The most common approach for this purpose is the one developed by:

EVANNO, G., S. REGNAUT, and J. GOUDET. 2005. Detecting the number of clusters of individuals using the software structure: a simulation study. Molecular Ecology 14(8): 2611–2620.

Or the link to the paper:

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-294X.2005.02553.x/full

Good luck

As a general rule, independently of the specific software used, such kinds of analysis model the probability of K given the genotypes and return a probability for each individual to belong to each of K clusters. Approaches to find the best value of K, therefore, can be based either on attempting to maximize P(K|G) or, using individual genotype probabilities, on minimising the prediction error in a cross-validation scheme.

I am not sure about the software STRUCTURE, but ADMIXTURE (https://www.genetics.ucla.edu/software/admixture/) implements a nice cross-validation feature that allows -together with the number of iterations to convergence- to determine the value of K that best fit the data.

Dear Gregor,

As far as I understand your question, you have analyzed 189 SNP markers in 189 individuals derived from crossing between 11 parents, I think before getting started with STRUCTURE analysis, you should first assess mixing within loci. Good mixing across loci produces linkage equilibrium. If you find linkage disequilibrium in a sample, it means the individuals are not drawn from a single well-mixed population and there must be population substructure in your sample. In this case you should proceed with STRUCTURE analysis or any other Bayesian clustering programs such as BAPS (yielding better resolution than STRUCTURE) to identify clusters within the analysed sample. Since the 189 individuals are not sampled from natural populations, but are instead produced by a cross sourced from different progenitors, I think you should consider K from 1 to 10 given that the progeny (189 lines) are the only ones included in the analysis.

I hope this would help, good luck!

You should use the Evanno method from Evanno et a. (2005). A very easy way to do it is using the program STRUCTURE HARVESTER. Here is the citation:

Earl DA, VonHoldt BM. 2011. Structure Harvester: a website and program for visualizing  STRUCTURE output and implementing the Evanno method. Conservation Genetic Resources 4, 459-461.

Good luck!