Can the sums possibly add up to provide evidence for the transmigration of souls?
According to the latest evidence the number of people who have ever lived on earth is > 100 billion ( > 0.1 trillion!). The number living today is 6-7 billion. Going back about 20 years there was a study which suggested that there are more people alive today than have ever existed before. I remember a christian priest appearing on TV to claim that this was proof enough that reincarnation could not take place.
Clearly the population trend from say 2000 years ago is one of expansion, so where do souls come from in the first place? The only 'evidence' for reincarnation lies in the brainwashing of people by some religions, as about half the world's population appear to believe in this.
The soul of Adam would still be alive in a body today, unless it has been liberated somewhere along the generations.