Ribosomal DNA (rDNA) is the genetic loci that encodes rRNA in eukaryotes. It is typically arranged as tandem repeats that vary in copy number within the same species. We have recently shown that rDNA repeats copy number in the yeast Saccharomyces cerevisiae is controlled by cell volume via a feedback circuit that senses cell volume by means of the concentration of the free upstream activator factor (UAF). The UAF strongly binds the rDNA gene promoter, but is also able to repress SIR2 deacetylase gene transcription that, in turn, represses rDNA amplification. In this way, the cells with a smaller DNA copy number than what is optimal evolve to increase that copy number until they reach a number that sequestrates free UAF and provokes SIR2 derepression that, in turn, blocks rDNA amplification. Here we propose a mathematical model to show that this evolutionary process can amplify rDNA repeats independently of the selective advantage of yeast cells having bigger or smaller rDNA copy numbers. We test several variants of this process and show that it can explain the observed experimental results independently of natural selection. These results predict that an autoregulated feedback circuit may, in some instances, drive to non Darwinian deterministic evolution for a limited time period.