We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate analytic solution and also by numerical simulation, and use it to make predictions about the distribution of extinctions and species lifetimes that we would expect to see in real ecosystems. It should be possible to test these predictions against the fossil record. The model indicates that a possible mechanism for mass extinction is the coincidence of a large coevolutionary avalanche in the ecosystem with a severe environmental disturbance.