Punnett Squares Honors Genetics Ms. Gaynor Chapter 11 (Part 2) Punnett Squares Honors Genetics Ms. Gaynor

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

Probability Rules Probability Rule #1 The multiplication rule (“and”) States that the probability that 2 or more independent events will occur together is the product (x ing) of their individual probabilities

Sperm R r 1⁄2 1⁄4 Eggs Rr Segregation of alleles into eggs  Rr Segregation of alleles into eggs alleles into sperm R r 1⁄2 1⁄4 Sperm Eggs

Probability Rule #2 The rule of addition (“or”) States that the probability that any 1 of 2 or more exclusive events will occur is calculated by adding (+ ing) together their individual probabilities

IN SUMMARY: 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 Problems Ms. Gaynor 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

Mendel’s Results Does Mendel’s segregation model account for the 3:1 ratio he observed in the F2 generation of his numerous crosses? We can answer this question using a Punnett square, which shows a genetic 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)

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

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 = the GENOTYPE probabilities (expected results) of offspring Ex: 50 % AA and 50 % Aa Phenotypic Ratio = the PHENOTYPE probabilities (expected results) of offspring Ex: 100% Tall

Ratios Can be expressed as a: DECIMAL Ex: 0.75 and 0.25 FRACTION 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

4 different types of monohybrid crosses COMPLETE DOMINANCE: 4 different types of monohybrid crosses

#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

#2: Homozygous Recessive x Homozygous Recessive Mom’s genotype (hh) x Dad’s genotype (hh) short Short h h h Genotypic ratio = 100% hh (4:0) Phenotypic ratio = 100% short (4:0) hh

#3: Homozygous Dominant x Heterozygous Mom’s genotype (HH) x Dad’s genotype (Hh) Tall Tall H H H h Genotypic ratio = 50% HH, 50% Hh (2:2) Phenotypic ratio = 100% Tall (4:0) HH Hh

#4: 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 an individual with the dominant phenotype with an individual that is homozygous recessive for a trait

Conduct a test cross, where the unknown dominant individual is crossed with the known recessive . 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 = 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!

Dihybrid Crosses How are two characters transmitted from parents to offspring? As a package? Independently?

Dihybrid Crosses crosses involveing 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 Produces four possible phenotypes in the F2 generation

Using the information from a dihybrid cross, Mendel developed the law of independent assortment Each pair of alleles segregates independently during gamete formation

For the following genotype, how many DIFFERENT gametes can be formed? AaBBCcDdeeFf 10 different A, a, B, C, c, D, d, e, F, f

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 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

The Laws of Probability Control Mendelian Inheritance Mendel’s laws of segregation and independent assortment Reflect the rules of probability

Probability Rules and Dihybrid Crosses A dihybrid or other multicharacter cross Is equivalent to two or more independent monohybrid crosses occurring simultaneously In calculating the chances for various genotypes from such crosses Each character first is considered separately and then the individual probabilities are multiplied together