Genetics & Probability Mendels laws: segregation independent assortment reflect same laws of probability that apply to tossing coins or rolling dice What is Probability? Probability is the likelihood that a particular event will occur. It does not ALWAYS happen (think Deal or No Deal) Can be written as a decimal, percentage, ratio, or fraction How do we use the principles of probability in our daily lives? Ex. Horse racing NCAA March Madness Superbowl Coin Toss Las Vegas $$$$$ Probability & genetics Calculating probability of making a specific gamete is just like calculating the probability in flipping a coin probability of tossing heads? 50% probability making a gamete PP P P PpPp P p 50% 100% Determining probability Number of times the event is expected Number of times it could have happened What is the probability that you picked an odd number when picking from 1-10? There are five odd numbers between 1 and 10. Or you can express it as a fraction: 5/10. Since it's a fraction, why not reduce it? The probability that you will pick an odd number is 1/2. Probability can also be expressed as a percent...1/2=50% Or as a decimal...1/2=50%=.5 Chance that 2 or more independent events will occur together probability that 2 coins tossed at the same time will land heads up Or.25 or 25% or 1:4 probability of Pp x Pp pp Rule of multiplication 1/2 x 1/2 = 1/4 Terminology and Directions ALLELES = (WARNING - THIS WORD CONFUSES PEOPLE; READ SLOW) alternative forms of the same gene. Hair Texture Gene- Straight (S) or Curly (s) One form of the gene codes for curly hair. A different code for of the same gene makes hair straight. So the gene for hair texture exists as two alleles --- one curly code (s), and one straight code (S). Alleles Dominant (Capital Letter) Shows up more in a population, Expresses itself when it is present Recesive (Small Letter) Shows up less in a population, only shows when there is no dominant trait. GENOTYPE = the genes present in the DNA of an organism. We will use a pair of letters (ex: Tt or YY or ss, etc.) to represent genotypes for one particular trait. There are always two letters in the genotype -one letter (gene) from mama organism -one letter (gene) from papa organism Phenotypes PHENOTYPE = how the trait physically shows-up in the organism. Wanna know the simplest way to determine an organism's phenotype ? Look at it. Examples of phenotypes: blue eyes, brown fur, striped fruit, yellow flowers. VOCAB Now, turns out there are three possible GENOTYPES two big letters (like "TT"), one of each ("Tt"), or two lowercase letters ("tt"). Since WE LOVE VOCABULARY, each possible combo has a term for it. Hetero/ Homo TTwo capital (TT) or TTwo lowercase (tt) in the GENOTYPE CCalled HOMOZYGOUS (("homo" means "the same"). SSometimes the term "PUREBRED" is used instead of homozygous. Heterozygous When the GENOTYPE is made up of one capital letter & one lowercase letter (ex: Tt) it's called HETEROZYGOUS ("hetero" means "other"). Just to confuse you, a heterozygous genotype can also be referred to as HYBRID. Let's Summarize: Genotype = genes present in an organism (usually abbreviated as two letters) AA = homozygous = pure Aa = heterozygous = hybrid aa = homozygous = pure Quick Review Genotype= genes of the organism Letters ex. TT or Tt or tt. Phenotype= the physical appearance of a trait in an organism What it physically looks like. The Letters are chosen for the Dominant trait of the allele. Homozygous and Heterozygous When we have two capital or two lowercase letters in the GENOTYPE (ex: TT or tt) it's called HOMOZYGOUS ("homo" means "the same"). Sometimes the term "PUREBRED" is used instead of homozygous. When the GENOTYPE is made up of one capital letter & one lowercase letter (ex: Tt) it's called HETEROZYGOUS ("hetero" means "other"). Just to confuse you, a heterozygous genotype can also be referred to as HYBRID. Dominant and Recessive Dominant (Capital Letter) Shows up more in a population, Expresses itself when it is present Recesive (Small Letter) Shows up less in a population, only shows when there is no dominant trait. Punnet Square Help determine the probability of getting a gene, not what you actually get Basic punnet squares look like window panes or tic tac toe boards. OR Baby steps of Punnet Squares 1. Determine and write down the genotypes of the parents 2. Draw a punnet