Lecture 5: Genetic Variation and Inbreeding. September 7, 2012

Transcription

1 Lecture 5: Genetic Variation and Inbreeding September 7, 01

2 Announcements I will be out of town Thursday Sept 0 through Sunday, Sept 4 No office hours Friday, Sept 1: Prof. Hawkins will give a guest lecture about transposable elements

3 Computer Lab Access Schedule is posted on the door and on the website Hari will be holding his office hours in the lab Updated hours will be on class homepage

4 Last Time Hardy-Weinberg Equilibrium Using Hardy-Weinberg: Estimating allele frequencies for dominant loci Variance of allele frequencies for dominant loci Hypothesis testing

5 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 N e and H E : RAPD SSR Allozyme

6 Today 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

7 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. 006 PNAS 103:1376

8 Example: Merling Pattern in collies Homozygous wild-type Heterozygotes Homozygous mutants M 1 M 1 N=6,498 M 1 M N=3,500 M M N= 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?

9 Why does the merle coat coloration occur in some breeds but not others? How did we end up with so many dog breeds anyway?

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11 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

12 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

13 Inbreeding can be quantified by probability (f) an individual contains two alleles that are Identical by Descent P A 1 A A 3 A 4 A 1 A A 3 A 4 F 1 A 1 A 3 A A 3 A 1 A 3 A A 3 A 3 A 5 F A 3 A 3 A A 3 A 3 A 3 A A 3 Identical by descent (IBD) Identical by state (IBS) Identical by descent (IBD)

14 Nomenclature D=X=P: frequency of AA or A 1 A 1 genotype R=Z=Q: frequency of aa or A A genotype H=Y: frequency of Aa or A 1 A genotype p is frequency of the A or A 1 allele q is frequency of the a or A allele All of these should have circumflex or hat when they are estimates: pˆ

15 Effect of Inbreeding on Genotype Frequencies D D D D = = = = fp fp p p p p fp (1 fp fp fp(1 f ) p) fp is probability of getting two A 1 alleles IBD in an individual p (1-f) is probability of getting two A 1 alleles IBS in an individual D = p + R q + fpq = fpq fpq H = pq Inbreeding increases homozygosity and decreases heterozygosity by equal amounts each generation Complete inbreeding eliminates heterozygotes entirely

16 Fixation Index The difference between observed and expected heterozygosity is a convenient measure of departures from Hardy-Weinberg Equilibrium F H H H E O = = 1 E H H O E Where H O is observed heterozygosity and H E is expected heterozygosity (pq under Hardy-Weinberg Equilibrium)

17 IBS IBD Assume completely inbred fraction (f) and noninbred fraction (1-f) in population H = pq(1 f ) + f H = pq(1" f ) f =1" H pq (0) F =1" H O H E If departures from Hardy Weinberg are entirely due to inbreeding, f can be estimated from Fixation Index, F

18 Effects of Inbreeding on Allele Frequencies D + 1 = p0 fp0q0 H 1 = p 0 q 0 " fp 0 q 0 p i = D i + 1 H i Allele frequencies do not change with inbreeding Loss of heterozygotes exactly balanced by gain of homozygotes p 1 = (p 0 + fp 0 q 0 ) + 1 (p 0 q 0 " fp 0 q 0 ) = p 0 + p 0 q 0 = p 0 + p 0 (1" p 0 ) = p 0 + p 0 " p 0 p 1 = p 0

19 Extreme Inbreeding: Self Fertilization Common mode of reproduction in plants: mate only with self Assume selfing newly established in a population ½ of heterozygotes become homozygotes each generation Homozygotes are NEVER converted to heterozygotes

20 Self Fertilization Aa Self-Fertilizations A a A AA Aa a Aa aa ½ Aa each generation ½ AA or aa (allele fixed within lineage) A A AA Self-Fertilizations A A AA AA AA AA

21 Decline of Heterozygosity with Self Fertilization 1 H 1 = H 1 H t H 0 = t 1 Steady and rapid decline of heterozygosity to zero AA or aa H t = 1 t H 0. Aa

22 Partial Self Fertilization Mixed mating system: some progeny produced by selfing, others by outcrossing (assumed random) H t = T pq + S t 1 aa H. Rate of outcrossing = T Rate of selfing = S T+S=1 AA Heterozygosity declines to equilibrium point Aa

23 What determines the equilibrium frequency of heterozygotes in a population with mixed selfing and outcrossing?