Max-Planck Institute for Biogeochemistry
Jena, Germany
A global distribution of biodiversity inferred from
climatic constraints: Results from a process-based
modelling study
Postprint version*
Axel Kleidon, Harold A. Mooney
published in:
Global Change Biology
reference:
A. Kleidon, Harold A. Mooney (2000) A global distribution
of biodiversity inferred from climatic constraints: Results
from a process-based modelling study. Global Change
Biology, 6 (5), 507-523.
web link:
http://www3.interscience.wiley.com/journal/117991450/home
Contact:
Dr. Axel Kleidon
Biospheric Theory and Modelling Group
Max-Planck-Institut für Biogeochemie
Hans-Knöll-Str. 10 • Postfach 10 01 64
07745 Jena • Germany
e-mail:
Ph:
Fax:
web:
[email protected]
+49-3641-576-217
+49-3641-577-217
gaia.mpg.de
* A postprint is a digital draft of a research journal article after it has been peer reviewed. A draft
before peer review is called a preprint. Postprints may sometimes be the same as the published
version, depending on the publisher. (source: wikipedia.org)
A GLOBAL DISTRIBUTION OF BIODIVERSITY
INFERRED FROM CLIMATIC CONSTRAINTS:
RESULTS FROM A PROCESS-BASED MODELLING STUDY
Authors:
Axel Kleidon and Harold A Mooney
Department of Biological Sciences
Stanford University, Stanford, CA 94305, USA
Phone:
Fax:
e-mail:
(650) 723-1530
(650) 723-9253
[email protected]
Corr. Author:
Axel Kleidon
Keywords:
biodiversity, climate, allocation, generic plant model,
plant functional types, biome distribution
Running Title:
Modelling biodiversity
revised version
11/1/99
Global Change Biology
in press
Modelling Biodiversity (Kleidon & Mooney)
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ABSTRACT
We investigated the connection between plant species diversity and climate by using a
process-based, generic plant model. Different “species” were simulated by different values for
certain growth-related model parameters. Subsequently, a wide range of values were tested in the
framework of a “Monte Carlo” simulation for success, that is, the capability of each plant with
these parameter combinations to reproduce itself during its lifetime. Species diversity was
approximated by the range of successful parameter combinations. This method was applied to a
global grid, using daily atmospheric forcing from a climate model simulation. The computed
distribution of plant “species” diversity compares very well with the observed, global-scale
distribution of species diversity, reproducing the majority of “hot spot” areas of biodiversity. A
sensitivity analysis revealed that the predicted pattern is very robust against changes of fixed
model parameters. Analysis of the climatic forcing and of two additional sensitivity simulations
demonstrated that the crucial factor leading to this distribution of diversity is the early stage of a
plant’s life when water availability is highly coupled to the variability in precipitation because in
this stage root-zone storage of water is small. We used cluster analysis in order to extract
common sets of species parameters, mean plant properties and biogeographic regions (biomes)
from the model output. The successful “species” cannot be grouped into typical parameter
combinations, which define the plant’s functioning. However, the mean simulated plant
properties, such as lifetime and growth, can be grouped into a few characteristic plant
“prototypes”, ranging from short-lived, fast growing plants, similar to grasses, to long-lived, slow
growing plants, similar to trees. The classification of regions with respect to similar
combinations of successful “species” yields a distribution of biomes similar to the observed
distribution. Each biome has typical levels of climatic constraints, expressed for instance by the
number of “rainy days” and “temperature days”. The less the number of days favorable for
growth, the greater the level of constraints and the less the “species” diversity. These results
suggest that climate as a fundamental constraint can explain much of the global scale, observed
distribution of plant species diversity.
Modelling Biodiversity (Kleidon & Mooney)
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1
INTRODUCTION
It has long been observed that tropical ecosystems are vastly more diverse than temperate
ones and many hypotheses have been proposed to explain this general feature of ecosystems
across the globe (see for instance Ricklefs and Schluter 1993, Heywood 1995). Here, we aim to
focus on plant species diversity, in particular as it relates to climate. There are a series of studies
which have successfully correlated gradients in observed plant species diversity with variations
in the climatic environment. Currie and Paquin (1987), for instance, were able to show a high
correlation between mean annual evapotranspiration and the distribution of tree species diversity
in North America, and Adams and Woodward (1989) extended this approach by demonstrating
that this correlation can also account for the intercontinental differences in tree species diversity
of temperate forests in North America, Europe and East Asia. Such relationships can also be
found in the tropics, e.g. as reported by Gentry (1988).
However, such correlations cannot provide a mechanistic understanding for the causes of
biodiversity. In this paper, we examine biodiversity from a process-based perspective by asking
which climatic conditions allow for high diversity in plant growth strategies. This perspective is
motivated by the dominant role of climate for a wide range of biological processes, from the
exchange fluxes of water and carbon to the distribution of species across the world. Climate
substantially constrains ecosystem activity and the distribution through its supply of water,
radiation and heat. These constraints have successfully been used to predict biospheric aspects
such as the net primary productivity (e.g. Rosenzweig 1968, Lieth 1975) and the large-scale
distribution of major biomes (e.g. Box 1981, Prentice et al. 1992). This leads us to the question
of how much the global distribution of species diversity is the consequence of climatic
constraints. More specifically, we ask from a process-based perspective which climatic regime
supports the highest diversity of plant growth strategies (or “species”), expressed in terms of its
allocation and phenology patterns.
Modelling Biodiversity (Kleidon & Mooney)
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In order to compute species diversity from climate, we develop a simple, process-based
simulation model of a generic plant, embedded in a land surface scheme. In the model, the plant
starts growing from a “seed”1 (an initial amount of assimilates) once environmental conditions
are favorable. During its lifetime, it allocates assimilates to six carbon pools: reproduction,
leaves, roots, structural above- and belowground, and storage. Once the storage pool becomes
zero the “plant” dies. The carbon pools in turn determine land surface parameters such as leaf
area index, vegetative coverage, surface albedo and soil storage capacity of plant-available water
(or rooting depth). These parameters affect the simulated land surface hydrology and
consequently net primary production (NPP), that is, the supply of assimilates. This construct
leads to an interaction between allocation strategies, plant development and land surface
hydrology under fixed atmospheric conditions. Our intention is to specifically examine the
potential singular role of atmospheric conditions as a central driving force for the patterning of
biodiversity. In view of this, we have purposefully omitted the aspects of competition among
plants, nutrient dynamics and interactions with microclimate. Within the model, processes such
as NPP, allocation and evapotranspiration, are all formulated in a uniform way. The “plants”
only differ with respect to the values of 12 chosen model parameters. It is these parameters alone
which determines the “plant’s” individual behavior (mainly in terms of its allocation and
phenology patterns). The idea behind this is to allow for as many growth strategies as possible,
thus making the model itself as universal as possible. This approach allows us to compute
species diversity by testing which combinations of parameter values lead to a successful “plant”
in a range of climates.
