In Guns, Germs, and Steel, Jared Diamond says that archaeologists can tell when and where agriculture arose by dating evidence of domesticated plants and animals. This information can be tricky when trying to determine where agriculture first arose, however, because it is not always the case that those animals and plants were first domesticated in the location they were found. In Egypt, for example, the archaeological evidence shows that farming was gradually adopted, which he interprets to mean that they adopted certain agricultural practices from their neighbors rather than inventing them by themselves. In areas where the archaeological record is complete, scientists can actually trace the physical changes in species of plants and animals as they became domesticated:
Most domesticated plant and animal species differ morphologically from their wild ancestors: for example, in the smaller size of domestic cattle and sheep, the larger size of domestic chickens and apples, the thinner and smoother seed coats of domestic peas, and the corkscrew-twisted rather than scimitar-shaped horns of domestic goats. Hence remains of domesticated plants and animals...can be recognized and provide strong evidence of food production at that place and time...
Further, scientists can determine where plants and animals were first domesticated by looking at the genetic record, which can, along with understanding the range of the wild species, determine when and where they diverged from their wild ancestors. Diamond lists five locations where it is certain that people invented agriculture separately (though, it should be noted, some archaeologists disagree.) They are the Fertile Crescent, China, Mexico, the Andes, and Eastern North America. The African Sahel, West Africa, Ethiopia, and New Guinea are also candidates, but less evidence exists.