Vegetatio 83: 49-69, 1989.
© 1989 Kluwer Academic Publishers. Printed in Belgium.
49
A theory of the spatial and temporal dynamics of plant communities
Thomas Smith 1,2, 3 • Michael Huston 1
1Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA;
z Department of Environmental Biology, Research School of Biological Science, Australian National
University, Canberra ACT 2601, Australia; 3present address: Department of Environmental Sciences,
Clark Hall, University of Virginia, Charlottesville, VA 22903, USA
Accepted 18.5.1989
Keywords: Competition, Individual-based model, Plant functional type, Resource gradient, Succession,
Tradeoff, Zonation
Abstract
An individual-based model of plant competition for light that uses a definition of plant functional types
based on adaptations for the simultaneous use of water and light can reproduce the fundamental spatial
and temporal patterns of plant communities. This model shows that succession and zonation result from
the same basic processes. Succession is interpreted as a temporal shift in species dominance, primarily
in response to autogenic changes in light availability. Zonation is interpreted as a spatial shift in species
dominance, primarily in response to the effect of allogenic changes in water availability on the dynamics
of competition for light. Patterns of succession at different points along a moisture gradient can be used
to examine changes in the ecological roles of various functional types, as well as to address questions
of shifts in patterns of resource use through time.
Our model is based on the cost-benefit concept that plant adaptations for the simultaneous use of two
or more resources are limited by physiological and life history constraints. Three general sets of adaptive
constraints produce inverse correlations in the ability of plants to efficiently use (1) light at both high and
low availability, (2) water at both high and low availability, and (3) both water and light at low availabilities.
The results of this type of individual-based model can be aggregated to examine phenomena at several
levels of system organization (i.e., subdisciplines of ecology), including (1)plant growth responses over
a range of environmental conditions, (2) population dynamics and size structure, (3) experimental and
field observations on the distribution of species across environmental gradients, (4) studies of successional pattern, (5)plant physiognomy and community structure across environmental gradients, and
(6) nutrient cycling.
Introduction
Consistencies in the relationship between environmental conditions and plant communities
have been the basis for explaining vegetation pat-
terns at both global and local scales (Holdridge
1967; Whittaker 1956, 1975; Walter 1973;
Ellenberg 1978; Box 1981), as well as the basis for
classifying the plants themselves (e.g., Raunkiaer
life forms, early vs. late successional, and gap vs.
50
non-gap). However, there is as yet no general
theory that links vegetation patterns to basic plant
processes (Drury & Nisbet 1973; Austin 1985;
McGraw & Wulff 1983; Ehleringer et aL 1986).
Huston & Smith (1987) showed that a single
mechanism of interaction among individual
plants (competition for light) could produce a
wide variety of successional patterns depending
on the correlation between a set of life history and
physiological characteristics. Here we extend this
approach by using a specific pattern of correlations between physiological and life history
traits to explain the basic spatial and temporal
patterns of vegetation.
These specific correlations result from fundamental physiological and energetic constraints on
the capture and use of resources by plants. The
constraints affect the ability of a plant to (1) tolerate low levels of a resource while maintaining the
ability to grow rapidly at high levels of the same
resource; and (2)simultaneously use different
types of resources when levels of both resources
are low.
The consequences of these correlations are
shifts in the relative competitive ability of different
types of plants along environmental gradients
(Huston & Smith 1987). We use these correlations to develop a functional classification of
plant types. We then explore the implications of
this classification using an individual-based
model of the nonequilibrium competitive interactions between plants which both respond to
and modify resource levels in their environment.
This approach demonstrates how different
functional strategies of resource use allow plants
to fill different ecological roles under different
resource conditions. It explains why some plants
are early successional species in some environments and late successional species in other
environments, as well as demonstrates the common processes underlying both temporal and spatial gradients of vegetation pattern.
Constraints on resource use by plants: the tradeoff
model
The pattern of correlations among plant characteristics that we use as the basis for our theory of
vegetation dynamics is derived from the general
principles of cost-benefit analysis as it has been
applied to plant physiology and allocation of
resources (Orians & Solbrig 1977; Mooney &
Gulmon 1979, 1982; Bloom etal. 1985; Chapin
et al. 1987; Givnish 1986).
