Mutations in plants helped farmers to domesticate wild crops. Some crops, such as wheat, had evolved to drop their seeds and so reproduce, but farmers harvested and replanted the mutation of wheat that kept its seeds in the air; the result was that the mutated wheat became the dominant species. Diamond comments that:
If one carries out such a genetic analysis for major ancient New World crops many of them prove to include two or more of those alternative wild variants, or two or more of those alternative transforming mutations.
(Diamond, Guns, Germs, and Steel, Google Books)
By examining the mutations that are unique to domesticated crops, agriculturalists can see how those mutations were spread around the world; some wild plants without the mutations still exist, and so it can be estimated both how long ago the mutation was adopted, and how far it spread by human interference. Non-indigenous plants were carried to new areas and planted by farmers, and they became indigenous through this activity; therefore, the study of domesticated plants versus wild plants shows how farmers exploited mutation to create new crops.
One place to find the answer to this is in Chapter 7. In that chapter (starting on p. 121 in the paperback edition), Diamond explains why mutations are important in agriculture. He says that there were many plants that were not very useful to humans until they mutated. They might have developed mutations for smaller or larger seeds, for example. They might also have mutated so that they could fertilize themselves. Both of these types of mutations could be very helpful.
When these mutations arose, farmers would select those plants and plant more of them. The mutant plant, then, would become more common in a given area. Archaeologists can then look to see when that sort of mutant plant first appeared in different areas. By looking at this, they can see how agriculture spread because they assume that the mutation was spread through agriculture.
You can also find more about this in chapter ten, where it talks about the significance of different mutations and variations in more detail, explaining why they can be used to trace the spread of agriculture. It starts on p.176 in the paperback.
At the start of agriculture, wild wheat seed was able to plant itself by virtue of its shape...but it didn't have the yield nor nutrition of what the mutated seeds had, the farmed seeds. And the mutated seeds didn't have the ability to fall to the earth and plant themselves like their wild cousin...it required manual labor to plant the farm seed.