Soil Biodiversity Programme Modelling Initiative
Preliminary Report No. 1: Modelling carbon flux in soil ecosystems: quantifying
indirect effects of biota and physical, chemical and biological interactions.
Authors: M. Toal (CEH Monks Wood), A. Meharg (University of Aberdeen)
31/8/00
1
Report No. 1
Modelling carbon flux in soil ecosystems: quantifying indirect effects of biota
and physical, chemical and biological interactions.
Introduction
Modelling is an ideal technique to simulate nutrient and energy flux in soil
ecosystems. However, a number of limitations in current soil ecological models have
been recognised. Process-based approaches (Molina et al., 1983; Parton et al., 1988;
Svendsen et al., 1995) aim to predict carbon turnover at the field or ecosystem level
over extended timescales (years to decades). This approach has been criticised due to
its inability to account for the impact on carbon transformations of perturbation within
the biotic community (McGill, 1996). This is a serious criticism as the majority of
nutrient transformations in soils are mediated by soil biota. Modelling techniques that
explicitly describe the role of biota in the nutrient cycling process (organismorientated models), have been developed to counter this criticism (DeRuiter et al.,
1993; Hunt et al., 1987). Organism-orientated models (based on soil food webs)
quantify nutrient fluxes by calculating carbon and nitrogen transformation by a range
of biotic functional groups. However, these models have also been criticised for
examining system dynamics from a purely trophic perspective, where the ‘links’ in
these models represent solely the material flow of carbon between organisms. These
models have been criticised for not including non-trophic effects of soil organisms
which may have an indirect effect on nutrient cycling (e.g. amendment of the physical
structure of soil), (Brussard, 1998) (Ettema, 1998).
2
Soil ecosystems are structured due to complex interactions between physical,
chemical and biological attributes (Figure 1). These interactions are both direct and
indirect and an array of non-linear processes and positive and negative feedbacks exist
within the soil ecosystem. In recent years, a number of reviews have emphasised the
need to consider these indirect, non-linear and feedback effects when attempting to
understand the functioning of the soil community (Lavelle et al., 1997) (Brussard,
1998) (Smith et al., 1998) (Young et al., 1998). The consensus of opinion in these and
other reviews is that studies must be undertaken to devise new quantitative theory in
order to increase ecological realism in nutrient cycling models (Smith et al., 1998)
(Lavelle, 2000). Advances in modelling theory are urgently needed as there are a
number of crucial areas which have received little quantitative study. For example,
certain groups of organisms directly transform only a small amount of energy or
nutrients, but play a disproportionately large role in amending the physical structure
of the soil (e.g. ecosystem engineers). The action of ecosystem engineers is important
as it has a large indirect effect on organisms which do control the majority of energy
and nutrient flux in soil systems (e.g. bacteria and fungi) through affecting soil
structure and consequently air and water availability (Jones et al., 1994) (Lawton,
1994) (Jones et al., 1997). Soil fauna also comminute SOM, which increases plant
litter surface area and hence, its’ susceptibility to microbial attack (Brown, 1993;
Lavelle et al., 1997; Seastedt, 1984). Thus, organisms which do little to alter the
chemical nature of SOM may still influence the rate of nutrient cycling in soil
communities by affecting the physical nature of carbon substrates via metabiosis
(Waid, 1999). These indirect effects which may strongly influence carbon cycling
have received little systematic study from a modelling perspective. Without a
quantitative understanding of the indirect effect of ecosystem engineers and other soil
3
fauna on nutrient and energy flux, we cannot hope to build accurate models of the soil
community (Brussard, 1998) (Ettema, 1998).
To build models that take account of these crucial areas, a model structure such as that
illustrated in Figure 2 must be adopted, as opposed to the purely trophic model
structure illustrated in Figure 3, on which most organism-orientated models are based.
Models that include indirect effects of organisms on nutrient cycling and physicalchemical-biological interactions have seldom been formulated before, yet this
approach is fundamental if the functioning of soil ecosystems is to be understood in
detail (Smith et al., 1998) (Lavelle, 2000). This paper suggests a quantitative
framework for modelling carbon flux in soils where both direct and indirect
interactions between physical, chemical and biological attributes are accounted for at
the core of model structure.
It must be stressed that this model in its present state is not a fully calibrated
prediction of the dynamics of carbon in a real soil ecosystem. For example, specific
models of carbon flow describe compartment sizes with units such as g C mm-3. By
contrast, this model uses units such as w C svol, describing a mass of C (w C) in a
defined soil volume (svol). This step has been taken as this paper describes a model
