Evolvability is the capacity of a population to generate heritable variation that can be acted upon by natural selection. This ability influences the adaptations and fitness of individual organisms. By viewing this capacity as a trait, evolvability is subject to natural selection and thus plays a critical role in eco‐evolutionary dynamics. Understanding this role provides insight into how species respond to changes in their environment and how species coexistence can arise and be maintained. Here, we create a G‐function model of competing species, each with a different evolvability. We analyze population and strategy (= heritable phenotype) dynamics of the two populations under clade initiation (when species are introduced into a population), evolutionary tracking (constant, small changes in the environment), adaptive radiation (availability of multiple ecological niches), and evolutionary rescue (extreme environmental disturbances). We find that when species are far from an eco‐evolutionary equilibrium, faster‐evolving species reach higher population sizes, and when species are close to an equilibrium, slower‐evolving species are more successful. Frequent, minor environmental changes promote the extinction of species with small population sizes, regardless of their evolvability. When several niches are available for a species to occupy, coexistence is possible, though slower‐evolving species perform slightly better than faster‐evolving ones due to the well‐recognized inherent cost of evolvability. Finally, disrupting the environment at intermediate frequencies can result in coexistence with cyclical population dynamics of species with different rates of evolution.