The idea that there are any large-scale trends in the evolution of biological organisms is highly controversial. It is commonly believed, for example, that there is a large-scale trend in evolution towards increasing complexity, but empirical and theoretical arguments undermine this belief. Natural selection results in organisms that are well adapted to their local environments, but it is not clear how local adaptation can produce a global trend. In this paper, I present a simple computational model, in which local adaptation to a randomly changing environment results in a global trend towards increasing evolutionary versatility. In this model, for evolutionary versatility to increase without bound, the environment must be highly dynamic. The model also shows that unbounded evolutionary versatility implies an accelerating evolutionary pace. I believe that unbounded increase in evolutionary versatility is a large-scale trend in evolution. I discuss some of the testable predictions about organismal evolution that are suggested by the model.