6.5. Traits and Probability. Punnett squares illustrate genetic crosses.

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1 6.5 Traits and Probability VOCABULARY Punnett square monohybrid cross testcross dihybrid cross law o independent assortment probability Key Concept The inheritance o traits ollows the rules o probability. S Punnett squares illustrate genetic crosses. A monohybrid cross involves one trait. A dihybrid cross involves two traits. Heredity patterns can be calculated with probability. John Innes Archives > R. C. Punnett igure 5. R. C. Punnett developed the Punnett square as a way to illustrate genetic crosses. Connect to Your World I you have tried juggling, you know it can be a tricky thing. Keeping three laming torches or clubs in motion at the same time is a challenge. Trying to keep track o what organism has which genotype and which gamete gets which allele can also be a lot to juggle. ortunately, R. C. Punnett developed a method to keep track o all o the various combinations graphically. Punnett squares illustrate genetic crosses. Shortly ater Mendel s experiments became widely known among scientists, a poultry geneticist named R. C. Punnett, shown in igure 5., developed the Punnett square. A Punnett square is a grid system or predicting all possible genotypes resulting rom a cross. The axes o the grid represent the possible gamete genotypes o each parent. The grid boxes show all o the possible genotypes o ospring rom those two parents. Because segregation and VISUAL VOCAB The Punnett square is a grid system or predicting possible genotypes o ospring. Parent alleles A a Parent alleles A AA Aa ertilization are random events, each combination o alleles is as likely to be produced as any other. By counting the number o squares with each genetic combination, we can ind the ratio o genotypes in that generation. I we also know how the genotype corresponds to the phenotype, we can ind the ratio o phenotypes in that generation as well. Let s briely review what you ve learned about meiosis and segregation to examine why the Punnett square is eective. Both parents have two alleles or each gene. These alleles are represented on the axes o the Punnett square. During meiosis, the chromosomes and, thereore, the alleles are separated. a Aa aa possible genotypes o ospring Chapter 6: Meiosis and Mendel 73

2 Each gamete gets one o the alleles. Since each parent contributes only one allele to the ospring, only one allele rom each parent is written inside each grid box. ertilization restores the diploid number in the resulting ospring. This is why each grid box has two alleles, one rom the mother and one rom the ather. Since any egg has the same chance o being ertilized by any sperm cell, each possible genetic combination is equally likely to occur. Explain What do the letters on the axes o the Punnett square represent? A monohybrid cross involves one trait. Thus ar, we have studied monohybrid crosses, crosses that examine the inheritance o only one speciic trait. Three example crosses are used below and on the next page to illustrate how Punnett squares work and to highlight the resulting ratios or both genotype and phenotype. IGURE 5. Homozygous-Homozygous recessive parent () dominant parent () Homozygous-Homozygous Suppose you cross a pea plant that is dominant or purple lowers with a pea plant that is recessive or white lowers. To determine the genotypic and phenotypic ratios o the ospring, irst write each parent s genotype on one axis: or the purple-lowered plant, or the white-lowered plant. Every gamete rom the purple-lowered plant contains the dominant allele,. Every gamete rom the white-lowered plant contains the recessive allele,. Thereore, 00 percent o the ospring have the genotype,. And 00 percent o the ospring have purple lowers, because they all have a copy o the dominant allele, as shown in igure 5.. igure 5.3 Heterozygous-Heterozygous parent () parent () Heterozygous-Heterozygous Next, in igure 5.3, you can see a cross between two purple-lowered pea plants that are both (). rom each parent, hal the ospring receive a dominant allele,, and hal receive a recessive allele,. Thereore, one-ourth o the ospring have a dominant genotype, ; hal have a genotype, ; and oneourth have a recessive genotype,. Both the and the genotypes result in purple lowers. Only the genotype results in white lowers. Thus, the genotypic ratio is :: o dominant:: recessive. The phenotypic ratio is 3: o purple:white lowers. George D. Lepp/Corbis 74 Unit 3: Genetics

3 Heterozygous-Homozygous inally, suppose you cross a pea plant that is or purple lowers () with a pea plant that is recessive or white lowers (). As beore, each parent s genotype is placed on an axis, as shown in igure 5.4. rom the parent with white lowers, the ospring each receive a recessive allele,. rom the parent, hal the ospring receive a dominant allele,, and hal receive a recessive allele,. Hal the ospring have a genotype,. Hal have a recessive genotype,. Thus, hal the ospring have purple lowers, and hal have white lowers. The resulting genotypic ratio is : o : recessive. The phenotypic ratio is : o purple:white. Suppose we did not know the genotype o the purple lower in the cross above. This cross would allow us to determine that the purple lower is, not dominant. A testcross is a cross between an organism with an unknown genotype and an organism with the recessive phenotype. The organism with the recessive phenotype must be recessive. The ospring will show whether the organism with the unknown genotype is, as above, or dominant. Apply rom an 3 cross, what percent o ospring would have purple lowers? igure 5.4 HETERozygous-Homozygous parent () recessive parent () George D. Lepp/Corbis QUICK LAB Inerring Using a Testcross Suppose you work or a company that sells plant seeds. You are studying a plant species in which the dominant phenotype is pink lowers (PP or Pp). The recessive phenotype is white lowers (pp). Customers have been requesting more plants with pink lowers. To meet this demand, you need to determine the genotypes o some o the plants you are currently working with. Problem What is the genotype o each plant? Procedure. Suppose you are presented with Plant A o the species you are studying. It has pink lowers. You want to determine the genotype o the plant.. You cross Plant A with Plant B o the same species. This plant has white lowers and a known genotype o pp. 3. The resulting cross yields six plants with pink lowers and six plants with white lowers. Use Punnett squares to determine the genotype o Plant A. Materials pencil paper Analyze and Conclude. Apply What is the genotype o Plant A? Explain how you arrived at your answer.. Apply What are the possible genotypes and phenotypes o ospring i Plant A is crossed with a plant that has a genotype o PP? 3. Calculate What ratio o dominant to recessive phenotypes would exist i Plant A were crossed with a plant that has a genotype o Pp? 4. Evaluate Is Plant A the best plant, in terms o genotype, that you can work with to produce as many o the requested seeds as possible? Why or why not? Which genotype would be best to work with? Chapter 6: Meiosis and Mendel 75

