Background: Speciation is driven by many different factors. Among those are trade-offs between different ways an organism utilizes resources, and these trade-offs can constrain the manner in which selection can optimize traits. Limited migration among allopatric populations and species interactions can also drive speciation, but here we ask if trade-offs alone are sufficient to drive speciation in the absence of other factors. Results: We present a model to study the effects of trade-offs on specialization and adaptive radiation in asexual organisms based solely on competition for limiting resources, where trade-offs are stronger the greater an organism’s ability to utilize resources. In this model resources are perfectly substitutable, and fitness is derived from the consumption of these resources. The model contains no spatial parameters, and is therefore strictly sympatric. We quantify the degree of specialization by the number of ecotypes evolved and the niche breadth of the population, and observe that these are sensitive to resource influx and trade-offs. Resource influx has a strong effect on the degree of specialization, with a clear transition between minimal diversification at high influx and multiple species evolving at low resource influx. At low resource influx the degree of specialization further depends on the strength of the trade-offs, with more ecotypes evolving the stronger trade-offs are. The specialized organisms persist through negative frequency-dependent selection. In addition, by analyzing one of the evolutionary radiations in greater detail we demonstrate that a single mutation alone is not enough to establish a new ecotype, even though phylogenetic reconstruction identifies that mutation as the branching point. Instead, it takes a series of additional mutations to ensure the stable coexistence of the new ecotype in the background of the existing ones. Conclusions: Trade-offs are sufficient to drive the evolution of specialization in sympatric asexual populations. Without trade-offs to restrain traits, generalists evolve and diversity decreases. The observation that several mutations are required to complete speciation, even when a single mutation creates the new species, highlights the gradual nature of speciation and the importance of phyletic evolution.