Does a mathematical model in which reproduction eventually falls below doubling disprove the law of doubling?

No. The law of doubling holds in principle, not down to the last detail. The fact that it eventually weakens serves the same purpose as the law itself: the survival and balance of species.

The model describes something true. When a species divides, one half is often stronger than the other. Some die, others mix with different lines. So in the end not everything doubles exactly, and a smaller factor remains. But this does not contradict the law. It only shows that the law is a general principle and does not apply mathematically down to the finest detail.

Without the principle of doubling, life would have come to a halt somewhere in the distant past. The rapid development we see in the history of life could not have taken place. Doubling secures the survival of species.

But if the law worked completely and without limits, the earth would long ago have been overcrowded. Even our own bodies would be so full of bacteria that survival itself would be endangered. So the weakening of the law also makes sense. It serves the same purpose as the law itself.

Together the two create a balance. Growth and limitation work hand in hand. The verses above say that God has created everything in due measure and causes everything to grow in the right proportion. A new model that describes this measure more precisely therefore disproves nothing. If anything, it shows how finely balanced this order is.