We take each unique set of these parameter values as representative of a plant “species”
since it defines the individual functioning of the “plant”. We call a “species” successful only if it
is able to reproduce, meaning that its allocation to reproduction during its lifetime exceeds the
initial amount of assimilates. For these parameters we take a large set of random numbers to give
us many random “species”. The motivation for this is to test the greatest variety of plant growth
1
We put terms that usually relate to real plants such as “species” and “seed” in quotation marks to emphasize that
these terms refer to the associated attributes in the model and not to the real world.
Modelling Biodiversity (Kleidon & Mooney)
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strategies (as many different “species”) as possible. We test these “species” to see whether or not
they are successful under different atmospheric forcings. Using output from a climate model on a
global grid, we are then able to compute the number of successful “species” in any land region of
the world. The number of successful “species” is then taken as an estimate for species diversity.
The analysis of the model output enables us to determine the climatic characteristics of
high diversity in detail within the model context. Since we know the climatic forcing which led
to the distribution of “species” diversity, it is therefore possible to extract the climatic aspects
that constrain growth strategies and thus lead to this distribution. Furthermore, the analysis can
be extended to test for the existence of “species” with similar sets of parameters, similar regions
with respect to combinations of successful “species” (that is, biomes), and “plants” that appear
similar in their realized mean lifetime properties.
In the next section we provide a detailed description of the plant model, the parameters
which define a “species” and give an overview of the land surface scheme. Section 3 describes
the setup of the simulation, the methods to assess the sensitivity of the computed diversity
pattern, and the tools to analyze the successful “species”. The results are presented and discussed
in section 4 as well as their limitations. We close with a summary and conclusion in section 5
which includes a discussion on the implications and prospects for future work.
Modelling Biodiversity (Kleidon & Mooney)
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2
MODEL DESCRIPTION
The rationale for the model development was to create a generic model of a plant, in
which the basic processes are formulated in a simple and universal way. The simplicity of the
model is a necessary requirement for conducting a Monte Carlo simulation on a global grid (see
section 3). Most of the model formulation, as well as the choice of constant model parameters, is
based on standard formulations used in models for the land surface and the terrestrial biosphere,
see e.g. ECHAM 4 (Roeckner et al. 1996) for the land surface component and CASA (Potter et
al. 1993), SDBM (Knorr and Heimann 1995), SILVAN (Kaduk and Heimann 1996) for the
biospheric component. An overview of the model structure is shown in Figure 1.
Generic Plant Component
The generic plant model’s state variables, parameters, and parameter values are
summarized in Table 1. The generic plant is represented by six carbon pools: a combined
assimilates and storage pool (A), reproductive (”seeds”, S), leaves (L), structural aboveground
(WL), fine roots (R) and structural belowground (WR). All carbon pools are initially empty. Once
growing conditions are favorable, germination is initiated by setting the assimilates pool to an
initial amount A0. Carbon is then allocated to the six pools and land surface parameters are
derived from the pool sizes. These land surface parameters affect the processes at the land
surface (see next subsection) and net primary productivity (NPP). NPP in turn forms the input to
allocation. Death occurs if the amount of carbon in the assimilate pool is zero (A = 0). The
formulation of these processes contain a series of parameters p1 … p12, which define a “species”
(or growth strategy). All of these parameters range between zero and one (The range of some
parameters is extended by using them in the exponent). A “species” is successful if it is able to
reproduce, that is, that the size of the reproductive pool S exceeds the initial amount of
assimilates A0 within the plant’s lifetime (i.e. S > A0). These parameters and their description are
summarized in Table 2. The components of the model are described in full detail below:
Modelling Biodiversity (Kleidon & Mooney)
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Growing conditions: Growing conditions are formulated in terms of soil wetness ƒW ( =
actual amount of moisture stored in the rooting zone W over the storage capacity WMAX, both
quantities used in the land surface component, see next subsection), temperature T, and time
constants W and T :
G RO W,W
G RO W,T
W
t
W
1
T
t
t
G RO W,W
T
t
with
W
W
G RO W,T
1
t
T
t
with
T
W
;
WMAX
T
;
T TCrit
10 4 p1
W
T
10 4 p 2
2
2
(1)
The quantities at the time t - t represent the values of ƒGROW,W and ƒGROW,T from the previous
time step. The parameters p1 and p2 are associated with time constants, describing the memory to
the past environmental conditions. A value close to zero represents a short memory while a large
value describes a long memory. Germination and growth occur if both functions are above a
value of 0.5:
0;
G RO W,W
or
G RO W,T
G RO W
1;
G RO W,W
and
G RO W,T
0.5
0.5
0.5
0.5
(2)
Germination: Germination is initiated whenever growing conditions are favorable. It is
implemented by setting the assimilates carbon pool to an initial value A0 given by
A0
108 p3
7
A00
(3)
The supply of seeds is not limited.
Allocation and Senescence: Allocation to growth (leaves, roots, structure) occurs when
Modelling Biodiversity (Kleidon & Mooney)
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growing conditions are favorable (ƒGROW = 1). It is proportional to the size of the assimilates pool
A and to a set of fixed parameters. Allocation to reproduction is enabled (ƒSEED = 1) once the
assimilates pool exceeds the initial amount A0, that is, A > A0. Once initiated, is not affected by
the growing conditions. Senescence is based on time averaged net primary production ƒNPP:
NPP
NPP
t
NPP
1
NPP
t
t
with
NPP
104 p 4
2
NPP
(4)
where NPP is the simulated, actual net primary production given by eqn. 12. The parameter p4 is
associated with a time constant NPP, describing the memory to the past NPP conditions. A
value close to zero represents a small persistence during periods of negative NPP while a value
close to one represents large persistence. Senescence is initiated when ƒNPP is less than zero:
0
1
SEN
0
0
NPP
NPP
(5)
During periods of senescence, a constant rate of carbon cSEN is removed from the leaves (L) and
roots (R) pools (see below for partitioning).
