Presentation on theme: "Hardy Weinberg: Population Genetics"— Presentation transcript:
1 Hardy Weinberg: Population Genetics Using mathematical approaches to calculate changes in allele frequencies…this is evidence of evolution.
2 Hardy-Weinberg equilibrium Hypothetical, non-evolving populationpreserves allele frequenciesnatural populations rarely in H-W equilibriumuseful model to measure if forces are acting on a populationmeasuring evolutionary changeG.H. Hardy (the English mathematician) and W. Weinberg (the German physician) independently worked out the mathematical basis of population genetics in Their formula predicts the expected genotype frequencies using the allele frequencies in a diploid Mendelian population. They were concerned with questions like "what happens to the frequencies of alleles in a population over time?" and "would you expect to see alleles disappear or become more frequent over time?"G.H. HardymathematicianW. Weinbergphysician
3 Evolution of populations Evolution = change in allele frequencies in a populationhypothetical: what conditions would cause allele frequencies to not change?very large population size (no genetic drift)no migration (no gene flow in or out)no mutation (no genetic change)random mating (no sexual selection)no natural selection (everyone is equally fit)H-W occurs ONLY in non-evolving populations!
4 Populations & gene pools Conceptsa population is a localized group of interbreeding individualsgene pool is collection of alleles in the populationremember difference between alleles & genes!allele frequency is how common is that allele in the populationhow many A vs. a in whole population
5 H-W formulas Alleles: p + q = 1 Individuals: p2 + 2pq + q2 = 1 B b BB
6 Origin of the Equation p2 + 2pq + q2 Assuming that a trait is recessive or dominantAllele pairs AA, Aa, aa would exist in a populationp + q = 1The probability that an individual would contribute an A is called pThe probability that an individual would contribute an a is called qBecause only A and a are present in the population the probability that an individual would donate one or the other is 100%p2 + 2pq + q2Male Gametes A(p)Male Gametes a(q)Female gametes A(p)AAp2AapqFemale Gametes a(q)aaq2
7 Hardy-Weinberg theorem Counting Allelesassume 2 alleles = B, bfrequency of dominant allele (B) = pfrequency of recessive allele (b) = qfrequencies must add to 1 (100%), so:p + q = 1Frequencies are usually written as decimals!BBBbbb
8 Hardy-Weinberg theorem Counting Individualsfrequency of homozygous dominant: p x p = p2frequency of homozygous recessive: q x q = q2frequency of heterozygotes: (p x q) + (q x p) = 2pqfrequencies of all individuals must add to 1 (100%), so:p2 + 2pq + q2 = 1BBBbbb
9 Practice Problem:In a population of 100 cats, there are 16 white ones. White fur is recessive to black.What are the frequencies of the genotypes?
10 Use Hardy-Weinberg equation! q2 (bb): 16/100 = .16q (b): √.16 = 0.4p (B): = 0.6p2=.362pq=.48q2=.16BBBbbbMust assume population is in H-W equilibrium!What are the genotype frequencies?
11 Answers: Assuming H-W equilibrium: Expected data Observed data 2pq=.48q2=.16Assuming H-W equilibrium:Expected dataBBBbbbp2=.20p2=.742pq=.102pq=.64q2=.16q2=.16Sampled data 1:Hybrids are in some way weaker.Immigration in from an external population that is predomiantly homozygous BNon-random mating... white cats tend to mate with white cats and black cats tend to mate with black cats.Sampled data 2:Heterozygote advantage.What’s preventing this population from being in equilibrium.bbBbBBObserved dataHow do you explain the data?How do you explain the data?
12 Tips for Solving HW Problems: Solve for q first.Then solve for p.Don’t assume you can just solve for p2 if only given dominant phenotypic frequency.READ carefully!!! HW Math is fun
13 Homework:Answer all the questions on the “Hardy Weinburg Practice Problems” handoutComplete the following prelab questions:List the conditions for a Hardy-Weinberg Population.Write a hypothesis for expected allele outcome for Case 1.Write down the formula of how to determine the allele frequencies.Write a hypothesis for expected allele outcome for Case 2.Write a hypothesis for expected allele outcome for Case 3.