To maintain life across a fluctuating environment, cells alternate between phases of cell division and quiescence. During cell division, the spontaneous mutation rate is expressed as the probability of mutations  per  generation (Luria and Delbrück, 1943; Lea and Coulson, 1949), whereas during quiescence it will be expressed  per  unit of time. In this study, we report that during quiescence, the unicellular haploid fission yeast accumulates mutations as a linear function of time. The novel mutational landscape of quiescence is characterized by insertion/deletion (indels) accumulating as fast as single nucleotide variants (SNVs), and elevated amounts of deletions. When we extended the study to 3 months of quiescence, we confirmed the replication-independent mutational spectrum at the whole-genome level of a clonally aged population and uncovered phenotypic variations that subject the cells to natural selection. Thus, our results support the idea that genomes continuously evolve under two alternating phases that will impact on their size and composition.