from one individual form clumps in the presence of serum from the other individual. This discovery led to our ability to administer compatible blood transfusions that do not kill the recipient. Clumps form in incompatible transfusions because specific proteins in the serum, called antibodies, react with foreign, or “nonself,” cells. The antibodies react with proteins on the surface of nonself cells, called antigens. Blood compatibility is determined by a set of three alleles (IA, IB, and iO) at one locus, which determine the antigens on the surface of red blood cells. Different combinations of these alleles in different people produce four different blood types, or phenotypes: A, B, AB, and O. The AB phenotype found in individuals of IAIB genotype is an example of codominance—these individuals produce cell surface antigens of both the Aand B types.

Some alleles have multiple phenotypic effects

Mendel’s principles were further extended when it was discovered that a single allele can result in more than one phenotype. When a single allele has more than one distinguishable phenotypic effect, we say that the allele is pleiotropic. A familiar example of pleiotropy involves the allele responsible for the coloration pattern (light body, darker extremities) of Siamese cats, discussed later in this chapter. The same allele is also responsible for the characteristic crossed eyes of Siamese cats. Although these effects appear to be unrelated, both result from the same protein producedunder the influence of the allele.

Gene Interactions

Thus far we have treated the phenotype of an organism, with respect to a given character, as a simple result of the alleles of a single gene. In many cases, however, several genes interact to determine a phenotype. To complicate things further, the physical environment may interact with the genetic constitution of an individual in determining the phenotype.

Some genes alter the effects of other genes

Epistasis occurs when the phenotypic expression of one gene is affected by another gene. For example, several genes determine coat color in mice. The wild-type color is agouti, a grayish pattern resulting from bands on the individual hairs. The dominant allele B determines that the hairs will have bands and thus that the color will be agouti, whereas the homozygous recessive genotype bb results in unbanded hairs, and the mouse appears black. A second locus, on another chromosome, affects an early step in the formation of hair pigments. The dominant allele A at this locus allows normal color development, but aa blocks all pigment production. Thus, aa mice are all-white albinos, irrespective of their genotype at the B locus. If a mouse with genotype AABB (and thus the agouti phenotype) is crossed with an albino of genotype aabb, the F1 mice are AaBb and have the agouti phenotype. If the F1 mice are crossed with each other to produce an F2 generation, then epistasis will result in an expected phenotypic ratio of 9 agouti:3 black:4 albino. (Can you show why? The underlying ratio is the usual 9:3:3:1 for a dihybrid cross with unlinked genes, but look closely at each genotype, and watch out for epistasis.) In another form of epistasis, two genes are mutually dependent: The expression of each depends on the alleles of the other. The epistatic action of such complementary genes may be explained as follows: Suppose gene A codes for enzyme A in the metabolic pathway for purple pigment in flowers, and gene B codes for enzyme B: In order for the pigment to be produced, both reactions must take place. The recessive alleles a and b code for nonfunctional enzymes. If a plant is homozygous for either a or b, the corresponding reaction will not occur, no purple pigment will form and the flowers will be white.

Hybrid vigor results from new gene combinations and interactions

If Mendel’s paper was the most important event in genetics in the nineteenth century, perhaps an equally important paper in applied genetics was published early in the twentieth century by G. H. Shull, titled “The composition of a field of maize.” Farmers growing crops have known for centuries that mating among close relatives (known as inbreeding) can result in offspring of lower quality than those from matings between unrelated individuals. The reason for this is that close relatives tend to have the same recessive alleles, some of which may be harmful, as we saw in our discussion of human pedigrees above. In fact, it has long been known that if one crosses two true-breeding, homozygous genetic strains of a plant or animal, the result is offspring that are phenotypically much stronger, larger and in general more “vigorous” than either of the parents. Shull began his experiment with two of the thousands of existing varieties of corn (maize). Both varieties produced about 20 bushels of corn per acre. But when he crossed them, the yield of their offspring was an astonishing 80 bushels per acre. This phenomenon is known as heterosis (short for heterozygosis), or hybrid vigor. The cultivation of hybrid corn spread rapidly in the United States and all over the world, quadrupling grain production. The practice of hybridization has spread to many other crops and animals used in agriculture. The actual mechanism by which heterosis works is not known. A widely accepted hypothesis is overdominance in which the heterozygous condition in certain important genes is superior to either homozygote.

