Cool, a question I can answer! You asked specifically about fruits and vegetables. The other now-removed post talked about two North American fruits that are not widely consumed anymore (even if they were never really crops in that they weren't `domesticated' under most definitions of the term---just employed in foraged and horticultural settings), but I do take some issue with their response for the broader general question. Unless they are including Mexico and Central America in their definition of South America, the assertion that so few fruits and vegetables originated elsewhere is not accurate. Mesoamerican domesticates include corn, tomatillos, squash, prickly pears, agave (check your liquor and sweetener aisle), vanilla, peppers, avocado, jicama, guava, beans, and if we're a little looser with Mesoamerica's southern boundary, we can add cacao, sweet pumpkin, and manioc. Strawberries and most compound berries are also North American.
To really get at your question of `lost crops' though, we have to look more towards seed crops---i.e. grains, and pseudograins. You'll notice that of the most important grains in modern economic and culinary terms, only maize comes from the New World. The rest (wheat, oats, barley, rice, millet, oats) are all from the Old World. But ancient Mesoamericans had four other grain-like crops at their disposal---two species of amaranth (Amaranthus hypocondriacus and A. cruentus), goosefoot, and chia. In South America, they had their own species of amaranth (A. caudatus), plus quinoa which has survived until today. In North America, they used goosefoot, sunflower seeds, erect knotweed, marsh elder, and maygrass before maize came in and likely supplanted some of them during the Late Woodland period.
But the question remains... why were some crops abandoned in favor of others? I can't speak at length for most of these particular crops, but I can speak at length about one in particular---Amaranth, particularly the one grown in Central Highland Mexico (A. hypocondriacus). I also touch on how Ancient Mesoamericans relied on plants we'd today call 'weeds'. Some of these lost crops are today considered weeds, and in a monocrop-intensive agricultural system like the one we inherited from Europeans these are to be avoided. Thus, at least one reason why some of the crops were lost is because they've never really been planted in extensive settings and are difficult to maximize yields under monocropping systems.
The following is an excerpt from my dissertation---due next Friday from which I am procrastinating. Part of the argument I'm trying to make in this chapter is that scholars have paid too much attention to maize, and haven't done enough to consider lost crops such as the ones you're asking about.:
Although ethnohistoric data from just before conquest suggests that amaranth production was an major subsistence activity in Prehispanic times, it had nearly dwindled out of existence by the mid-twentieth century. The Aztec tribute lists in the Codex Mendoza mention that the Triple Alliance demanded a tribute in amaranth approximately equal to that in maize (Mohar Bettancourt 1976; Berdan and Anawalt 1996). Besides its importance in resource provisioning, amaranth also played an important role in the ritual economy. At the trecena festivals held at the beginning of each month, the Aztec would create statues of their god Huitzilopochtli out of popped amaranth seed glued with concentrated maguey sap. The statue would then be consumed by the festival participants at the end of the rituals (Broda, Montúfar López 2013). It is quite likely that this ancient important ritual is the reason why amaranth is so scarce today.
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