Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend the “Rule-of-Four,” initially used in calculus reform efforts, to a “Rule-of-Five” framework for models and modeling that is inclusive of varying disciplinary definitions of each. This unifying framework allows us to both build on strengths that each discipline and its students bring, but also identify gaps in modeling activities practiced by each discipline. We also discuss benefits to student learning and interdisciplinary collaboration.

Abstract Quantitatively linking individual variation in functional traits to demography is a necessary step to advance our understanding of trait-based ecological processes. We constructed a population model for Asclepias syriaca to identify how functional traits affect vital rates and population growth and whether trade-offs in chemical defence and demography alter population growth. Plants with higher foliar cardenolides had lower fibre, cellulose and lignin levels, as well as decreased sexual and clonal reproduction. Average cardenolide concentrations had the strongest effect on population growth. In both the sexual and clonal pathway, the trade-off between reproduction and defence affected population growth. We found that both increasing the mean of the distribution of individual plant values for cardenolides and herbivory decreased population growth. However, increasing the variance in both defence and herbivory increased population growth. Functional traits can impact population growth and quantifying individual-level variation in traits should be included in assessments of population-level processes.