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 dominantto 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 theoryis 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 homozygousfor 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 recombinantphenotypes. 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 assortmentis 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.