Over thousand years historians have debated why Rome fell. Some look at culture, some at economy and others at biology. Perhaps they are all right.
All agree that morals weakened. Family values were gradually abandoned especially in the White upper classes. This lead to the fall in the birth rate.
Then there was immigration from the south and naturally they had higher average birth rate. This naturally led to a change in the racial composition of Rome and Greece.
At the same time the currency was inflated and prices were regulated. This obviously destroyed the economy and led to the economic disintegration of the empire. On the other hand this might have been a blessing since that led to the Germanic invasions which invogarated the gene pool. This was coumpounded by the fact that for hundred of years the birth rate of the Germanic invaders was higher. Especially France, England and North Italy became Germanized again.