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POPULATION GENETICS

Population Genetics is the study of genetics at the population level Mendelian Population is a group of sexually reproducing organisms with a close degree of genetic relationship

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POPULATION GENETICS

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  1. Population Genetics is the study of genetics at the population level Mendelian Population is a group of sexually reproducing organisms with a close degree of genetic relationship Gene Pool is a mixture of the genetic units (Genes or Gametes) produced by a Mendelian population from which the next generation arises. Alleles occur in this pool Evolution: Through events such as natural selection, migration, or mutation, the gene pool changes as new alleles enter or existing alleles exit the pool. These changes are the basis for evolution POPULATION GENETICS

  2. Probability works for individuals but how about populations? • You are a plant breeder and were given a field with 1000 plants • 450 red, 300 pink, and 250 white • Assuming these plants mate randomly, what will the proportions of these colors be in the next generation?

  3. Definitions • Frequency • The number (count) of an item within a population • Example: 450 red snapdragons • Relative Frequency • The proportion (fraction) of an item within a population • Example: 450 / 1000 = 0.45 = 45% red snapdragons

  4. What will the proportions of these colors be in the next generation? • How do we solve this problem? • Determine the relative frequency of each genotype and allele • relative frequency of RR = x = #RR / #individuals (N) • x = 450/1000 = 0.45 • relative frequency of RW = y = #RW / #individuals (N) • y = 300/1000 = 0.30 • relative frequency of WW = z = #WW / #individuals (N) • z = 250/1000 = 0.25 • Note: x + y + z = 1

  5. What will the proportions of these colors be in the next generation? • Calculating relative allele frequency • Frequency of allele R = p • p(R) = total # of R alleles from each genotype divided by total # of alleles (2N) • p(R) = [(2 × # RR) + (# RW)] / (2N) • p(R) = [(2 × 450) + (300)] / (2 × 1000) = 0.6 • Frequency of allele W = q • q(W) = total # of W alleles from each genotype divided by sample size (N) • q(W) = [(2 × # WW) + (# RW)] / (2N) • q(W) = [(2 × 250) + (300)] / (2 × 1000) = 0.4 • Note: p + q = 1

  6. What have we done so far? • Calculated the relative frequency of each genotype in the population (x, y, & z) • Calculated the relative frequency of each allele in the population (p & q) • What next?

  7. What will the proportions of these colors be in the next generation? • Now examine all possible mating types. How many are there? • 3 types of male (RR, RW, & WW)  3 types of female (RR, RW, & WW) = 9 possible crosses • Calculate the probability each type of cross will occur

  8. Note: All the cells add up to 1! Males RR (0.45) RW (0.30) WW (0.25) 0.1350 RR (0.45) 0.2025 0.1125 Females 0.0900 0.1350 0.0750 RW (0.30) 0.0750 WW (0.25) 0.1125 0.0625 Perhaps a table would be helpful... • What is the probability that heterozygotes will mate? • frequency RW males  frequency RW females • 0.30  0.30 = 0.09 (this is the middle cell of the table) • Therefore, mating among heterozygotes is expected to occur 9% of the time

  9. What will the proportions of these colors be in the next generation? • We’ve calculated the probability of each mating type • What next? • We need to determine what type of offspring will come from each mating type… We already know how to do this…

  10. Probability of each genotype in the offspring • To predict genotype frequencies in the offspring we use: • frequency of each mating type • RW  RW = 0.3  0.3 = 0.09 • frequency of offspring resulting from each mating type • 25% RR, 50% RW, 25% WW

  11. PARENTS RESULTING GENOTYPE OF OFFSPRING MATING (type) FREQUENCY RR RW WW RR x RR RR x RW RR x WW RW x RW RW x WW WW x WW Probability of each genotypein the offspring

  12. Males RR (0.45) RW (0.30) WW (0.25) 0.1350 RR (0.45) 0.2025 0.1125 Females 0.0900 RW (0.30) 0.1350 0.0750 0.0750 WW (0.25) 0.1125 0.0625

  13. PARENTS MATING (type) FREQUENCY RR RW WW RR x RR 0.2025 0.2025 RR x RW RR x WW RW x RW RW x WW WW x WW Probability of each genotypein the offspring GENOTYPE FREQUENCY OF RESULTING OFFSPRING

  14. Males RR (0.45) RW (0.30) WW (0.25) 0.1350 RR (0.45) 0.2025 0.1125 Females 0.0900 RW (0.30) 0.1350 0.0750 0.0750 WW (0.25) 0.1125 0.0625 OR = add the probabilities How do we combine these? (AND or OR) is the question: Probability: RW male & RR female AND RR male & RW female Probability: RW male & RR female OR RR male & RW female

  15. PARENTS GENOTYPE FREQUENCY OF RESULTING OFFSPRING MATING (type) FREQUENCY RR RW WW RR x RR 0.2025 0.2025 .135 + .135 = .27 .5.27 = .135 .5.27=.135 RR x RW RR x WW 0.225 0.225 RW x RW 0.09 .25.09=.0225 .5.09=.045 RW x WW 0.15 .5.15=.075 .5.15=.075 WW x WW 0.0625 0.0625 1 0.36 0.48 0.16 Probability of each genotypein the offspring .25.09=.0225 • If we consider all possible matings, the genotypic frequencies of the offspring will be: • x(RR) = 0.36 • y(RW) = 0.48 • z(WW) = 0.16

  16. What are the allele frequencies? • p(R) = (rel freq RR) + 0.5 × (rel freq RW) p(R) = 0.36 + (0.5 ×0.48) = 0.6 • q(r) = (rel freq WW) + 0.5 ×(rel freq RW) q(W) = 0.16 + (0.5 × 0.48) = 0.4 • NOTE: THESE ARE THE SAME AS WE SAW IN THE PARENTS • They are in equilibrium • What will the relative genotypic frequencies be in the next generation? x(RR) = 0.36, y(RW) = 0.48, z(WW) = 0.16 • Genotypic frequencies achieve equilibrium after one generation of random mating • Try this yourself at home to check

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