  Systems of interacting species, such as biological environments or chemical
reactions, are often described mathematically by sets of coupled ordinary
differential equations. While a large number $\beta$ of species may be involved
in the coupled dynamics, often only $\alpha < \beta$ species are of interest or
of consequence. In this paper, I explore how to build reduced models that
include only those given $\alpha$ species, but still recreate the dynamics of
the original $\beta$-species model. Under some conditions detailed here, this
reduction can be completed exactly, such that the information in the reduced
model is exactly the same as the original one, but over fewer equations.
Moreover, this reduction process suggests a promising type of approximate model
-- no longer exact, but computationally quite simple