square of appropriate size 3. Split the letters of the parents and put them on the outside 4. Do the punnet square 5. Summarize the results by showing genotypic and phenotypic ratios Punnet Square Practice Steps 1 -Determine the genotypes of the parents and write them down Tall (T) is dominant to short pea plants (t). Cross a short pea plant with one that is heterozygous for tallness. What are the parents genotypes? tt x Tt Cross a short pea plant with one that is heterozygous for tallness. What are the parents genotypes? tt x Tt T t t 3. Draw a p-square 4. Split the letters of the parents and put them on the outside 5. Do the punnet square Tt tt Summarize the results by showing genotypic and phenotypic ratios Genotypic Ratio (letters) TT- 0 or 0/4 or 0% Tt- 2 or 2/4 or 50% tt- 2 or 2/4 or 50% Phenotypic (looks) Tall- 2 or 2/4 or 50% Short- 2 or 2/4 or 50% Tt tt TtTt t Decide what the genotypes of the parents are In humans, brown eyes, B, are dominant to blue eyes, b. If the father has brown eyes and is homozygous dominant for the trait, BB, and the mother has blue eyes and is homozygous recessive for the trait, bb, what are the possible genotypes and phenotypes of their offspring. Father-homozygous dominant-BB Mother-homozygous recessive-bb Then, write the genotype for one parent across the top of the punnett square, and the genotype for the other parent along the left side of the square. BB b b Fill in the boxes inside with whatever letter are on top and to the left of them BB b b The genotypes inside the boxes represent the possible gene combination of their offspring Each box is a 25% or chance So, the genotypes of all the offspring in this genetic cross would be Bb Because there is at least one dominant allele the phenotype (appearance) would also be dominant all offspring would have brown eyes BB b b Bb Try another punnett square Two brown eyed parents, who are both heterozygous for the trait, Bb, mate. What are the chances they will have a blue eyed child? Step 1 What are the genotypes of the 2 parents? Step 3 Bb b B Step 4 Bb b B BB bbBb Step 5 Genotypes of offspring BB-1/4 or 25% Bb-1/2 or 50 % Bb-1/4 or 25% Phenotypes of offspring Brown eyes (BB and Bb)- 3/4 or 75% Blue eyes (bb)-1/4 or 25% Probability of blue eyed child=1/4 or 25 % Bb b B BB bbBb Biology What is a dihybrid cross? Work 2 genes at once Find the expected offspring for both traits They are a little more work than the monohybrid cross, but So much fun!! Steps to solving a dihybrid problem 1. Read the problem and find the two separate traits. Sample problem: In Springfield, red hair (H) is dominant to blue hair (h) and having four fingers (F) on your hand is dominant to having five fingers (f). If Side Show Bob and Mrs. Van Houten get married and decide to have a little brother for Millhouse, what is the chance that the newborn will have red hair and five fingers if Side Show is heterozygous for red hair and heterozygous for four fingers and Mrs. Van Houten has blue hair and is homozygous for four fingers? Genotypes 2. Find the two parents and write down their genotypes. HhFf x hhFF What do they Want? 3. Read the question and see what you have to look for. Do they want you to find a ratio, percent, fraction, or do they want you to list all possibilities? Math Class 4. Once you have found all the information, you can start to set up the problem by finding the gametes for each parent by using FOIL. FOIL stands for First, Outside, Inside, Last FOIL Here is an example of how to use FOIL: (a + b) * (c + d) First = (a + b) * (c + d) = ac Outside = (a + b) * (c + d) = ad Inside = (a + b) * (c + d) = bc Last = (a + b) * (c + d) = bd So our pairs are: ac, ad, bc, bd Parent Genotypes Now try it with the parents alleles Side Show = HhFf So, HF, Hf, hF, hf Mrs. Van Houten = hhFF So, hF, hF, hF, hF DiHybrid (Double Cross) 5. Once you have the gametes, you have to line them up in a punnett square. You are going to need a bigger square! Put the gametes of one parent across the top of the square and the other down the side of the square HF Hf hF hf hF 6. Now you have to do the actual cross. This is a single box example. Remember to always put the two like alleles back together, The same letters go together, and The capital letter should go first Keep the same sequence of alleles (letters) HhFF HF hF Fill in the rest of the box! HhFFHhFfhhFFhhFf