Math Biology Seminar: Tomas Veloz

The decline of the Earth's biodiversity is a threat to the ecosystems in the planet. Ecological systems are faced with species extinctions and invasions and one fundamental question is how systems vary when they suffer these changes. In particular, a major problem in theoretical ecology is to resolve how ecosystem features such as resilience, resistance, robustness, or in wider terms, stability respond to changes in species diversity, richness, connectivity, or in wider terms, complexity. This question is known as the Complexity-Stability problem. We propose a novel formalism to deal with this problem. Chemical Organization Theory (COT) is a formalism for modeling self-organizing systems. Although COT is inspired by problems in biochemical systems, it has much broader applicability. The elements of the formalism are resources and reactions, where a reaction (e.g. a+b-> c+d) maps a combination of resources (in an abstract sense) onto a new combination. Thus, a reaction represents an elementary process that converts resources into new resources. Reaction networks tend to self-organize into invariant reaction sub-networks, called organizations. They represent all the possible attractors of the reaction networks dynamics. Thus, COT provide a simple model that links the structure and dynamics of stable community systems: an organization is able to constantly recreate its own components. In this seminar, we introduce the mathematical framework of COT, explain how to model ecological relationships and ecosystems using COT, and present some illustrative examples.