The environment affects gene action

The phenotype of an individual does not result from its genotype alone. Genotype and environment interact to determine the phenotype of an organism. Environmental variables such as light, temperature, and nutrition can affect the translation of a genotype into a phenotype. A familiar example of this phenomenon involves the Siamese cat. This handsome animal normally has darker fur on its ears, nose, paws and tail than on the rest of its body. These darkened extremities normally have a lower temperature than the rest of the body. Afew simple experiments show that the Siamese cat has a genotype that results in dark fur, but only at temperatures below the general body temperature. If some dark fur is removed from the tail and the cat is kept at higher than usual temperatures, the new fur that grows in is light. Conversely, removal of light fur from the back, followed by local chilling of the area, causes the spot to fill in with dark fur. Two parameters describe the effects of genes and environment on the phenotype:

Penetrance is the proportion of individuals in a group with a given genotype that actually show the expected phenotype.

Expressivity is the degree to which a genotype is expressed in an individual.

For an example of environmental effects on expressivity, consider how Siamese cats kept indoors or outdoors in different climates might look.

Most complex phenotypes are determined by multiple genes and environment

The differences between individual organisms in simple characters, such as those that Mendel studied in peas, are discrete and qualitative. For example, the individuals in a population of peas are either short or tall. For most complex characters, however, such as height in humans, the phenotype varies more or less continuously over a range. Some people are short, others are tall, and many are in between the two extremes. Such variation within a population is called quantitative, or continuous, variation. In most cases, quantitative variation is due to two factors: multiple genes, each with multiple alleles, and environmental influences on the expression of these genes. Geneticists call the genes that together determine a complex character quantitative trait loci. Identifying these loci is a major challenge and an important one. For example, the amount of grain that a variety of rice produces in a growing season is determined by many interacting genetic factors. Crop plant breeders have worked hard to decipher these fac-tors in order to breed higher-yielding rice strains. In a similar way, human characteristics such as disease susceptibility and behavior are caused in part by quantitative trait loci.

Genes and Chromosomes

The recognition that genes occupy characteristic positions on chromosomes and are segregated by meiosis enabled Mendel’s successors to provide a physical explanation for his model of inheritance. It soon became apparent that the association of genes with chromosomes has other genetic consequences as well. We mentioned above that genes located on the same chromosome may not follow Mendel’s law of independent assortment. What is the pattern of inheritance of such genes? How do we determine where genes are located on a chromosome and the distances between them? The answers to these and many other genetic questions were worked out in studies of the fruit fly Drosophila melanogaster. Its small size, its ease of cultivation, and its short generation time made this animal an attractive experimental subject. Beginning in 1909, Thomas Hunt Morgan and his students pioneered the study of Drosophila in Columbia University’s famous “fly room” where they discovered the phenomena described in this section. Drosophila remains extremely important in studies of chromosome structure, population genetics, the genetics of development and the genetics of behavior.

Genes on the same chromosome are linked

Some of the crosses Morgan performed with fruit flies resulted in phenotypic ratios that were not in accord with those predicted by Mendel’s law of independent assortment. Morgan crossed Drosophila of two known genotypes, BbVgvg X bbvgvg, for two different characters, body color and wing shape:

B (wild-type gray body), is dominant over b (black body)

Vg (wild-type wing) is dominant over vg (vestigial, a very small wing)

Morgan expected to see four phenotypes in a ratio of 1:1:1:1, but that is not what he observed. The body color gene and the wing size gene were not assorting independently; rather, they were for the most part inherited together. These results became understandable to Morgan when he assumed that the two loci are on the same chromosome— that is, that they are linked. After all, since the number of genes in a cell far exceeds the number of chromosomes, each chromosome must contain many genes. The full set of loci on a given chromosome constitutes a linkage group. The number of linkage groups in a species equals the number of homologous chromosome pairs. Suppose, now, that the Bb and Vgvg loci are indeed located on the same chromosome. Why, then, didn’t all of Morgan’s F1 flies have the parental phenotypes—that is, why did his cross result in anything other than gray flies with normal wings (wild-type) and black flies with vestigial wings? If we assumed that linkage is absolute — that is, that chromosomes always remain intact and unchanged — we would expect to see just those two types of progeny. However, this is not always what happens.

