Mendel’s Second Experiment The Inheritance of Two Traits: The Inheritance of Two Traits: Does the inheritance of one characteristic influence the inheritance of another characteristic? Does the inheritance of one characteristic influence the inheritance of another characteristic? For example: Does pea shape influence pea color? For example: Does pea shape influence pea color?

Mendel performed a Dihybrid Cross He crossed two pea plants that differed in two traits. He crossed two pea plants that differed in two traits. P generation: Pure round & yellow (RRYY) P generation: Pure round & yellow (RRYY) P generation:Pure wrinkled Green (rryy) P generation:Pure wrinkled Green (rryy) What do you think the results were? What do you think the results were? The F1 generation will be heterozygous for both traits: RrYy Mendel's Experiments

Moving On to Two Traits at a Time Keep T and t for tall and short plants, respectively. Keep T and t for tall and short plants, respectively. Add R and r for round and wrinkled seeds, respectively. Add R and r for round and wrinkled seeds, respectively. A double heterozygote male produces four types of gametes. A double heterozygote male produces four types of gametes.

Cross with a Female Double Heterozygote A double heterozygote female produces four types of eggs. A double heterozygote female produces four types of eggs.

Crossing the Double Heterozygotes The male passes on his alleles, two per gamete The male passes on his alleles, two per gamete

Crossing the Double Heterozygotes The female passes on her alleles, two per egg. The female passes on her alleles, two per egg.

Double Heterozygote Cross: Assessing the Resultant Genotypes At least one T yields tall stature. At least one T yields tall stature. At least one R yield round seeds. At least one R yield round seeds. Thus, there are 9 ways (gray) to produce tall, round- seeded offspring. Thus, there are 9 ways (gray) to produce tall, round- seeded offspring.

Double Heterozygote Cross: Assessing the Resultant Genotypes Again, at least one T yields tall stature. Again, at least one T yields tall stature. And one R is required for round seeds, so rr must produce wrinkled seeds. And one R is required for round seeds, so rr must produce wrinkled seeds. Thus, there are 3 ways (lighter gray) to produce tall, wrinkly seeded offspring Thus, there are 3 ways (lighter gray) to produce tall, wrinkly seeded offspring

The Third Phenotype in a Double Heterozygote Cross Two t alleles yield short stature. Two t alleles yield short stature. At least one R produces round seeds. At least one R produces round seeds. Thus, there are 3 ways (lightest gray) to produce short offspring with round seeds. Thus, there are 3 ways (lightest gray) to produce short offspring with round seeds.

The Fourth Phenotype in a Double Heterozygote Cross Two t alleles yield short stature. Two t alleles yield short stature. Two r alleles produce wrinkled seeds. Two r alleles produce wrinkled seeds. There is only 1 way to produce short offspring with wrinkled seeds. There is only 1 way to produce short offspring with wrinkled seeds. 10v/media/ch08/dihybrid_v2.html

The F1 generation were all round and yellow What happens when you cross F1 with a F1? What happens when you cross F1 with a F1? The F2 generation: 9 round and yellow 3 round and green 3 wrinkled and yellow 1 wrinkled and green These results represent a phenotypic ratio of 9:3:3:1

Law of Independent Assortment The inheritance of alleles for one trait does not affect the inheritance of alleles for another trait. The inheritance of alleles for one trait does not affect the inheritance of alleles for another trait. This means that different pairs of alleles are passed to the offspring independently of each other. This means that different pairs of alleles are passed to the offspring independently of each other. A pea plant’s ability to produce white flowers instead of purple ones does not influence the same plant’s ability to produce round peas instead of wrinkled peas A pea plant’s ability to produce white flowers instead of purple ones does not influence the same plant’s ability to produce round peas instead of wrinkled peas mations/content/independentassortment.html mations/content/independentassortment.html mations/content/independentassortment.html mations/content/independentassortment.html

The Rules of Probablity Probablity scale ranges from 0-1 Probablity scale ranges from 0-1 An event that is certain to occur has a probability of 1, while an even that is certain NOT to occur has a probability of 0. An event that is certain to occur has a probability of 1, while an even that is certain NOT to occur has a probability of 0. E.g. chances of rolling 3 on a die: 1/6 E.g. chances of rolling 3 on a die: 1/6 The probabilities of all possible outcomes for an event must add up to 1. The probabilities of all possible outcomes for an event must add up to 1.

The Rule of Multiplication How do we determine the chance that two or more independent events will occur together in some specific combination? How do we determine the chance that two or more independent events will occur together in some specific combination? –Compute the probability for each independent event, then multiply these individual probabilities to obtain the overall probability of these events occurring together. –E.g. What is the chance that two coins tossed simultaneously will land heads up?  1/2 x 1/2 = 1/4 –If an F1 plant has a genotype Pp, what is the probability that a particular F2 plant will be pp?

