The MEL model is a quantitative synthesis of the
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, Ni),
biomass in vegetation (BC, BN),
and soil detritus (DC, DN).
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 (Ni) and is
proportional to the surface area of vegetation
that is active in uptake of that element (Si).
We have examined several alternate formulations of
the uptake equation (Rastetter and Shaver 1992),
and currently use one in which Si is
a fractional power function of vegetation biomass.
There is a diminishing return in Si
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 (BC + qBN,
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 Vi
(no units), which can change through time as the
availability of, or requirement for, resource
i changes. Because Vi
is the fraction of the total uptake
effort, the sum of the Vi
for all resources must be 1, which implies that
(i.e., increases in one Vi
must be compensated by a net decrease in sum of
the other Vi). All else
being constant, acquisition of resource i
increases monotonically (but not necessarily
linearly) with increasing Vi
and uptake of resource i is zero
when Vi 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
MBL MEL Version I
Initial two element model, plant pools
Rastetter et al., 1992
MBL MEL Version II
Added soil pools
Rastetter et al., 1997
MBL MEL Version III
version with N fixation and DON fluxes
Herbert et al., 1999
Rastetter et al., 2001
Rastetter et al., 2005
MBL MEL Version 3.5
Daily version of MBL
MEL version III. There are two
subversions of this version, a single
soil layer version and a 4 soil layer
MBL MEL Version 4
Daily model with eight
Rastetter et al., in
MBL MEL by clicking here
•Species, community and ecosystem level
consequences of the interactions among multiple
resources (DEB-0108960), June 2001 – May 2005.
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
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:
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
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.
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
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