Biomathematics Seminar Series - Francis Poulin (Nov. 17, 2026)

Speaker: Francis Poulin (University of Waterloo)

Title: From NPZD to the Biological Carbon Pump: A Simple Model with Multiple Carbon Pathways

Abstract: 

The ocean takes up a large share of the carbon dioxide released by human activity, and much of that uptake depends on biology. Phytoplankton fix dissolved inorganic carbon. That carbon then moves through grazers, detritus and dissolved organic matter, and some of it is eventually stored at depth. This set of processes is known as the biological carbon pump. Nutrient–Phytoplankton–Zooplankton–Detritus (NPZD) models are a classic and mathematically appealing way to describe plankton ecosystems, but they track only nitrogen. If carbon is simply tied to nitrogen through a fixed stoichiometric ratio, it has no independent dynamics, and the model cannot store carbon or delay its return.

In this talk I present NPZDCO, a minimal extension of NPZD that adds carbon and oxygen. It includes phytoplankton exudation of dissolved organic carbon and zooplankton respiration. These additions give carbon several recycling pathways that act on different time scales: a fast loop through detritus, a slower loop through dissolved organic carbon, and a direct return through respiration. I will discuss the model’s structure, its conservation laws (total nitrogen, total carbon, and a local coupling between carbon and oxygen through redox chemistry), and how the arrangement of pathways determines where carbon goes, how long it stays there, and how quickly it returns. The model sits between simple NPZD models and complex biogeochemical models. I will also show reaction–diffusion simulations computed with numerical schemes built to keep concentrations positive and conserve mass exactly.