In Hinduism's beliefs about re-incarnation or more aptly the 'transmigration of souls' people's souls can go into rocks and and animals after death if they have not lived a good/holy live.

So you could say that people's souls were being stored into other animals or even the earth. So really there was no theological problem.

I don't have any page references but the above appears in the Bhagavad Gita and the Uppanishads.

As a disclaimer, no answer to a theological question like this can hope to fully encompass all faiths and interpretations of scripture. I will confine myself to Buddhism; however, please bear in mind I am only giving one possible interpretation of one scripture of that faith.

I take your question as assuming that all souls must, instantly, be converted into a new life. There is no reason that this need be the case. Indeed, the Buddha himself taught that there exist an “infinite, unfathomable number of souls” which hardly corresponds to the population at this or any other time. So the present human population cannot be assumed to have any correlation whatsoever to a “maximum” number of souls, after which more must be created.

However, this all glosses over the main issue. The Buddha taught his followers:

"All living beings, whether born from eggs, from the womb, from moisture, or spontaneously; whether they have form or do not have form; whether they are aware or unaware, whether they are not aware or not unaware, all living beings will eventually be led by me to the final Nirvana, the final ending of the cycle of birth and death. And when this unfathomable, infinite number of living beings have all been liberated, in truth not even a single being has actually been liberated."

The concluding line seems a paradox; it is in fact one of Buddhism’s most profound doctrines. For,

“if a disciple still clings to the arbitrary illusions of form or phenomena such as an ego, a personality, a self, a separate person, or a universal self existing eternally, then that person is not an authentic disciple."

A true disciple of the Buddha cannot speak of any number of beings, since such beings would exist in and of themselves. Thus, the concept of numbering souls to keep up with population growth becomes absurd. The dilemma simply does not exist.

This doctrine is known as anatman as opposed to atman. Both of my quotations come from the Buddhist scripture commonly referred to as the Diamond Sutra. If you are interested, the scripture is beautiful, fairly brief, and available for free online. If you want an hard copy, Thich Nhat Hahn’s The Diamond that Cuts through Illusion provides both the text and Hahn’s very readable commentary.

Source: The Diamond Sutra Chapter 3