structure, as opposed to giving specific numerical predictions for a defined
ecosystem. If this model approach was adopted, then site/ecosystem specific
calibration experiments could be carried out. This model merely provides a
quantitative structural framework on which future models of soil ecosystems could be
based.
4
Methodology
Modelling carbon flux in soils
Paustian (1994) outlines two main methods of modelling carbon flux in soils,
‘Process-orientated’ modelling (where models focus on aggregated processes
mediating the movement and transformations of matter or energy; soil organisms are
implicit in the model formulation) and ‘Organism-orientated’ modelling (where
models quantify the flow of nutrients and energy through soil biota, and explicitly
describe functional or taxonomic groups of organisms in the structure of the model).
A detailed mechanistic, organism-orientated model would be the ideal technique to
quantify carbon flux as the direct and indirect effects of organisms would be explicitly
described. However, organism-orientated models are highly data demanding and we
do not yet possess sufficient theory or empirical data to describe the interrelationships
between a number of important organisms at a mechanistic level. For example, we do
not know the extent to which pore size distribution and pore connectivity are
influenced by enchytraeids and earthworms, hence we cannot produce accurate
mechanistic models for soil water and air content, which are important influences on
microfloral growth (and hence carbon flux). A range of physical, chemical and
biological interactions that are fundamental to soil function have yet to be
quantitatively described. However, a number of workers are beginning to examine
methods of constructing a range of mechanistic models (Anderson et al., 1997)
(Davidson and Park, 1998) (Otten and Gilligan, 1998; Otten et al., 1999) (Bailey et
al., 2000). These studies provide an excellent basis for building overarching
mechanistic models of organism growth and carbon flux, but due to incomplete
5
modelling theory and a lack data describing a number of soil processes, we cannot as
yet produce large scale mechanistic models of the soil ecosystem. Yet there is a
pressing need to find a quantitative, predictive methodology to describe carbon flux in
soils which reflects the ecological realism of field conditions. Therefore, how should
tractable modelling of carbon flux within the soil ecosystem be approached today?
This report describes a modelling methodology that builds on existing information
about a number of soil processes. The methodology is termed ‘micro-process’
modelling. A micro-process model can be defined as a model that includes the
resultant effects of biological-chemical-physical interactions, but does not
mechanistically describe them. For example, in a micro-process model, the
mechanistic effect of fauna on soil structure, and the subsequent effect of soil
structure on air and water and eventually microflora, is bypassed. For example, the
feedback effect of fauna on microbial growth, (illustrated in Figure 2) is described by
a statistical relationship between faunal biomass, a soil structural parameter and water
percolation rate. The water content of the soil then affects microbial growth rate. The
micro-process methodology borrows from both organism-orientated approaches (in
that the effects of specific groups of organisms are described) and process-orientated
approaches (in that statistical relationships, as opposed to mechanistic explanations
are used to describe model linkages). Micro-process models can be seen as an
example of an ‘integrated’ approach (Paustian, 1994).
The relationships between organisms and their physico-chemical environment in these
micro-process models could gradually be replaced by more mechanistic treatments of
soil systems as the knowledge front within soil ecology advances. These micro-
6
process models could bridge a gap between the present knowledge base, where a
dearth of models exists, and the future, where we will have an increased
understanding of the mechanistic nature of soil interrelationships (Figure 4).
To illustrate this proposed method, a micro-process carbon flux model has been
constructed describing a simple biological-chemical-physical soil system. Direct and
indirect effects of the interacting soil attributes (e.g. water, carbon substrates and
microflora) are described within a spatio-temporal context.
A general methodology for constructing microprocess models of carbon flux in
soil ecosystems
The model is dynamic as it describes C flux/C compartmentalisation in the soil
system through time. It is also defined on a spatial basis, according to soil horizons.
Figure 5 illustrates a column of soil divided into three horizons (each horizon is
represented by a structurally identical submodel). The submodels could be defined for
any spatial scale desired, (e.g. cm3, dm3 etc.). Each submodel could also be adjusted
to give different horizons (or adjacent soil ‘columns’) different numerical values for
their parameters to simulate spatial heterogeneity. The novelty of this approach is that
both direct and indirect effects on carbon flux are described within the model
structure and physical-chemical-biological interactions are accounted for.
7
Model attributes
Physical

