Written Assignment 2

Even with perfect information, it can still be impossible to know a genetic outcome with certainty. It’s like flipping a coin: you can know every last detail about the coin, but you still can’t know whether the coin will land on heads or tails when flipped. The best you can do is define the probability of each possible outcome. The rules of probability have a central role in genetics, for two reasons. First, Mendel described the process of segregation, in which each gamete receives only one copy of each gene present in somatic cells. As a result, for each gene the individual carries, the likelihood that the sperm or egg will include one allele is the same as the likelihood that it will include the other allele. It is impossible to know which allele it will be. Second, as we learned in Chapter 8, all of the sperm or eggs produced by an individual are genetically different from one another, and any one of those gametes may be the gamete involved in fertilization. Like segregation, fertilization is a chance event. In games of chance, as well as in matings, we can make predictions based on probabilities. If an individual is homozygous for a trait, 100% of his or her gametes will carry that allele. An individual heterozygous for a trait has a 50% probability of carrying the dominant allele and a 50% probability of carrying the recessive allele. What is the probability that an offspring will be homozygous for albinism (mm) if the male parent is heterozygous for albinism (Mm) and the female parent is albino (mm)? To get the mm outcome, two events must occur. First, the father’s gamete must carry the recessive allele (m), and second, the mother’s gamete must carry the recessive allele (m). In this case, the probability of a homozygous recessive offspring is 0.5 (the probability that the father’s gamete carries m) times 1.0 (the probability that the mother’s gamete carries m), for a probability of 0.5, or 50%, or 1/2 (1 in 2). This is a general rule when determining the likelihood of a complex event occurring: if you know the probability of each component that must occur, you multiply all the probabilities together to get the overall probability of that complex event occurring.

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Consider an example that involves Tay-Sachs disease. As described in Chapter 4, Tay-Sachs is caused by malfunctioning lysosomes that do not digest cellular waste properly. It leads to death in early childhood. Tay-Sachs occurs if a child inherits two recessive alleles (t) for the Tay-Sachs gene. If each parent is heterozygous for the Tay-Sachs gene (Tt), what is the probability that their child will have Tay-Sachs disease? Half the father’s sperm will have the dominant T allele and half will have the t allele. So the probability of the child inheriting the t allele is 0.5. Half of the mother’s eggs will have the T allele, while the other half have the t allele, so the probability of the child inheriting the t allele from its mother is also 0.5. And the overall probability of the child having Tay-Sachs disease is 0.5 × 0.5 = 0.25, or 1 in 4. Of course, if the couple has only one child, we can’t predict with certainty whether the child will have Tay-Sachs. The mathematical probability tells us, however, that if the couple had an infinite number of children, we could expect that one-fourth of them would have Tay-Sachs disease.

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Suppose you are in charge of the alligators at a zoo. Some of your individuals come from a population in which white, albino alligators have occasionally occurred, although none of your current alligators are white. Because white alligators—those having two recessive pigmentation alleles, mm (the letter “m” refers to the color pigment melanin)—are popular with zoo visitors, you would like to produce some via a mating program. The problem is that you cannot be certain of the genotype of your alligators. The problem is that you cannot be certain of the genotype of your alligators. They might be homozygous dominant, MM, or they might be heterozygous, Mm. In either case, their phenotype is normal coloration. Determining the genotype of a particular alligator is a challenge to animal breeders, but not an insurmountable one. Genes may be invisible, but their identity can be revealed by a tool called the test-cross.