The tradeoff between tolerance to low resource
conditions and maximum potential growth rate
under high resource conditions (Fig. 1) is a wellknown consequence of the physiological and
energetic constraints on plants (e.g., Parsons
1968a). This type of tradeoff has been reported for
different light conditions (Grime & Jeffrey 1965;
Loach 1967; Boardman 1977; Bazzaz 1979), different soil water conditions (Ellenberg 1953,
1954; Gates 1968; Parsons 1968b; Kozlowski
1982; Zimmermann & Brown 1971; Zimmermann & Milburn 1982), and different nutrient
supply conditions (Mitchell & Chandler 1939;
Grime 1974, 1977, 1979; Chapin 1980; Chapin
etaL 1986, 1987; Bryant etal. 1983).
High
_.1
_<
F-
,,,<
F--
O
fl_
"i-
x
<
Low
High
Low
RESOURCE AVAILABILITY
Fig. 1. Growth rate in relation to resource availability for
plants of two degrees of tolerance. Note the inverse relationship between the resource level where the growth rate is zero
(x intercept of the curves) and the maximum rate of growth
achieved under high resource conditions (based on Larcher
1975; Bazzaz 1979; Orians & Solbrig, 1977; Chapin et al.
1986).
51
To illustrate our use of the 'tradeoff model' for
explaining vegetation dynamics, we will limit our
discussion to traits related to the use of water and
light, two resources that often limit plant growth
(Clements et al. 1929; Daubenmire 1947; Walter
1964, 1968, 1971, 1973; Gates 1980). Our focus
on constraints related to these two resources
encompasses the fundamental tradeoffs between
water loss and CO2 uptake through stomata, as
well as the tradeoffs between aboveground and
belowground resource allocation. In addition, the
availability of these two resources varies greatly
over a wide range of spatial and temporal scales,
and thus can be expected to explain a large
proportion of the variation in plant community
structure over a range of scales.
We do not intend to present a comprehensive
model of vegetation dynamics, but rather to
illustrate the robust predictions that result from
applying the tradeoff model in the context of an
individual-based model of plant competition. To
keep our example simple, we limit our consideration to a subset of physiological and life history
traits that apply specifically to carbon gain in
terrestrial woody plants. We focus on vegetative
growth and carbon gain, and do not explicitly
consider reproduction because carbon is the basic
currency of all plant growth (Bazzaz & Reekie
1985), and limitations on carbon gain will limit
reproduction as well as vegetative growth. Inclusion of short-term environmental variability in our
model is easily done, but to simplify the presentation of our example, we will consider only plants
that respond to a particular scale of resource
variability. For example, long-lived perennials
that integrate a wide range of resource conditions
respond to resource variation at a very different
temporal scale than do annuals that complete
their life cycle following a single rainstorm. We
specifically discuss the spatial and temporal
dynamics of woody plant communities that occur
along a moisture gradient from desert shrubland
to savannah to rainforest.
The consequences of constraints on the simultaneous use of light and water by individual plants
are summarized in the following three premises.
Premise I.
A plant that can photosynthesize at
high rates and grow rapidly under conditions of
high light is unable to survive at low light levels
(i.e., it is shade-intolerant). Conversely, a plant
that is able to grow in low light (shade-tolerant
plant) has a low maximum rate of growth and
photosynthesis even under high light conditions
(Bazzaz 1979; Bazzaz & Pickett 1980; Larcher
1980).
Premise 2.
A plant that can grow rapidly and/or
reproduce abundantly under conditions of high
available soil moisture is unable to survive under
dry conditions (i.e., it is intolerant to low
moisture). Conversely, a plant adapted to survive
and reproduce under dry conditions is unable to
grow rapidly and/or reproduce abundantly even
with high soil moisture availability (tolerant to low
moisture) (Parsons 1968b; Orians & Solbrig
1977).
Tolerances to conditions of low light
and low moisture are interdependent and inversely correlated. Adaptations that allow a plant
to grow at low light levels restrict its ability to
survive under dry conditions. Conversely, adaptations that allow survival under dry conditions
reduce the plant's ability to grow in low light.
Thus no woody plant can simultaneously have a
high tolerance for low levels of both resources.
Premise 3.
We will use these premises to characterize different types of plants, as well as differences
between individuals of the same type growing
under different conditions. Application of these
premises to situations in which many individual
plants interact with each other and with their
environment is the basis of our theory of the spatial and temporal dynamics of vegetation.
Mechanisms underlying tradeoffs in the use of
light and water
These premises represent the consequences at the
whole-plant level of a large suite of physiological
processes and life history strategies involved in
the efficient use of different levels of the same
52
resource and of different resources. The mechanisms involved in these tradeoffs include all levels
of a plant's structure, from its enzyme systems
and organelle structure to its branching pattern
and leaf angle.
