Punnett Squares Honors Biology Ms. Day Lecture #25 Punnett Squares Honors Biology Ms. Day

What is “Probability”? Why did Mendel get his results? What is the probability that Mendel would get his results EACH time? PROBABILITY = likelihood (chance) that an event will happen

2 Probability Rules Multiplication Rule What are the chances of _?_ AND _?_ happening at the same time? MULTIPLY probability of EACH event happening TOGETHER Addition Rule What are the chances of _?_ OR _?_ happening at same time? ADD the probability of EACH event happening TOGETHER

Probability Example Problem Ms. Day has 4 sisters. What is the probability that this will happen (her mother having 5 girls in a row)? ½ x ½ x ½ x ½ x ½ =?? 0.03125 or 3.125 % chance

Monohybrid Cross Dihybrid Cross a cross between 2 individuals that looks at 1 trait There are 4 different types Ex: freckles OR dimples a cross between 2 individuals that looks at the possibilities of inheriting 2 DIFFERENT traits at one time Ex: Freckles AND dimples Dihybrid Cross

What is a Punnett Square? a diagram (box) used to predict the probabilities of the possible outcomes for offspring that will result from a cross between 2 parents SHOWS EXPECTED RESULTS (not necessarily actual!!!!!)

Law of Segregation Germ Line Cell a A Gamete (sperm or egg) a A

Monohybrid Punnett Square Mom’s genotype (Hh) x Dad’s genotype (hh) Tall Short Mom’s allele #1 Mom’s allele #2 H h Dad’s Allele #1 h Allele #2 h Hh hh

Genotypic Ratio vs. Phenotypic Ratio Genotypic Ratio (Probability or Frequency) = the GENOTYPE probabilities (expected results) of offspring Ex: 50 % AA and 50 % Aa Phenotypic Ratio (Probability or Frequency) = the PHENOTYPE probabilities (expected results) of offspring Ex: 100% Tall

Probabilities can be expressed as a: DECIMAL Ex: 0.75 and 0.25 FRACTION Ex: ¾ and ¼ PRECENTAGE Ex: 75% and 25% RATIO Ex: 3: 1

Punnett Square Hh hh Genotypic ratio = 50 % Hh, 50% hh Phenotypic ratio = 50 % Tall, 50% short Hh hh

Ex#1: Homozygous Dominant x Homozygous Recessive Mom’s genotype (HH) x Dad’s genotype (hh) Tall Short H H h Genotypic ratio = 100% Hh (4:0) Phenotypic ratio = 100% Tall (4:0) Hh

Ex #2: Heterozygous x Heterozygous Mom’s genotype (Hh) x Dad’s genotype (Hh) Tall Tall H h H h Genotypic ratio = 25% HH, 50% Hh, 25% hh (1:2:1) Phenotypic ratio = 75% Tall, 25% short (3:1) HH Hh hh

3 Genotype Phenotype Purple 1 White 2 Ratio 3:1 Ratio 1:2:1 PP Figure 14.6 3 1 2 Phenotype Purple White Genotype PP (homozygous) Pp (heterozygous) pp Ratio 3:1 Ratio 1:2:1

The Testcross Allows us to determine the genotype of an organism with the dominant phenotype, but unknown genotype Genotype is not immediately obvious Cross: dominant phenotype individual x homozygous recessive for same trait (H _ ?_ x hh)

Mom’s genotype (H?) x Dad’s genotype (hh) Test Cross Mom’s genotype (H?) x Dad’s genotype (hh) Tall Short H ? h Genetypic ratio = ? Phenotypic ratio =? IF THERE ARE ANY SHORT OFFSPRING, THEN WE KNOW THE UNKNOWN GENOTYPE HAS TO BE Hh HH ?h Hh

Mendel’s 2nd Law: law of independent assortment says that the genes are inherited independently of other genes Occurs during Metaphase I Mendel assumed traits occur on different chromosomes!

DIHYBRIDS Review… Mendel’s 1st Law: law of segregation says that the each gamete gets 1 allele PER GENE Mendel’s 2nd Law: law of independent assortment says that the genes are inherited independently of other genes

Dihybrid Crosses crosses involving crossing 2 DIFFERENT traits at one time Example: Mate 2 parents and look at the probability of seeing 2 traits, such as: eye color AND hair color freckles AND dimples

How do You Do Dihybrid Crosses? 2 ways 1. one BIG Punnett Square (16 boxes instead of 4) 2. Make 2 separate Punnett Squares 1 square for EACH trait Then use PROBABILITY RULES and MULTIPLY

One BIG Punnett Square 1. Find the possible gametes using F.O.I.L method (ONLY 1 “letter” per gene) AaBb x AABb AB AB Ab Ab aB AB ab Ab

2. Place the gametes in the Punnett Square & fill in boxes AB Ab aB ab AB Ab AABB AABb AaBB AaBb AAbB AAbb AabB Aabb

Genotypic Ratio AAbB = 8/16 or 1/2 AaBB = 2/16 or 1/8

Phenotypic Ratio A= freckles, a= no freckles B = Dimples, b= no dimples AAbB = 8/16 (50%) freckles, dimples AaBB = 2/16 (12.5%) freckles, dimples Aabb = 2/16 (12.5%) freckles, no dimples AABB= 2/16 (12.5%) freckles, dimples AAbb = 2/16 (12.5%) freckles, no dimples So…12/16 (75%) freckles AND dimples 4/16 (25%) freckles AND no dimples

Now…the easier way! Write out a key for EACH trait AA, Aa= Freckles, aa= No freckles BB, Bb= Dimples, bb= No dimples Figure out the genotypes of EACH parent and put them together Draw 2 Punnett squares & figure out the FRACTION ratio of possible genotype and phenotypes Draw punnett square #1 for trait #1 Draw punnett square #2 for trait #2 Figure out genotype/phenotype possibilities of offspring by multiplying fractions

AaBb x aabb AA, Aa= Tall aa= short BB, Bb= Black bb= white ½ Bb ½ bb ½ Aa ½ aa ½ Black ½ white ½ Tall ½ short So… babies could look: 25% Black & Tall (½ * ½) 25% white & tall (½ * ½) 25% Black & short (½ * ½) 25% white & short (½ * ½) Bb bb Aa aa

Probability Rules and Dihybrid Crosses A dihybrid or other multicharacter cross Is equivalent to two or more independent monohybrid crosses occurring simultaneously (AT THE SAME TIME)