Genes can be exchanged between chromatids

Absolute linkage is extremely rare. If linkage were absolute, Mendel’s law of independent assortment would apply only to loci on different chromosomes. What actually happens is more complex and therefore more interesting. Chromosomes are not unbreakable, so recombination of genes can occur. That is, genes at different loci on the same chromosome do sometimes separate from one another during meiosis. Genes may recombine when two homologous chromosomes physically exchange corresponding segments during prophase I of meiosis — that is, by crossing over. Recall from Chapter 9 that the DNA is replicated during the S phase, so that by prophase I when homologous chromosome pairs come together to form tetrads, each chromosome consists of two chromatids. The exchange event involves only two of the four chromatids in a tetrad, one from each member of the homologous pair, and can occur at any point along the length of the chromosome. The chromosome segments involved are exchanged reciprocally, so both chromatids involved in crossing over become recombinant (that is, each chromatid ends up with genes from both of the organism’s parents). Usually several exchange events occur along the length of each homologous pair.

When crossing over takes place between two linked genes, not all progeny of a cross will have the parental phenotypes. Instead, recombinant offspring appear as well, as they did in Morgan’s cross. They appear in proportions called recombinant frequencies, which are calculated by dividing the number of recombinant progeny by the total number of progeny. Recombinant frequencies will be greater for loci that are farther apart on the chromosome than for loci that are closer together, because an exchange event is more likely to occur between genes that are far apart than between genes that are close together.

Geneticists can make maps of chromosomes

If two loci are very close together on a chromosome, the odds of crossing over between them are small. In contrast, if two loci are far apart, crossing over could occur between them at many points. In a population of cells undergoing meiosis, a greater proportion of the cells will undergo recombination between two loci that are far apart than between two loci that are close together. In 1911, Alfred Sturtevant, then an undergraduate student in T. H. Morgan’s fly room, realized how that simple insight could be used to show where different genes lie on a chromosome in relation to one another. The Morgan group had determined recombinant frequencies for many pairs of linked genes. Sturtevant used these recombinant frequencies to create genetic maps that showed the arrangement of genes along the chromosome. Ever since Sturtevant demonstrated this method, geneticists have mapped the chromosomes of eukaryotes, prokaryotes, and viruses, assigning distances between genes in map units. A map unit corresponds to a recombinant frequency of 0.01; it is also referred to as a centimorgan (cM), in honor of the founder of the fly room. You too, can work out a genetic map.

Sex Determination and Sex-Linked Inheritance

In Mendel’s work, reciprocal crosses always gave identical results; it did not matter, in general, whether a dominant allele was contributed by the mother or by the father. But in some cases, the parental origin of a chromosome does matter. For example, as we saw at the beginning of this chapter, human males inherit hemophilia Afrom their mother, not from their father. To understand the types of inheritance in which the parental origin of an allele is important, we must consider the ways in which sex is determined in different species.