Change in Pool Sizes: The dynamics of the carbon pools are expressed by the following
differential equations:
dA
dt
dL
dt
dR
dt
dS
dt
dWL
dt
dWR
dt
NPP
AS
AL
AR
A
AL
1
LW
A
LD
c SE N
AR
1
RW
A
RD
cSEN
AS
A
AL
LW
A
AR
RW
A
(6)
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The parameters ƒXY are given by
p5
AS
AL
AR
LW
RW
LD
RD
p5
p6
p5
p6
p5 p6
p9
p10
0 ;
p6
p7
p7
p8
SEED
p7
p8
G RO W
p7
p8
G RO W
SEN
(7)
0
0
p11 ; SEN
0
; SEN
1 p11 ; SEN
0
0
These factors are assumed to remain constant during the time step of integration so that analytical
solutions of eqns. (4) are used in the model.
Land surface parameters: Land surface parameters, needed by the land surface
component, consist of maximum soil storage capacity of plant available water in the rooting zone
WMAX, leaf area index LAI, supply for transpiration TrSupply, vegetative coverage ƒVEG, forest
cover ƒFOR, surface albedo a, and the storage capacity of the canopy WLMAX. The use of these
parameters for simulating land surface processes is described in the section “Land Surface
Component” below. They are computed from the carbon pools according to:
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WMA X
LAI
max WMA X,0 , cW MA X
c LA I L
TrSupply cTR S R
W
VEG
1 e
k LA I
F OR
1 e
c FOR WL
a
VEG
WLMA X
WR
aV E G
1
VEG
aSO IL
cW LMA X LAI
(8)
The conversion constants and their values are summarized in Table 3.
Most of these parameterizations are commonly used in terrestrial biogeochemical models:
leaf area index LAI being proportional to the size of leaf carbon pool, vegetative coverage ƒVEG
being an exponential function of LAI, the surface albedo a being a weighted combination of a
fully vegetated surface and bare soil and the size of the rainfall interception storage WLMAX being
proportional to the leaf area index LAI. The formulations regarding root properties (WMAX and
TrSupply) are obtained from first principles. The motivation for using a square-root relationship
for the soil water storage capacity comes from Shinozaki et al.’s pipe model (1964). This
conceptual model views the root system as an assemblage of pipes which connect the root ends
(the organs responsible for water absorption from the soil) with the leaves. The pipe model is
capable of reproducing the observed shape of plant forms. We assume a uniform density of root
ends within the rooting zone/soil volume WMAX and obtain a square root relationship between
depth and biomass WR. Furthermore, we assume the supply for transpiration/soil water uptake
capacity to be proportional to the fine root biomass R and to soil wetness. The parameterization
of forest coverage ƒFOR is taken as an analogy to the formulation used for vegetative coverage
ƒVEG. These land surface parameters form the input for the land surface component (see
subsection below).
Net Primary Productivity (NPP): NPP is computed from the difference between gross
primary productivity (GPP) and autotrophic respiration (RES). GPP is calculated as a function of
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the photosynthetically active radiation (PAR, taken as 55% of the incoming solar radiation) and a
number of limiting factors i (Monsi and Saeki 1953, Monteith 1977):
GPP
cG PP
LU E
H2 O
T
VEG
PAR
(9)
The limiting factors i are given by:
LU E
p12
H 2O
1 e
T
tanh
T
TrSupply TrDe mand
15 C
8 C
0.5
(10)
LUE represents a constant parameter which increases the light use efficiency with the tradeoff of
increasing respiration rate at the same time (see below, eqn. 11). This mechanism has been
incorporated in order to allow for different values of light use efficiency and is motivated by
observations that increased light use efficiency is associated with higher respiration rates (e.g.
Bazzaz and Pickett 1980). It is also motivated by the observations that the plant’s nitrogen status
correlates with photosynthesis (Field and Mooney 1986) as well as respiration (Ryan 1995). The
factor H2O represents the water limitation of productivity and is taken to be a function of the
ratio of actual evapotranspiration to potential evapotranspiration. TrSupply is the supply rate for
evapotranspiration (eqns. 8) and TrDemand is the atmospheric demand for transpiration (as
computed in the land surface component, see below). The factor T reduces productivity at low
temperatures T. The motivation for using the hyperbolic tangent is to obtain a net temperature
dependence of NPP (that is, in combination with respiration, see eqns. (11) and (12) below)
similar to the one used in the CASA model (Potter et al. 1993). The dependence of GPP on
atmospheric carbon dioxide concentration is not included in this model.
Respiration RES is taken as proportional to a Q10 relationship and to biomass:
RES
LUE
Q10
T 10 C
10 C
cRES,1 L R
cRES,2 WL
WR
(11)
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NPP is then obtained by the difference between (9) and (11):
NPP
GPP
RES
(12)
Land Surface Component
The land surface model is based on the land surface parameterization of the ECHAM 4
atmospheric General Circulation Model (Roeckner et al. 1996). Two main modifications have
been made to this land surface scheme: First, we use the supply-demand approach of Federer
(1982) to allow for offline simulations (i.e. without an interacting atmosphere), using the
equilibrium evapotranspiration rate of McNaughton and Jarvis (1983) as an approximation for
the demand. The supply for transpiration TrSupply is computed from soil wetness and fine root
biomass (see eqn. 8). Second, we include a sub-rooting zone soil layer. This layer is fed by the
drainage from the rooting zone. Water is only removed with an increase in the rooting zone depth
or when its content exceeds its capacity (set to 1000 mm). The idea of including an additional
layer is to adequately simulate enhanced plant water availability with downward root growth. The
downward root growth (that is, an increase in the extent of the rooting zone WMAX) leads to an
adjustment of the soil water content of the rooting zone W, determined by
W
WMA X
WSU B
WSU B, MA X
(13)
with WSUB and WSUB,MAX being the water content and the storage capacity of the sub-rooting
zone layer. This adjustment is the result of the distinction between the rooting zone and subrooting zone in the soil column.
The land surface component consists of four budget equations for moisture stored in the
vegetation’s canopy (WL), in the snow cover (WS), in the rooting zone of the soil (W) and in a
zone below the rooting zone (WSUB). This scheme runs on a daily time step, using daily forcing
Modelling Biodiversity (Kleidon & Mooney)
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of precipitation, 2m air temperature, incoming shortwave radiation and net emission of longwave
radiation. From precipitation and air temperature, snowfall is computed as in Wigmosta et al.
(1994). Snowmelt is computed according to the day-degree formula, using a melt rate of 3.22
mm d-1 °C-1. Precipitation is first intercepted by the canopy, using a maximum storage capacity
of WLMAX (eqn. 8). Throughfall and snowmelt form the input for soil infiltration. Surface runoff
is computed from infiltration, soil moisture and surface heterogeneity according to Dümenil and
Todini (1992). Drainage from the rooting zone is computed from soil wetness and feeds the subrooting zone reservoir WSUB. The net surface albedo is computed from the value given in eqn. 6
and the fraction of snow and forest cover. The albedo determines the net amount of absorbed
solar radiation which is needed to compute the demand for evapotranspiration. Total
evapotranspiration is the composite of evaporation from the canopy, bare soil, and snow and
transpiration. Transpiration is taken as the minimum of supply and demand.
