Hey everyone.
Has anyone read the Mol Ecol paper by Ferretti et al. 2013: Population genomics from pool sequencing? Specifically, has anyone tried to use their calculation of Fst from estimated nucleotide diversity?
For some reason, what ever I do I keep getting an Fst of zero -- even for very simple data with only two populations and very different nucleotide diversities. I have attached the equations, a description of the parameters, and my calculations to this question.
It could be that I have misread something important, or my order of operations in the summations is wrong.
For pooled data, being able to use nucleotide diversity to calculate Fst would be such a huge advantage to any study. Can anyone see what I have done wrong?
Hi @Xavier!
In this calculation you are not working with individuals: the value of pi is calculated from pooled NGS protocol; essentially, you don't have individual level data, but instead population level data. Theta for this calculation is a population parameter; you find the pairwise version of theta from each population to calculate Ht.
Regardless, I have run this calculation with different numbers, and Ht always ends up equalling Hs. In a real population genetic study, if a population has a value of 0.1, and another has a value of 0.9, the Fst should come out reasonably close to 1.0.
What I want to know is if the order of operations is wrong.
Dear Joshua,
The Fst equation looks for differentiation among populations. In this approach, Hs is calculated as the mean of variability within populations and Ht is the total variability if all populations were considered as a single population. Ht can be calculated as the variability within populations plus the among variability of all combinations of two populations.
In your calculation you assume that pi_A is the mean of the two populations, which is wrong. The pi_among is the average pairwise difference of the individuals of the two populations together, and will only be equal to the mean of within populations if the same variants are shared among the populations and in the adequate frequencies.
For example, if I have two populations of variability 0.1 and 0.1 but the variants at each population are located at different positions, the pi_among can be much higher that 0.1 because many variants will be fixed in the other population.
In your example of populations of 0.1 and 0.9 you need to calculate from the observed data what is the variability among populations.
Sebastian and Xavier are right. Example: Sequences from two (haploid) populations
pop1:
ACAAAT
ACAAGT
pop2:
CCAAGT
CCAAGT
In this case, the internal variability Hs is 1/6=0.167 for pop1 and 0 for pop2. However, the average pairwise nucleotide diversity between the populations is 0.25 because of the fixed difference A/C between populations in the first base.
Thanks so much Sebastian and Luca for your responses! I get it now.
Also, Luca, thanks for your paper; despite my wee blunder, I really liked your study and it has been super useful with helping me get my head around NGS.