John 15

In parable, the Savior taught his disciples -

"I AM the true vine, and my Father is the husbandman." (New Testament John 15:1)

And of his disciples he taught -

"Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit." (New Testament John 15:2)

Which purging he explains -

"Now ye are clean through the word which I have spoken unto you." (New Testament John 15:3)

The Savior makes it perfectly clear that the branch depends upon the vine to bring forth fruit, saying -

"Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.
5 I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing." (New Testament John 15:4 - 5)

Those that refuse to depend or "abide in the vine" -

"...he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned." (New Testament John 15:6)

But those who truly "abide in the vine" -

"If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you.
8 Herein is my Father glorified, that ye bear much fruit; so shall ye be my disciples." (New Testament John 15:7 - 8)

It is clear that the branches are dependent upon the vine, not vice versa. Branches grow out of the vine. The branch cannot survive on its own. As the Savior reminds us -

"Ye have not chosen me, but I have chosen you, and ordained you, that ye should go and bring forth fruit, and that your fruit should remain: that whatsoever ye shall ask of the Father in my name, he may give it you." (New Testament John 15:16)

President John Taylor wrote -

“As a Saint you say, ‘I think I understand my duty, and I am doing very well.’ That may be so. You see the little twig: it is green; it flourishes and is the very picture of life. It bears its part and proportion in the tree, and is connected with the stem, branches, and root. But could the tree live without it? Yes, it could. It need not boast itself and get uplifted and say, ‘How green I am! and how I flourish! and what a healthy position I am in! How well I am doing! and I am in my proper place and am doing right.’ But could you do without the root? No: you bear your proper part and position in the tree. Just so with this people. When they are doing their part—when they are magnifying their calling, living their religion, and walking in obedience to the Spirit of the Lord, they have a portion of his Spirit given to them to profit withal. And while they are humble, faithful, diligent, and observe the laws and commandments of God, they stand in their proper position on the tree: they are flourishing; the buds, blossoms, leaves, and everything about them are all right, and they form a part and parcel of the tree. . . .” (John Taylor in JD, 6:108.)

As members of the Church, if we do receive constant nourishment and strength that comes from the Savior, through his words and his atonement, by the power and guidance of the Holy Ghost, we will wilt and dry and will eventually fall from the vine.