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3
METHODS
This section describes the methods we apply to: (i) calculate the distribution of species
diversity using the model of section 2; (ii) estimate the sensitivity of the predicted pattern to
changes in fixed model parameters (see Tables 1 and 3); (iii) isolate the underlying mechanism
and causes for this pattern; and (iv) group the successful “species” with respect to different
characteristics.
Distribution of species diversity: The coupled plant growth - land surface model runs on a
global grid, comprising of all 1,821 non-glaciated land grid points of the ECHAM 4 GCM
(Roeckner et al. 1996, approx. 2.8° lat * 2.8° lon in T42 resolution). First, the land surface
scheme is integrated without the plant component for 2 years to yield an equilibrium in the water
content of the soil. It is then integrated for 20 years including the plant growth model using a
daily time step. Daily “weather” input of precipitation, incoming shortwave radiation, net
longwave emission and near surface (2m) air temperature is taken from model output of a ten
years simulation of the ECHAM 4 GCM (Hagemann and Kleidon, 1999), which is used twice in
order to obtain forcing for 20 years. The model starts in January, and after one “plant” dies, it is
replaced by a new “seed” throughout the simulation period.
In principle, the total range of successful “species” can be obtained by testing all possible
“species” parameter combinations p1…p12 for success (i.e. S > A0). This would involve a
tremendous numerical task, which would lead to 1012 simulations for each grid point if, for
instance, 10 evenly spaced values for each parameter were used. As a more practical alternative,
we employ the Monte-Carlo technique (e.g. Press et al., 1992), the idea of which is to efficiently
evaluate the function (that is, success of a “species”) for a large number of random parameter
combinations or “species”. With a sufficiently large number of combinations, the ratio of the
number of successful “species” to the total of all tested “species” will attain a constant value and
thus represents a good approximation for the total range of successful “species”. We evaluate the
model for a total of 1000 combinations (i.e. 1000 random ”species”) of the model parameters pi
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(Table 2) on each grid point, each being run for a length of 20 years. Relative species diversity
among regions is then approximated by the number of successful “species”. We will be referring
to this setup as the “standard” simulation.
Sensitivity of the results. We conduct a sensitivity analysis to estimate the robustness of
the computed pattern of species diversity with respect to the constant parameters (respiration
costs cRES,1, light use efficiency cGPP, specific storage capacity cWMAX, specific uptake capacity
cTRS, initial storage capacity WMAX,0 , specific leaf area cLAI, and critical temperature TCrit, see
Tables 1 and 3). We examine these sensitivities by conducting additional simulations and we
evaluate them by correlating the patterns with the “standard” pattern on a grid point basis. The
correlation coefficient r2 describes the similarity of the two patterns, while the linear regression
coefficient a describes the similarity in magnitude. The sensitivity to the constant parameters is
obtained from simulations of 20 years length for a subset of 500 random “species” in which each
of the parameters listed above are doubled and halved from their values as specified in section 2
(except for the critical temperature, where the values are changed by ± 5°C). In addition we
perform a long simulation of 500 years for a subset of 200 “species” to test the sensitivity of the
predicted pattern to the simulation period.
Mechanism. To get a first impression of the causes for the predicted diversity pattern, the
computed species diversity is correlated with mean climatic variables. Furthermore, two
additional model simulations are then conducted in order to test how important plant
establishment is for the predicted pattern of diversity. In a first model simulation (“initial stage”),
the size of the soil moisture storage capacity is prescribed at its initial value throughout the
simulation (i.e. WMAX = WMAX,0). This simulation represents a close coupling of the plant’s water
availability to atmospheric variability/precipitation because soil moisture storage in the rooting
zone is fixed to be small. In a second simulation (“mature stage”), optimised values for soil
moisture storage capacity (Kleidon and Heimann, 1998) - taken as being representative of the
mature plant stage - are prescribed throughout the simulation. These values allow optimum
access to water stored in the soil and are either limited by precipitation input (in arid regions) or
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by evapotranspiration use (in humid regions). The use of these values represents a decoupling of
the plant’s water availability from short-term variability and the plant is therefore essentially
exposed to mean “climatic” water availability. Both simulations are conducted for a simulation
period of 20 years for the same 1000 random “species” as in the “standard” simulation.
Grouping of “successful species”. The successful “species” and the associated plant
properties of the “standard” simulation are investigated using cluster analysis (e.g. Späth, 1985).
A cluster is defined as an object of similar data points. The similarity of data points is measured
by their Euclidian distances to the cluster center. We use the “minimal distance method” to
obtain the clusters as described by Späth (1985). Given a fixed number of clusters, this method
iteratively minimizes the variance within a cluster. The quality of clustering can be described by
the ratio of the between-cluster-variance to the within-cluster-variance. A ratio greater than one
implies that the cluster points are separated; the greater the ratio, the better the separation. This
ratio will be referred to as “separation” in the following sections.
This method is used to identify:
(i)
possible similarities in successful “species” as defined by the parameters, using
each set of parameter values as data points (“parameter groups”).
(ii)
groups of characteristic plant lifetimes and biomass partitioning as a result of the
implementation of the successful “species”, using the lifetimes and sizes of
biomass pools at the end of a lifecycle of all plants as data points (“characteristic
plant prototypes”).
(iii)
typical combinations of successful “species” in different regions, using the set of
successful “species” of each grid point as data points. Each of the resulting
clusters can be interpreted as a biome.
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We then take the “biome” classification and use it as a basis for an investigation of
similar characteristics in climate and in the “species” parameters. To begin with, we compute the
number of days without stress with respect to water (precipitation) and temperature for each
“biome”. We define “rainy days” as days at which precipitation exceeds the water equivalent of
net radiation, “temperature days” as days at which the air temperature is greater than 10°C (TCrit),
and “growing days” as days at which both conditions are met. Next, we conduct a variable
selection analysis to the model parameters of all “species” within each “biome”. This technique
applies cluster analysis to each of the 12 “species” parameters. The parameter which clusters best
(highest separation) is the best constrained parameter and consequently the most important for
this particular “biome”. We determine the separation for each parameter for up to certain number
of clusters (20% of the data points) and assess the significance of the separation by comparing it
to the separation obtained by random samples. The separation values of the important parameters
are then reported as multiples of the separation of random samples.
