Probability & Punnett Squares

1. Probability & Punnett Squares

2. Bell Ringer What do these pictures show? What is unusual about this hand and foot? Look closely!!

3. Bell Ringer cont. • The hand and foot have six fingers and toes instead of five. • This is the result of a genetic disorder referred to as Polydactyly – having more than five digits.

4. Bell Ringer cont. What religious group do these people belong to? They are Amish - lead a simple life centered on family and religion. Large population resides in Lancaster County, PA.

5. Bell Ringer Cont. The Amish live separately from the rest of society. They typically marry only other Amish people. What if I told you Polydactyly is more common among the Amish than in the general population. Why do you think that is true? Why might it someday be important for you to know if you are a carrier for a genetic disease?

6. Objectives • As a result of this lesson you (my students) • will be able to: • Explain how geneticists use the principles of probability • Describe how geneticists use Punnet Squares • Distinguish between the concepts heterozygous and homozygous • Solve genetic problems using a PunnetSquare

7. What is Probability? Probability is a number that describes the likelihood that a particular event will occur Example: A coin flip What are the possible outcomes when you flip a coin? Answer: There are two – it could land heads up or tails up

8. What is Probability? Cont. Probability is the likelihood that a particular event will occur Example: A coin flip What are the chances a coin will land heads up? Answer: 50% or ½ What are the chances a coin will land tails up? Answer: 50% or ½

9. What is Probability? Cont. If you flip a coin 3 times in a row, what is the probability it will land heads up every time? Each coin flip is an independent event – each time the coin is flipped, the probability of it landing heads up is ½ . The probability of flipping 3 heads in a row is: ½ x ½ x ½ = 1/8 Remember: Past outcomes do not effect future outcomes!

10. How does Probability relate to Genetics? • The principles of probability can be used to predict the outcomes of genetic crosses! Coin Toss Lab • Suppose that you were to toss a coin 20 times. Predict how many times the coin would land on heads and how many times would it land on tails. • Let’s do it.

11. Coin Toss Lab Discussion • Did your results equal your calculated probabilities? • What did you notice as your number of tosses increased? Answer: The more times you tossed your coin, the closer your actual results should have been to your predicted probability. Probable outcomes are not always equal to actual outcomes; however, the two should get closer as the number of trials increases.

12. Genotype and Phenotype Review • What is genotype? • FF • Ff • ff • An organism’s genetic makeup. An organisms particular combination of alleles. • What is phenotype? • An organism’s physical appearance. The phenotype is determined by the genotype. When an organism is heterozygous the dominant allele will be expressed. • FF or Ff • ff

13. Human traits review When an organism has two identical alleles for a particular trait (ex. TT or tt), it is said to be _______. Answer: Homozygous When an organism has two different alleles for the same trait (ex. Tt), it is said to be _________. Answer: Heterozygous

14. Human traits review This girl is displaying one of the traits we spoke of. Which one? Answer: Widow’s Peak What is her phenotype? Answer: She has a Widow’s Peak What is a possible genotype given that Widow’s Peak is a dominant allele? Answer: WW or Ww

15. Punnett Squares Let’s combine our knowledge of probability with our understanding of genotype and phenotype.

16. What is a Punnet Square? • The Punnett square is a diagram that is used to predict an outcome of a particular cross or breeding experiment. • It is named after Reginald C. Punnett, who devised the approach, and is used by biologists to determine the probability of an offspring having a particular genotype.

17. How do you construct a Punnett Square? • Start by drawing a box and dividing it into four squares.

18. How to construct a Punnett Square (cont.) • Write the male parent’s alleles (RR) along the top of the square and the female parent’s alleles along the left side (Rr). R R Dad R r Mom

19. How to construct a Punnett Square (cont.) • Copy the female parent’s alleles into the boxes to the right. Dad R r R R R r r r Mom

20. How to construct a Punnett Square (cont.) • Copy the male parent’s alleles into the boxes beneath them. Dad R r R R R R r r r r R r Mom

21. Punnet Squares • The completed Punnett square shows all the possible combinations in the offspring. Dad R r R R R R r r r r R r Mom

22. Why use a Punnet square? • You can use a Punnet square to calculate the probability that offspring with a certain combination of alleles will result.

23. For example in: R R R r r r R r R r What is the probability that the offspring will be RR? R 1 in 4 or 25% What is the probability that the offspring will be rr? 1 in 4 or 25% r What is the probability that the offspring will be Rr? 2 in 4 or 50%

24. Now let’s see what happens… • We are going to mate a black guinea pig (homozygous: BB) with a white guinea pig (homozygous: bb). • Create a Punnet square to determine the probability of having a white guinea pig (remember that uppercase letters mean the trait is dominant, this means uppercase will mask the recessive trait b)

25. However • If we mate a black guinea pig (heterozygous: Bb) with a white guinea pig (homozygous: bb). • What is the probability of having a white guinea pig? (once again, remember that uppercase letters mean the trait is dominant, this means uppercase will mask the recessive trait b)

26. Closure Let’s return to our Bell Ringer… What is the genetic disorder that is displayed in this picture? Answer: Polydactyly Polydactyly is a dominant genetic disorder. John is heterozygous for Polydactyly – What is his genotype? Answer: Pp What is John’s phenotype? Answer: He displays the symptoms of the disorder – he has six toes.

27. Closure cont. John (Pp) marries Diane who is homozygous for Polydactyly. What are the chances they will have a child who is homozygous for Polydactyly? Use a Punnett Square to answer the question!

28. Closure cont. Answer: 2/4 or 50% P p P P

29. Answer the following questions in your notebook • What is probability? • If you know the parents’ alleles for a trait how can you use a Punnet square to predict the probable genotypes of the offspring? • Define genotype and phenotype. • Explain how two organisms can have the same phenotype but different genotypes. Give an example.