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The HKA Test <ul><li>(Hudson, Kreitman & Aguad é (1987)  Genetics  116) </li></ul><ul><li>θ  = 4N μ </li></ul><ul><li>N = ...
The HKA Test <ul><li>The HKA test is a “within species, between species” test </li></ul><ul><ul><li>The neutral mutation r...
The HKA Test <ul><li>… And </li></ul><ul><ul><li>Interspecific divergence to estimate  μ   </li></ul></ul>MRCA Species A S...
The HKA Test <ul><li>θ  and  μ  are calculated to estimate N </li></ul><ul><li>Selection is inferred when N varies between...
The HKA Test <ul><li>Hypothetical scenario 2: </li></ul>Locus 1 Locus 2 B A B A θ 1  = 100 θ 2  = 10 θ 1 / θ 2  = 10 θ 1  ...
The HKA Test <ul><li>The devil’s in the details: </li></ul><ul><ul><li>HKA (1987) proposed using  X 2  as a goodness-of-fi...
The HKA Test <ul><li>Coalescent simulations: </li></ul><ul><ul><li>Usually one locus is “known” to be neutral </li></ul></...
The HKA Test <ul><li>Compare the “neutral” simulation’s distribution to “selected” locus: </li></ul><ul><ul><li>Use  X 2  ...
The HKA Test <ul><li>With the HKA test you can ask:  </li></ul><ul><li>“ Can the differences between the two loci be expla...
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The HKA Test

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The HKA Test

  1. 1. The HKA Test <ul><li>(Hudson, Kreitman & Aguad é (1987) Genetics 116) </li></ul><ul><li>θ = 4N μ </li></ul><ul><li>N = effective population size; μ = mutation rate </li></ul><ul><li>HKA teases apart which is responsible for θ , thereby testing for selection </li></ul><ul><li>Expectations under the neutral model: </li></ul><ul><ul><li>All loci share the same N </li></ul></ul><ul><ul><li>Each locus has its own characteristic neutral μ </li></ul></ul>
  2. 2. The HKA Test <ul><li>The HKA test is a “within species, between species” test </li></ul><ul><ul><li>The neutral mutation rate ( μ ) drives both intraspecific polymorphism and intraspecific divergence </li></ul></ul><ul><li>HKA test uses this to test for selection </li></ul><ul><ul><li>Intraspecific polymorphism from ≥2 loci to estimate θ … </li></ul></ul>Locus 1 Locus 2
  3. 3. The HKA Test <ul><li>… And </li></ul><ul><ul><li>Interspecific divergence to estimate μ </li></ul></ul>MRCA Species A Species B μ = d /2T μ = substitutions per site per year d = distance in substitutions per site between two sequences T = divergence time DNA sequences
  4. 4. The HKA Test <ul><li>θ and μ are calculated to estimate N </li></ul><ul><li>Selection is inferred when N varies between loci </li></ul><ul><li>Hypothetical scenario 1: </li></ul>Locus 1 Locus 2 B A B A θ 1 = 100 θ 2 = 10 θ 1 / θ 2 = 10 θ 1 > θ 2 , but μ 1 > μ 2 in a corresponding fashion Difference in θ explained by different μ , which neutrally varies from locus to locus N is the same for both loci: No selection μ 1 = d 1 /2T 1 μ 2 = d 2 /2T 2 μ 1 = 50 μ 2 = 5 μ 1 / μ 2 = 10
  5. 5. The HKA Test <ul><li>Hypothetical scenario 2: </li></ul>Locus 1 Locus 2 B A B A θ 1 = 100 θ 2 = 10 θ 1 / θ 2 = 10 θ 1 > θ 2 , but μ 1 = μ 2 Difference in θ can only be explained by difference in N One locus has an apparent reduction of N – infer Selection! μ 1 = d 1 /2T 1 μ 2 = d 2 /2T 2 μ 1 = 20 μ 2 = 20 μ 1 / μ 2 = 1 By the way: θ 1 = 4N 1 μ 1 θ 2 = 4N 2 μ 2 μ 1 = d 1 /2T 1 μ 2 = d 2 /2T 2 and… so, between species d is a measure of μ
  6. 6. The HKA Test <ul><li>The devil’s in the details: </li></ul><ul><ul><li>HKA (1987) proposed using X 2 as a goodness-of-fit test to see if the observed variables match the expected </li></ul></ul><ul><ul><li>Variables: </li></ul></ul><ul><ul><ul><li>Segregating sites – to calculate θ </li></ul></ul></ul><ul><ul><ul><li>Divergence between species – a measure of μ </li></ul></ul></ul><ul><ul><li>The real data is the observed, what’s the expected? </li></ul></ul><ul><ul><ul><li>Coalescent simulations of the neutral model! </li></ul></ul></ul><ul><ul><ul><li>Use known variables to seed simulations </li></ul></ul></ul>
  7. 7. The HKA Test <ul><li>Coalescent simulations: </li></ul><ul><ul><li>Usually one locus is “known” to be neutral </li></ul></ul><ul><ul><li>Use this one to seed simulations to get distribution </li></ul></ul>Use L2 parameters Simulate 1000 times Lots of variation around θ and μ Creates a distribution L1 L2 B A B A θ 1 = 58 μ 1 = 14 θ 2 = 10 μ 2 = 13
  8. 8. The HKA Test <ul><li>Compare the “neutral” simulation’s distribution to “selected” locus: </li></ul><ul><ul><li>Use X 2 test with 2*(No. loci)-2 degrees freedom </li></ul></ul><ul><ul><li>The more loci, the more statistical power you have </li></ul></ul>
  9. 9. The HKA Test <ul><li>With the HKA test you can ask: </li></ul><ul><li>“ Can the differences between the two loci be explained by variation under the neutral model?” </li></ul><ul><ul><li>Yes : explained by neutral variation of μ ; no selection </li></ul></ul><ul><ul><li>No : explained by non-neutral variation in N; N differs from neutral expectations and therefore locus has undergone selection </li></ul></ul>

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