Soil moisture content
Chemical

Recalcitrant carbon substrates – Represents the bulk of soil organic matter (SOM).

Labile carbon substrates – Represents the soil pool of carbon substrates that is
available for utilisation by microflora.
Biological

Worms – This group represents fauna which physically affect soil physical
structure (they are an example of an ecosystem engineer). The amendments to soil
structure then affect soil moisture content and consequently microbial growth.
These organisms also ‘comminute’ the recalcitrant SOM, making it more readily
available for microfloral utilisation.

Microflora – This represents a generic soil microbial biomass.

Grazers – This group represents protozoa/nematodes/microarthropods which graze
the microflora. These fauna are assumed not to amend the physical structure of the
soil.

Roots – Roots manifest themselves as carbon inputs into the system (dead roots
and exudations).
8
Model relationships (qualitative description)
The carbon inputs into the model are derived from soil organic matter and root
exudations. Water (i.e. rainfall) is also needed as an input. The biotic community
(worms, microflora and grazers) then interacts with the chemical and physical
attributes of the system and carbon is cycled. The relationships between the model
attributes are qualitatively described in Tables 1 to 3.
It is realised that not all links have been made even for this simple system (e.g.
leaching of carbon substrates, invasion of adjacent soil columns by microflora etc).
Furthermore, the microflora are represented by a single compartment within the
model, whereas thousands of different genotypes of soil fungi and bacteria coexist
under field conditions. The model has been purposefully oversimplified as this is
only an illustration of the ‘micro-process’ method. If this method is considered
worthy of further analysis, then a future study could calibrate the model on a sitespecific basis.
Model relationships (Quantitative description)
The overall model describes the dynamics of carbon flow in a column of soil from a
semi-natural ecosystem, to a depth that encompasses the rooting zone (Figure 5). The
depth profile is divided into three horizons, each represented by a similar submodel
(Figure 6, with component definitions in Tables 4 and 5). The timestep of the model is
9
1 day and the duration of the model run is three years (1095 timesteps). These spatial
and temporal scales have been arbitrarily selected for illustrative purposes; they could
be adjusted, depending on model requirements and data availability. All model
compartment definitions, units and initial values are given in Tables 4 and 5. The
following sections describe the quantitative links between model attributes.
Physical parameters
Soil Moisture Content – Soil moisture content is determined by rainfall and water
percolation rate. Rainfall figures are taken from the Sourhope Automatic Weather
Station (daily rainfall figures in mm). The AWS data for 1999-2000 is used in all
three years of the model run. The rainfall is input into the uppermost submodel
(submodel 1, Figure 5). First order kinetics are assumed to describe percolation, hence
if a pulse input of water is input into submodel 1 at t = 0, the dynamics of water
percolation are illustrated in Figure 7. A number of studies have demonstrated that
worms increase water percolation rates in soils by a factor ranging from 2 to 10
(Tisdall, 1978) (Edwards et al., 1979) (Clements, 1982) (Lee and Foster, 1991).
Hence it was assumed in the model that a relationship existed between water
percolation rate and worm biomass. The derivation of this relationship and the
equations that describe the effect of worm biomass on soil structure and hence
percolation rate are given are given in Appendix 1. The methodology given in
Appendix 1 was used to derive equations 1 to 4, which describe water flux down the
soil column.
10
Biological parameters
Microflora - Monod kinetics have been used in the majority of models describing
carbon utilisation by microflora (Smith, 1982) (Darrah, 1991a; Darrah, 1991b) (Scott
et al., 1995) (Blagodatsky and Richter, 1998a) (Kreft et al., 1998). Hence Monod
kinetics have also been assumed to adequately describe microfloral population
dynamics (Equations 5 and 6) in the present model. Table 4 contains kinetic
parameter definitions. It is assumed that microbial growth is affected by soil moisture
according to the relationship illustrated in Figure 8. Figure 8 is a plot of maximum
growth rate against a parameter v, a measure of soil moisture, where v is defined as
the instantaneous soil moisture content/maximum soil moisture content at saturation
(Equation 7). Low values of v describe drought conditions, whereas high values can
be interpreted as waterlogged or flooded conditions. As can be seen, it is assumed that
microbial growth rate is lowered under conditions of drought or waterlogging. In
order to modify the Monod equation to account for soil moisture, a parameter p was
formulated to amend the microfloral growth rate (Figure 9 and equations 5 and 8),
where p is controlled by v. As can be seen, the factor max/p approaches max under
optimal water conditions, because p tends to 1, leading to maximal microfloral growth
rates. Conversely, the factor max/p becomes very small at the extremes of water
condition as p increases under drought or flooded conditions, leading to lowered
microbial growth rates. To avoid max/p tending to 1/infinity, the value of p was
truncated to 5 at v0.05 and v0.95. This approach is based on (and extends) the
relationship between soil moisture and maximal growth rates described in Scott et al.
(1995), where different values of max are given, depending on the moisture content of
11
the soil.
Microbial death and waste production are assumed to follow first order kinetics and
these processes are accounted for in equation 5. Microfloral respiration must also be
affected by soil moisture, and is described by equation 6.
Worm biomass – Worms are treated as being an ‘influence’ only, they do not
represent a physical compartment of C within the system. However, a submodel of
