Understanding how the contents of university mathematics education (UME) came to be what they currently are, as well as how they evolve (or are submitted to inertia) under various sorts of institutional conditions and constraints is an endeavor undertaken by the Anthropological Theory of the Didactic (ATD) under the name didactic transposition. In this paper, we present a reflexive analysis of transposition processes that we participated in when the first author (a mathematician and UME researcher) was given the responsibility of teaching and orchestrating a biocalculus course for more than 700 first-year biology students tutored by 10 mathematics instructors. The course material was developed on the basis of the official syllabus and materials provided by the second author, an evolutionary anthropologist familiar with quantitative approaches in biology. Didactic transposition processes will be modeled and discussed using ATD theoretical constructs in order to provide answers to the following research questions: What set of conditions and constraints allowed the emergence of a biocalculus course at the University of Montpellier (UM, France)? What are the characteristics of the transposition phenomena that took place, as compared to a more classical calculus course (such as the one that preceded it in Montpellier)?