God's people are represented as the olive branches in Romans 11. That particular tree has significance throughout the bible. In the Mediterranean and a few other places it grows naturally. As such it grew wild in those lands. It's oil is still one of the three main ingredients in the food of that area, along with grape and wheat.
Scripture says that Jesus is the true vine. Any vine thereon which does not bear fruit God is cut off. (John 15:1). Wheat represents mankind. It can either be good seed or bad, and it can either bear fruit or not. (John 12:24). And then we have the fruit of the olive tree. It's branches represent God's chosen people. Paradise (Canaanland) was promised to be naturally the Hebrews because God made a covenant with Abraham. From his tree a seed would grow to save the world. That seed was to produce God in the flesh who was called Jesus, Joshua in Hebrew, which means "deliverer". Abraham knew that God spoke both of the land of milk and honey and Heaven itself!
Joshua in the Old Testament was a deliverer. His name even meant that. Joshua was born to deliver. Moses led the Hebrew people out of the wilderness, but it was Joshua who delivered them to the promised land. Joshua was the seed of Abraham just as Jesus is. (I use the present tense because Jesus IS - he is eternal). You see, everything has always been about Jesus. God had one plan for the salvation of mankind, and it was always Jesus and salvation by grace. God didn't need a Plan B because of his power and foreknowledge.
The Tree of Life in the Garden of Eden bore fruit. We know it was twelve spiritual fruits, but we were never informed what it's natural fruit was. It makes sense that the natural growing olive tree represents the supernatural God in his natural form - the flesh. That is a rational thought because of the agony of Jesus in the Garden of Gethsemane before he died. Therein still grows the oldest olive trees in the world. It has been verified that some olive trees alive today are 2000 years old (Wikipedia). Perhaps, when Jesus was at Gethsemane some of the same trees with him in the Garden of Eden were still extant. Indeed, the Garden of Eden may have had at it's center what became Gethsemane. (See my commentary on this hypothesis at http://kentuckyherrin.blogspot.com/2017/06/the-garden-of-eden-jerusalem.html). It makes sense that Jesus would come home to prepare for his own death. I say this because the Tree of Life represents Jesus Christ. He existed in Paradise on earth, and still does in the heavenly Paradise, It seems logical that his cup was emptied in Paradise where he sweated as if his own blood.
It is no coincidence that Gethsemane means "pressed out", and the oil of the olive was pressed out, just as Jesus's own water was pressed from his body. The Olive Tree is a very likely candidate for the physical tree of life, just as Jesus is for the spiritual Tree.
Paul uses the olive branches analogy in Romans 11 to represent the Hebrew people who are naturally God's. Those Hebrews who believed in Jesus in ancient times were those olive branches in the analogy. Of course the mystery of God of which Paul spoke meant that salvation was never by works but always by grace. As such the grounded and faithful Hebrew people were Christians before Christ came. They had faith that he would die for their sins. Abraham followed the Word on Mt. Moriah (Calvary), and that Word was Jesus (John 1). Abraham even mimicked God in his willingness to do what God would do with his own Son! Never forget that mankind were Christians from the creation! It was the Voice of Jesus who spoke to Adam way back in the cool of the evening.
With the branches of the olive tree which failed to be fruitful, those limbs were cut off, and new ones grafted onto the tree. It would appear that the limbs of the tree were the specific symbol of the Hebrews, the ones grafted on - the Gentiles, but the tree itself was representative of Jesus. The sap of the olive tree represents his blood which he sweated out at Gethsemane. God is the root from which the Tree grew. (See my blog on the mystery and the Tree of Life at http://kentuckyherrin.blogspot.com/2014/08/the-mysteryand-low-hanging-fruit.html). I also believe that the Tree of Life, not only was representative of Jesus but also the cross: http://kentuckyherrin.blogspot.com/2013/10/whatever-happened-to-tree-of-life.html).
Adam was not only the forebear of the Jews but all mankind. As the Hebrew people were condemned to die because of Adam, the Gentiles were as well. The mystery of God was that grace was the way to salvation, but that it was for all mankind! (See http://kentuckyherrin.blogspot.com/2015/11/the-mystery-of-god-mystery-of-christ.html). Romans 11 is Paul relating the mystery of God to the Romans. At that moment, it was revealed by Paul that Jesus didn't come just to save the Jews but them as well. JHVH was no longer the invisible Hebrew God but the visible God of all! At the moment Paul related this, it was revealed to the world that Jesus died for all! This Gentile born in little Shopville, Kentucky, was born-again in Clayton, Indiana, and of the same everlasting covenant as was Abraham!