4 A dihybrid cross involves two traits. CONNECT TO Law o Segregation As you learned in Section 3, Mendel s irst law o inheritance is the law o segregation. It states that organisms inherit two copies o each gene but donate only one copy to each gamete. Biology VIDEO C L I P HMDScience.com Premium Content Law o Independent Assortment igure 5.5 DiHyBrid Cross This dihybrid cross is -. generation YR Yr yr yr YR YYRR YYRr YyRR All o the crosses discussed so ar have involved only a single trait. However, Mendel also conducted dihybrid crosses, crosses that examine the inheritance o two dierent traits. He wondered i both traits would always appear together or i they would be expressed independently o each other. Mendel perormed many dihybrid crosses and tested a variety o dierent combinations. or example, he would cross a plant with yellow round peas with a plant with green wrinkled peas. Remember that Mendel began his crosses with purebred plants. Thus, the irst generation ospring () would all be and would all look the same. In this example, the plants would all have yellow round peas. When Mendel allowed the plants to selpollinate, he obtained the ollowing results: 9 yellow/round, 3 yellow/wrinkled, 3 green/round, green/wrinkled. Mendel continued to ind this approximately 9:3:3: phenotypic ratio in the generation, regardless o the combination o traits. rom these results, he realized that the presence o one trait did not aect the presence o another trait. His second law o genetics, the law o independent assortment, states that allele pairs separate independently o each other during gamete ormation, or meiosis. That is, dierent traits appear to be inherited separately. The results o Mendel s dihybrid crosses can also be illustrated with a Punnett square, like the one in igure 5.5. Drawing a Punnett square or a dihybrid cross is the same as drawing one or a monohybrid cross, except that the grid is bigger because two genes, or our alleles, are involved. or example, suppose you cross two plants with yellow, round peas that are or both traits (). The our allele combinations possible in each gamete YR, Yr, yr, and yr are used to label each axis. Each grid box can be illed in using the same method as that used in the monohybrid cross. A total o nine dierent genotypes may result rom the cross in this example. However, these nine genotypes produce only our dierent Yr yr yr phenotypes. These phenotypes are yellow round, yellow wrinkled, green round, and green wrinkled, and they occur in the ratio o 9:3:3:. YYRr YyRR Note that the 9:3:3: phenotypic ratio results rom a cross between organisms that are or both traits. The phenotypic YYrr Yyrr ratio o the ospring will dier (rom 9:3:3:) i one or both o the parent organisms are yyrr yyrr or one or both traits. Yyrr yyrr generation 76 Unit 3: Genetics yyrr Analyze In IGURE 5.5, the boxes on the axes represent the possible gametes made by each parent plant. Why does each box have two alleles?

5 HMH Heredity patterns can be calculated with probability. Probability is the likelihood that a particular event will happen. It predicts the average number o occurrences, not the exact number o occurrences. number o ways a speciic event can occur Probability = number o total possible outcomes Suppose you lip a coin. The number o total possible outcomes is two: heads up or tails up. The probability that it would land heads up is /, or one out o two. The probability that it would land tails up is also /. Next, suppose you lip two coins. How one coin lands does not aect how the other coin lands. To calculate the probability that two independent events will happen together, multiply the probability o each individual event. The probability that both coins will land heads up, or example, is / 3 / = /4. These probabilities can be applied to meiosis. Suppose a germ cell undergoes meiosis in a plant that is or purple lowers. The number o total possible outcomes is two because a gamete could get a dominant or a recessive allele. The probability that a gamete will get a dominant allele is /. The probability that it will get a recessive allele is also /. I two plants that are or purple lowers ertilize each other, the probability that both egg and sperm have a dominant allele is / 3 / = /4. So, too, the probability that both have a recessive allele is /4. There is also a /4 chance that a sperm cell with a dominant allele will ertilize an egg with a recessive allele, or that a sperm cell with a recessive allele will ertilize an egg with a dominant allele. These last two combinations are basically the same. In either case, the resulting plant will be. Thus, the probability that a pea plant will be or this trait is the sum o the probabilities: /4 + /4 = /. Apply Explain how Mendel s laws relate to probability. 6.5 Reviewing ormative Assessment Main Ideas. What do the grid boxes in a Punnett square represent?. Why does the expected genotypic ratio oten dier rom the expected phenotypic ratio resulting rom a monohybrid cross? 3. How did Mendel s dihybrid crosses help him develop his second law? Critical thinking 4. Calculate What would be the phenotypic ratios o the ospring resulting rom the ollowing cross: YYRr 3? 5. Predict I you are working with two tall pea plants and know that one is Tt, how could you determine the genotype o the other plant? igure 5.6 PROBABILITY And HEREDITY The coins are equally likely to land heads up or tails up. Two sides o coin H T H Two sides o coin Sel-check Online HMDScience.com Premium Content T 4 HH 4 HT 4 HT 4 TT CONNECT TO Adaptation 6. You have seen that onequarter o ospring resulting rom two parents are recessive. Yet or some genes, the recessive allele is more common in the population. Explain why this might be. Chapter 6: Meiosis and Mendel 77