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Section 11.2

Section 11.2. Applying Mendel’s Principles. Probability and Punnett Squares. During Mendel’s crosses with pea plants  he carefully categorized and counted the offspring to create data Through analysis  principles of probability can be used to explain the results of genetic crosses

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Section 11.2

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  1. Section 11.2 Applying Mendel’s Principles

  2. Probability and Punnett Squares • During Mendel’s crosses with pea plants he carefully categorized and counted the offspring to create data • Through analysis  principles of probability can be used to explain the results of genetic crosses • Probability – likelihood that a particular event will occur • EX: flipping a coin – 2 possible outcomes (heads or tails)  probability of either outcome is equal for every flip (1/2 = 50%)

  3. Probability • Flip a coin  50% of either outcome • Flip a coin 3 times  each flip is an independent event with ½ probability of landing heads up: • Probability of flipping 3 heads in a row = ½ * ½ * ½ = 1/8 • Multiplying individual probabilities tells us: • Past outcomes do not affect future outcomes

  4. Using Segregation to Predict Outcomes • Allele segregation during gamete formation is every bit as random as a coin flip • So principles of probability can be used to predict the outcomes of genetic crosses • Mendel’s P1 Cross: • True-breeding tall x true-breeding short • Offspring: ????

  5. Mendel’s F1 Cross F1 plants were both tall When crossed  produced a mixture of tall and short plants If each plant had 1 tall allele and 1 short allele, and if alleles segregated as Mendel thought, then ½ the gametes produced would carry the short allele The only way to produce a short plant is for 2 gametes carrying the t allele to combine

  6. Using Segregation to Predict Outsomes • Each F2 gamete has ½ chance of carrying the t allele • There are 2 gametes, so probability = ½ * ½ = 1/4 • ~ ¼ of F2 offspring should be short, and remaining ¾ should be tall • 3 dominant : 1 recessive showed up consistently in Mendel’s experiments • For each of his experiments: 1/4 showed traits controlled by recessive allele & ¾ showed traits controlled by dominant allele • Segregation did occur according to Mendel’s model

  7. Using Segregation to Predict Outcomes • F2 generation – not all have same characteristics or the same combinations of alleles • TT vs. Tt – both tall, but only 1 has identical alleles • Homozygous – have 2 identical alleles for a particular gene (TT) (tt) • Heterozygous – organism that have 2 different alleles for the same gene (Tt)

  8. Probabilities Predict Averages • Probabilities predict average outcome of a large number of events • To get the expected 50:50 ratio, you may have to flip the coin many times • Larger number of offspring = results closer to predicted values • May need hundreds or thousands of individuals for ratios to come very close to matching the predictions

  9. Genotype and Phenotype • Every organism has a genetic makeup as well as a set of observable characteristics. • Phenotype – physical traits (tallness) • Genotype – genetic makeup (TT, Tt, tt) • Genotype of an organism is inherited • Phenotype is largely determined by genotype • 2 organisms may have same phenotype but have different genotypes

  10. Using Punnett Squares One of best ways to predict outcome of a genetic cross is by using a diagram Punnett square – use mathematical probability to help predict the genotype and phenotype combinations in genetic crosses

  11. Constructing a Punnett Square Make a square Follow principle of segregation to write all possible combinations of alleles in the gametes produced by one parent at the top edge of the square Segregate and write the other parent’s alleles along the left edge Every possible genotype is written into the boxes within the square, just as they might appear in the F2 generation Page 316 – step by step instructions

  12. Independent Assortment Does the segregation of 1 pair of alleles affect another pair? Does gene that determines shape of a seed affect the gene for seed color? To find out, Mendel followed 2 different genes as they passed from one generation to the next 2-factor = dihybrid = involves 2 different genes 1-factor = monohybrid

  13. The 2-Factor Cross: F1 Mendel crossed true-breeding plants that produced only round yellow peas with plants that produced wrinkled green peas Round yellow = RRYY Wrinkled green = rryy All F1 offspring produced round yellow peas Alleles for round and yellow are dominant Genotype in each of F1 plants = RrYy Heterozygous for both seed shape and see color Cross did not indicate whether genes assort (segregate) independently Cross provided hybrid plants needed to breed F2 generation

  14. The 2-Factor Cross: F2 Mendel crossed F1 plants to produce F2 offspring F1 plants formed by fusion of gamete w/ dominant RY alleles with another gamete carrying the recessive ry alleles Did this mean that the 2 dominant alleles would always stay together, or would they segregate independently, so that any combination of alleles was possible? F2 plants produced 556 seeds. Mendel compared their variation 315 = round and yellow (parental phenotype) 32 = wrinkled and green (parental phenotype) 209 = combinations of phenotypes  combinations of alleles not found in either parent Alleles for seed shape segregated independently of those for seed color Genes that segregate independently do not influence each other’s inheritance

  15. F2 Conclusions Mendel’s experimental results very close to 9:3:3:1 ratio predicted by the Punnett square Principle of Independent Assortment – genes for different traits can segregate independently during the formation of gametes. Independent assortment helps account for many genetic variations observed in plants, animals, etc – even when they have the same parents

  16. Summary of Mendel’s Principles Mendel’s principles of heredity, observed through patterns of inheritance, form the basis of modern genetics The inheritance of biological characteristics is determined by individual units called genes, which are passed from parents to offspring. Where 2 or more forms (alleles) of the gene for a single trait exist, some alleles may be dominant and others may be recessive. In most sexually reproducing organisms, each adult has 2 copies of each gene – one from each parent. These genes segregate from each other when gametes are formed. Alleles for different genes usually segregate independently of each other

  17. Summary of Mendel’s Principles Don’t only apply to plants Thomas Hunt Morgan (early 1900s) – used fruit flies to advance the study of genetics A single pair can produce hundreds of flies Tested all of Mendel’s principles Learned that they applied to flies and other organisms as well Mendel’s basic principles can be used to study the inheritance of human traits and to calculate the probability of certain traits appearing in the next generation

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