The HKA Test

The HKA Test
(Hudson, Kreitman & Aguad é (1987) Genetics 116)
θ = 4N μ
N = effective population size; μ = mutation rate
HKA teases apart which is responsible for θ , thereby testing for selection
Expectations under the neutral model:
All loci share the same N
Each locus has its own characteristic neutral μ

The HKA Test
The HKA test is a “within species, between species” test
The neutral mutation rate ( μ ) drives both intraspecific polymorphism and intraspecific divergence
HKA test uses this to test for selection
Intraspecific polymorphism from ≥2 loci to estimate θ …
Locus 1 Locus 2

The HKA Test
… And
Interspecific divergence to estimate μ
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

The HKA Test
θ and μ are calculated to estimate N
Selection is inferred when N varies between loci
Hypothetical scenario 1:
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

The HKA Test
Hypothetical scenario 2:
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

The HKA Test
The devil’s in the details:
HKA (1987) proposed using X 2 as a goodness-of-fit test to see if the observed variables match the expected
Variables:
Segregating sites – to calculate θ
Divergence between species – a measure of μ
The real data is the observed, what’s the expected?
Coalescent simulations of the neutral model!
Use known variables to seed simulations

The HKA Test
Coalescent simulations:
Usually one locus is “known” to be neutral
Use this one to seed simulations to get distribution
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

The HKA Test
Compare the “neutral” simulation’s distribution to “selected” locus:
Use X 2 test with 2*(No. loci)-2 degrees freedom
The more loci, the more statistical power you have

The HKA Test
With the HKA test you can ask:
“ Can the differences between the two loci be explained by variation under the neutral model?”
Yes : explained by neutral variation of μ ; no selection
No : explained by non-neutral variation in N; N differs from neutral expectations and therefore locus has undergone selection

The HKA Test

by guest45b507 on Oct 19, 2007

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