Lecture #28 Punnett Squares Honors Biology 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

2 Probability Rules Multiplication Rule What are the chances of _?_ AND _?_ happening at the same time? MULTIPLY 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. 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 =?? or % chance

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  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 Dad’s Allele #2 h HhHhh HhHhh

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 HhHhh HhHhh Genotypic ratio = 50 % Hh, 50% hh Phenotypic ratio = 50 % Tall, 50% short

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 h Genotypic ratio = 100% Hh (4:0) Phenotypic ratio = 100% Tall (4:0) HhHhHhHh HhHhHhHh

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

#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) HHhHh HhHhh

Figure Phenotype Purple White Genotype PP (homozygous) Pp (heterozygous) Pp (heterozygous) pp (homozygous) 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)

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

Mendel’s 2 nd 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  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 AaBb x AABbABAb aBAB abAb

2. Place the gametes in the Punnett Square & fill in boxes AB Ab aB ab AB Ab AB Ab AABBAABbAaBBAaBb AAbBAAbbAabBAabb AABBAABbAaBBAaBb AAbBAAbbAabBAabb

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

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)