Modelling forest ecosystems: the Edinburgh Forest Model
John H. M. Thornley
Centre for Ecology & Hydrology, Edinburgh, EH26 0QB, UK.
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Abstract
Reasons for building an ecosystem model are discussed, stressing the importance of
objectives. A model is required for any research programme aiming to take a firm
grasp of forest responses. The Edinburgh Forest Model (EFM) is outlined. This is a
standard model of the genre, taking account of pools and fluxes of carbon (C),
nitrogen (N) and water. It comprises tree, soil and water submodels. The tree
submodel has a phenology submodel. There is an optional aphid submodel. The
system has the usual environmental and management drivers. Evergreen or
deciduous forests can be simulated, as even-aged stands of trees in a plantation or,
using stand averages with self-thinning and regeneration, natural forests. Some
typical simulations and applications of the model are listed, illustrating the scope of
the model. Mechanistic models provide a framework for integrating complexity,
clarifying thought, unifying results, understanding why they arise, and making
predictions about future time courses of these ecosystems.
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Introduction
Many of the ideas and principles of modelling in agriculture and plant ecology can be traced
back to de Wit (1970), who pioneered crop simulation.
In a modelling project, it is important first to define objectives, as there are many different
reasons for building a model. Controversy is often rooted in differing objectives. Ecosystem
modelling is essentially a long-term commitment of ten years and more. Short-term work is
usually superficial. The learning curve is long, and covers many different areas (biology,
mathematics, computing). Team-work and collaboration are important.
The need for mechanistic mathematical models is driven by the increasingly quantitative
nature of biological data, the widening knowledge base, the requirement for integrating the
behaviour of different parts of a complex system when seeking understanding, the
imperative of being able to predict possible futures reliably, and is facilitated by the rapid
advances in computer technology.
Above all, models provide clarity of thought, and are now accepted as de rigeur for any
research programme which aims to take a firm grasp of the forest responses. Mechanistic
models are required to provide the understanding needed for appropriate and flexible
management of forests, whatever the prevailing environmental or economic objectives. The
models are necessarily large, reflecting the complexity of the forest ecosystem. The
challenge is to develop models of “engineering strength”. This requires a suitable research
environment: stable, multidisciplinary, and well-connected to experimental programmes; it
must also support for the four essential legs of an ecosystem model: research, development,
documentation, and application. Some researchers are dismayed by the fragmentation of
much plant ecosystem modelling work.
The Edinburgh Forest Model (EFM)
Most plant ecosystem models are now quite similar: a reasonable level of consensus is
emerging. The EFM is mechanistic, dynamic, and deterministic. The principal objective has
been to obtain an understanding of the important factors determining forest ecosystem
responses in Britain. The model is written on approximately two to three levels of
description, descending to the level of aggregated biochemistry. The model accounts for the
pools and fluxes of carbon (C), nitrogen (N) and water in the forest. There are submodels
for the tree, litter and soil, water, aphids, and phenology. The usual environmental and
management inputs drive the system. The model employs standard methods for modelling
continuous dynamic systems, with ordinary non-linear differential equations. The rates of
processes are functions of the state variables.
Tree submodel
The tree is assumed to comprise foliage, branches, stem, coarse roots and fine roots &
mycorrhyza. Within these categories, there is a further decomposition into aggregated
biochemistry and meristem cells.
Key assumptions
Dry matter is regarded as being “structural” or substrates. This assumption decouples
sources from sinks, which have different environmental dependencies. It permits a
more meaningful calculation of growth and allocation.
Within-plant allocation (shoot:root ratio) is calculated using the mechanistic
transport-resistance approach.
Using a photosynthetic protein pool, photosynthetic acclimation to light, nitrogen, CO2
(down-regulation) and temperature is simulated.
Photosynthetic contributions of sunlit and shade leaves in the canopy are separately
calculated.
Foliage and fine root structural material are assigned an age structure.
