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Topics for Today • Review of Dihybrid Cross - Relationship with molecular/chromosomal behavior • Deductions from Pedigrees • Calculation of Genetic Probabilities Mendel’s Interpretations Reinterpretted Mendel’s Interpretation Traits do not blend but are determined by unchangeable units x Our Interpretation Genes proteins traits Mendel’s Interpretations Reinterpretted Mendel’s Interpretation Each trait is determined by two units Our Interpretation Two homologous chromosomes Mendel’s Interpretations Reinterpretted Mendel’s Interpretation The two units may or may not be identical Our Interpretation A a Genes come in different forms, alleles, which make different protein Mendel’s Interpretations Reinterpretted Mendel’s Interpretation One character form is recessive to or dominant over another Our Interpretation P >p p >P Mendel’s Interpretations Reinterpretted Mendel’s Interpretation The two character forms carried by a heterozygote are passed to progeny with equal likelihood Law of Segregation Our Interpretation Mendel’s Interpretations Reinterpretted Mendel’s Interpretation Different traits assort independently Law of Independent Assortment Our Interpretation Different traits assort independently Law of Independent Assortment Different traits assort independently Law of Independent Assortment RRYY RRYy RrYY RrYy RRYy RRyy RrYy Rryy RrYY RrYy rrYY rrYy RrYy Rryy rrYy rryy Deductions from Pedigrees • Pedigree with ephemeral trait (Fig. 2) • Pedigrees with other kinds of traits (next week) • Genetic counseling (later today) Deductions from Pedigrees How is the trait inherited? AA-? A- Try dominant A-? Deductions from Pedigrees How is the trait inherited? aa aa aa aa aa aa aa aa aa aa aa aa aa aa aa A- aa A- aa Any problem? Deductions from Pedigrees How is the trait inherited? aa aa Try recessive Deductions from Pedigrees How is the trait inherited? AA- A- AA- A- A- A- A- A- A- A- A- A- A- aa A- aa ACan we get more? Deductions from Pedigrees How is the trait inherited? Which one gave a? Which one gave a? AA- A- AA- A- A- A- A- Aa A- A- Aa A- A- aa A- aa ACan we get more? Deductions from Pedigrees How is the trait inherited? Which one gave a? Which one gave a? A- What about outsiders? A- Aa AA- A- A- A- A- Aa Aa A- Aa A- A- aa A- aa ACan we get more? What about outsiders? Deductions from Pedigrees How is the trait inherited? AAA Aa AA- A- A- A- A- Aa Aa AA Aa AA A- aa A- aa A- Genetic Counseling Make the problem concrete Will our children be normal ? ? ? What’s the probability that a child of III.5 x III.6 will will have be aa? CS? Genetic Counseling AAA A- aa A- A- A- A- A- A- Parse the problem A- AA A- A- (start simple) Child will be aa if: III5 is Aa AND III6 is Aa AND III5 Probability: a AND III6 a Genetic Counseling AAA A- aa A- A- A- A- A- A- Solve each segment A- AA A- A- Child will be aa if: III5 is Aa AND III6 is Aa AND III5 Probability: II2 is Aa AND II2 1 a 1/2 1/2 a AND III6 a 1/2 Genetic Counseling AAA A- aa A- A- A- A- A- A- Solve each segment A- AA A- A- Child will be aa if: III5 is Aa AND III6 is Aa AND III5 Probability: 1/2 1/2 1/2 a AND III6 a 1/2 Genetic Counseling AAA A- aa A- A- A- A- A- A- Put parts together A- AA A- A- Child will be aa if: III5 is Aa AND III6 is Aa AND III5 Probability: Multiply? Add? a AND III6 a 1/2 1/2 1/2 1/2 … intersection union… mutually … independent… exclusive… fewer more possibilities possibilities Union of possibilities Probability that progeny of Aa x Aa has A phenotype Male (Aa) makes gamete Gets A from female OR gets A from male Female (Aa) makes gamete Rule of addition union mutually exclusive A a A AA Aa a aA aa Gets aA OR AA OR Aa P(A-) = 1/4 + 1/4 + 1/4 = 3/4 Intersection of possibilities Probability that progeny of Aa x Aa has a phenotype Male (Aa) makes gamete Gets a from female AND gets a from male Female (Aa) makes gamete Rule of multiplication intersection independent A a A AA Aa a aA aa Gets a from female AND gets a from male P(aa) = 1/2 x 1/2 = 1/4 Genetic Counseling AAA A- aa A- A- A- A- A- A- Put parts together A- AA A- A- Child will be aa if: III5 is Aa AND III6 is Aa AND III5 Probability: Multiply? Add? a AND III6 a x x x 1/2 1/2 1/2 1/2 … intersection union… mutually … independent… exclusive… 1/16 fewer more possibilities possibilities Example illustrating Rule of Complementation • Suppose there are two genes (A, B) that are required for dark hair • A defect in any one of them will produce light hair • What is the probability that a person will have light hair? Make problem concrete: Light hair if A- OR B- Parse problem: P(A- OR B-) = P(A-) + P(B-) Is Rule of Addition valid here? Is possession of A- and possession of B- mutually exclusive? P(A How to Calculate OR Probability of light hair P(A-) P(A-) + P(B-)? B) P(B-) Not mutually exclusive. P(A-B-) added twice P(A How to Calculate OR Probability of light hair B) P(A-) + P(B-)? Not mutually exclusive. P(A-B-) added twice P(A-) x P(B-)? Gives intersection, not union P(A How to Calculate OR Probability of light hair P(A-) P(B-) P(A-): probability of possessing defective allele of gene A B) P(A How to Calculate OR Probability of light hair not A- P(not A-) = 1 - P(A-) probability of not possessing defective allele of gene A B) P(A How to Calculate OR Probability of light hair P(A-) P(B-) P(B-): probability of possessing defective allele of gene B B) P(A How to Calculate OR Probability of light hair not B- P(not B-) = 1 - P(B-) probability of not possessing defective allele of gene B B) P(A How to Calculate OR Probability of light hair not A- P(not A-) = 1 - P(A-) probability of not possessing defective allele of gene A B) P(A How to Calculate OR Probability of light hair B) not AAND not B- P(not A- and not B-) = [1 - P(A-)] x [1 - P(B-)] probability of not possessing either defective allele P(A How to Calculate OR Probability of light hair B) A- OR Bnot A- AND not B- P(A- or B-) = 1 - [1 - P(A-)] x [1 - P(B-)] probability of possessing either defective allele How likely to get hemophilia? •There are five known alleles for the clotting factor protein Factor VIII (H1-, H2-, H3-, H4-, H5-). •Three of them (H3-, H4-, H5-) cause hemophilia. H3-is the probability hemophilia •What that a person will have one of the H4-defective hemophilia three alleles and thus get hemophilia? H5hemophilia -, +H4-, OR H5-??? H4 P(H3 ) = P(H3-) + P(H4-) + P(H5-) Rule of addition Union? … but is possession of the alleles mutually exclusive? Union of possibilities Male (Aa) makes gamete A a P(A) = 0.5 P(a) = 0.5 Female (Aa) makes gamete A P(A) = 0.8 AA Aa a P(a) = 0.2 aA aa P(A-) = 0.4 + 0.4 + 0.1 = 0.9