Evolutionary game theory (EGT)---overwhelmingly employed today for the study of cooperation in various systems, from microbes to cancer and from insect to human societies---started with the seminal 1973 paper by Maynard Smith and Price showing that limited animal conflict can be selected at the individual level. Owing to the explanatory potential of this paper and enabled by the powerful machinery of the soon-to-be-developed replicator dynamics, EGT took off at an accelerated pace and began to shape expectations across systems and scales. But, even as EGT has expanded its reach, and even as its mathematical foundations expanded with the development of adaptive dynamics and inclusion of stochastic processes, the replicator equation remains, half a century later, its most widely used equation. Owing to its early development and its staying power, the replicator dynamics has helped set both the baseline expectations and the terminology of the field. However, much like the original 1973 paper, replicator dynamics rests on the assumption that individual differences in reproduction are determined only by the payoff from the game (i.e., in isolation, all individuals, regardless of their strategy, have identical intrinsic growth rates). Here, we argue that this assumption limits the scope of replicator dynamics to such an extent as to warrant not just a more deliberative application process, but also a reconsideration of the broad predictions and terminology that it has generated. Simultaneously, we reestablish a dialog with ecology that can be mutually fruitful, e.g., by providing an explanation for how diverse ecological communities can assemble evolutionarily.