AbstractIn plants, most competition is resource competition, where one plant simply preempts the resources away from its neighbors. Interference competition, as the name implies, is a form of direct interference to prevent resource access. Interference competition is common among animals that can physically fight, but in plants, one of the main mechanisms of interference competition is allelopathy. Allelopathic plants release cytotoxic chemicals into the environment which can increase their ability to compete with surrounding organisms for limited resources. The circumstances and conditions favoring the development and maintenance of allelochemicals, however, are not well understood. Particularly, despite the obvious benefits of allelopathy, current data suggest it seems to have only rarely evolved. To gain insight into the cost and benefit of allelopathy, we have developed a matrix game to model the interaction between plants that produce allelochemicals and plants that do not. Production of an allelochemical introduces novel cost associated with both synthesis and detoxifying a toxic chemical but may also convey a competitive advantage. A plant that does not produce an allelochemical will suffer the cost of encountering one. Our model predicts three cases in which the evolutionarily stable strategies are different. In the first, the nonallelopathic plant is a stronger competitor, and not producing allelochemicals is the evolutionarily stable strategy. In the second, the allelopathic plant is the better competitor, and production of allelochemicals is the more beneficial strategy. In the last case, neither is the evolutionarily stable strategy. Instead, there are alternating stable states, depending on whether the allelopathic or nonallelopathic plant arrived first. The generated model reveals circumstances leading to the evolution of allelochemicals and sheds light on utilizing allelochemicals as part of weed management strategies. In particular, the wide region of alternative stable states in most parameterizations, combined with the fact that the absence of allelopathy is likely the ancestral state, provides an elegant answer to the question of why allelopathy seems to rarely evolve despite its obvious benefits. Allelopathic plants can indeed outcompete nonallelopathic plants, but this benefit is simply not great enough to allow them to go to fixation and spread through the population. Thus, most populations would remain purely nonallelopathic.