Innovation, competition, diversification: a tree form dynamics of long-term development

This paper provides an individual-based foundation for the logistic and Lotka-Volterra equations which describe the diffusion of an innovation or the competition between old and new alternatives, then presents two extensions of this basic model. First, it extends the short-term competition to a long-term process characterized by a sequence of innovations and substitutions. Next, by allowing the substitutions to be incomplete, it extends the unidimensional process to a tree-form multidimensional one featuring diversification throughout the long-term development.