carbon utilisation by worms could be added to the model if required (Whalen et al.,
1999). Figure 10 illustrates worm ‘residency’ in the rooting zone through time, where
the population is at a minimum during summer and at a maximum during the late
autumn/early winter period (Gerard, 1967). Fauna are known to indirectly increase the
decomposition rate of SOM through activities such as comminution (Seastedt, 1984)
(Brown, 1993) (Lavelle et al., 1997). Hence the overall model must include a
quantitative description of the indirect effect of fauna on SOM dynamics. It is
assumed that the functioning of worms (e.g. comminution) acts to increase the
availability of C to microbes. Therefore, within the structure of the model, it is
assumed that fauna act upon the decomposition rate kd , which controls the transfer of
carbon from the recalcitrant C to the labile C compartment. Specifically, a minimum
rate (kd_min) has been assumed for transfer of C from recalcitrant to labile OM in the
absence of worms. The action of worms increases the rate constant kd until a
maximum decomposition rate is reached (kd_max) at maximum worm biomass (Emax).
The presence of worms can increase the decomposition rate of SOM by a factor of 1.5
to 10 when compared to scenarios where worms have been deleted (Cortez, 1998)
12
(Yamashita and Takeda, 1998). An increase in the rate constant kd due to the presence
of worms was conservatively estimated from within this range, i.e. it was assumed
that kd_max = 2* kd_min. Equation 11 describes the effect of fauna on decomposition. In
equation 11, the constant Cd is the increase in recalcitrant C decomposition rate, over
and above the minimum rate, caused by faunal processing at Emax. In order to avoid
dividing a zero by Emax, Et should be given a very small conditional value (e.g.
0.000001) if Et = 0.
Grazers - The biomass of the grazers is assumed to be directly proportional to that of
the microflora, and death and excretion are described by first order rate constants.
Equation 9 describes the dynamics of C-flux through the grazers.
Chemical parameters
The carbon inputs into the model are ultimately derived from carbon fixation in the
above ground plant biomass. Inputs are in two forms – dead roots (deposited into the
recalcitrant C pool) and root exudations (deposited into the labile C pool). Plant
derived carbon inputs are related to carbon fixation throughout the year, however,
there is little quantitative data presently available on the dynamic input of carbon into
SOM from exudation and root turnover in relation to primary production. Hence both
Ir and Il will be given constant values throughout the year.
13
Cr – The recalcitrant substrates are a recipient compartment for carbon losses from the
roots due to death. The recalcitrant substrates represent the bulk of SOM and these
substrates depolymerise to the labile substrate pool obeying first order kinetics,
amended by the effect of comminution by worms. Ir is increased due to root death
(which is assumed to vary under drought or flooding, influenced by p, equation 10)
and microfloral and grazer death. Equation 11 describes the dynamic behaviour of the
recalcitrant SOM C.
Cl – The labile substrate pool is increased due to root exudation, Cr depolymerisation
and grazer and microfloral waste production. Cl is decreased due to microbial
utilisation of labile carbon substrates. It is assumed that root biomass decreases down
the soil profile, therefore Ir and Il are given decreasing values with depth (Table 5). Il
is decreased due to root death (which is assumed to vary under drought or flooding,
influenced by p, equation 12). Equation 13 describes the dynamic behaviour of the
labile C.
Results
The model was run using the simulation package ModelMaker 4.0.1. Examples of
model output are given in Figures 11 to 13. The advantage of this modelling approach
is that various hypotheses can be tested within the model (e.g. effects on carbon flux
of group deletions, reductions in biomass, differences in water conditions, carbon
input levels, spatial differences etc, plus many more with increased model
complexity). For example, if worms are deleted (thus decreasing water percolation
14
rate and production of labile substrates from recalcitrant SOM), the carbon cycle
within the model system is altered (Figure 13). As can be seen, when worms are
deleted, the water content of the submodels is increased (with frequent flooding), the
microbial biomass is lowered and decomposition of the recalcitrant SOM (Cr) is
impaired. This build up of recalcitrant SOM may then impact on plant productivity, as
demonstrated in ecotoxicological studies where deletion of earthworms due to the
build up of soil pollutants leads to an increase in SOM levels and a decrease in plant
productivity (Coughtrey et al., 1979; Spurgeon and Hopkins, 1999). This result
should be treated with caution as a host of other influences are not included, but this
merely demonstrates how the model could be used to study the dynamics of the soil
ecological community. The model provides a quantitative, rather than qualitative,
framework to answer questions posed by authors such as Jones et al. (1994), who ask
‘How should we model [ecological] engineering?’. The structure of the model itself is
elastic, therefore if a sufficient number of fundamental soil functions are included, the
approximate behaviour of the system could be tractably simulated. If model
complexity was increased and calibration properly attempted, predictions could be
made under a range of scenarios and tested against reality. This model is a device
which could be used to tie together the results of diverse projects within the field of
soil ecology.
This modelling methodology has advantages over previous methods as biological,
chemical and physical attributes of the system are seen as being equally important and
direct and indirect effects are quantitatively described at the core of the model
structure.
15
Obviously, there are a great many areas where further model development is
necessary. A number of these improvements to model structure are listed below.

