A three-state, discrete-time Markov chain is used to model the dynamics of energy flow in a tri-trophic food web. The distribution of energy in the three trophic levels is related to the rates of flow between the trophic levels and calculated for the entire range of possible flow values. These distributions are then analysed for stability and used to test the idea that plants are resource-limited and herbivores are predation-limited. Low rates of death and decomposition, when coupled with low rates of herbivory and carnivory, tend to destabilize this food web. Food webs with higher rates of death and decomposition are relatively more stable regardless of rates of herbivory and carnivory. Plants are more prone to resource-limitation and herbivores are, in general, limited by their predators, which supports Hairston et al. (Am. Nat. 94 (1960) 421). The rate of decomposition often mediates the roles of top-down and bottom-up control of energy flow in the food web.