The world's major grains are listed on pg. The major producing countries are listed on pg. Populations are variable. They are stable only for a given situation. A change in selection pressure will cause a change in the genetics of the plant involved.
Domestication is an evolutionary process under the influence of man.
Usually a slow process. As long as gatherers only gather, they exert little selective pressure. If anything, they would favor shattering types. This was true for grass harvesting by most of the North American Indians. They bent the grass over and hit the heads with a stick to loosen the grains.