Perhaps the most fundamental constraint upon
plants results from the inherent conflict between
carbon dioxide uptake and water loss. Much of
our understanding of this topic is based on work
on enzyme systems and morphology at the leaf
level (Medina 1971; Cowan 1982; Farquhar &
Sharkey 1982; Farquhar &von Caemmerer 1982;
Field & Mooney 1986). Some progress has been
made in understanding how this conflict is
resolved at the level of the whole plant (e.g., Tolley
& Strain 1984, 1985; Teskey & Shrestha 1985;
Cowan 1986; McCree 1986; Schulze 1986;
Turner 1986; Schulze et al. 1987). However, the
way in which the multiple chemical and physical
processes within a plant are integrated to regulate
the growth of a whole plant is a major area of
ongoing research, the discussion of which is
beyond the scope of this paper. We focus on the
consequences of these and other tradeoffs for the
growth of whole plants.
One of the best-known consequences of the
constraints on use of different types of resources
is the tradeoff in allocation of energy to roots
versus aboveground structures. The implications
of the root:shoot ratio have been extensively discussed (Struik & Bray 1970; Aung 1974; Kramer
& Kozlowski 1979; Schulze 1982, 1986;
McMurtrie & Wolf 1983; Givnish 1986; Hunt &
Nicholls 1986; Tilman 1988). In general, when
water and nutrients are plentiful in relation to
light, plants invest relatively little energy in roots,
but spend most of their energy on aboveground
parts to capture light. In contrast, when water and
nutrients are limiting to plant growth, plants must
invest heavily in roots at the expense of their
aboveground parts. Competition for light becomes relatively unimportant under these conditions, but competition for water and nutrients
may be intense. Thus root :shoot ratios vary
widely in proportion to the relative availability of
light in relation to moisture and nutrients. Variation in root:shoot ratios occurs both between
species adapted to different resource conditions
and between individuals of a single species that
are grown under different conditions.
Other responses of the whole plant to reduced
light include increases in (1) leaf area/leaf weight;
(2) leaf weight/whole plant weight; (3) leaf
area/root surface; and (4) stem height/stem
biomass (Loach 1967; Kozlowski 1976, 1982;
Kramer 1983; Kramer & Kozlowski 1979;
Zimmermann & Brown 1971 ; Fitter & Hay 1981 ;
Withers 1979). These responses tend to be greater
in plants that are less tolerant of shade (i.e., they
have greater morphological plasticity). Each of
these responses or mechanisms can impose
limitations on the plant's ability to survive other
stresses such as reduced availability of moisture
or nutrients, fire, or herbivory (see Oosting &
Kramer 1946; Keever 1950; Bryant etal. 1983;
Chapin etal. 1987; Osmond etal. 1987). Responses to moisture or nutrient limitation are
often the opposite of the responses to reduced
light (Kramer 1969; Struik & Bray 1970;
Kozlowski 1976, 1982; Fitter & Hay 1981;
Chapin 1980; Chapin etal. 1986; Schulze 1986;
Schulze etal. 1987), with corresponding decreases in the efficiency of light use. For example,
any decrease in the leaf area ratio (the ratio of
phytosynthetic surface to total respiring plant
biomass), such as may result from decreased
water availability, will increase the whole-plant
light compensation level and reduce the net carbon gain.
Constraints on the use of resources at different
levels of availability also affect growth rate and
size. In general, species adapted to high levels of
resource availability can have a wide range of
growth rates, depending on patterns of energy
allocation to growth versus reproduction, mechanical structure, chemical defenses, other physiological processes, the rate of respiration, etc. (Paul
1930; Monsi 1968; Monsi & Murata 1970;
Zahner 1970; Mooney 1972; Whittaker 1975;
Mooney & Gulmon 1979; Gifford & Evans 1981 ;
Bazzaz etal. 1987). However, among plants
adapted to low resource conditions, the range of
growth rates is narrowly restricted and the rates
are much lower because of the adaptations
53
required for growth under such conditions
(Chapin 1980).
Few of these specific mechanisms apply over
the entire range of conditions under which plants
are found, and few apply to all levels or sizes of
plant structure (e.g., leaves versus whole plants,
herbaceous vs. woody plants, and annuals vs.
perennials). Yet taken together, these diverse
mechanisms form a consistent pattern oftradeoffs
that can be generalized to the correlation pattern
that we use as the basis of our theory of vegetation
dynamics.