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In the test-cross, you cross (i.e., mate) an individual exhibiting a dominant trait but whose genotype is unknown with an individual that is homozygous recessive. Then you examine the phenotypes of their offspring. To breed an albino alligator, you could borrow an albino alligator from another zoo and breed your unknown-genotype alligator (genotype: M_) with that albino alligator (genotype: mm). There are two possible outcomes, and they will reveal the genotype of your M_ alligator. If your alligator is homozygous dominant (MM), it will contribute a dominant allele, M, to every offspring. Even though the albino alligator will contribute the recessive allele, m, to all of its offspring, all the offspring of this cross will be heterozygous, Mm, and none of them will be albino. If, on the other hand, your M_ alligator is heterozygous, Mm, half of the time it will contribute a recessive allele, m, to the offspring. In every one of those cases, the offspring will be homozygous recessive and thus albino. So the cleverness of the test-cross is that when you cross your unknown-genotype organism with an individual showing the recessive trait (and so having the known genotype of mm), the offspring will reveal the previously unknown makeup of the parent. To be confident in concluding that the unknown-genotype alligator has the MM genotype, though, you’d have to observe many, many offspring. After all, even if its genotype is Mm, quite a few offspring in a row might be normally pigmented, with the genotype Mm. Eventually, however, a heterozygous individual is likely to produce an offspring with the homozygous recessive genotype, mm, and the albino phenotype.

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Prospective parents may want to know the likelihood of having a child with a particular genetic disease, say hemophilia. Geneticists who study diseases may want to know how a particular disease or trait is inherited. Is it recessive or dominant? Is it carried on the sex chromosomes or on one of the other chromosomes? A pedigree is a type of family tree that can help answer these questions. In a pedigree, information is gathered from as many related individuals as possible across multiple generations. Starting from the bottom, each row in the chart represents a generation, listing all of the children in their order of birth, their sex, and whether or not they have a particular trait. Working up the pedigree, the children’s parents are indicated and, above them, their parents’ parents, for as far back as data are available. Squares represent males and circles represent females, and these shapes are shaded to indicate that an individual exhibits the trait of interest. Sometimes the genotype (as much of it as is known) is also listed for each individual. The pedigree is analyzed for patterns of inheritance. For dominant traits, all affected individuals must have at least one parent who exhibits the trait. In contrast, for recessive traits, an individual may exhibit a recessive trait even if neither parent exhibits the trait. In this case, the individual’s parents must be heterozygous for that trait. The pedigree can also help to determine whether a trait is carried on the sex chromosomes (X or Y, which we discuss in Section 9.13) or on one of the non-sex chromosomes (also called autosomes). Traits that are controlled by genes on the sex chromosomes are called sex-linked traits. Recessive sex- linked traits, for example, appear more frequently in males than in females, whereas dominant sex-linked traits appear more frequently in females. These patterns may become obvious only on inspection of a large pedigree.

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Anury is a condition seen in dogs and some other animals in which the animal has no tail. The pedigree reveals that anury is inherited as a recessive trait, because unaffected parents can have offspring with the disorder. Can you determine the genotype of the individual labeled “1” in Figure 9-16? Why must that female be heterozygous (Aa) for anury? (By the way, an individual that carries one allele for a recessive trait, and so does not exhibit the trait but can have offspring that do, is referred to as a carrier of the trait.) Must her mate have the same genotype? On the same pedigree, note that two individuals in the second row of the pedigree have a puppy (indicated by “?”). What is the probability that this puppy has anury? Examine the pedigree carefully and see whether you can come up with the answer. In the cross producing the mystery puppy, the father has anury and so must be homozygous recessive; he will definitely pass on one a to the son. The mother’s genotype can be AA, Aa, or aA, given that both of her parents are heterozygous. Consequently, she has a 2/3 (2 in 3) probability of being a carrier of the a allele. If she is, then there is a 1/2 (50%) chance that she will pass the allele on to her offspring, and he will have anury. The probability, therefore, is 2/3 × 1/2 = 1/3, or a 1 in 3 chance that the puppy will have anury. As we’ll discuss in later sections of this chapter, some traits may not show complete dominance and many traits are also influenced by the environment, so it is not always obvious what a trait’s mode of inheritance is. In such cases, the more individuals we can include in the pedigree, the more accurate the analysis. Some human pedigrees contain thousands of individuals and stretch back six or more generations. With some other species it is possible to analyze tens of thousands of individuals per generation for a dozen or more generations. This is why plants and small insects (among other organisms) are excellent for studying inheritance patterns. Once we have an idea about how a trait is inherited, we can identify individuals who are carriers of a recessive trait and make informed predictions about a couple’s risk of having a child with a particular disorder. This knowledge can be useful in conjunction with prenatal testing and treatment.

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