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4
RESULTS AND DISCUSSION
Computed Distribution of Species Diversity, Sensitivity and Mechanism
Global distribution of species diversity. The computed distribution of species diversity is
shown in Figure 2a. Out of the 1000 random “species” tested for success, a maximum of 84 was
achieved in the tropical Andes mountain range (out of a total of 87 successful “species”
globally). Only 11% of the total, non-glaciated land area has a relative “species” diversity of
more than 50%, while 49% of the total land area has a relative “species” diversity of less than
10%. The maxima of “species” diversity (“hot spot” areas) are achieved in the Andean mountains
and the Central Amazon basin, at the Brazilian Atlantic coast, central and South Africa,
Madagascar and Southeast Asia. Regions with high diversity are simulated in the southeast of the
United States, Central America, East Africa, and China. Desert and tundra regions yield the
lowest diversity. This computed pattern of “species” diversity compares well with observations
(e.g. Scheiner and Rey-Benayas 1994, Barthlott et al. 1996, 1999). In particular, most of the “hot
spot” areas of maximum biodiversity are well reproduced. For comparison, a map of species
diversity based on observations (Barthlott et al., 1996, 1999) is shown in Figure 2b. Note that the
modelled distribution was grouped into 9 groups similar to the scale used in Figure 2b.
However, there are a few shortcomings of the model. For example, Australia is poorly
reproduced. In this case, this can be attributed to a poor performance of the climate model
simulation and consequently of the climatic forcing used for our model. There are also some
smaller scale peaks of diversity which are not resolved by the model, for instance in California,
the Cape region (Fynbos) and Chile. This can be attributed to the low climate model resolution
which does not adequately resolve the orographic gradients. While these weaknesses may be
reasonably explained, the large-scale pattern of biodiversity is nevertheless very well reproduced
and this therefore suggests that climate is indeed a major constraint for biodiversity.
Sensitivity to simulation period. In order to test the sensitivity of the results to the length
of the simulation period, one long simulation was conducted for 500 years for a subset of 200
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“species”. The results of this simulation are virtually identical with the “standard” simulation
with respect to the successful “species” and their distribution. By this we demonstrate that the
length of the simulation period of 20 years chosen for most simulations is sufficient.
Sensitivity to constant parameter values. The results of the sensitivity simulations are
summarized in Table 4. Even though the constant model parameters (Tables 1 and 3) were
considerably changed in the sensitivity simulations, the correlations with the “standard” pattern
are between 92% and ≈ 100%. This means that the use of drastically different model parameter
values does not affect the general predicted pattern of “species” diversity and thus does not alter
the ultimate outcome. However, the magnitude of “species” diversity does vary, and depends the
most strongly on the values of light use efficiency (cGPP), the specific supply rate (cTRS) and the
specific respiration rate (cRES). These parameters directly relate to the carbon balance (light use
efficiency, specific respiration rate) and the carbon-water interaction (specific uptake rate per
root biomass). This is a reasonable outcome since it is the carbon balance which ultimately
determines the amount of carbon allocated to reproduction in terms of its magnitude and
therefore the success of a “species”. Consequently, the magnitude of the predicted pattern is
affected. The results are similar for the patterns of simulated mean plant productivity. Here, the
magnitude responds most strongly to light use efficiency (cGPP). The insensitivity of the relative
distribution of “species” diversity supports the idea that this pattern is predominantly a
consequence of the atmospheric forcing.
Mechanism. Table 5 shows the correlations between the “species” diversity with climatic
variables for the “standard” simulation as well as for the two sensitivity simulations “initial
stage” and “mature stage”. The mean number of “growing days” correlates best with “species”
diversity (linear correlation coefficient r2 = 0.78). The “initial stage” simulation is essentially
identical with the “standard” simulation, whereas the “mature stage” is more diverse and the
correlations to climatic variables are substantially different. In particular, the low correlations
with both, mean precipitation and number of “rainy days”, demonstrate that the abundance of
“species” is considerably less constrained by water availability since sufficient soil water is
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accessible to the plant.
These two simulations emphasize that it is the survival of the initial stage of plant
development especially which is critical for the “species” ’ success, since at this stage, the plant’s
water availability is tightly related to precipitation (as reflected by the number of “rainy days”)
since access to soil storage is limited. During plant growth, increasing storage of carbon
assimilates helps to survive unfavorable growing periods, and a root system provides access to
water stored in the soil. Consequently, the plant progressively decouples itself from the
atmospheric variability. In addition, good growing conditions in turn favour high plant
productivity which leads to a correlation between “species” diversity and mean plant NPP (Table
5).
Common Characteristics of the Successful “Species”
“Parameter Groups”: A total of 87 successful “species” were analyzed with respect to
similar “species” parameter values. The separation of the clusters attains unity with 16 clusters
and does not achieve values greater than 2.3 (with 40 clusters). This means that the successful
“species” parameter combinations do not cluster well, taking into account that we only have 87
data points (successful “species”). Thus, the successful “species” cannot be grouped into a few
common functional units.
“Characteristic Plants”. The “standard” simulation yielded roughly 160,000 successful
“plants” globally for the whole simulation period, which were then analyzed for similarities in
mean lifetime properties (lifetime, mean growth or NPP, mean allocation to carbon pools). A
good separation was obtained with as little as five clusters (Table 6). The five clusters can be
assigned to “characteristic plant types”, ranging from short-lived, fast growing plants (i.e.
grasses) to long-lived, slow growing plants (i.e. trees). The distribution of these “characteristic
plant types” (not shown) are similar to what one would expect for the distribution of grasses
(“plant types” 1, 2, 3) and trees (“plant types” 4, 5). “Plant types” 1 and 3 are the most abundant
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and can be found in most regions except for some deserts (Sahara, inner Asia) and tundra regions
(Northern Alaska/Canada and Northern Siberia). Less frequently found are “plant types” 2 and 4,
the former more abundant in the tropics and the latter more abundant in the arctic. “Plant type” 5
mainly occurs in all forested regions. These results imply that similar “plant” characteristics can
be produced by a wide range of parameter combinations or “species”.
“Biomes”. The 1,821 model grid points were analyzed with respect to similar
occurrences of successful “species”. The regions cluster well, and the classification for 8 clusters
is shown in Figure 3 (separation = 3.5). The obtained classification is similar to observed
distributions of major biomes (e.g. Matthews 1983, Olson et al 1983). An association to each
group with a biome is given in Table 7. Note that desert and arctic regions, which are vastly
different in their climates, are nevertheless classified in the same group (this also applies to a
lesser extent to cluster 7, representing mainly boreal, but also a few arid regions). This grouping
effect is attributable to the clustering of regions with a low number of “species”.