(a)
LOW
aNil
0
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8~
DECxIFMEu/~SlNGowTH
nr~
~/C
' OV
IBl N
ILEDI M I T ~
oz
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nr
iii
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0k-
RATE
TO TOLERANCES
HIGH
HIGH
LOW
SHADE TOLERANCE
Plant functional types
(b)
The consequences of the three premises for use of
light and water are summarized in Fig. 2a, which
illustrates two main points. First, growth rate
decreases as tolerance to either low light or low
water availability increases. Thus, the highest
growth rate is found in the upper right hand
corner, which represents the lowest tolerance for
low levels of light and water. Second, there is a
limit to the combined tolerance to low light and
water levels. This is illustrated by the diagonal
boundary, which limits woody plant strategies to
the combination of traits represented by the upper
right half of the figure. By plant strategy, we mean
a combination of plant characteristics related to
the use of fight and water, including the resource
allocation patterns reflected in maximum growth
rate, maximum size, and maximum age, along
with the plant's growth response to different combinations of light and water availability.
For the sake of our example, we divide the
continuum of plant strategies illustrated in Fig. 2a
into discrete functional types (Fig. 2b). We have
arbitrarily selected 15 functional types to represent the range of woody plant strategies for light
and water use. The number of functional types
that can or should be distinguished along the continuum, or in any particular situation, is a topic
that we will not address here.
The specific traits that we use to define
functional types in our model are given in Table 1.
These parameters are used with the growth
LOW •
123
UA
0
1
\
2
3
4
6
7
8
10
11
~
\;3
0
Z
112
I.U
_-I
o
HIGH
HIGH
SHADETOLERANCE
5
112
114
•
LOW
Fig. 2. (a) Possible w o o d y plant strategies for light a n d w a t e r
use, illustrating some of the consequences of the tradeoffs
described in the three premises. The highest rate of growth
(carbon gain) is in the upper right corner of the figure, and
growth decreases with increasing tolerance to low levels of
light and/or water. (b) Division of the continuum of woody
plant strategies into the 15 discrete functional types used in
the computer simulations. Each functional type is defined by
maximum growth rate, shade tolerance, and tolerance to low
moisture levels, as definedby the parameters in Table 1. The
same labelingfor these 15functional types is used throughout
the paper.
response equations to define the growth of each
functional type for all combinations of light and
water availability.
The growth of an individual plant of a specific
functional type under different combinations of
light and water availability can be represented as
54
Table 1. Parameters and growth response equations for 15 functional types used in model simulations and figures 2 through 8.
Species
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Growth rate
(relative
diameter
increment)
Maximum
height
(m)
Maximum
age
(years)
Drought
tolerance
DRTOL 1
Shade
tolerance
1.0
1.3
1.7
2.2
2.9
1.0
1.3
1.7
2.2
1.0
1.3
1.7
1.0
1.3
1.0
36
34
31
28
24
31
28
24
20
24
20
15
15
10
5
500
296
175
103
61
296
175
103
61
175
103
61
103
61
61
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.5
0.5
0.6
1
2
3
4
5
2
3
4
5
3
4
5
4
5
5
Light response
Light compensation
level LC z
Scale factor
SF1 z
Scale factor
SF22
0.015
0.024
0.039
0.063
0.100
0.026
0.043
0.069
0.110
0.047
0.076
0.121
0.083
0.133
0.146
1.00
1.00
1.02
1.20
1.75
1.00
1.02
1.20
1.75
1.02
1.20
1.75
1.20
1.75
1.75
10
6
4
2
1
6
4
2
1
4
2
1
2
1
1
S M G F = (DRTOLi-DRT)/DRTOLi, where S M G F is the soil moisture growth factor, D R T O L i is the drought tolerance of
functional type i calculated as the proportion of the growing season below the soil wilting point above which the plant cannot
maintain positive net growth and DRT is the proportion of the growing season below wilting point for a specific simulation.
2 L T G F = SF1 i • (1.0-exp(-SF2 i * (AL-LCi)))-(1.0-SMGF), where L T G F is the light growth factor scaled as a proportion of the
maximum growth rate for a given functional type, AL is the available light expressed as a proportion of full sunlight, LC is
the light compensation level for favorable moisture conditions (from Table 1), SF1 is a parameter to scale the light curve to
asymptote at 1.0, and SF2 is a parameter that determines the initial slope of the light response curve. A multiplier is set to
zero if its calculated value becomes negative. These equations were used to generate the response surfaces in Fig. 3.
a three-dimensional response surface, with wholeplant carbon gain on the vertical axis and with
light and water availability on the x and y axes
(Fig. 3). These response surfaces reflect the consequences of the tradeoffs described in the three
premises. Fig. 3b represents the hypothesized
growth-response surface for a plant with intermediate tolerance for both low light and low
moisture levels, and it illustrates the interdependence of light use and water use (Premise 3). The
response surface can be envisioned as a series of
light-response curves (here, integrated to wholeplant carbon gain) that have been calculated
under a range of moisture conditions.