Sex is determined in different ways in different species

In corn, a plant much studied by geneticists, every diploid adult has both male and female reproductive structures. The tissues in these two types of structures are genetically identical, just as roots and leaves are genetically identical. Plants such as corn, in which the same individual produces both male and female gametes, are said to be monoecious (from the Greek, “one house”). Other plants, such as date palms and oak trees, and most animals are dioecious (“two houses”), meaning that some individuals can produce only male gametes and the others can produce only female gametes. In other words, dioecious organisms have two sexes. In most dioecious organisms, sex is determined by differences in the chromosomes, but such determination operates in different ways in different groups of organisms. For example, the sex of a honeybee depends on whether it develops from a fertilized or an unfertilized egg. A fertilized egg is diploid and gives rise to a female bee—either a worker or a queen, depending on the diet during larval life (again, note how the environment affects the phenotype). An unfertilized egg is haploid and gives rise to a male drone: In many other animals, including humans, sex is determined by a single sex chromosome, or by a pair of them. Both males and females have two copies of each of the rest of the chromosomes, which are called autosomes. Female grasshoppers, for example, have two X chromosomes, whereas males have only one. Female grasshoppers are described as being XX (ignoring the autosomes) and males as XO (pronounced “ex-oh”): Females form eggs that contain one copy of each autosome and one X chromosome. Males form approximately equal amounts of two types of sperm: One type contains one copy of each autosome and one X chromosome; the other type contains only autosomes. When an X-bearing sperm fertilizes an egg, the zygote is XX, and develops into a female. When a sperm without an X fertilizes an egg, the zygote is XO, and develops into a male. This chromosomal mechanism ensures that the two sexes are produced in approximately equal numbers. As in grasshoppers, female mammals have two X chromosomes and males have one. However, male mammals also have a sex chromosome that is not found in females: the Y chromosome. Females may be represented as XX and males as XY: Males produce two kinds of gametes. Each gamete has a complete set of autosomes, but half the gametes carry an X chromosome and the other half carry a Y. When an X-bearing sperm fertilizes an egg, the resulting XX zygote is female; when a Y-bearing sperm fertilizes an egg, the resulting XY zygote is male.

The X and Y chromosomes have different functions

Some subtle but important phenotypic differences show up clearly in mammals with abnormal sex chromosome constitutions. These conditions, which result from nondisjunctions, as described in Chapter 9, tell us something about the functions of the X and Y chromosomes. In humans, XO individuals sometimes appear. Human XO individuals are females who are physically moderately abnormal but mentally normal; usually they are also sterile. The XO condition in humans is called Turner syndrome. It is the only known case in which a human can survive with only one member of a chromosome pair (here, the XY pair), although most XO conceptions terminate spontaneously early in development. XXY individuals also occur; this condition is known as Klinefelter syndrome. People with this genotype are sometimes taller than average, always sterile and always male. These observations suggested that the gene that determines maleness is located on the Y chromosome. Observations of people with other types of chromosomal abnormalities helped researchers to pinpoint the location of that gene:

Some XY individuals are phenotypically women and lack a small portion of the Y chromosome.

Some men are genetically XX and have a small piece of the Y chromosome present but attached to another chromosome.

The Y fragment that is missing and present in these two examples, respectively, contains the maleness-determining gene, which was named SRY (sex-determining region on the Y chromosome).

The SRY gene encodes a protein involved in primary sex determination—that is, the determination of the kinds of gametes that will be produced and the organs that will make them. In the presence of functional SRY protein, the embryo develops sperm-producing testes. (Notice that italic type is used for the name of a gene but roman type is used for the name of a protein.) If the embryo has no Y chromosome, the SRY gene is absent, and thus the SRY protein is not made. In the absence of the SRY protein, the embryo develops egg-producing ovaries. In this case, a gene on the X chromosome called DAX1 produces an anti-testis factor. So the role of SRY in a male is to inhibit the maleness inhibitor encoded by DAX1. The SRY protein does this in male cells, but since it is not present in females, DAX1 can act to inhibit maleness. Primary sex determination is not the same as secondary sex determination, which results in the outward manifestations of maleness and femaleness (body type, breast development, body hair, and voice). These outward characteristics are not determined directly by the presence or absence of the Y chromosome. Rather, they are determined by genes scattered on the autosomes and X chromosome that control the actions of hormones, such as testosterone and estrogen. The Y chromosome functions differently in Drosophila melanogaster. Superficially, Drosophila follows the same pattern of sex determination as mammals—females are XX and males are XY. However, XO individuals are males (rather than females as in mammals) and almost always are indistinguishable f

Date: 2014-12-22; view: 1712