HhFFHhFfhhFFhhFf HhFFHhFfhhFFhhFf HhFFHhFfhhFFhhFf HF Hf hF hf hF Genotypic Ratio 7. Find the genotypic ratio HhFF = 4/16 (25%) HhFf = 4/16 (25%) hhFF = 4/16 (25%) hhFf = 4/16 (25%) Phenotypic Ratio 8. Find the phenotypic ratio Red hair, four fingers = 8/16 (50%) Blue hair, four fingers = 8/16 (50%) Answer the Question 9. Now, dont forget to answer the question! If Side Show Bob and Mrs. Van Houten get married and decide to have a little brother for Millhouse, what is the chance that the newborn will have red hair and five fingers if Side Show is heterozygous for red hair and heterozygous for four five fingers and Mrs. Van Houten has blue hair and is homozygous for four fingers? 0% Review: Dominant/Recessive One allele is dominant over the other (capable of masking the recessive allele) PP = purple pp = white Pp = purple Review Problem: Dominant/Recessive In pea plants, purple flowers (P) are dominant over white flowers (p) show the cross between two heterozygous plants. PpPp P p pp Pp PP - PP (1); Pp (2); pp (1) - ratio 1:2:1 - purple (3); white (1) - ratio 3:1 GENOTYPES: PHENOTYPES: Incomplete Dominance Incomplete dominance is when one allele is not completely dominant over the other. The alleles do not blend, but the phenotype is a blending of the two traits. Incomplete Dominance Ex. Flower Color in 4 Oclocks RR = redrr = whiteRr = pink Problem: Incomplete Dominance Show the cross between a pink and a white flower. - Rr (2); rr (2) - ratio 1:1 - pink (2); white (2) - ratio 1:1 R r rrrr rrRr rr Rr GENOTYPES: PHENOTYPES: Codominance Codominance are when the alleles are neither dominant or recessive. In cases of codominance, both traits are expressed in the offspring Symbols are always written as capital letters. Example of Codominance In chickens- they are either white, black or black and white The colors are comdiminant Another Example of Codominance White and red are codominant. Cows are white, red or red and white Codominance The heterozygous condition, both alleles are expressed equally Sickle Cell Anemia in Humans NN = normal cells SS = sickle cells NS = some of each Problem: Codominance Show the cross between an individual with sickle-cell anemia and another who is a carrier but not sick. N S SSSS SS - NS (2) SS (2) - ratio 1:1 - carrier (2); sick (2) - ratio 1:1 GENOTYPES: PHENOTYPES: Multiple Alleles There are more than two alleles for a trait Blood type in humans Blood Types? Type A, Type B, Type AB, Type O Blood Alleles? A, B, O (in book I A, I B, I) Rules for Blood Type A and B are codominant AA = Type A BB = Type B AB = Type AB A and B are dominant over O AO = type A BO = type B OO = type O Blood Also Shows Codominance Problem: Multiple Alleles Show the cross between a mother who has type O blood and a father who has type AB blood. - AO (2) BO (2) - ratio 1:1 - type A (2); type B (2) - ratio 1:1 GENOTYPES: PHENOTYPES: O O ABAB AO BO AO BO Problem: Multiple Alleles Show the cross between a mother who is heterozygous for type B blood and a father who is heterozygous for type A blood. -AB (1); BO (1); AO (1); OO (1) - ratio 1:1:1:1 -type AB (1); type B (1) type A (1); type O (1) - ratio 1:1:1:1 GENOTYPES: PHENOTYPES: A O BOBO AB OO BO AO Sex-Linked Inheritance Traits that are only found on the X or Y chromosome Colorblindness and Hemophilia are examples of sex-linked traits. These genes are recessive and found only on the X chromosome. Sex-linked Punnet Squares Constructed the same way as a regular Punnet Square. Alleles are placed next to the X chromosome. Sex-linked Punnet Squares X B X b X b X b X B Y X b Y XbXb Y Definition Some traits are determined by the combined effect of two or more pairs of alleles. These traits are called polygenic traits. Each gene contributes a small but additive effect to the trait. Other names for polygenic traits are multi- factorial traits, or quantitative traits. Polygenic traits are continuous Because so many alleles contribute to the final phenotype, a variety of phenotypes can occur! For example, height is a polygenic trait. If you look around, you will notice there are not two set heights, but rather a continuum of height among your classmates. Another example of a polygenic trait: Hair Color Hair color is controlled by alleles on chromosomes 3, 6, 10, and 18. The more dominant alleles that appear in the genotype, the darker the hair!