Can we compare two LD decay curves by statistical test to say they are different?

Question

[Hann]

Hello,

Is it possible to compare two curves and say they are different not just by eyes, but providing statistical test?

Here is LD decay plot of two plant species. And by eyes, I see the difference in which the blue one decay faster at the beginning.

The Genome-wide LD decay was calculated by PopLDdecay software by calculating the pairwise linkage disequilibrium.

Is it possible to provide a statistical test? to support this sentence: "Genome-wide linkage disequilibrium (LD) analyses revealed a faster LD decay in wild (r2 ∼ 0.17 at 70 kb) compared to cultivated group(r2 ∼ 0.20 at 70 kb)"

[Asaf]

Something looks weird in the blue line, it looks like it's not decaying, can it be that every pair of SNPs will have a correlation r^2 of 0.15? Maybe you have a bias in the population? I'm not sure if there is a test to compare the two plots but you can take the same pairs of SNPs and compute the correlation between them in both populations then compare the coefficients using a paired t-test.

[Hann]

This was my initial plan, but using paired t-test you compare the means between two related groups. Does it make sense to compare the two means of curves?

[Asaf]

No, that's not what I meant. Select a group of SNP pairs with a certain distance range (100kb +- 10kb for instance) then for each pair compute the correlation using each population, you now have paired measurements that you can compare. You can repeat the process for several point along the curve. The LD drop curve is deceiving, it's a smoothing of averaging of r^2 values in bins of distances, it looks pretty but actually very much noisy.

[Hann]

Very good. Now I understand your point. Thanks a lot!

And with vcftools http://vcftools.sourceforge.net/man_latest.html I can define the physical window

Example: --ld-window-bp 100000 compute the LD between SNPs being maximum 100 kb apart

Answer 1

[hewm2008]

1. You can compare the distance between the two groups when R^2=0.2. In theory, the distance of the cultivated group will be longer.
2. The two lines intersect, the main reason is that your sample size is too small, and the sample size of the two groups is also very different. You can try to draw the picture with the same sample size.

[Hann]

You are right! The sample size of the two groups are very different, the cultivated group with 157 individuals, while the wild group is only 14 individuals.

What do you mean by comparing the distance R^2=0.2? Just by saying:

Genome-wide linkage disequilibrium (LD) analyses revealed a faster LD decay in wild (r2 ∼ 0.2 at 400 bp) compared to cultivated group(r2 ∼ 0.20 at 70 kb)

Reviewers asked for a statistical test to support this sentence (>_<")

[hewm2008]

Yes, you can read more other paper how to description sush as follow: https://www.researchgate.net/figure/Comparison-of-LD-decay-in-the-wild-species-and-each-variety-complex-of-domesticated_fig3_301344878