If a parent has a genotype YyRr, what is the probability of an F2 plant having the genotype YYRR? If a parent has a genotype YyRr, what is the probability of an F2 plant having the genotype YYRR?

The Rule of Addition What is the probability that an F2 plant from a monohybrid cross will be heterozygous? What is the probability that an F2 plant from a monohybrid cross will be heterozygous? –There are two ways F1 gametes can combine to produce a heterozygous result. The dominant allele can come from the ovum and the recessive allele from the sperm or vice versa. By the rule of addition, the probability of an event that can occur in two or more different ways is the sum of the separate probabilities of those ways. By the rule of addition, the probability of an event that can occur in two or more different ways is the sum of the separate probabilities of those ways. –1/4 + 1/4 = 1/2

Using rules of probability to solve genetics problems Imagine a trihybrid cross Imagine a trihybrid cross –P: purple flowerp: white flower –Y: yellow seedy: green seed –R: Round seedr: wrinkled seed PpYyRr x Ppyyrr What fraction of offspring will exhibit the recessive phenotype for at least two of the three traits? PpYyRr x Ppyyrr What fraction of offspring will exhibit the recessive phenotype for at least two of the three traits? Solution: List all possible genotypes: Solution: List all possible genotypes: –ppyyRr, ppYyrr, Ppyyrr, Ppyyrr, ppyyrr –Next use rule of multiplication to calculate the individual probabilities for each of the genotypes –Use rule of addition to pool the probabilities for fulfilling the condition of at least two recessive traits.

Solution: PpYyRr x Ppyyrr ppyyRrxx= ppYyrrxx= Ppyyrrxx= PPyyrrxx= ppyyrrxx= ____________________________________ Chance of at least 2 recessive traits =

Test Crosses A test cross can be used for both monohybrid and dihybrid crosses to determine the genotype of an unknown individual. A test cross can be used for both monohybrid and dihybrid crosses to determine the genotype of an unknown individual. It involves crossing the unknown genotype with a homozygous recessive individual. It involves crossing the unknown genotype with a homozygous recessive individual. The results will determine the unknown genotype. The results will determine the unknown genotype.

Examples: Monohybrids In a monohybrid test cross involving height, if all offspring are tall, one can deduce that the original genotype was TT (homozygous). In a monohybrid test cross involving height, if all offspring are tall, one can deduce that the original genotype was TT (homozygous). If 50% of the off spring are tall and the other 50% dwarf, one can deduce that the original genotype was Tt (heterozygous) If 50% of the off spring are tall and the other 50% dwarf, one can deduce that the original genotype was Tt (heterozygous) Examples: Dihybrids In test cross involving shape and color, if it produces plants that show the dominant phenotype for both traits that is round and yellow, one can conclude that the original genotype was RRYY. In test cross involving shape and color, if it produces plants that show the dominant phenotype for both traits that is round and yellow, one can conclude that the original genotype was RRYY. If the original plant is heterozygous (RrYy), the cross will produce a 25% chance for each combination. If the original plant is heterozygous (RrYy), the cross will produce a 25% chance for each combination. 25% Round and Yellow 25% Round and Green 25% Round and Yellow 25% Round and Green 25% Wrinkled and Yellow 25% Wrinkled and Green 25% Wrinkled and Yellow 25% Wrinkled and Green

Beyond Mendel’s Laws Incomplete Dominance Incomplete Dominance Co-Dominance Co-Dominance Multiple Alleles Multiple Alleles

Incomplete Dominance Occurs when neither of the alleles for a certain trait is dominant. Occurs when neither of the alleles for a certain trait is dominant. This gives rise to an intermediate expression found in individuals that are heterozygous. Ex. White flowers and Red flowers are homozygous, Pink flowers are heterozygous. This gives rise to an intermediate expression found in individuals that are heterozygous. Ex. White flowers and Red flowers are homozygous, Pink flowers are heterozygous.

Co-Dominance Both alleles for a trait are dominant and are both expressed in a heterozygous individual. Both alleles for a trait are dominant and are both expressed in a heterozygous individual. Which of the following offspring would represent co-dominance from the mating of a pure black rooster and a white hen? Which of the following offspring would represent co-dominance from the mating of a pure black rooster and a white hen? Black chicken Black chicken White chicken White chicken Grey chicken Grey chicken Black and White Black and White chicken. chicken.

Multiple Alleles Occurs when a gene has more than two alleles. Occurs when a gene has more than two alleles. Ex. Human blood has 3 alleles: A, B, O Ex. Human blood has 3 alleles: A, B, O Phenotype (blood type) Genotype A I A I A or I A i B I B I B or I B i ABIAIBIAIB O i