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Lecture 5: Genetic Variation and Inbreeding August 31, 2015 Last Time Sandy Simon guest lecture: measuring genetic variation at the nucleotide level Before that: Hardy-Weinberg Equilibrium Using Hardy-Weinberg: Estimating allele frequencies for dominant loci Variance of allele frequencies for dominant loci Hypothesis testing If nucleotides occur randomly in a genome, which sequence should occur more frequently? AGTTCAGAGT AGTTCAGAGTAACTGATGCT What is the expected probability of each sequence to occur once? How many times would each sequence be expected to occur by chance in a 100 Mb genome? What is the expected probability of each sequence to occur once? AGTTCAGAGT What is the sample space for the first position? A T Probability of “A” at that position? 1 G 4 C Probability of “A” at position 1, “G” at position 2, “T” at position 3, etc.? 1 1 1 1 1 1 1 1 1 1 x x x x x x x x x 0.2510 9.54 x10 7 4 4 4 4 4 4 4 4 4 4 AGTTCAGAGTAACTGATGCT 0.2520 9.09 x10 13 How many times would each sequence be expected to occur in a 100 Mb genome? AGTTCAGAGT 9.54x10 10 95.4 7 8 AGTTCAGAGTAACTGATGCT 9.09x10 10 9.1x10 13 8 5 Why is this calculation wrong? AGTTCAGAGTAACTGATGCT AGT TCA GAG TAA CTG ATG CT UCA AGU CUC AUU GAC UAC GA Ser Cys Phe Ile Asp Tyr UGA AGU CUC AUU GAC UAG GA Stop Cys Phe Ile Asp Stop A P( A B) P( A) P( B) P( A B), B P( A B ) P( A | B ) P( B ), Today Measures of diversity More Hardy-Weinberg Calculations Merle Patterning in Dogs First Violation of Hardy-Weinberg assumptions: Random Mating Effects of Inbreeding on allele frequencies, genotype frequencies, and heterozygosity 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) more general: what’s left over after calculating expected homozygosity n H E 1 p 2i , i 1 Homozygosity is overestimated at small sample sizes. Must apply correction factor: Correction for bias in parameter estimates by small sample size n 2N 2 HE 1 p i , 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 1 pi = Frequency of each allele: 2N 2N 1 1 1 H E(max) 1 1 2 N 2N 2N i 1 2 N Does this make sense? 2N 2 2 Applying small sample correction factor: n 2N 2N 2N 1 2 HE 1 p i 1 2 N 1 i 1 2 N 1 2 N Also see Example 2.11 in Hedrick text Observed Heterozygosity Proportion of individuals in a population that are heterozygous for a particular locus: HO N N ij H ij Where Nij is the number of diploid individuals with genotype AiAj, and i ≠ j, And Hij is frequency of heterozygotes with those alleles Difference between observed and expected heterozygosity will become very important soon This is NOT how we test for departures from HardyWeinberg equilibrium! Alleles per Locus Na: Number of alleles per locus Ne: Effective number of alleles per locus Same as ne in your text If all alleles occurred at equal frequencies, this is the number of alleles that would result in the same expected heterozygosity as that observed in the population Ne 1 Na 2 p i i 1 , Example: Assay two microsatellite loci for WVU football team (N=50) Calculate He, Na and Ne Locus A Locus B Allele Frequency Allele Frequency A1 0.01 B1 0.3 A2 0.01 B2 0.3 A3 0.98 B3 0.4 n 2N 2 HE 1 p i , 2 N 1 i 1 Ne 1 Na 2 p i i 1 , Measures of Diversity are a Function of Populations and Locus Characteristics Assuming you assay the same samples, order the following markers by increasing average expected values of Ne and HE: RAPD SSR Allozyme Example: Merle patterning in dogs Merle or “dilute” coat color is a desired trait in collies, shetland sheepdogs (pictured), Dachshunds and other breeds Homozygotes for mutant gene lack most coat color and have numerous defects (blindness, deafness) Caused by a retrotransposon insertion in the SILV gene Clarke et al. 2006 PNAS 103:1376 Example: Merling Pattern in collies Homozygous wild-type M1M1 N=6,498 Heterozygotes Homozygous mutants M1M2 M2M2 N=3,500 N=2 Is the Merle coat color mutation dominant, semi-dominant (incompletely dominant), or recessive? Do the Merle genotype frequencies differ from those expected under Hardy-Weinberg Equilibrium? Why does the merle coat coloration occur in some breeds but not others? How did we end up with so many dog breeds anyway? Nonrandom Mating: Inbreeding Inbreeding: Nonrandom mating within populations resulting in greater than expected mating between relatives Assumptions (for this lecture): No selection, gene flow, mutation, or genetic drift Inbreeding very common in plants and some insects Pathological results of inbreeding in animal populations Recessive human diseases Endangered species http://i36.photobucket.com/albums/e4/doooosh/microcephaly.jpg Important Points about Inbreeding Inbreeding affects ALL LOCI in genome Inbreeding results in a REDUCTION OF HETEROZYGOSITY in the population Inbreeding BY ITSELF changes only genotype frequencies, NOT ALLELE FREQUENCIES and therefore has NO EFFECT on overall genetic diversity within populations Inbreeding equilibrium occurs when there is a balance between the creation (through outcrossing) and loss of heterozygotes in each generation Inbreeding can be quantified by probability (f) an individual contains two alleles that are Identical by Descent P A1A2 F1 A3A4 A1A3 F2 A 3A 3 A 2A 3 A2A3 Identical by descent (IBD) A 1A 2 A3A4 A1A3 A2A3 A3A5 A3A3 A2A3 Identical by state (IBS) Identical by descent (IBD)