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.
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
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
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
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
(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
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
MBL MEL Version I
Initial two element model, plant
Rastetter et al., 1992
MBL MEL Version II
Added soil pools
Rastetter et al., 1997
MBL MEL Version
species version with N fixation
and DON fluxes
Herbert et al.,
Rastetter et al., 2001
Rastetter et al., 2005
MBL MEL 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
with eight resources.
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
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:
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
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. 2013.
Recovery from disturbance requires
resynchronization of ecosystem nutrient
cycles. Ecological Applications
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