Modeling Systems of Interacting Specialists

Many natural and artificial systems can be described abstractly as a collection of interacting entities that must meet two requirements for survival. First, entities must maintain their individual viability through some homeostatic process that consumes resources obtained from other entities in their environment. Additionally, the system must produce a pattern of resource flows among entities that creates suitable conditions for their mutual viability. We define a hybrid model that focuses on these general features. It is an abstract representation designed to capture the resource production and exchange processes that are essential to such diverse arrangements as firms interacting to form an economy, species interacting to form an ecosystem, and multi-cellular organisms. These diverse systems can be studied by setting terms and parameters of the generic model; thus, insights obtained from the study of one system can be transferred to systems that are superficially dissimilar but share common core dynamics. The model uses a set of coupled non-linear first-order differential equations to describe the dynamics of individual entities. Entities are coupled through discrete exchange events in which they seek to satisfy their resource requirements given the environmental conditions they experience. We configure the model to analyze the behavior of three disparate systems. One examines how differential production efficiencies can lead to competitive exclusion in a system of entities having complementary resource requirements. A second explores how a population of entities adapts to balance requirements for both robustness and efficiency under different exogenous stress regimes. The third considers a hierarchical system of embedded entities to investigate the effects of different patterns of system-level exchange on the internal properties of compound entities.