F3 test detect somewhat ancient gene flow

Dear @bumblenick

I have both wild and domesticated populations. From the analysis of inferred ancestral components (using admixture software), I found some wild individuals contained domesticate components (about 50%). So I want to use the three-population test to test whether these individuals have gene flow from the domesticated populations. But the results are all non-negative, meanwhile, I also do this at the individual level, the results are same as the population level. But from the results, I can see the f_3 values for these admixtured individuals (SRR1576679,BS1,ERR340348) are smaller than the unadmixtured individuals (ERR340329,ERR340333,ERR340335,ERR340341) when do analysis at individual level. I guess this admixture event may be ancient (about several thousands generations ago). So I want to know can I get some more information from the following results when the f_3 value is non-negative and can three-population test detect ancient gene flow? Thanks.

snps: 16016002
Source 1 Source 2 Target f_3 std. err Z SNPs
result: ERR340334 A14 BS1 0.079671 0.005448 14.624 12914067
result: ERR340334 A14 ERR340329 0.602950 0.036776 16.395 13012058
result: ERR340334 A14 ERR340333 0.404647 0.025341 15.968 13052431
result: ERR340334 A14 ERR340335 0.334453 0.020576 16.255 13053033
result: ERR340334 A14 ERR340341 0.487972 0.026363 18.510 12994993
result: ERR340334 A14 ERR340348 0.106602 0.006818 15.636 12944510
result: ERR340334 A14 SRR1576679 0.084376 0.004683 18.016 12857869

Best
Zhuqing

Start with the reported three-population test results and the AdmixTools behavior they describe; the issue names no source files, tests, or entry points. Determine whether the non-negative f3 values indicate a defect or expected behavior, and document a clear explanation or reproducible next step.