I don't know what the fruit of sycamore trees might be – I only know the ones with seeds that we used to spin like helicopter blades when kids. Fruit was absent. However, sycamores introduced into the Levant did bear fruit of some kind and they were introduced by the Philistines – or that is the claim of a team of Israeili researchers and archaeologists – go to http://phys.org/print359978639.html
They examine Bronze and Iron Age sites in the southern Levant, both Philistines and non-Philistines, and came up with the claim they introduced three plants – the sycamore tree (from the eastern Mediterranean), cumin (also from the eastern Mediterranean and not native to the Levant) and the opium Poppy (which is said to have an origin in western Europe). The point being made is that the three plants chosen have different points of origin which may reflect a diverse origin of the Philistines themselves, such as the Aegean region, Anatolia, and Cyprus (which was already known but here it is given some biological props). They eventually disappeared as a distinct group by 600BC which is probably due to hybridisation with native Canaanites.
One animal, also hybridised, did not disappear, and that is the European pig (which mixed with local pig breeds led to even wild pigs becoming more like European pigs than Near Eastern breeds. Pigs do actually live in the wild in the Near East, solely because they are not eaten due to religious reasons. The Philistines liked their pigs.