Wild olive trees grow throughout the island and they produce perfectly tiny olives with a thin and bitter skin. However, though the oil from wild olives is supposedly superior to that of domesticated varieties, the yield is much, much lower. And so the grafting game begins. Wild olive trees grow throughout the island and they produce perfectly tiny olives with a thin and bitter skin. However, though the oil from wild olives is supposedly superior to that of domesticated varieties, the yield is much, much lower. And so the grafting game begins.