Processes generating heterogeneity in genomic divergence are currently a much-debated issue. Initially, all highly divergent regions were attributed due to adaptation or even to "speciation islands". The field has since come to recognize that such heterogeneity even arises in the absence of selection and that many different processes, most of all variation in recombination rate, but also selection against universally deleterious genes (background selection), gene richness and GC content affect divergence landscapes throughout the genome. An additional, fairly recently proposed mechanism, is that incompatibility among alleles in highly variable species arise more often in certain regions of the genome and thereby generate divergence peaks. This idea is theoretically supported and may play a large role for divergence and speciation in general, however, empirical evidence is very scarce. We have generated data to test for the relative roles of incompatibilities and adaptation for genomic divergence between S. dioica and S. latifolia. To detect loci or regions associated with adaptation, we produced ddRAD seq data for recombinant hybrids from an earlier four-year transplant experiment into sites of each species. We are using GWAS on cumulative fitness determined in the transplant experiment (GEMMA). To detect loci associated with environmentally independent incompatibilities we generated ddRADseq data from a series of reciprocal back-crosses. In these crosses, we can detect allelic incompatibilities in the form of transmission biases. Such incompatibilities can arise at various stages, for example, as early as pollen or ovule production, alternatively, during gamete interactions or even shortly after zygote formation. The two datasets, form the transplant experiment and from the crosses, will be informative on their own while the comparisons of the number and genomic location of the loci associated will either adaptation or transmission bias will allow us to assess the relative contribution of incompatibilities or adaptation to genomic divergence. We will assess genomic divergence at loci of interest using further pre-existing ddRADseq data (range-wide population samples) and plan to add more data on an outgroup to be able to analyze which of the alternative alleles has evolved recently. In addition to the above analyses we plan to use a forthcoming reference sequence of our study species together with collaborators to answer simliar research questions and improve and complement our earlier analyses.