Ammonia fluxes through the stomates are calculated. Although these fluxes are small,
they can be significant in low N deposition ecosystems.
Weaknesses
No explicit representation of plant proteins, except for the photosynthetic protein pool.
No direct representation of development in relation to reproductive growth, e.g. seed
production, soil seed banks, and seed germination.
Soil submodel
Key assumptions
The soil submodel is standard in most respects. Where the present formulation departs
from many other models is:
Ammonium N and nitrate N pools are separately represented.
Non-symbiotic N fixation is calculated. Forests often grow under very low N inputs.
Albeit small, non-symbiotic N fixation in the soil is then a crucial input, determining
long-term responses.
A soluble carbon pool represents C substrates in the soil such as carbohydrates and
organic acids. This pool drives C leaching, microbial growth, and non-symbiotic N
fixation.
Weaknesses
Only a single soil horizon is considered.
Only a single microbial pool is included.
Water submodel
Key assumptions
A mechanistic physico-chemical basis is chosen for this submodel.
Plant water potential and its components are represented.
Soil water potential and soil hydraulic conductivity are calculated from soil relative water
content.
The plant cells are elastic. Osmotic effects are included.
Water fluxes are driven by water potential gradients (but see Roderick, 2001).
Weaknesses
A single horizon for soil water in used.
The soil is assumed homogeneous.
Simple and quite widely used equations are used to calculate soil water potential and soil
hydraulic conductivity from soil water content, which arguably, rarely apply to real
soils with their complex pore size distributions, worm-holes, and cracks.
Key assumptions of the aphid submodel
Key assumptions
This model is based on that of Newman et al. (2003), who considered cereal and grass
aphids.
Aphid growth and development is linked to the quantity and quality of C and N substrates
available in the phloem, in this case the C and N substrate concentrations in the
foliage.
In addition to the adult morphs (wingless and winged), four developmental morphs
(instars) are represented in order to give an adequate description of aphid dynamics.
Effects of temperature, nutritional status and aphid number density on development,
fecundity, mortality and allocation of offspring to wingless or winged, are considered.
Weaknesses
No representation of sexual processes or overwintering eggs.
Possible effects of day length and tree phenology are not included.
Parameterization is general, and is possibly more applicable to cereal and grass aphids
than to the spruce aphid.
Predicted aphid dynamics appear unrealistic, but the reasons for this are not yet
understood.
Key assumptions of the phenology submodel
Key assumptions
This functions essentially as a seasonal clock, driven by temperature. It times events
such as bud burst, dormancy onset and leat fall, end of dormancy, and the
acquisition of competence to respond to forcing temperatures.
A cyclical scheme allows one season to affect the next.
Weaknesses
No effects of tree size or substrate status on phenology.
Doubts about the stability of the scheme for particular environments.
Applications of the Edinburgh Forest Model
Some applications of the EFM are briefly described in order to show the range of
investigations that lie within its scope.
Dynamics and death of an even-aged unthinned plantation
The model was allowed to run until a numerical instability occurs, which is construed as tree
death. The instability cannot be avoided or significantly delayed by (for instance) decreasing
the integration interval. It occurred after one to three hundred years, depending on
conditions. The model permits one to examine the physiological events which give rise to
tree death, giving rise to an hypothesis for “natural” tree death.
Dynamics of a thinned plantation over a 60-year rotation
Growth, yield and tree characteristics have reasonable values. These simulations were
used to calibrate the model.
Response of a thinned conifer plantation to N fertilizer
The effects of a single application of N fertilizer were simulated. The response can be
significant, small or even negative depending on timing and the N-status of the forest.
Beech plantation dynamics
The phenology clock times events such as bud burst, leaf fall etc which are applied to the
model when it is running in deciduous mode. Some biological and management parameters
are changed when the model is applied to a beech plantation. After this re-calibration, the
model simulated beech plantation dynamics satisfactorily.
