Biological aging is characterized by an age-dependent increase in the probability of death and by a decrease in the reproductive capacity. Individual age-dependent rates of survival and reproduction have a strong impact on population dynamics, and the genetic elements determining survival and reproduction are under different selective forces throughout an organism lifespan. Here we develop a highly versatile numerical model of genome evolution – both asexual and sexual – for a population of virtual individuals with overlapping generations, where the genetic elements affecting survival and reproduction rate at different life stages are free to evolve due to mutation and selection. Our model recapitulates several emerging properties of natural populations, developing longer reproductive lifespan under stable conditions and shorter survival and reproduction in unstable environments. Faster aging results as the consequence of the reduced strength of purifying selection in more unstable populations, which have large portions of the genome that accumulate detrimental mutations. Unlike sexually reproducing populations under constant resources, asexually reproducing populations fail to develop an age-dependent increase in death rates and decrease in reproduction rates, therefore escaping senescence. Our model provides a powerful in silico framework to simulate how populations and genomes change in the context of biological aging and opens a novel analytical opportunity to characterize how real populations evolve their specific aging dynamics.