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Variation and probability

Variation and probability. Gamete production is source of variation and genetic diversity, an advantage of sex. As a result of segregation and independent assortment, lots of combinations possible. 2 n possibilities exist for diploids where n = haploid number of chromosomes

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Variation and probability

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  1. Variation and probability • Gamete production is source of variation and genetic diversity, an advantage of sex. • As a result of segregation and independent assortment, lots of combinations possible. • 2n possibilities exist for diploids where n = haploid number of chromosomes • In humans, this is 8 million different gametes • Crossing over during meiosis creates even more combinations of genetic information • This diversity important in evolution, survival.

  2. Trihybrid cross • Mendel also crossed peas and looked at inheritance of 3 traits simultaneously. • These showed independent assortment also. • A Punnett square to determine the phenotypic ratios would be unwieldy • It would require an 8 x 8 matrix: 64 squares • Because independent events are involved, one can use the product law • Multiply each probability. • Simplest way: forked-line method = branch diagram

  3. Product law • Product law used to calculate odds of an outcome from independent events • Flip a coin: heads or tails, 50:50 chance (1/2) • Flip a coin 3 times, get 3 heads; the next flip, there’s still a 50:50 chance of getting a head. • The chance of getting 4 heads in a row: • ½ x ½ x ½ x ½ = 1/16 the product law. • Odds of round, yellow seeds in a cross of Ww GG x Ww gg: ¾ x 4/4 = 3/4

  4. Sum Law • The sum law: outcomes of events are independent, but can be accomplished in more than one way. Flip a penny and a nickel: odds of 1 heads and 1 tails? There are 4 possible outcomes from this flip. 1 head, 1 tail can be from the penny being heads (odds 1/4), but also from the nickel (1/4): ¼ + ¼ = ½

  5. Branch diagram for figuring trihybrid cross Crossing 2 individuals heterozygous for all 3 traits:Ww Gg Pp x Ww Gg Pp What proportion of the offspring are expected to have round, green peas and purple flowers, where W is round, w is wrinkled; G is yellow, g is green; and P is purple and p is white? W_ gg P_ ¾ x ¼ x ¾ = 9/64

  6. Alterations to Mendel • Incomplete or partial dominance • Codominance • Multiple alleles • Lethal alleles • Gene interactions • Sex-linked, sex-limited, & sex-influenced • Effect of environment • Extranuclear inheritance

  7. Incomplete or partial dominance One allele only partially masks the other. Half as much enzyme makes half as much pigment. Phenotypic ratio is the same as genotypic: 1:2:1 www.people.virginia.edu/ ~rjh9u/snapdragon.html

  8. Partial dominance-2 • Partial dominance is not a common visual phenotype • A molecular phenotype showing partial dominance is more common • One allele instead of 2 is producing enzyme, so on a gel, a protein band is half as intense.

  9. Codominance • M and N blood groups: LM LN • Glycoprotein on blood cell surface • If one of each allele, both expressed. • Phenotype indicates genotype. • Heterozygote cross: shows 1:2:1 ratio http://boneslab.chembio.ntnu.no/Tore/Bilder/BlodMN.jpg

  10. Multiple alleles • In peas, Mendel following the inheritance of two contrasting traits, e.g. purple vs. white flowers • Often, more than two alleles for a trait exist. • Study of multiple alleles requires a population! • In diploid organisms, an individual can only have a maximum of two alleles. (2 different alleles) • In populations, many different alleles may be present. • Classic example: the ABO blood group system

  11. ABO Blood groups Series of sugars added to cell lipid creates trait. Genotypes include: AA, AO = type A BB, BO = type B OO = type O AB = type AB where A and B are co-dominant, O is recessive. In AB and O, the genotype is known from the phenotype. http://science.uwe.ac.uk/StaffPages/na/abo_ho2.gif

  12. Lethal alleles • In genetic crosses, information is obtained by examining the phenotype of the offspring. • In some instances, the genotype is lethal • Lethality may present itself late in life (Huntington Disease) or may result in no offspring. • Example: Fur color in mice: Agouti on left, yellow on right. http://www.cumc.columbia.edu/news/in-vivo/Vol1_Iss21_dec18_02/img/obesity-mice.jpg

  13. Lethal alleles-2 • If certain genotypes are lethal, results of a cross may be quite confusing. • Agouti x agouti = all agouti • Yellow x yellow = 2/3 yellow, 1/3 agouti • Agouti x yellow = ½ yellow, ½ agouti • 2:1 ratio is tip-off that something odd happens • Homozygous for yellow is lethal, so that genotype is NOT represented. • For lethality, yellow allele acts as recessive. • For coat color, yellow allele acts as dominant • A = agouti, Ay = yellow. Heterozygote is yellow.

  14. Complex inheritance and dihybrid crosses • Example: inheritance of simple trait and multiple allele trait: albinism and ABO • Crossing of heterozygotes • Mm (albinism) and AB (blood type) • Assume independent assortment • Simple trait shows 3:1 ratio, co-dominant trait shows 1:2:1 ratio • Phenotypic classes in offspring no longer 9:3:3:1 • Actually come out 3:6:3:1:2:1 • Complex inheritance produces odd ratios.

  15. Really good practice problems • http://www.biology.arizona.edu/mendelian_genetics/mendelian_genetics.html • Do all the problems from the links “Monohybrid cross” and from “Dihybrid cross”.

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