The trend is to use a combination of tools and strategies to nail down the causal genes and figure out different alleles. All you need to be aware of those tools and strategies and they will help you find your way out when you are stuck.
Take a look at this paper, Parallel domestication of the Shattering1 genes in cereals, at Nature Genetics. It contains the map-based cloning of Sh1, haplotype analysis and association mapping, diverse origins of sorghum, comparative genomics across cereals, rice mutant analysis, and maize high-resolution QTL analysis with GBS markers. You will have to praise either the mother nature or the wisdom of ancient farmers who made this transition from the hunter-gatherer stage to agriculture.
[Question, what do we mean by "parallel"?]
[Answer: first "parallel" is among different species, and second "parallel" is about different domesticated alleles]
Here is another paper from our group, Presence of tannins in sorghum grains is conditioned by different natural alleles of Tannin1, at PNAS. It involves QTL mapping, meta-QTL fine mapping, association mapping, transformation validation with an Arabidopsis mutant, and nucleotide diversity analysis across wild, landraces, and cultivars. More broadly, it involves domestication, natural selection, and health benefit. Technically, you will see the effect of allele frequency in association mapping, and the general direction of the research => “haplotype”.