1. Competition for resources often contributes strongly to defining an organism's ecological niche. Endogenous biological rhythms are important adaptations to the temporal dimension of niches, but how other organisms influence such temporal niches has not been much studied, and the role of competition in particular has been even less examined. We investigated how interspecific competition and intraspecific competition for resources shape an organism's activity rhythms. 2. To do this, we simulated communities of one or two species in an agent‐based model. Individuals in the simulation move according to a circadian activity rhythm and compete for limited resources. Probability of reproduction is proportional to an individual's success in obtaining resources. Offspring may have variance in rhythm parameters, which allow for the population to evolve over time. 3. We demonstrate that when organisms are arrhythmic, one species will always be competitively excluded from the environment, but the existence of activity rhythms allows niche differentiation and indefinite coexistence of the two species. Two species which are initially active at the same phase will differentiate their phase angle of entrainment over time to avoid each other. When only one species is present in an environment, competition within the species strongly selects for niche expansion through arrhythmicity, but the addition of an interspecific competitor facilitates evolution of increased rhythmic amplitude when combined with additional adaptations for temporal specialization. Finally, if individuals preferentially mate with others who are active at similar times of day, then disruptive selection by intraspecific competition can split one population into two reproductively isolated groups separated in activity time. 4. These simulations suggest that biological rhythms are an effective method to temporally differentiate ecological niches and that competition is an important ecological pressure promoting the evolution of rhythms and sleep. This is the first study to use ecological modeling to examine biological rhythms.