‘Opening out the boxes’ – At present, the model has only one compartment
representing microflora. In reality, there is immense microbial diversity under
field conditions. Methods to account for this diversity in model structures need to
be developed (see report No. 2). Variations in microbial physiology could also be
taken into account, using techniques such as those described in Blagodatsky et al.,
(1998).

Improve the description of water flow down the soil profile to increase
hydrological realism in the model structure.

The model in its present state assumes that microbial growth is limited by soil
moisture alone. However, the effect of limitation in a number of parameters could
be accounted for. Values for a range of p inhibition constants could be defined for
temperature, pH, C/N ratio of carbon inputs etc.

Above ground plant productivity models could be mechanistically linked to the
below ground carbon cycling model.

A number of other functional groups could be included in the model, such as
mycorrhizae, based on models of carbon flow through individual groups (Staddon,
1998).
Conclusions
A model framework has been forwarded that can account for direct and indirect
16
interactions within the soil food web and physical-chemical-biological interactions.
This model could not directly be applied to the field site to make site specific
predictions of carbon flux in its present state. The model described in this report is a
framework on which to build more ecologically realistic models of nutrient flux,
which will eventually elucidate factors which control nutrient dynamics in soil
systems. Further collaboration with other workers is needed to amend the model
structure and tune parameter values (e.g. Mark Bailey: microbial diversity and water
stress; David Hopkins: effect of worms on soil structure; Phil Ineson: quantifying
carbon inputs into the system).
17
Model equations
Water percolation – Equations 1 to 4 describe the flow of water down the soil profile from one
submodel to the next.


S
dW1
 R   kw _ min  t cw  W1

dt
Sop 

Equation 1



S
S
dW2 
  kw _ min  t cw  W1   k w _ min  t cw  W2


dt
Sop 
Sop 


Equation 2



dW3 
S
S
  kw _ min  t cw  W2   kw _ min  t cw  W3


dt
Sop 
Sop 


Equation 3

dWS 
S
  kw _ min  t cw  W3

dt
Sop 

Equation 4
Generic submodel dynamics – Equations 5 to 13 describe the within submodel dynamics.
Equations 5 to 13 are repeated for each sub-model.
 max
Cl
dM
p

M  k1 M  k 2 M  k 3 M
dt
K m  Cl
Equation 5
max
C
dMCO2  1  Y  p l

M

dt
 Y  K m  Cl
v
Equation 6
Wn
Wmax
Equation 7
18
p  0.25
1
v(1  v)
Equation 8
dG
 k3 M  k 4 G  k 5 G  k 6 G
dt
Equation 9
I r  I r _ min p ; If p > 5, I r  1.1
Equation 10