The response surfaces of Fig. 3 illustrate important consequences of the interaction between light
use and water use. With decreasing moisture
availability, the level of light necessary for photosynthetic carbon gain to equal respiratory carbon
loss (i.e., the whole-plant light compensation
point) is higher than it is for higher moisture
availability. Therefore, the maximum growth
achieved under high light levels is lower when
moisture availability is reduced.
The consequences of the tradeoffs in Premises
1 and 2 are seen most clearly in comparisons
between different functional types of plants.
Figs. 3a and c show hypothesized growthresponse surfaces for two functional types of
plants with contrasting patterns of light and water
use. Fig. 3a represents the growth-response surface for a plant that is tolerant of low light levels
but intolerant of low moisture levels (cf.
Premise 3). This plant's response to light under
high moisture conditions forms a classic shadetolerant light-response curve. This curve contrasts with the growth-response curve of the
functional type in Fig. 3c, which is typical of
55
(a) F U N C T I O N A L T Y P E 1
~r
"
S
'
(b) F U N C T I O N A L T Y P E 10
(cJ F U N C T I O N A L TYPE 15
.
:) •
< 0u. 0,67
O
0.67
H7
01
033
'
'
///.-~-.- ,'
•
"
~
' ~
~,
'
,
i
~
H GH .~,
~. ' ' ' i' L-;~ S'~
,~
" ~ e L E t.tOt~T
0
~2
0.3:
HIGH
/
-',
I
VAII'~81E LIOHT
0
~.~'~"
Fig. 3. Growth response surfaces for three functional types showing growth rate in relation to light and moisture levels. (a) High
shade tolerance with low tolerance for low moisture (type 1, Figs 2, 4-7); (b) Intermediate shade tolerance with intermediate
tolerance to low moisture (type 10, Figs 2, 4-7); and (c) Low shade tolerance with high tolerance to low moisture (type 15,
Figs 2, 4-7).
shade-intolerant plants. Note that the shadeintolerant type (Fig. 3c) requires a higher minim u m light level for growth (light compensation
point) under high levels of moisture availability
but it is able to continue growth at much lower
levels of water availability than is the shadetolerant type (Fig. 3a).
In the rest of the paper, we will focus on these
functional types of plants rather than on plant
species per se. For many ecological applications,
such as models of global vegetation pattern, this
classification is likely to be more useful than a
taxonomic one because it is based on inherent
physiological and life history properties rather
than on systematics.
Our definition of functional type is analogous
to the concept of guild that has been applied to
animals (Root 1967). Accordingly, all members of
a functional type use the same type of resources
in more or less the same way, and thus can be
considered functional redundants. Differences
within a functional type (i.e., between guild members) tend to be much finer than the differences
between types. This use of functional type contrasts with traditional descriptions of plant strategies or roles in a community. In our system, a
plant can have different roles in different communities, depending on the environmental conditions and the presence of various other species
(see results).
The specific shapes of the response surfaces we
use in our model actually represent hypotheses
about the interaction of constraints on light and
water use. However, our functional classification
of plants does not depend on the exact details of
the response surfaces, but only on the general
validity of physiological and life history correlations expressed in the tradeoff model. The same
general approach to cost-benefit tradeoffs in
plants has been used as the basis for explanations
of such characteristics as leaf size and shape
(Parkhurst & Loucks 1972; Givnish 1978, 1979),
leaf type in arid environments (Orians & Solbrig
1977), plant height (Givnish 1982; Chazdon
1986), plant photosynthesis (Mooney & Gulmon
1979; Cowan 1986), the ability to use multiple
resources (Chapin etal. 1987), and herbivore
defense and nutrient use (Mooney & Gulrnon
1982; Bryant etal. 1983; Coley etal. 1985).
The shapes of the response surfaces could be
determined empirically with appropriate experiments. The multi-factorial physiological experiments needed to quantify the precise shape of
these response surfaces have not yet been performed at the whole plant level (see Osonubi &
Davies 1980; Brun & Cooper 1967; Linder et al.
