Buddha explains concept of “transmigration”

Buddha says:

“Like everything else in nature, the life of man is subject to the law of cause and effect. The present reaps what the past has sown, and the future is the product of the present. But there is no evidence of the existence of an immutable ego-being, of a self which remains the same and migrates from body to body. There is rebirth but no transmigration.” 15

“Is not this individuality of mine a combination, material as well as mental? Is it not made up of qualities that sprang into being by a gradual evolution? The five roots of sense-perception in this organism have come from ancestors who performed these functions. The ideas which I think came to me partly from others who thought them, and partly they rise from
combinations of the ideas in my own mind. Those who have used the same sense-organs, and have thought the same ideas before I was composed into this individuality of mine are my previous existences; they are my ancestors as much as the I of yesterday is the father of the I of to-day, and the karma of my past deeds conditions the fate of my present existence.” 16

http://www.arthursbookshelf.com/Buddhism/The%20Gospel%20of%20Buddha%20-%20Paul%20Carus.pdf

Paarsurrey says:

So Buddha’s concept of transmigration is different from what Hindus believe or the Buddhists of different denominations believe perhaps influenced by some Hindus at some point of time in the pase. Buddha believes transmigration not after the end of one’s life but in one’s own life,as one progress from one stage to another stage from the basic savage human being to the the ethical, moral and spiritual higher forms , such stages could be denoted in symbols resembling to the animals on ones vertical evolution.