WI: Limited Columbian Exhange in Antiquity

Assume a limited contact between Mediterranean/West Africa and the New World. It could be so limited that no reliable records are maintained. A few brave Carthaginians make it across the Atlantic and back, or whatever floats your boat. We'll assume a time frame of anywhere between, say, the death of Alexander and the fall of the Western Empire. Again, whatever works. This is short-term contact, a few trading missions that, while successful, eventually cease for whatever reason.

The important part is the exchange of, at minimum: major cereal crops such as maize and wheat, and old world domesticated animals such as cattle, horses, and pigs. Other crops and animals can be included as plausiblity allows. Assume limited enough contact to preclude major epidemics immeaditely (though animal domestication may allow for future local epidemics to start in the New World).

After contact is re-lost, what broad strokes might you see occuring in both hemispheres?
 
For reasons lost to history Ramses II of Egypt was buried with tobacco and one of his ladies-in-waiting had nicotine and cocaine in her hair shafts [both New World products] .This means there's a good possibility that there may have very brief exchange between Egypt and the New World millennia before Columbus OR these items just kept being passed from one outpost to another until they made it Egypt where they were consumed.
 
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