Population bottlenecks are stochastic events that strongly condition the structure and evolution of natural populations. Their effects are readily observable in highly heterogeneous populations, such as RNA viruses, since bottlenecks cause a fast accumulation of mutations. Considering that most mutations are deleterious, it was predicted that the frequent application of bottlenecks would yield a population unable to replicate. However, in vitro as well as in vivo systems evolving through bottlenecks present a remarkable resistance to extinction. This observation reveals the robustness of RNA viruses and points to the existence of internal mechanisms which must confer a high degree of adaptability to fast mutating populations. In this contribution, we review experimental observations regarding the survival of RNA viruses, both in laboratory experiments and in natural populations. By means of a simple theoretical model of evolution which incorporates strong reductions of the population size, we explore the relationship between the number of replication rounds that a single founder particle undergoes before the next bottleneck is applied, and the mutation rate in a particular environment. Our numerical results reveal that the mutation rate has evolved in a concerted way with the degree of optimization achieved by the population originated from the founder particle. We hypothesize that this mechanism generates a mutation-selection equilibrium in natural populations that maximizes adaptability while maintaining their structure.