Each of the groups is characterized by distinct levels of stress, ranging from little (group
1: “tropical rainforest”) to high (group 8: “desert or tundra”). In Figure 4 we show the mean
growing conditions for each group, expressed by the number of “rainy days”, “temperature days”
and “growing days”. Parallel to the increase of stress or climatic constraints (that is, a decrease in
the number of growing days) is a continual decrease of mean diversity from 75% for group 1
(“tropical rainforest”) down to 1% for group 8 (“desert or tundra”). Groups 1, 2, 3 and 5 are
mostly restricted by moisture availability in an increasing order (“growing days” equals “rainy
days”), while both, moisture and temperature, together impose constraints on groups 4, 6, 7, and
8 (“growing days” are less than “rainy days” or “temperature days”).
Within each of the groups, the “species” display similar characteristics in that the range of
certain parameters is constrained. This is exemplified by the outcome of the variable selection
analysis, which is shown in Table 7. In most groups, the “seed” size is most constrained,
implying that the specified range of possible values in the model description (eqn. 2) is too large.
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Otherwise, there is a general tendency for either more strongly constrained parameters or more
parameters being constrained with increased levels of climatic constraints (that is, from group 1
to group 8).
These results lead to the following interpretation. The cluster analysis on similar
occurrences of successful “species” led in fact to a classification of climate. Within each group,
there are similar levels of climatic constraints. These lead to similar occurrences of “species”
within the group, indicating that the range of values for a certain set of parameters is restricted.
The set of parameters and the strength of the constraints differ among the groups, with a general
trend towards increased restrictions and consequently a decrease in “species” diversity from
group 1 (“tropical rainforest”) to group 8 (“desert or tundra”).
Summary of the Mechanism and Implications
Climate and species diversity. The results can be summarized into a general mechanism
by which climate limits plant species diversity. Variability in the growing conditions determines
the number of “good growing days” for plant development during the early stage, thus
determining the rate of survivorship and establishment. Later stages of the plant’s life are less
affected by variability because the plant decouples itself from its environmental variability by
storing carbon and growing a root system. “Good growing days” are usually also associated with
a “good” climate, leading to high productivity. Note though that good growing conditions are not
defined in terms of solar radiation or net available energy, but purely on the number of days with
rainfall and temperature greater than 10°C. It is thus not the high productivity per se which leads
to high diversity in the model. A high productivity can also be achieved in a mature stage with a
well developed root system with more environmental variability, for instance, with less “rainy
days” but an equal amount of mean precipitation. It may be pointed out that this concept for plant
species diversity in fact contradicts the energy-diversity hypothesis, see e.g. Hutchinson 1959,
since it is not the net available energy which leads to high diversity. Nevertheless, a higher NPP
is beneficial for the success of a “species” because, compared to the same “species” with lower
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NPP, it leads (i) to a higher allocation to reproduction thus a higher chance for success and (ii) to
a higher chance to decouple itself from variability in the growing conditions through carbon
storage and/or allocation to roots. This general aspect agrees with model studies which show the
importance of roots/soil water storage for land surface functioning (e.g. Milly and Dunne 1994,
Kleidon and Heimann 1998).
Plant functional types. As discussed above, climate imposes constraints on only a certain
range of parameter values, which reduces the diversity under less favorable growing conditions.
However, other parameters remain unconstrained which prohibits the classification of the
successful “species” into common parameter groups. However, the model is capable of
producing “characteristic plants” (grasses and trees) and a reasonable “biome” distribution. What
this suggests is that there is a large redundancy in the range of parameter values, and that this
redundancy does not show up in the resulting plant properties. This redundancy could
nevertheless be of crucial importance for the functioning of ecosystems (e.g. enhanced stability,
Tilman and Downing 1994) and their ability to adapt to environmental change. This in turn will
have important implications for the future development of dynamic global vegetation models
(e.g. Foley et al. 1996), which are often based on the principle of plant functional types. It would
seem that, by basing these models on plant functional types, the model ecosystem is reduced to a
sparse one, and resembling a case of very low species diversity. However, we did not test here
how different the species function in terms of carbon and water exchange in a competitive
environment which would be needed to assess the potential bias in these models.
Limitations
conceptual limitations: Diversity here only refers to functional diversity to the extent of
which these functions are incorporated in the model. Consequently one would expect that with
more included functionality in the model, one might find an even stronger gradient between high
and low diversity regions. Also, not considered are other effects that may constrain biodiversity,
such as competition, nutrient dynamics, and interaction with the microclimate. These factors
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could act to further constrain the possible range of parameter values. The distribution computed
here should therefore be seen as an upper bound for species diversity.
model limitations: Even though the model used here is fairly complex in its overall
formulation (section 2), the processes associated with carbon and water are still formulated in a
crude way and could be improved in future versions. One aspect, for instance, is soil hydrology,
which has been incorporated by a one-layer “bucket” type model. Especially when extending the
model’s complexity by including competition among plants, a vertical refinement in the soil
hydrology scheme is ultimately necessary. Also neglected is capillary rise of moisture from
below the rooting zone, which could be seen as an additional source of moisture (Levine and
Salvucci, 1999). One could expect that the inclusion of this aspect could lead to an increase in
simulated diversity since the relative importance of “rainy days” would be reduced.
complexity: The overall distribution of “species” diversity is quite simple, since it can be
well described by the number of “good growing days”. It would therefore seem that the model
can be vastly simplified, and would still capture the large-scale pattern. However, such
simplification would be at the expense of the model being less based on individual processes.
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5.
CONCLUSION
In this paper we successfully computed a global distribution of “species” diversity from
climate using a model of a single, generic plant. Our results suggests that climatic constraints are
important factors which can explain a large extent of the observed global distribution of plant
species diversity. These constraints can be expressed in the number of “good growing days” and
represent variability in the growing conditions rather than mean climate per se. These “good
growing days” restrict the survivorship of the model plants in the early stage of development.
Consequently, climate acts as a “sieve” which sorts out more and more “species” with increasing
levels of climatic constraints, resulting in more restricted growth strategies and thus a less diverse
range of species.
So far, the model consists of only isolated plants. This is, however, consistent with our
aim which was namely to conduct an investigation of solely the climatic constraints on
biodiversity. The very good agreement with observations support the reach of this study.
