There really is no standard way to report STRUCTURE results, unfortunately. Many people expect the delta K statistic from Evanno. The key for delta K is that you need multiple iterations of each K value and runs across multiple K values. The method to calculate the statistic assumes there are multiple runs per K value to calculate a standard deviation. The parameter settings (e.g. MCMC reps, burn-in, model choice) need to be the same across those runs. Even when these settings are consistent there is still variability in the analysis, hence the development of the delta K statistic.

Because of this variability, it is important to report on how much variation there is across STRUCTURE runs. Often it is assumed that less variability for a K value means it is a stronger biological pattern. It is important to provide the biological context as well: don't interpret the barplot at face-value, make sure it makes sense with what you know about the system. I think it is wise to complement a STRUCTURE analysis with something like a PCA or NJ tree tom provide an additional perspective.

I echo all of Justin's thoughts and would also add that the Evanno method isn't always the best at identifying the uppermost hierarchical level of structure if sampling is uneven across groups (Puechmaille 2016; see link). I've had more luck obtaining sensible K values with the Puechmaille "supervised" estimators. Different methods will of course yield slightly different answers sometimes, so default to what makes sense given your system and species. Article The program STRUCTURE does not reliably recover the correct ...

I agree with both comments above. Without having testing multiple K values you cannot assess delta K, but any way Evanno's approach is not a silver bullet.

The first question you need to ask yourself is whether you absolutely need to find a best K. Eventually each K tested may have its own interest...

If anyway you really want to assess a best K, you can of course use Evanno approach but it is very sensible to outliers. Alternatively you can always show in a graph the evolution of you lnP across different runs and K. I also agree with Justin than it is as important to assess if your different runs provide similar pictures (you may use eventually software like Clumpp for this).

The K-value is fit by running structure across a number of possible k-values. If you only use one k-value (seems you only did K=2) then it will not be able to calculate delta K. You do need to run the k-values from 1 through some number usually 8 or so - depends on the size of your study system. It seems that you have 6 groups or sites tested, so this would be the smallest maximum K-value to test. Then you will see the delta K come up in harvester b/c delta K is calculated on the difference between loglik at k and k+1 with a penalty for increased variance that arises when the program "over-clusters". You can run a pre-determined K=2, but only if you are making a specific test on this question and you don't have reason to believe there is other genetic structure.

I have used the structure output (log lik with variance among iterations) and delta K to support a conclusion. Structure is difficult b/c there are user-defined values (like K) and biases ( like sample size) that can cause issues. I've also used a second method like K-means analysis to support the conclusion based on structure. I would put my trust in this order: 1) structure output; 2) k-means; 3) delta K. Prichard et al. (2010) manual for the revised structure program describes in detail how to ask questions about K and interpret the output (available on their website).

I have found a 10k burn in and 100k iterations as sufficient for my data sets. I do a minimum of 10 runs per K-value. I tested a recent data set for sample size bias based on Puechmeille et al. study, but did not find it to be a problem in that data set. If you sampled fairly evenly and representatively across groups then it should not be a problem.

Thank you all for the answers,

Dear Dana, of course I have run K=1-10 (only put here the best picture for myself). Once also tried K=30 :-) Several different run-burnin and K value i have tried...

K3 and K 4 are attached but i guess they do not seems pretty well descript my sample structure. May be K=3... What do you think?

Thanks

Just eye-balling the results you just provided, I would guess that the Puechemaille estimators (and other methods) would point to K=2, because at K=3 or higher, you have sites 1-5 sharing approximately equal proportions of different clusters. Meaningful population signals beyond K=2 would result if at least one of your sites shared a majority genomic proportion to each cluster; otherwise, these equally-assigned clusters are spurious and do not add much to the interpretation.

If you are interested in trying to delineate "weak" population signals, you might try using your sampling locations as model priors ('locprior' option) in the admixture model. The Structure User Guide goes into good detail on why one might want to do this and how to adjust settings.

i want to see the loglik plot with variance. Interesting data. K4 is over-clustering. I would try running sites 1-5 to see what happens. Looks like the data patterns are consistent and k2 is the cleanest.

What I'm missing here is your underlying question. What are you trying to find out? Maybe Structure isn't the best way to go forward.

In my opinion, Structure is one of the most misused softwares in the history of population genetics. It suffers from high type 2 errors, and (like any other clustering method) fails to catch any hierarchical population structure that may be present. The results are also not a proof of anything, they are IMHO merely a hypothesis of population structure. So it should only be used for data-exploration. But for data-exploration there are easier and better options, like PCA, DAPC, ...

Dear Türker, It would be as a result of the limited numbers of used microsattellites or the same PICs for the used primers. What about the migration rate among your populations? Although you found K=2, the populations did not distinctly separate and the first figure seems like a result of admixed populations. It would be better to see the log graph. You can check it via Structure Harvester.