### Abstract:

A generalized mathematical model of ecosystems is
developed. The model begins with the general class of
systems known as state-determined systems, in which the
time-derivative of each state variable is a function of some
subset of the set of all system state variables and
.environmental parameters. A formal basis is presented for
considering the steady-state behavior of such systems in
terms of isoclines, drawing upon the fields of graph theory,
linear algebra, and differential equations.
The simplifying capabilities of hierarchy theory are
invoked to mitigate the adverse effects of model complexity.
Like the theory of isocline analysis, the particular
formulation of hierarchy theory presented is phrased in
graph-theoretic terms, enabling the model to be developed as
a technique for analyzing the steady-state behavior of
hierarchical systems. The role of inter-level time scale
heterogeneity in hierarchical organization is discussed.
As an illustration of its ability to portray the
behavior of spatially-nested hierarchies, the model is used
to provide a perspective on data from the climax vegetation
of the Great Smoky Mountains. The effects of time scale
heterogeneity are also illustrated by using the model to
organize data sets from several vegetation/avian communities
across the United States. The vegetation is taken to behave
with a lower characteristic frequency than the relatively
rapidly-developing avian subcommunity, thus constraining the
latter in a hierarchical fashion.
In order to understand in a more general way the role
such a model might play in advancing ecological
understanding, a broad framework is presented for analyzing
the role of conceptual structures in science and the place
of models in these structures. A view of models as
scientific metaphors is advanced as an alternative to the
pictorial/realist interpretation of models. Given this
understanding of models in general, the proposed model and
its underlying assumptions are compared and contrasted with
a set of four partial conceptual structures drawn from the
fields of systems ecology, plant ecology, natural resource
economics, and organismic systems theory.