However, other factors naturally affect the realized species diversity of ecosystems. For instance,
competition would certainly act to further constrain the range of successful “species”. As a way
of developing this research further, one could extend this approach by including the aspect of
competition between plants into the model as well as the interaction of plants with the surface
energy balance. More specifically, this would permit us then (i) to compare the importance of
climate to the effect of competition, and (ii) to model and assess the effect of diverse versus
sparse ecosystems on exchange fluxes of carbon and water on a global scale.
ACKNOWLEDGEMENTS
A. K. would like to acknowledge the financial support of the Alexander-von-Humboldt
Foundation through a Feodor Lynen Fellowship. Partial support was also provided by NASA
through a grant from the EOS program (grant number NAS5-31726). We profited from a number
of fruitful discussions with our colleagues at Stanford, in particular from Arestotelino Ferreira
about the statistical evaluations of the model output. We would like to thank the reviewers for
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their constructive comments. The computations were performed at the German Climate
Computing Center (DKRZ), Hamburg, Germany.
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TABLE CAPTIONS:
TABLE 1: State variables and parameters of the generic plant model. “gC” refers to grams of
carbon per m-2, “W” refers to W m-2.
TABLE 2: Summary of growth strategy or “species” parameters. This table summarises the
parameters in the model description which define a growth strategy or “species”. Column 2 gives
a brief description of the effect of this parameter on the plant behaviour and column 3 gives the
equation in which the parameter occurs. All of these parameters range between zero and one. All
are associated with benefits and trade-offs. For instance, a low value for p1 yields a slow
response to soil moisture conditions, resulting in a careful, conservative growth strategy while a
high value results in a fast response to soil moisture conditions, thus a opportunistic growth
strategy.
TABLE 3: Parameters and state variables of the interface between the land surface model and
the generic plant model.
TABLE 4: Sensitivity of the model to constant parameters. The simulations are sorted in
increasing order of maximum species diversity relative to the “standard” simulation (last
column). The names in the first column refer to the parameter modifications (see Tables 1 and 3).
The columns show the linear correlation coefficient r2 and the slope between the “species”
diversity and mean plant net productivity of the sensitivity simulation and the “standard”
simulation respectively.
TABLE 5: Correlations between simulated diversity and environmental variables. Given are the
correlation coefficients r2 for the correlation between the diversity distributions for the three
simulation and with the “standard” distribution as well as the slope, mean annual precipitation,
number of “growing days” and mean plant net primary production (NPP). In the “initial stage”
simulation, the soil water storage capacity is prescribed to the initial value WMAX,0 (set to 50 mm)
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and in the “mature stage” simulation to a large value (generally much greater than 50 mm).
TABLE 6: Cluster analysis on characteristic “plants”. Simulated plant properties of successful
“species” were analysed for similar properties (lifetime, mean growth rate, mean allocation) of all
grid points. The five clusters are well separated (separation = 12.8, number of data points =
158232). The clusters are sorted by increasing lifetime. Some “plants” may not have ended their
life cycle during the simulation. Their lifetime refers to the age at the end of the simulation
period (applies especially to cluster 5). The association given in the last column is based on the
general strategy and the geographical distribution of each of the characteristic “plants” (not
shown).
TABLE 7: Variable selection analysis on growth strategy parameters of all successful “species”
within a “biome”. Shown are the biogeographical clusters (as in Figure 3a), the associated biome
types, and the most constrained/important parameters (Table 2). The values in parentheses are the
maximum attained separation, expressed as a multiple of the separation of random samples.
Separations less than 1.2 are not shown.
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TABLE 1:
symbol
description
value or unit
___________________________________________________________________________
state variables
A
assimilates/storage carbon pool
S
reproduction carbon pool
L
leaves carbon pool
WL
structural aboveground carbon pool
R
roots carbon pool
WR
structural belowground carbon pool
allocation
ƒAL
ƒAS
ƒAR
ƒLW
ƒRW
ƒLD
ƒLR
allocation from assimilates to aboveground growth
allocation from assimilates to reproduction
allocation from assimilates to belowground growth
relative allocation to aboveground structure vs. leaves
relative allocation to belowground structure vs. roots
senescence of leaves
senescence of roots
phenology
ƒGROW,T
ƒGROW,W
ƒNPP
ƒGROW
ƒSEN
ƒSEED
time weighted temperature conditions
time weighted soil moisture conditions
time weighted productivity conditions
0: no growth, 1: growth
0: no senescence, 1: senescence
0: no reproduction, 1: reproduction
time scales
T
W
SEN
response time to temperature conditions
response time to soil moisture conditions
response time to productivity conditions
carbon fluxes
gC
gC
gC
gC
gC
gC
0…1
0…1
0…1
0…1
0…1
0…1
0…1
0…1
0…1
gC
days
days
days
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GPP
RES
NPP
gross primary productivity
autotrophic respiration
net primary productivity
gC
gC
gC
productivity limitations
LUE
plant specific light use efficiency (also affects respiration) 0…1
H2O
water limitation
0…1
T
temperature limitation
0…1
parameters
A0
A00
cGPP
“species” seed size (= initial amount of carbon)
reference seed size
maximum light use efficicency
gC
1 gC
0.2 gC/(W d)
cRES,1
respiration rate for leaf and root biomass
10-3 gC/(gC d)
cRES,2
cSEN
Q10
Tcrit
respiration rate for structural biomass
amount of carbon reduction during senescence
respiration coefficient
critical temperature for growing conditions
10-4 gC/(gC d)
1 gC/d
2
10 °C
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TABLE 2:
parameter
description
equation
___________________________________________________________________________
p1
growth response time to moisture conditions
(1)
p2
growth response time to temperature conditions
(1)
p3
initial amount of assimilates (“seed size”)
(3)
p4
senescence response time to net productivity conditions
