Virginia Tech Mathematics Colloquium – Fall 2026

Classical population models often rely on simple, unstructured differential equations that assume uniform life stages and instantaneous growth. In reality, species have stage-specific traits and behavioral adaptations that require more complicated mathematical tools. In this talk, I will illustrate how applied mathematicians collaborate with biologists to build mechanistic, first-principles models that capture multi-scale ecological dynamics. We begin with grazing, introducing co-limitation functions to capture how nutrient limitations alter feeding behavior. We then transition to growing up, using stage-structured and delay differential equations to model how high nutrient demands in juveniles create developmental bottlenecks. We demonstrate how stage-specific nutrient demands shift stability boundaries and control population oscillations under enrichment. Ultimately, we show how matching the right mathematical framework to biological reality uncovers novel dynamical behaviors and yields deeper insights into complex ecological systems.

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