Application of Network Particle Tracking (NPT) in open compartmental systems
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Compartment models are often used to represent and study biological and ecological systems. They are modeled as directed graphs, describing flows of a conserved quantity (eg. mass, energy, a specific molecule, etc.) among a set of compartments. Various measures have been defined to capture universal system-wide properties of these models. In this thesis, we introduce a method that eliminates these shortcomings. Using a stochastic individual based algorithm called Network Particle Tracking (NPT), we come up with simulation-based definitions for storage analysis. While both definitions agree for steady-state systems, the NPT-based definition works for dynamic systems as well. We use the same methodology to study other interesting properties of mass and energy distribution within ecological networks. An important system-wide property storage analysis quantifies how each environmental input gets shared among all compartments. Application of current storage analysis is restricted to steady-state models. It cannot be utilized to study dynamic systems. This is a major limitation as most ecosystems experience seasonal changes. Another property, residence time (RT), is a widely used concept representing the average time the flow material stays in a compartment (or the system) at equilibrium. Residence time distribution (RTD) offers more detailed information about the behavior of the flow material within the system. These properties get quite difficult to compute for large and complex networks. Tracing the movement of tagged flow material in the system, similar to tracer experiments, could be used study these essential properties.