(4)
p5
allocation to reproduction
(7)
p6
allocation to aboveground growth
(7)
p7
allocation to belowground growth
(7)
p8
allocation to storage
(7)
p9
relative allocation to aboveground structure
(7)
p10
relative allocation to belowground structure
(7)
p11
relative senescence aboveground
(7)
p12
light use efficiency regulation
(10)
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TABLE 3:
parameter
description
value
___________________________________________________________________________
transpiration
TrDemand
demand for transpiration
TrSupply
supply for transpiration, depending on R
cTRS
conversion factor for R to TrSupply
0.5 mm/(gC d)
land surface parameters needed by the land surface model
WMAX
plant available soil moisture storage capacity, depending on WR
LAI
leaf area index, depending on L
ƒVEG
fraction of vegetation cover
ƒFOR
forest cover
a
surface albedo
conversion parameters
aSOIL
albedo of bare soil
aVEG
albedo of vegetation cover
0.20
0.12
cFOR
conversion factor for WL to ƒFOR
0.002 m2/gC
cLAI
specific leaf area, conversion factor for L to LAI
0.03 m2/gC
cWLMAX
conversion factor for L to WL,MAX
0.2mm/m2
cWMAX
conversion factor for WR to WMAX
k
light extinction coefficient
WL,MAX canopy interception storage
WMAX, 0
minimum value for WMAX
20 mm (gC/m-2)-1/2
0.5
0.2 mm m-2
50 mm
state variables of the land surface model
WSNOW amount of water stored in snow cover
WL
amount of water intercepted by the canopy
WS
amount of water stored in the rooting zone of the soil
WSUB
amount of water stored below the rooting zone of the soil
Modelling Biodiversity (Kleidon & Mooney)
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TABLE 4:
sensitivity
simulation
diversity
correlation
productivity
slope
correlation
slope
relative
diversity
___________________________________________________________________________
0.5 * cGPP
92 % 0.53
97 % 0.38
60 %
0.5 * cLAI
92 % 0.54
97 % 0.78
65 %
0.5 * cTRS
94 % 0.58
97 % 0.97
68 %
2.0 * cRES
94 % 0.64
97 % 0.85
73 %
2.0 * cLAI
95 % 0.83
97 % 1.08
93 %
0.5 * WMAX,0
97 % 0.91
98 % 0.97
95 %
Tcrit + 5°C
98 % 0.99
≈100 % 1.00
98 %
≈100 % 1.00
99 % 0.86
100 %
Tcrit - 5°C
98 % 1.02
≈100 % 1.00
100 %
2.0 * cWMAX
98 % 1.08
94 % 1.27
100 %
2.0 * WMAX,0
97 % 1.14
99 % 1.07
105 %
0.5 * cRES
96 % 1.37
97 % 1.19
128 %
2.0 * cTRS
95 % 1.49
98 % 1.11
133 %
2.0 * cGPP
94 % 1.50
97 % 2.62
135 %
0.5 * cWMAX
Modelling Biodiversity (Kleidon & Mooney)
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TABLE 5:
“standard”
diversity
mean
number of
precipitation “growing days”
mean
plant NPP
___________________________________________________________________________
“standard” diversity
(100 %)
66 %
78 %
83 %
“initial stage” diversity
99.96 %
66 %
78 %
82 %
38 %
50 %
67 %
(slope = 1.003)
“mature stage” diversity
57 %
(slope = 1.59)
Modelling Biodiversity (Kleidon & Mooney)
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TABLE 6:
cluster
lifetime
growth
structure
association
-2
-1
days
gC m d
(%)
___________________________________________________________________________
3
279
3.4
9
“grass”
1
735
2.2
12
“grass”
4
1519
2.5
16
“tree?”
2
2727
1.7
18
“shrub?”
5
5839
0.5
15
“tree”
Modelling Biodiversity (Kleidon & Mooney)
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TABLE 7:
cluster
association (“biome”)
most constrained
parameters
____________________________________________________________________________
1
“tropical rainforest”
p3 (80)
2
“tropical forest”
p3 (173), p4 (1.5)
3
“tropical seasonal forest”
p3 (129), p6 (2.9), p8 (1.5),
p1 (1.2)
4
“evergreen forest”
p3 (56), p1 (2.3), p4 (1.4),
p5 (1.4), p11 (1.3), p6 (1.2)
5
“grassland”
p3 (16), p4 (1.5), p5 (1.5),
p2 (1.4)
6
“temperate deciduous forest”
p3 (77), p6 (3.0)
7
“grassland or boreal forest”
p6 (3.8), p5 (2.9), p10 (1.9),
p9 (1.7), p2 (1.6)
8
“desert or tundra”
p5 (2.9), p6 (2.0), p1 (1.8),
p9 (1.8), p4 (1.7), p8 (1.4),
p12 (1.3), p3 (1.2)
Modelling Biodiversity (Kleidon & Mooney)
page 41 of 45
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FIGURE CAPTIONS:
FIGURE 1: Schematic diagram of the model setup. The model consists of a generic plant
component which simulates the development of an isolated plant and a land surface component
which primarily simulates land surface hydrology. The two components interact through land
surface parameters, which are derived from the plant’s state and through the land surface
conditions (mainly soil moisture availability), which is simulated by the land surface component.
FIGURE 2: Global distribution of species diversity. The top map (a) shows the simulated
distribution of species diversity. The values are grouped into 9 groups: (1) < 2%, (2) 2 - 4%, (3) 4
- 10%, (4) 10 - 20%, (5) 20 - 30%, (6) 30 - 40%, (7) 40 - 60%, (8) 60 - 80%, and (9) ≥ 80% of
the maximum diversity value simulated. The bottom map (b) shows a map based observations
(Barthlott et al. 1996, 1999) for comparison. Note that the scaling is similar in both maps. Figure
2b is available on the internet at http://www.botanik.uni-bonn.de/system/biomaps.htm.
FIGURE 3: Biogeographic classification of regions. The map shows a regional classification
with respect to similar sets of successful “species”. This classification was obtained by applying
cluster analysis to the set of successful “species” at all grid points. The groups are sorted in an
increasing order of climatic constraints (see Figure 4). Each of the groups can be associated
mainly with one major biome (see Table 7 for associations). Within each group, a distinct set of
model parameters is most constrained (Table 7).
FIGURE 4: Mean climatic conditions within each “biome”, expressed in terms of days with
favourable growing conditions (precipitation and temperature). The “biomes” are sorted in an
increasing order of climatic constraints, thus decreasing in terms of diversity. The mean diversity
of the “biomes” are (top to bottom): 75%, 48%, 30%, 29%, 12%, 12%, 5% and 1% respectively
of the maximum achieved value. Error bars denote one standard deviation.
Modelling Biodiversity (Kleidon & Mooney)
page 42 of 45
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FIGURE 1:
Modelling Biodiversity (Kleidon & Mooney)
page 43 of 45
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FIGURE 2:
Modelling Biodiversity (Kleidon & Mooney)
page 44 of 45
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FIGURE 3:
Modelling Biodiversity (Kleidon & Mooney)
page 45 of 45
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FIGURE 4:
Tropical
Rainforest
Tropical
Forest
Tropical
Seasonal
Forest
Evergreen
Forest
Grassland
Temperate
Deciduous
Forest
Grassland
or Boreal
Forest
Desert or
Tundra
0
20
40
60
80
100
Frequency (%)
Rainy Days (P>1 mm/d)
Temperature Days (T>10°C)
Rainy + Temperature Days (P>1mm/d and T>10°C)