F2 utility in admixtools?

[DanielEPlatt]

I have been trying to get admixtools utilities to yield a bias-corrected f2 by feeding f3(b;a,a) or f4(b,a;b,a), but these utilities complain and will not produce meaningful output for those instances. How do I get f2(a,b) from ADMIXtools?

[DanielEPlatt]

I figured out a way to compute F_2's from F_3's - which meets my needs.

[bumblenick]

The clean way to do this is to run qpfstats and then qpfmvFlexible and you get standard errorsNickSent from my iPhoneOn Jul 26, 2025, at 1:34 PM, DanielEPlatt ***@***.***> wrote:DanielEPlatt left a comment (DReichLab/AdmixTools#117) I figured out a way to compute F_2's from F_3's - which meets my needs. —Reply to this email directly, view it on GitHub, or unsubscribe.You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[DanielEPlatt]

Wow!! Thank you for your quick reply, Nick!

From d^2(a,b) := F_2(a,b), I derived: d^2(a,b) = F_2(a,c) + F_2(b,c) - 2 F_3(a,b; c) for any c by injecting a -c+c in the (a-b) terms. d^2(a,b) = ⟨(a-c+c-b)⋅(a-c+c-b)⟩.

I also got F_3 (a,b;c)=⟨(c-a)⋅(c-b)⟩=⟨(c-b+b-a)⋅(c-b)⟩=⟨(c-b)⋅(c-b)⟩+⟨(b-a)⋅(c-b)⟩=F_2 (b,c)-F_3 (a,c;b), so that

F_3 (a,b;c)+F_3 (a,c;b)=F_2 (b,c)
F_3 (b,c;a)+F_3 (b,a;c)=F_2 (c,a)
F_3 (c,a;b)+F_3 (c,b;a)=F_2 (a,b)

with the last two by cyclic permutations. Adding the 1st two and subtracting the third (just like getting Christoffel symbols from derivatives of the metric tensor):

F_3 (b,a;c)=1/2 (F_2 (b,c)+F_2 (c,a)-F_2 (a,b))

SO - inserting this into the expression for d^2(a,b):

d^2 (a,b)=F_3 (b,c;a)+F_3 (a,c;b)

This seems to me an improvement over the frequently published 1-F_3(a,b;c) with c being some outgroup (Mbuti), computed with outgroup = true. BTW: nene of my F_3's are in the outgroup form...

This leave a couple other questions I had: 1) Should I be using "outgroup" = true? 2) How are these normalized? (They seem a bit odd - not that that would matter to MDS except that I'd hope they were all normalized the same way...)

PS> I'd used the above to compute my d^2's -- seemed to work. PLUS, standard error propagation for sums of F_3's works -- EXCEPT I don't know how these will be correlated, which will impact my estimate. Does the approach you suggest solve that problem?