E
dCr
 I r  k2 M  k5G   kd _ min  t cd  Cr
dt
Emax 

Equation 11
Il 
Il _ max
p
; If p > 5, I r  1.2
Equation 12
max
max
Cl


dCl
Et
p
 1 Y  p
 I l   kd _ min 
cd  Cr  k1M  k4G 
M 
M

dt
Emax 
K m  Cl
 Y  K m  Cl

19
Cl
Equation 13
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22
Tables
Table 1 – Physical attributes of the microprocess model
Table 2 – Chemical attributes of the microprocess model
Table 3 – Biological attributes of the microprocess model
Table 4 – Microprocess model parameter definitions
Table 5 – Initial values for selected variables
Figures
Figure 1 – Soil attribute interactions
Figure 2 – A schematic representation of a model containing both direct and indirect
influences on carbon flux in soils
Figure 3 – A schematic representation of a trophic model of carbon flow in soils
Figure 4 – Temporal development of soil ecological models
Figure 5 – An illustration of the hierarchical approach to micro-process modelling
Figure 6 – Expanded micro-process submodel (solid lines represent the physical flow
of carbon or water. Dashed lines represent ‘influence’ of one model attribute on
another – no physical flow of substances occurs along a dashed line)
Figure 7 – The temporal behaviour of water percolating down a soil column after a
pulse input at t = 0.
Figure 8 – The relationship between maximal microbial growth rate and soil
moisture.
Figure 9 – The relationship between the moisture inhibition factor p and soil moisture
content
Figure 10 – Worm biomass in the rooting zone throughout the timescale of the model
run.
Figure 11 – Dynamic behaviour of carbon in each model compartment through time
(submodel 1)
Figure 12 – Depth profile of microfloral biomass in model system with time
(submodels 1 to 3)
Figure 13 – Effect of ecosystem engineer deletion on soil moisture, microbial
biomass and recalcitrant SOM carbon (submodel 1)
23
Table 1
Attribute
Affects:
Directly/indirectly?
Soil moisture
microflora
Directly (microfloral
growth is negatively
affected by drought or
flooding)
Dead root carbon inputs
Directly (inputs increase
under drought or flooding,
due to increased root
death)
Root exudations
Directly (inputs decrease
under drought or flooding
due to increased root
death)
Attribute
Affects:
Directly/indirectly?
Labile carbon substrates
Microflora
Directly by providing an
energy source for
microfloral growth
Recalcitrant carbon
substrates
Labile carbon substrates
Directly by providing a
further carbon source for
the labile carbon pool
Table 2
24
Table 3
Attribute
Affects:
Directly/indirectly?
Worms
Soil moisture
Directly, by altering
percolation rate
Carbon substrates
Directly, by increasing
decomposition rate of
recalcitrant carbon to
labile carbon through
comminution
microflora
Indirectly, through the
effect of worms on water
and carbon substrate
balance
Labile carbon substrates
Directly (microflora use
labile carbon as an energy
source and return wastes to
labile C pool)
Recalcitrant carbon
substrates
Directly (due to death)
grazers
Directly (microbes provide
a food source for grazers)
microflora
Directly, by using
microflora as a foodsource
Microflora
Grazers
Carbon substrates (Cl and Directly (due to death and
Cr)
excretion)
Roots
Labile carbon substrates
Directly (increase Cl pool
by exudation)
Recalcitrant carbon
substrates
Directly (increase Cr pool
due to death of roots)
25
Table 4
Parameter
Definition
Initial
value/function
Units
(see notes)
0.0005
t-1
Table 2
Table 2
0.9
w svol-1
w svol-1
t-1
E
Faunally induced increase in decomposition
constant at Emax
Recalcitrant carbon pool
Labile carbon pool
Faunally induced increase in water
percolation constant at Emax
Worm population biomass
Figure 10
w svol-1
Emax
G
Ir_min
Il_max
k1
k2
k3
k4
k5
Maximum worm population in rooting zone
Grazer carbon pool
Dead root carbon input rate (minimum)
Exudate carbon input rate (maximum)
Microbial excretion rate
Microbial death rate
Grazing rate
Grazer excretion rate
Grazer death rate
10
Table 2
Table 2
Table 2
0.03
0.02
0.02
0.08
0.02
w svol-1
w svol-1
w svol-1 t-1
w svol-1 t-1
t-1
t-1
t-1
t-1
t-1
k6
kd_min
Km
kw_min
M
MCO2
p
R
S
Grazer respiration rate
Minimum recalcitrant C decomposition rate
Saturation constant for microfloral growth
Minimum water percolation rate
Microbial biomass carbon pool
Carbon dioxide pool
