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Lecture 5: Assaying Genetic Variation September 11, 2009 Exam 1 September 30 in lab I will be out of town September 26 through September Oct 2 Baneshwar will do review September 28 and Gancho Slavov will help out Old exam posted at: http://www.as.wvu.edu/~sdifazio/popgen/sched.html Last Time Hardy-Weinberg review More about dominant loci and allele frequencies Hypothesis testing Detecting departures from H-W Today Measures of genetic variation Hardy-Weinberg departures revisited Exact tests for assessing departures from expectations What is a Population? Operational definition: an assemblage of individuals Population genetics definition: a collection of randomly mating individuals Why does this matter? Measuring diversity Allele frequency is same as sampling probability Two allele system: frequency of one allele provides frequency of other: p and q Homozygotes: individuals with the same allele at both homologous loci Heterozygotes: individuals with different alleles at homologuous loci Dominance and Additivity Dominance: masking of action of one allele by another allele Homozygotes indistinguishable from heterozygotes Additivity: phenotype can be perfectly predicted from genotype Intermediate heterozygote Codominant: both alleles are apparent in genotype: does NOT refer to phenotype! http://bio.research.ucsc.edu/~barrylab/classes/animal_behavior/GENETIC.HTM#_Toc400823041 Hardy-Weinberg Law Hardy and Weinberg came up with this simultaneously in 1908 Frequencies of genotypes can be predicted from allele frequencies following one generation of random mating Assumptions: Infinite population Random mating No selection No migration No Mutation Hardy-Weinberg Law and Probability A(p) a(q) A (p) AA (p2) Aa (pq) a (q) aA (qp) aa (q2) p2 + 2pq + q2 = 1 Expected Heterozygosity If a population is in Hardy-Weinberg Equilibrium, the probability of sampling a heterozygous individual at a particular locus is the Expected Heterozygosity: 2pq for 2-allele, 1 locus system OR 1-(p2 + q2) or 1-Σ(expected homozygosity) n more general: what’s left over after calculating H E 1 p 2i , i 1 expected homozygosity Homozygosity is overestimated at small sample sizes. Must apply correction factor: 2N n Correction for bias in parameter estimates by HE 1 p 2i , small sample size 2 N 1 i 1 Maximum Expected Heterozygosity Expected heterozygosity is maximized when all allele frequencies are equal Approaches 1 when number of alleles = number of chromosomes 2N 1 2 2 2N 1 1 H E(m ax) 1 1 2N i 1 2 N 2N 2N Applying small sample correction factor: 2N n 2N 2N 1 HE 1 p 2i 1 2 N 1 i 1 2 N 1 2 N Departures from Hardy-Weinberg Chi-Square test is simplest (frequentist) way to detect departures from Hardy-Weinberg Compare calculated Chi-Square value versus “critical value” to determine if significant departures are delected Observed Heterozygosity Proportion of individuals in a population that are heterozygous for a particular locus: HO N ij Where Nij is the number of diploid individuals with genotype AiAj, and i ≠ j N Difference between observed and expected heterozygosity will become very important soon This is NOT how we test for departures from Hardy- Weinberg equilibrium! How do you calculate deviations from Hardy- Weinberg for this example? Observations of Malate Dehydrogenase Genotype Frequencies in Drosophila Meaning of P-value Probability of a Chi-square value of the calculated magnitude or greater if the null hypothesis is true Critical values are not magical numbers Important to state hypotheses correctly Interpret results within parameters of test p<0.05: The null hypothesis of no significant departure from Hardy- Weinberg equilibrium is rejected. Alternatives to Chi-Square Calculation If expected numbers are very small (less than 5), Chi-square distribution is not accurate Exact tests are required if small numbers of expected genotypes are observed Essentially a sample-point method based on permutations Sample space is too large to sample exhaustively Take a random sample of all possible outcomes Determine if observed values are extreme compared to simulated values Fisher’s Exact Test in lab last time Exact Tests for Detecting Departures from Expected Patterns Father of exact tests: R.A. Fisher Prompted by a dispute over tea Applying Fisher’s Exact Test to Hardy Weinberg Probability of observing a particular group of genotypes follows a multinomial probability distribution: N! 2N 2N P(Data) p1 11 p2 22 (2 p1 p2 ) N12 , N11!N 22!N12! Expected Expected Homozygote Heterozygote Frequency of Frequency of Counts Count Homozygotes Heterozygotes How extreme is your distribution of genotypes relative to what would be expected by chance if genotypes follow Hardy-Weinberg proportions? Probability of Observing Mdh Genotypic Distributions N! 2N 2N P(Data) 2N p1 11 p2 22 p3 33 (2 p1 p2 ) N12 (2 p2 p3 ) N 23 (2 p1 p3 ) N13 N11!N 22!N12!N 23!N13N 33 Is this an extremely low probability? How many combinations must we calculate? 114! = 2.5 x 10186 In practice, this sample space must be SAMPLED Monte-Carlo Markov Chain Methods often used Example: Merling Pattern in Dogs Merle or “dilute” coat color is a desired trait in collies and other breeds Homozygotes for mutant gene lack most coat color Heterozygotes Homozygous mutants Homozygous wild-type N=2531 N=197 N=18590