Simulation of natural forest
The EFM is able to simulate natural forest, deciduous or evergreen. This is achieved by
assuming empirical equations for tree mortality and regeneration but preserving the meantree concept of the model. While this will not help us understand the mechanisms of
mortality and regeneration in forests, it may help us understand the role of the processes of
mortality and regeneration in forest ecosystem responses.
Seasonal dynamics of natural conifer and beech forests
The equilibrium state of natural forests has interesting seasonal dynamics. These are very
different for conifer and deciduous forests.
Managing forests for wood yield and carbon storage
The EFM has been used to study theoretically which management regimes best achieve the
dual objectives of high sustained timber yield and high carbon storage (Thornley & Cannell,
2000b). The conclusions are interesting. They relate to the model as formulated and
parameterized at that time, but are likely to be of general validity.
More carbon was stored in the undisturbed forest than in any regime in which wood was
harvested (35.2 kg C m-2). Plantation management gave moderate carbon storage (14.3 kg
C m-2) and timber yield (15.6 m3 ha-1 year-1). But most notably, annual removal of 10 or 20%
of woody biomass per year gave both a high timber yield (25 m3 ha-1 year-1) and high carbon
storage (20 to 24 kg C m-2). The efficiency of the latter regimes could be attributed to high
light interception and net primary productivity, with less evapotranspiration and summer
water stress than in the undisturbed forest, high litter input to the soil giving high soil carbon
and N2 fixation, low maintenance respiration and low N leaching owing to soil mineral pool
depletion.
There is no simple inverse relationship between amount of timber harvested from a forest
and amount of carbon stored. Management regimes which maintain a continuous canopy
cover and mimic, to an extent, regular natural forest disturbance, realize the best
combination of high wood yield and carbon storage.
Aphid dynamics in natural conifer forest
The aphid model has been applied to the EFM running in evergreen natural forest mode in
an Eskdalemuir environment without any specific parameter adjustment. The
parameterization is mostly as described by Newman et al. (2003). Six treatments were
applied: mean temperature is raised by + 0, 2, 5 oC, times CO2 concentrations of 350, 700
mol µmol-1. In each case the forest is in an equilibrium state when 5 aphids stem-1 are
introduced at time zero.
At ambient Eskdalemuir temperatures (+ 0 oC), the aphids quickly die out at both CO2
concentrations. At + 2 oC, the aphid population settles down to a relatively low annually
cyclic value; the cycle amplitude is greater at high CO2 concentration (in other simulations
less growth occurs at high CO2 concentration - there can be profound differences between
short- and long-term responses to elevated CO2, particularly where N status is concerned:
Thornley & Cannell, 2000a). At + 5 oC, aphid growth is altogether more volatile: at low CO2
a stable annual cycle is achieved many years; at high CO2 the system appears to show
more of the characteristics of chaos. Higher aphid numbers are accompanied by decreased
phloem N and decreased leaf area indices.
The simulations suggest that temperature greatly affects both speed and volatility of aphid
infestation, with CO2 modulating the details of this response.
Aphid dynamics in a plantation
The simulated effects of aphid infestation on an evergreen plantation grown at Eskdalemuir
+ 5 oC were investigated. At raised temperatures, aphids flourish. Both leaf area index and
yield class are depressed considerably by aphid infestation. The general effect of aphid
introduction is to decrease growth, although relatively complex dynamics arises from the
interaction between the aphid life cycle and the changing nutrient status of an uninfected
plantation. The mechanistic structure of the model allows these complications to be
examined and their causes unravelled.
Climate change
The last application reported here is concerned with climate change, and the possible effects
of climate change on forests. Climate change experiments are usually short term, perhaps of
several years duration, and are often concerned with the responses to step-changes in
environmental variables. It is dangerous to extrapolate such results to the reality of climate
change which is slow, possibly spanning centuries, and may give ecosystems much time to
respond. Indeed, these and other simulation results suggest that the results of short-term
experiments can be misleading, even opposite to long-term effects.