1981 for factorial experiments involving leaf
response to light and temperature, to light and
CO2, and to light and nutrients, respectively).
Nonetheless, the overall patterns can be inferred
56
from basic models of plant physiology (e.g.,
Farquhar & v o n Caemmerer 1982) and from the
limited amount of whole plant experimental work
that has been done (Hunt & Nicholls 1986;
Wellington et al. in review).
Two aspects of the responses summarized in
Figs 2 and 3 are critical for understanding vegetation dynamics and plant distributions. The first
is the set of adaptations that allow a plant to
survive under a particular combination of
resource conditions. The second is the effect of
those adaptations on the distribution of that plant
type in communities of competitors across the
entire range of resource conditions. Inevitably,
the same adaptations that allow a plant to grow
well under one set of conditions will prevent it
from surviving under some other conditions.
A model of plant interactions based on functional
types
We examine the consequences of our functional
description of plants using the same type of model
that Huston & Smith (1987, see also Botkin et al.
1972; Shugart 1984) used to examine succession.
The relevant features of the model are (1)it is
based on individual plants; (2)individuals interact by depleting the level of a single resource,
light; and (3)the model determines the nonequilibrium dynamics of plant interactions by
tracking the growth of each individual.
We model tree growth in annual timesteps on
a grid composed of plots of ground scaled to the
area which can be dominated by a single individual of maximum size (Shugart & West 1979).
Birth, growth, and death of each individual on
each plot are followed, and the leaf areas of each
individual are integrated to determine the vertical
light profile in each plot. The model determines
the responses of each individual to available water
and light according to the response functions for
its specific functional type (i.e., the equations used
to generate the response surfaces in Fig. 3, see
Table 1 for parameters and equations). The model
of resource interactions is neither multiplicative
nor based on Liebig's law of the minimum; rather
it is based on the tradeoff model described earlier.
Light is the only resource for which plants compete in this model, and the only way in which
individuals interact is indirectly, through their
effect on light availability. The consequences of
competition for light are expressed as a decrease
in growth for each individual based on the amount
of light it receives and its type-specific lightresponse function for the current moisture conditions (e.g., Fig. 3). An increased probability of
mortality is associated with decreased growth. In
the model, individuals do not compete for water;
rather they experience a type-specific decrease in
their maximum growth rate and an associated
increase in the minimum light level needed to
support growth, both of which are proportional to
the degree of water availability in a particular
environment (Fig. 3). Functional types that are
intolerant of low water availability experience a
greater reduction in growth for a given degree of
water stress than do tolerant types.
In a simulation for a given set of initial resource
conditions, individuals of all functional types are
allowed to interact to produce an annual record
of the plant type composition, size distributions,
resource availability, etc., that result from their
particular resource use strategies. Reproductive
strategies are not considered explicitly, rather all
functional types are established at the same rate.
This type of individual-based model has been
widely used in forestry, agriculture, and population biology (Botkin et aL 1972; Shugart & West
1977; Shugart 1984; Pastor & Post 1985, 1986;
Huston & DeAngelis 1987; Huston & Smith
1987; Huston e t a L 1988).
Model results
Most previous applications of this general type of
individual-based forest model have focused on
succession and other patterns of vegetation
change that occur at a single location in space
(Shugart & West 1977; West et al. 1981; Pastor
& Post 1986; Huston & Smith 1987). Here we use
our definition of plant functional types together
with an individual-based model to investigate the
57
interaction of spatial and temporal patterns,
specifically (1)differences in successional patterns along a spatial gradient of water availability
and (2)temporal shifts in plant spatial distributions along gradients of water availability.
Simulations of the interactions between many
individuals of each of the 15 functional types were
aggregated to show the total biomass of each
functional type in a matrix of time (succession)
and space (a gradient of site water conditions).
Fig. 4 presents the resulting three-dimensional
surfaces of total biomass in relation to successional time and water availability for 5 of the
15 functional types.
Some of the important spatial and temporal
patterns embodied by these response surfaces can
be more clearly visualized using two-dimensional
figures that show the different patterns of succession that occur at different points along the
moisture gradient. Fig. 5 presents changes in
biomass through time for the dominant functional
types under 6 different moisture conditions. Temporal changes in the pattern of spatial zonation
are presented in Fig. 6, which shows the relative
biomass of 5 functional types along the same
gradient during early and late succession.
