Ecosystem Modeling

Modeling has become a useful tool for testing hypotheses concerning behavior and self-regulation of complex systems (e.g., Camilo and Willig 1995, B. Patten 1995, Ulanowicz 1995) and for predicting ecosystem responses to environmental changes, as well as ecosystem contributions to environmental change, especially carbon flux (e.g., Rastetter et al. 1991, Sarmiento and Le Quere 1996). The logistical difficulty of measuring and manipulating all ecosystem components and processes for experimental purposes has placed greater emphasis on modeling to simulate experimental conditions and to identify critical components and processes for further study.

Modeling at the ecosystem level necessarily starts with conceptual models of linkages among components and reflects the perception of individual modelers of the importance of particular components and interactions (e.g., Figs. 1.3, 11.6-11.9). Models differ in the degree to which species are distinguished in individual submodels or combined into functional group submodels (de Ruiter et al. 1995, Naeem 1998, Polis 1991b, Reagan et al. 1996) and to which light, water, and nutrient availability are integrated simultaneously with changes in ecosystem structure and composition (e.g., R. Waring and Running 1998). Obviously, conceptualizing the integration of the many thousands of species and other components in a given ecosystem is virtually impossible. However, some global-scale models distinguish the biota only at the community level, if at all. The degree to which individual species are distinguished influences the representation of the variety of interactions and feedbacks that influence ecosystem parameters (Naeem 1998, Polis 1991b, Reagan et al. 1996). Similarly, models based on a limited set of variables to predict a single type of output (e.g., carbon flux) may fail to account for effects of other variables (e.g., effects of limiting nutrients, such as nitrogen, on carbon flux) (R.Waring and Running 1998). More general models require simplifying assumptions to expand their application and may lose accuracy as a consequence.

After the conceptual organization of the model has been determined, interaction strengths are quantified (Figs. 11.14 and 11.15), based on available data, or subjected to sensitivity analysis to identify the range of values that represent observed interaction (e.g., Benke and Wallace 1997, Dambacher et al. 2002, de Ruiter et al. 1995, Parton et al. 1993, Rastetter et al. 1991, 1997, Running and Gower 1991). Direct and indirect interactions can be represented in transition matrix form. For example, see the following:

N1

N2

N3

N4 .

. Ni

N1

an

a 21

a 31

a 41 .

. a i1

N2

a12

a 22

a 32

a 42 .

. ai2

N3

a13

a 23

a 33

a 43 .

. a i3

N4

a14

a 24

a 34

a 44 .

. ai4

Nj

a1j

a 2j

a 3j

a 4j .

. a ij

where Nj is the ;'th ecosystem component and a is the relative effect (direct + indirect) of Nj on Ni. When Ni = Nj, aij represents intrinsic (intraspecific) effects on numbers or mass. Differential equations of the general form:

are used to calculate the transitional states of each component as input conditions change. Note the application of this inclusive equation to equations for growth of individual populations and interacting species in Chapters 6 and 8. Components must be linked so that changes in the number, mass, or energy or nutrient content of one component have appropriate effects on the numbers, masses, or energy or nutrient contents of other components. Models focused on species emphasize fluxes of energy or matter through food webs. Models focused on energy or matter pools emphasize fluxes of energy and matter among pools but may include important species that affect flux rates.

Ecosystem models are sensitive to effects of indirect interactions. Nutrient availability and directions of fluxes indirectly affect all organisms. For example, a direct predator-prey interaction reduces prey abundance and directs energy and nutrients through that predator, thereby indirectly affecting resources available for other organisms, as well as interactions between that prey and its competitors, hosts, and other predators (see Chapter 8). Ultimately, indirect effects

Fig. 11.14

Quantification of feeding rates (top), interaction strengths as per capita effects (bottom), and impact of these interactions on soil food web stability in conventional agriculture at Lovinkhoeve Experimental Farm, The Netherlands. From de Ruiter et al. (1995) with permission from the American Association for the Advancement of Science.

Fig. 11.15

Detail of carbon fluxes in the soil organic carbon submodel of the Century ecosystem model. This model can be coupled to the nitrogen submodel. From Parton et al. (1993) courtesy of the American Geophysical Union.

Fig. 11.15

Detail of carbon fluxes in the soil organic carbon submodel of the Century ecosystem model. This model can be coupled to the nitrogen submodel. From Parton et al. (1993) courtesy of the American Geophysical Union.

of this interaction can affect primary production, canopy cover, and resource availability in ways that determine climate, substrate, and resource conditions for the entire ecosystem. Nontrophic interactions are difficult to recognize and measure (Dambacher et al. 1999, 2002, O'Neill 2001); quantitative data are available for relatively few potential indirect interactions. Accordingly, the complexity of indirect, as well as direct, interactions is difficult to model but has important implications for how ecosystems respond to environmental changes (see Chapter 15).

A number of models have been developed to predict fluxes of energy or key elements, especially carbon or nitrogen, through ecosystems. However, as noted earlier in this chapter, interactions among various cycles (e.g., nitrogen and carbon cycles integrated through biomolecules, carbon and calcium cycles integrated in carbonates, or nitrogen and calcium cycles integrated through soil pH change) may confound predictions based on individual resources.

Comprehensive ecosystem models that integrate energy, carbon, water, and nutrient fluxes include FOREST-BGC/BIOME-BGC (Running and Gower 1991) and CENTURY (e.g., Fig. 11.15; Parton et al. 1993), which have been modified to represent a variety of ecosystem types. These models are useful for predicting global biogeochemical processes because they integrate common ecosystem processes in a logical framework; have minimum requirements for detail of inputs for ecosystem characteristics; and account for the mass balances of multiple nutrients moving through interacting plants, detritus, decomposers, and abiotic pools. This ecological stoichiometry (Daufresne and Loreau 2001, Sterner and Elser 2002) provides a tool for evaluating consequences of changes in mass balances among multiple elements as a result of changes in environmental conditions or community interactions. The effects of insects and other invertebrates have been incorporated poorly, or not at all, in these, or other, existing ecosystem models. At best, insects usually are combined as "insects" or "arthropods," thereby losing valuable information about this diverse group, species of which can respond dramatically and differentially to environmental change and have major effects on ecosystem properties (Chapters 12-14).

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