The "survival of the fittest" is the paradigm of Darwinian evolution in which the best-adapted replicators are favored by natural selection. However, at high mutation rates, the fittest organisms are not necessarily the fastest replicators but rather are those that show the greatest robustness against deleterious mutational effects, even at the cost of a low replication rate. This scenario, dubbed the "survival of the flattest", has so far only been shown to operate in digital organisms. We show that "survival of the flattest" can also occur in biological entities by analyzing the outcome of competition between two viroid species coinfecting the same plant. Under optimal growth conditions, a viroid species characterized by fast population growth and genetic homogeneity outcompeted a viroid species with slow population growth and a high degree of variation. In contrast, the slow-growth species was able to outcompete the fast species when the mutation rate was increased. These experimental results were supported by an in silico model of competing viroid quasispecies.