Microfloral maximal growth rate
Moisture inhibition parameter
Daily rainfall (Sourhope)
Soil structure parameter
0.05
0.0005
150
0.1
Table 2
0
4.0
Equation 8
Variable
0.0001
t-1
t-1
w svol-1
t-1
w svol-1
w svol-1
t-1
mm
-
v
Wmax
Wn
Ws
Y
Proportion of maximum moisture capacity
Maximum water capacity of submodel n
Initial water content of submodel n
Initial water content of sink
Microbial yield coefficient
Equation 7
20
10
0
0.5
f svol-1
f svol-1
f
w w-1
cd
Cr
Cl
cw
max
26
Notes
The units are arbitrary for this illustrative model. They could be adjusted to ng C cm -3
or mg C dm-3, depending on the requirements and scale of the model. In the above
table, the units are as follows:
w – unit of mass (e.g. ng, mg, g)
svol – unit of soil volume (mm-3, cm-3, dm-3)
t – unit of time (the time unit used in this model run is ‘day’)
f – unit of fluid (e.g. ml, l)
Table 5
1
Submodel
2
3
Initial Cr
2100
700
400
Initial Cl
10
7
2
Initial G
6
3
1
Irmin
0.2
0.1
0.05
Ilmax
6
3
1.5
Initial M
30
15
7.5
27
Figure 1
e.g.:
 Species diversity
 Interaction strength
 Physiological state
BIOLOGICAL
CHEMICAL
PHYSICAL
e.g.:
 C/N ratio
 pH
 P, K content
e.g.:
 Pore volume
 Moisture content
 Void space spatial
arrangement
28
Figure 2
Water
Air
CO2
microflora
Available
soil
carbon
Soil structure
fauna
Burrowing/
bioturbation
Comminution
Solid arrows: material flow of carbon
Dashed arrows: ‘influence’ of one component on another (no material flow of carbon)
Figure 3
microflora
Available
soil
carbon
fauna
29
CO2
Figure 4
Far future?
‘Ideal’ Mechanistic models of C flux
 Direct and indirect effects and
feedbacks quantitatively described
in a mechanistic manner.
 Phys/chem/biol interactions
quantitatively related
mechanistically
Near future
Microprocess models of C flux
 Direct and indirect effects on C
flux quantitatively described
using a small scale process model
methodology
 Phys/chem/biol interactions
quantitatively related
 Calibration by best available data
Present
Large scale process models/small scale
trophic models/empirical data
 Small number of structurally simple
trophic models
 Large amount of empirical data that
is not immediately amenable to
modelling.
 Poor understanding of
phys/chem/biol interactions, indirect
effects and feedbacks
30
Figure 5
SUB-MODEL 1
Rainfall
V
W1
FIELD-SCALE
MODEL
p
Ir
Il
F4
Cr
F5
Cl
M_CO2
F2
Water_flow
F6
F7
S
Sub1
Sub4
Out1
Out4
F1
M
F8
F3
Eworm_popn_lag
eworm_popn
F9
G_CO2
G
F1
Out1
SUB-MODEL 2
Rainfall
V
W1
Water flow
F4
In1
In3
Sub2
Sub5
Out2
Out5
p
Ir
Il
F4
Cr
F2
F5
Cl
F5
Water flow
M_CO2
F2
Water_flow
F6
F1
F7
S
In4
Sub3
Sub6
Out3
Out6
M
F8
F3
Eworm_popn_lag
In2
eworm_popn
F9
G_CO2
G
Out1
F3
F6
Water flow
C1
SUB-MODEL n
31
C2
Figure 6
Rainfall
V
W1
p
Ir
Il
F4
Cr
F5
Cl
M_CO2
F2
Water_flow
F6
F1
F7
S
M
F8
F3
Eworm_popn_lag
eworm_popn
F9
G
Out1
32
G_CO2
Figure 7
100
Water content (arbitrary units)
90
80
70
60
W1
W2
W3
Ws
50
40
30
20
10
0
0
10
20
30
40
50
Time
33
60
70
80
90
100
Figure 8
max
Microbial
growth
rate
min
Drought
Optimal
Soil moisture content
34
Flooding
Figure 9
5
4
p
3
2
1
0
0.05
0.50
v
(Wt/Wmax)
35
0.95 1
Figure 10
1
0
9
8
7
6
E
5
4
3
2
1
0
0
3
6
5
7
3
0
T
i
m
e
(
d
a
y
s
)
36
1
0
9
5
Figure 11
1000
Cr1
Cl1
grazers1
M1
M_CO2_1
g_CO2_1
100
10
1
0
365
730
1095
Time (days)
Figure 12
60
C content in each compartment (w/svol)
C content of each compartment (w/svol)
10000
50
40
M1
M2
M3
30
20
10
0
0
365
730
Time (days)
37
1095
Figure 13
7
0
-1 )
6
0
S
o
i
lw
a
t
e
rc
o
n
t
e
n
t(
+
w
o
r
m
s
)
S
o
i
lw
a
t
e
rc
o
n
t
e
n
t(
-w
o
r
m
s
)
5
0
4
0
Watervolume(fsvol
3
0
2
0
1
0
0
6
5
-1 )
6
0
M
i
c
r
o
b
i
a
lb
i
o
m
a
s
s(
+
w
o
r
m
s
)
M
i
c
r
o
b
i
a
lb
i
o
m
a
s
s(
-w
o
r
m
s
)
5
5
5
0
4
5
MicrobialC(wsvol
4
0
3
5
3
0
2
5
2
6
0
2
0
-1 )
2
5
0
0
2
4
0
0
2
3
0
0
2
2
0
0
2
1
0
0
RecacitrantSOMC(wsvol
2
0
0
0
1
9
0
0
1
8
0
0
1
7
0
0
R
e
c
a
l
c
i
t
r
a
n
tS
O
M
C
(
+
w
o
r
m
s
)
R
e
c
a
l
c
i
t
r
a
n
tS
O
M
C
(
-w
o
r
m
s
)
1
6
0
0
1
5
0
0
3
6
5
7
3
0
T
i
m
e
(
d
a
y
s
)
38
1
0
9
5
Appendix 1
Quantifying the effect of ecosystem engineers on soil processes – modelling the
influence of fauna on water percolation rates in soil.
It is widely recognised that certain species of fauna amend the physical structure of
soil, which in turn affects a number of ecosystem processes. The following section
