Model Description

The MEL model is a quantitative synthesis of the Mooney-Bloom-Chapin Resource-Optimization hypothesis of plant nutrition (Mooney 1972, Bloom et al. 1985, Chapin et al 1987; also called the "functional equilibrium hypothesis," Farrar and Jones 2000) within a whole-ecosystem context (Rastetter et al. 1997a).  The resource-optimization hypothesis predicts how plants should allocate their internal assets (biomass, proteins, carbohydrate...) to acquire resources from the environment (CO₂, NH₄, NO₃, water, light...).  In an environment where resource concentrations do not change, the optimum allocation of internal assets is one where all resources in the environment equally limit production (Chapin et al. 1987); otherwise too many assets would be expended toward acquiring a non-limiting resource and a reallocation of those assets toward limiting resources would therefore increase production.  Changes in resource availability and in metabolic requirements through time complicate this picture, but the overall concept still applies:  plants should constantly adjust the distribution of their internal assets to approach a more balanced rate of resource uptake from the environment (e.g., shifts in root-shoot ratios, allocation of N).  Selective pressure should strongly favor species that maintain a near optimum allocation pattern.  We use an analogous approach to simulate soil microbial processes.  However, because changes in microbial community composition and acclimation of microorganisms to changes in the environment are very much faster than acclimation in vegetation, we treat the reallocation of effort for soil processes as instantaneous.

Figure 1: The Multiple Element Limitation (MEL) Model for two elemental resources C and N (Rastetter et al. 1997).

Historically, MBL MEL has been  applied to the C and N cycles.  We therefore describe the model with reference to these specific elements.  In the model (Fig. 1), C and N are cycled among available inorganic pools (CO₂, N_i), biomass in vegetation (B_C, B_N), and soil detritus (D_C, D_N).  A microbial community is implied in the model structure, but its biomass is not explicitly represented.  Microbial biomass is assumed to be part of soil detritus. 

Inorganic N is depleted through losses from the ecosystem (N loss, e.g., leaching or gas fluxes), uptake by microbes (Immobilization), and uptake by vegetation (N Uptake). Inorganic N is replenished from sources outside the ecosystem (N Deposition) and by mineralization of soil organic matter (Mineralization).

Elements are taken up by vegetation at a rate that is a Michaelis-Menten function of element concentration (N_i) and is proportional to the surface area of vegetation that is active in uptake of that element (S_i). We have examined several alternate formulations of the uptake equation (Rastetter and Shaver 1992), and currently use one in which S_i is a fractional power function of vegetation biomass. There is a diminishing return in S_i and thus, in uptake, as biomass increases. However, this formulation does not capture late-successional decreases in leaf area observed in some forests.

Vegetation biomass is assumed to be roughly proportional to the amounts of the two elements in the vegetation. However, because the model allows transient deviations of the element ratio from a nutritionally balanced state, it would be inappropriate to calculate biomass based solely on one element or the other. Therefore, we calculate vegetation biomass based on the abundance of both elements (B_C + qB_N, where q is the optimum C:N ratio) and, for convenience, express it in C units.

The heart of the MEL model is the algorithm for reallocating plant assets expended toward resource acquisition (biomass, proteins, carbohydrate...).  We refer to these assets as the uptake effort and lump them into a single abstract variable.  We assume that the total uptake effort is limited, but increases with the vegetation biomass. The fraction of the total effort that is allocated toward the uptake of resource i is represented by the variable V_i (no units), which can change through time as the availability of, or requirement for, resource i changes.  Because V_i is the fraction of the total uptake effort, the sum of the V_i for all resources must be 1, which implies that

 (i.e., increases in one V_i must be compensated by a net decrease in sum of the other V_i).  All else being constant, acquisition of resource i increases monotonically (but not necessarily linearly) with increasing V_i and uptake of resource i is zero when V_i is zero.

MBL MEL version 4 broadens the application of the resource optimization hypothesis to interactions among more than two resources, including non-element resources (e.g., light and water), and among substitutable resources (e.g., NH₄ or NO₃ as sources of N). The approach is general enough that the model can now be extended to any number of element and non-element resources and to any number of substitutable resources.

 
Table 1: Key features of MBL MEL versions

Download MBL MEL by clicking here

Recent Projects

•Species, community and ecosystem level consequences of the interactions among multiple resources (DEB-0108960), June 2001 – May 2005.

Major Findings

Citations

Activities & Contributions

Citations

Herbert, D. A., E. B. Rastetter, G. R. Shaver, G. I. Ågren.  1999.  Effects of plant growth characteristics on biogeochemistry and community composition in a changing climate.  Ecosystems 2:367-382.

Herbert, D. A., M. Williams, and E. B. Rastetter. 2003. A modeled analysis of N and P limitation on carbon accumulation in an Amazonian forest site after alternate land-use abandonment. Biogeochemistry 65: 121-150.

Herbert, D. A., E. B. Rastetter, L. Gough and G. R. Shaver.  2004.  Species diversity across nutrient gradients: An analysis of resource competition in model ecosystems.  Ecosystems 7: 296-310.

Rastetter, E. B., G. I. Ågren and G. R. Shaver.  1997.  Responses of N-limited ecosystems to increased CO₂: A balanced-nutrition, coupled-element-cycles model.  Ecological Applications 7:444-460.

Rastetter, E. B., and G. R. Shaver.  1992.  A model of multiple element limitation for acclimating vegetation.  Ecology 73:1157-1174.

Rastetter, E. B., and G. R. Shaver.  1995.  Functional redundancy and process aggregation:  Linking ecosystems to species.  In:  C. G. Jones and J. H. Lawton (eds.) Linking Species and Ecosystems.  Chapman and Hall, New York, pp. 215-223.

Rastetter, E. B., S. S. Perakis, G. R. Shaver, and G. I. Ågren. 2005. Carbon Sequestration in Terrestrial Ecosystems Under Elevated CO₂ and Temperature:  Role of Dissolved Organic N Loss. Ecological Applications 15:71-86.

Rastetter, E.B., P.M. Vitousek, C. Field, G.R. Shaver, D. Herbert, G.I. Ågren. 2001. Resource Optimization and Symbiotic N Fixation. Ecosystems 4:369-388.

Rastetter, E.B., R.D. Yanai, R.Q. Thomas, M.A. Vadeboncoeur, T.J. Fahey, M.C. Fisk, B.L. Kwiatkowski, and S.P. Hamburg. In press. Recovery from disturbance requires resynchronization of ecosystem nutrient cycles. Ecological Applications - In press 2013. Zip file containing model description, parameter and driver files for all figures is available here.

This material is based upon work supported by the National Science Foundation under grants #OPP-9318529, OPP-9732281, DEB-9509613, DEB 0716067 (OPUS), DEB-0108960, ARC-0806329, EF-1065587, ARC-0856853, and DEB-0949420 and the Environmental Protection Agency under grants RFQ-RT-00-00107 and QT-RT-00-001667. Any opinions, findings, conclusions, or recommendations expressed in the material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or the Environmental Protection Agency.

Last Updated: 25 Feb 2013 BK