KEY CONCEPT The inheritance of traits follows the rules of probability.

Punnett squares illustrate genetic crosses. The Punnett square is a grid system for predicting all possible genotypes resulting from a cross. The axes represent the possible gametes (alleles) of each parent. The boxes show the possible genotypes of the offspring. The Punnett square yields the ratio of possible genotypes and phenotypes.

A monohybrid cross involves one trait. Monohybrid crosses examine the inheritance of only one specific trait. homozygous dominant-homozygous recessive: all heterozygous, all dominant Recall: What did Mendel call a homozygous plant such as FF or ff?

heterozygous-heterozygous—1:2:1 homozygous dominant: heterozygous:homozygous recessive; 3:1 dominant:recessive Apply: How did the white flower appear among the offspring if neither parent had white flowers?

heterozygous-homozygous recessive—1:1 heterozygous:homozygous recessive; 1:1 dominant:recessive A testcross is a cross between an organism with an unknown genotype and an organism with the recessive phenotype. Apply: From an FF x Ff cross, what percent of offspring would have purple flowers?

A dihybrid cross involves two traits. Mendel’s dihybrid crosses with heterozygous plants yielded a 9:3:3:1 phenotypic ratio. Mendel’s dihybrid crosses led to his second law, the law of independent assortment. The law of independent assortment states that allele pairs separate independently of each other during meiosis. Explain: Would the Punnett square represent the expected results if the genes for the two traits were inherited together?

Heredity patterns can be calculated with probability. Probability is the likelihood that something will happen. Probability predicts an average number of occurrences, not an exact number of occurrences. Probability = number of ways a specific event can occur number of total possible outcomes Probability applies to random events such as meiosis and fertilization. Apply: Explain how Mendel’s laws relate to probability.

Mendelian Inheritance Reflects Rules of Probability Rule of Multiplication: The probability that independent events will occur simultaneously is the product of their individual probabilities. What is the probability that you will roll a 6 and a 4? 1/6 x 1/6 = 1/36 chance

Mendelian Inheritance Reflects Rules of Probability Question: In a Mendelian cross between pea plants that are heterozygous for flower color (Pp), what is the probability that the offspring will be homozygous recessive? Answer: Probability that an egg from the F1 (Pp) will receive a p allele = ½ Probability that a sperm from the F1 will receive a p allele = ½ Overall probability that 2 recessive alleles will unite at fertilization: ½ x ½ = ¼

Mendelian Inheritance Reflects Rules of Probability Works for Dihybrid Crosses: Question: For a dihybrid cross, YyRr x YyRr, what is the probability of an F2 plant having the genotype YYRR? Answer: Probability that an egg from a YyRr parent will receive the Y and R alleles = ½ x ½ = ¼ Probability that a sperm from a YyRr parent will receive the Y and R alleles = ½ x ½ = ¼ Overall probability of an F2 plant having the genotype YYRR: ¼ x ¼ = 1/16

Mendelian Inheritance Reflects Rules of Probability Rules of Addition: The probability of an event that can occur in two or more independent ways is the sum of the separate probabilities of the different ways. What is the probability that you will roll a 6 or a 4? 1/6 + 1/6 = 2/6 or 1/3 chance

Mendelian Inheritance Reflects Rules of Probability Question: In a Mendelian cross between pea plants that are heterozygous for flower color (Pp), what is the probability that the offspring will being a heterozygote? Answer: There are 2 ways in which a heterozygote may be produced: the dominant allele may be in the egg and the recessive allele in the sperm, or the dominant allele may be in the sperm and the recessive allele in the egg.

Mendelian Inheritance Reflects Rules of Probability Probability that the dominant allele will be in the egg with the recessive in the sperm is ½ x ½ = ¼ Probability that the dominant allele will be in the sperm with the recessive in the egg is ½ x ½ = ¼ Therefore, the overall probability that a heterozygote offspring will be produced is ¼ + ¼ = ½