Fig. 7 illustrates the pattern ofbiomass along a
moisture gradient in absence of competition
between functional types (i.e., in a monoculture,
Fig. 7a) and in the presence of such competition
(i.e., in a polyculture, Fig. 7b). The same data
presented in Fig. 7b, on an absolute axis, are also
presented in Fig. 6b, on a relative axis.
Although the above four figures form the basis
for the following discussion of results, the output
of this individual-based model can be aggregated
in many additional ways to address different
ecological questions. For example, it is possible to
compute the spatial and temporal distribution of
specific resources that are affected by the plants,
as is illustrated in Fig. 8, which shows the vertical
distribution of leaf area and the available light at
ground level for three different levels of moisture.
Patterns at other levels of organization can also
be investigated using the model output. Population dynamics under different conditions can be
examined, such as the effect of different levels of
resource availability or of different types of
resources on size distributions (see Huston &
DeAngelis 1987). Community properties, such as
height structure or species diversity (see Huston
& Smith 1987), and ecosystem properties, such as
productivity, total biomass, decomposition rate,
nitrogen availability, etc., can be examined by
aggregating the model results for the appropriate
parameters (see Aber et al. 1979, 1982; Pastor &
Post 1985, 1986, 1988; Huston & Smith 1987;
Huston et al. 1988).
~NL-OWG
re) TYPE 1
I
(b)TYPE E
( c ) T Y P E 10
,
Uililli'iS'illlA'~
#)TYPE 13
,
,,,~,~
17-14411
(eJTYPE 15
.~.~...
Fig. 4. Three-dimensionalrepresentationof functionaltype biomass along spatial and temporal gradients, includingthe effects
of competition.The vertical axis represents the total biomass of each species at a specificpoint in time (succession)and space
(moisturegradient).The surfacescorrespondto species 1,6,10,13, and 15 from Figs 2 and 3. For each simulationall 15 functional
types from Table 1 (Fig. 2b) were included.
58
20
0
30
~
ORNL-DWG 1111-18724
ORNL-DWG 86-16717
100
)
-- DRY
15
I
<
IE
0
m
o
1314
0
40
i
f
25
]15
(b)
10
(c)
Z
W
75
m
O.
50
YEAR 4 0 0
(J
0
60
'°°I
25
0
1 (d)
(d) 0/~._,~
t
HIGH
LOW
MOISTURE
AVAILABILITY
~,.,.~6
Fig. 6. Species zonation along a moisture gradient at different stages of succession. The curves represent sections of
the surfaces of Fig. 4 at two points along the time axis, scated
as relative biomass.
ul
u)
ORNL-DWG 87-14487
_ ~OCULTURE
0
100
(f)
1
--
-
<
O
.~
1
__
~
15
POLYCULTURE
( b)
'
313
+
5O
6
2
- WET
0
100
200
YEAR
300
400
Fig. 5. Successional sequences resulting from competition
among the same functional types under different moisture
conditions. The curves represent sections of the surfaces of
Fig. 4, plus additional functional types from Table 1, at different points along the moisture axis.
HIGH
MOISTUREAVAILABILITY
LOW
Fig. 7. Simulated patterns of plant abundance along a
moisture gradient. (a)The response of 5 functional types
grown in monoculture, illustrating the similar physiological
optimum of each functional type; (b)The response of 5
functional types grown in competition with all 15 functional
types, illustrating the ecological optima of the functional
types.
59
Plant succession: dominance along temporal
gradients
Because of the tradeoffs involved in efficient use
of light at high versus low levels (Premise 1), there
is an inevitable shift in the competitive ability of
a functional type over the course of succession.
This shift in competitive ability results from the
decrease in light at ground level as plant height
and leaf area increase during succession. Thus,
successional dynamics are determined by the
inverse relationships between the various adaptations that confer superior competitive ability at
different points along an autogenically-controlled
temporal gradient of light availability (Clements
1916; Clements etal. 1929; Huston & Smith
1987).
We first consider simulations for specific levels
of water availability, along a gradient from dry to
wet. Under dry conditions, the possible light-use
strategies are limited to those that are relatively
shade-intolerant (Premise 3). Light at ground
30 t---
I
I
I
I
level is relatively high (cf. Fig. 8a) because leaf
area is limited by the need to reduce transpiration,
a high light compensation point, and by the allocation of carbon for water uptake and transport.
With the reduced number of functional types
capable of surviving under dry conditions, the
successional sequence is simple and short
(Figs 5a and b); there is little change in light
availability over time and little vertical stratification of the vegetation (Fig. 8a).
