The food hearth theory of Nikolai Vavilov is obviously outdated. In searching for later insights I stumbled on the Dictionary of cultivated plants and their centres of diversity (1975) by a student of Vavilov, PM Zhukovsky together with AC Seven. The book lists domesticated plants (for food as well as fodder, industrial and medicinal uses) using a centers of origin list expanded on that suggested by Vavilov. The differences can be seen above, for South America three centers are contracted into one, the Chinese center incorporates Japan, the Ethiopian center has disappeared in a vast African one and Australian, North-American and Euro-Siberian centers are added.
The entire Vavilovian system came under criticism from JR Harlan who in Agricultural Origins: Centers and Noncenters (1971) argues for three separate origins of agriculture and three non-centers (spanning 5000 to 10.000 km) where domestication took places in dispersed areas. Resulting in the map below. Note that the three temperate climate centers (Mexico, Near East China) are all matched by a tropical non center, and that the three centers are all thought to have independently developed writing. Very Neat.