Reference from which these applications of ENA are extracted:

Patten BC. 1997. Synthesis of chaos and sustainability in a nonstationary linear dynamic model of the American black bear (Ursus americanus Pallas) in the Adirondack Mountains of New York. Ecol. Model. 100, 11-42.

Here an application of a dynamic model is used to show the importance of indirect effects (see chapter 5) even within a linear approach.

There are many examples of indirect relationships in natural systems, some of them involving the global oneāthe biosphere. The majority of these relationships remain either overlooked or poorly understood (Krivtsov et al., 2000). To model such systems requires the use of many integrated submodels, due to the complexity of processes involved.

The knowledge that all species in nature are complexly interconnected directly and indirectly to all other biotic and abiotic components of their ecosystems is slow in being translated into models and even more in management practice.

An example for such a synthesis is the simulation model of a wildlife population, the American black bear (Ursus americanus Pallas) on the 6000ha Huntington Wildlife Forest in the central Adirondack Mountain region of upper New York State, USA (Costello, 1992). The model was designed to be conceptually complex but mathematically simple, so its behavior would derive more from biology and ecology than from mathematics. The STELLA II (High Performance Systems, Hanover, NH) model of the Adirondack black bear is linear, donor controlled, nonstationary, and phenomenological (Patten, 1983).

The model's purposes are to express black bear biology as a population system inseparable from its ecosystem and to demonstrate how chaos and sustainability can be realistically incorporated into models, minimizing the use of inappropriate mathematics that, though traditional or classical, may not be well chosen due to an inadequate rationale.

If envirograms for all the taxa and significant abiotic categories of the Huntington Wildlife Forest could be formed, then the centrum of each would account for one row and one column of an n X n interconnection matrix for the whole ecosystem. The centrum of each black bear envirogram for a life history stage would then represent one such row and column within the ecosystem matrix and from these indirect connections between bear and ecosystem compartments could be determined. Of course the forest ecosystem model does not exist, but the rationale for embedding the bear subsystem within it is clear, and the purpose of the envirograms was to implement this in principle by way of organizing relevant information for modeling.

A further criterion was that all the direct interactions between the bear compartments and the environment would be by mass energy transactions, enabling the conservation principle to be used in formulating system equations. The envirograms prepared for this model are depicted in Simek (1995) and were then used to construct a quantitative difference equation model employing STELLA II.

Quantification of the model is still approximate, based on general data and knowledge of the bear's life history, reproductive behavior, environmental relationships, and seasonal dynamics as known for the Huntington Forest and the Adirondack region. The equations are all linear, and donor controlled, with details of temporal dynamics introduced by non-stationary (time-varying) coefficients rather than by nonlinear state variables and constant coefficients.

The model's behavior is here described in detail only for the cub compartment and selected associated parameters (Figure 9.5). The other compartments behave with similar realism.

A baseline simulation was achieved which generated 33-64 individuals 6000ha during a typical model year; this is consistent with a mean of about 50 animals typically considered to occur on the Huntington property. Yearling M/F sex ratios generated by the

Figure 9.5 Submodel layer depiction of the cub compartment of the black bear model.

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