▪ Abstract  Computer models are used to mimic the early evolution of ancient vascular plants (tracheophytes). These models have three components: (a) an N-dimensional domain of all mathematically conceivable ancient morphologies (a morphospace); (b) a numerical assessment of the ability (fitness) of each morphology to intercept light, maintain mechanical stability, conserve water, and produce and disperse spores; and (c) an algorithm that searches the morphospace for successively more fit variants (an adaptive walk). Beginning with the most ancient known plant form, evolution is simulated by locating neighboring morphologies that progressively perform one or more tasks more efficiently. The resulting simulated adaptive walks indicate that early tracheophyte evolution involved optimizing the performance of many tasks simultaneously rather than maximizing the performance of one or only a few tasks individually, and that the requirement for optimization accelerated the tempo of morphological evolution in the Silurian and Devonian.