First therefore the simulated consequences of step changes to environmental factors are
examined, before considering the simulated consequences of realistic climate change
scenarios. The assumed climate change affects atmospheric CO2, atmospheric N
deposition and temperature only. For southern Scotland equilibrium conditions for a natural
conifer forest, the effects over twenty years of step changes to ambient CO2 (+ CO2:
doubled, from 350 to 700 µmol mol-1), N deposition (+ N: 10 to 30 kg N ha-1 year-1) and
temperature (+T: all temperatures increased by 5oC). The forest model is, using the
language of dynamic systems, a classical “stiff” system: the carbon dynamics are relatively
fast, whereas the longer-term behaviour depends on nitrogen, and its acquisition or loss by
the ecosystem. This can be seen by comparing the ratio of carbon input, of order 0.5 kg C
m-2 year-1, to the carbon content, of order 25 kg C m-2, giving a rate constant (by division) of
1/50 = 0.02 year-1, with the ratio of nitrogen input, of order 0.001 kg N m-2 year-1, to the
nitrogen content, of order 1 kg N m-2, giving a rate constant (by division) of 0.001/1 = 0.001
year-1. The latter is twenty times smaller, giving a correspondingly longer time constant. A
detailed explanation of ecosystem N dynamics for grassland is given by Thornley & Cannell
(2000a).
+CO2 and + T step changes give some immediate responses which are partially or even
completely reversed with the further passage of time: e.g. for net primary production, specific
leaf area, shoot:root ratio, foliage N content and soil mineral N. Responses to N (centre
column) are mostly simpler and smaller; note that equilibrium natural conifer forest is already
an N-rich system. Managed systems, where products are regularly removed, are relatively
N-poor and therefore can respond more strongly to increasing N. These results indicate
plainly the anomalous and possibly misleading responses which can be obtained from
short-term experimentation on the forest ecosystem.
The simulated effects of 250 years of climate change from 1850 to 2100 (using a standard
scenario), have also been investigated. The effects of the three assumed climate change
components (C, N and T) have been examined separately and in combination. High C
sequestration is favoured by high CO2 and low temperature; N deposition makes little
difference to this already N-rich ecosystem. On the other hand, net primary production is
maximized by increasing CO2 and temperature. Soil mineral N is decreased by + CO2, as
are N losses from the system, but these are increased by + N and + T. Leaf area index is
increased by + C, although other simulations can give a decrease and experimental work
gives a range of results (figure 4, Saxe et al., 1998).
Conclusions
The development of mechanistic models is part of a shift in research focus towards
quantitative explanation, integration of complexity, and prediction in the agricultural and
ecological sciences. A forest research program without a modelling component may be
critically emasculated by this missing dimension. To do such work successfully requires
appropriate organization and commitment. While models are, rightly, only a part of the
research scene, they provide a framework for ideas which can be helpful to all involved in
research and applications of that research.
Reference
De Wit C.T. (1970) Dynamic concepts in biology. I. Setlik (Ed.) Prediction and Measurement
of Photosynthetic Productivity, Pudoc, Wageningen, Netherlands 17-23.
Newman, J.A., Gibson, D.J., Parsons, A.J. and Thornley, J.H.M. (2003) How predictable
are aphid population responses to elevated CO2? Journal of Animal Ecology 72:
556-566.
Roderick, M.L. (2001) On the use of thermodynamic methods to describe water relations in
plants and soil. Australian Journal of Plant Physiology 28: 729-742.
Saxe, H., Ellsworth, D.A. and Heath, J. (1998) Tree and forest functioning in an enriched
CO2 atmosphere. New Phytologist 139: 395-436.
Thornley J.H.M. and Cannell M.G.R. (2000a) Dynamics of mineral N availability in
grassland ecosystems under increased [CO2]: hypotheses evaluated using the
Hurley Pasture Model. Plant and Soil 224: 153-170.
Thornley J.H.M. and Cannell M.G.R. (2000b) Managing forests for wood yield and carbon
storage: a theoretical study. Tree Physiology 20: 477-485.