It is a great pleasure to be part of the celebration of Nitant Kenkre's scientific career. In this paper, we review mathematical models for studying evolutionary branching and diversification in biology. We highlight insights provided by Nitant Kenkre's work in the early 2000s as part of the Consortium of the Americas for Interdisciplinary Science. We focus on the use of these models for understanding the conditions that promote phenotypic diversification and innovation in biological systems, understood as the branching of stationary solutions, and some of the ideas that emerged as part of the research Consortium. We highlight recent developments and applications of stochastic, nonlocal partial derivative formalisms.