describes a simple model which quantifies the effect of an ecosystem engineer (E) on
water percolation rate via amendment of the physical structure of soil.
Consider the percolation rate of water through a volume of soil as a first order process
(Equation 1)
dW
 I w  kwW
dt
Equation 1
Where W is the water content of soil volume V, Iw is the input rate of water into V and
kw is the rate constant controlling percolation rate of water out of V. It is assumed that
the action of E causes an increase in the number of burrows in soil (where worms are
an example of an ecosystem engineer), which acts to increase the percolation rate of
water (kw). The percolation rate kw will attain a maximum value (kw_max) if the E
population in soil volume V is at a maximum (Emax). kw will attain a minimum value
(kw_min) when E = 0. E will exert its effect on kw via its effect on soil structure, S.
Graphically, the relationship between the three quantities E, S and kw at equilibrium is
illustrated in Figure 1.
39
Figure 1
kw_max
Sop
Emax
0
00
t
t
0
0
t
As can be seen, at Emax, the physical state of the soil is at its optimal configuration
(Sop) producing a maximal percolation rate, kw_max. The variable S can be considered
as a quantity describing a physical attribute such as total earthworm burrow length in
soil volume V. However, the physical structure/state of the soil is not at equilibrium
under natural conditions; the physical state of the soil changes through time (e.g.
worms create burrows and the burrows themselves break down due to ageing and
bioturbation). Therefore, the dynamics between E, S and kw must be quantified.
Consider first a situation where burrows (an example of a biologically created soil
physical structure) are indestructible. Burrow creation is related to E biomass
according to the relationship illustrated in Figure 2:
Figure 2
Sop
Emax
0
tx
0
ty
40
tx
ty
However, burrows have a finite ‘lifespan’ (T). New structures will be created in
proportion to E biomass and old structures will be destroyed T timesteps after their
creation. Therefore:
Rate of change
of S
=
Production rate of new structure
Destruction rate
of old structure
Allowing one unit of E biomass to produce one unit of ‘structure’ per time period
gives:
dS
 ED
dt
Equation 2
Where D is the destruction rate of older structure, proportional to E at t-T. E and D are
illustrated in Figure 3 for the time period t = 0 to 365, where T = 30:
Figure 3
1
0
E
8
(equivalent to the 6
production
4
rate of S)
2
E
0
1
0
8
D
6
(equivalent to E
at time t-T)
4
2
D
0
0
41
6
0 1
2
0 1
8
0 2
4
03
0
0 3
6
0
T
im
e
A graph of S under the above conditions for the time period t = 0 to 365 is illustrated
in Figure 4:
Figure 4
3
0
0
2
5
0
2
0
0
S
1
5
0
1
0
0
5
0
0
0
S
3
6
5
7
3
0
1
0
9
5
T
i
m
e
The relationship between S and E has been defined (Equation 2). The next step is to
relate S to kw. In the absence of E in soil volume V, percolation rate (kw) is at a
minimum (kw_min). kw is increased in proportion to S until a maximum value is reached
(kw_max). Hence, the percolation rate through V can be separated into 2 components
according to equation 3, where x is the increase in percolation rate caused by E
through S.
kw _ max  kw _ min  x
The value of x is described by equation 4
42
Equation 3
x
St
cw
Sop
Equation 4
As can be seen, the factor St/Sop becomes 1 when St is at a maximum (Sop). Hence at St
= Sop, x = cw, where cw =kw_max-kw_min. In order to avoid dividing a zero by Sop, S
should be given a very small conditional value (e.g. 0.000001) if St = 0; this occasion
will arise if E = 0 for an extended period of time. In conclusion, equations 5, 6 and 7
relate ecosystem engineer biomass to water percolation rate.
kw  kw _ min 
St
cw
Sop
Equation 5
dS
 ED
dt
Equation 6
cw  kw _ max  kw _ min
Equation 7
It is realised that this is not a complete description of the effect of ecosystem
engineers on soil structure and consequently soil processes. There are a number of
areas where this model deviates from reality, however, no previous models have
attempted to include the dynamic effect of ecosystem engineers on soil processes and
this simple model is viewed as a first step towards increasing biological realism in
carbon flow models where the indirect effects of ecosystem engineers may be
important.
43