In fact, arid regions are characterized by an
absence of temporal shifts in species composition
following disturbance (Noy Meir 1973; Zedler
1981; Peet & Loucks 1977). For example, Hanes
(1971) described the patterns of vegetation
dynamics in arid chaparral plant communities as
'autosuccession', referring to the self-replacing
nature of the vegetation. Diversity both within
and between habitats changes relatively little
through the course of succession under these dry
conditions.
With increased moisture availability, shade
I
I
r
(e)
WET SITE
25
100
I-"1(3
80 ._%
20
z
v
=,,-I,
E
-.1 W
I-.
-I- 15
(3
LU
-r-
60 ~
u.a
u.z
0 ~
40 (.'3~
10
20
0
50%
Z q,
LU
(3
m
Id.I
0
0
50%
10%
0
10%
5%
0
5%
P E R C E N T A G E OF L E A F A R E A PER HEIGHT C L A S S
Fig. 8. Simulated vertical distribution of leaf area and associated light availability at ground level for three environments along
a moisture gradient. The leaf area distribution reflects the contribution of all functional types present under the specific moisture
conditions.
60
tolerance becomes a viable strategy. Indeed,
shade tolerance is necessary if a plant is to be able
to establish and survive as light is reduced by the
increased leaf area that plants can support under
moist conditions (Fig. 8b). Under moister conditions, additional functional types (those intolerant
of low water availability) are able to enter the
community, while the types that are tolerant to
low moisture are still able to survive, at least in the
high light conditions of early succession. This
increase in the number of functional types results
in a more complex successional sequence
(Fig. 5c, d, e), and allows vertical stratification of
the vegetation (Fig. 8b).
Under wet conditions (Fig. 50, survival in the
high light conditions of early succession is independent of tolerance to low moisture or light, and
all functional types can survive. However, shadeintolerant mesic types (with a low tolerance for
dry conditions) quickly dominate because their
growth rates are higher than those of either the
more shade-tolerant types or the more xeric types
(with high tolerance for dry conditions) (see Fig. 2
and Table 1). As light is reduced at ground level,
the ability to regenerate and grow under shaded
conditions becomes more important and the more
shade-tolerant types (e.g., type 6 in Fig. 5d, e),
regardless of moisture tolerance, begin to dominate. The most mesophytic shade-tolerant types
will eventually dominate under high moisture conditions (e.g., type 1 in Fig. 5e, f), because of their
shade tolerance and size. Note, however, that the
highly shade-tolerant types existing in the low
light levels of the forest floor are very sensitive to
water stress and could be severely affected by
extreme seasonality or occasional droughts
(Nutman 1937; Walter 1971).
Only when high moisture availability makes
shade tolerance a viable strategy can there be
complex vertical stratification of forest structure.
With increasing water availability, plant density
and leaf area can increase and available light at
ground level decreases (Fig. 8c). When there is
sufficient water to support a closed canopy
woodland, a vertical stratification of woody vegetation develops with a functionally and taxonomically distinct understory (White 1968; Smith &
Goodman 1986, 1987). The increased leaf area
results in a temporal shift in species composition
(i.e., succession) because the initial canopy dominants cannot regenerate under reduced light
availability.
The pattern of increasing vertical stratification,
increasing production, increasing leaf area index,
and increasing number of functional types continues as moisture availability increases, reaching
the highest levels under the most mesic conditions
(e.g., in a tropical rain forest).
Zonation: dominance along spatial gradients
Although zonation is a spatial phenomenon, it
also has a temporal component. Succession
occurs at every point along a spatial gradient, so
patterns of zonation may change over time. The
simulations presented in the context of succession
in Figs 4 and 5 can also be used to look at patterns of zonation.
Because plants found under dry conditions
have a low leaf area and small stature, light availability is relatively high at ground level (Fig. 8a).
Zonation of woody plants in arid regions generally
involves shade-intolerant species of increasing
size along gradients of increasing moisture availability. Although diversity within a zone is low,
many different zones can occur because slight
differences between soil types can result in significant differences in soil moisture under low rainfall
conditions.
Minimal overlap occurs between the zones
because shade intolerance precludes coexistence
through vertical stratification of light. As
Whittaker (1975) observed, 'Toward increasingly
unfavorable [xeric] environments there is a
stepping down of community structure and a
reduction of stratal differentiation, with generally
smaller number of growth forms arranged in fewer
and lower strata.' Because physiological limitations prevent the more mesic types from occurring
during any successional stage, there is little
change in the diversity of functional types through
time (Fig. 6).
Under wetter conditions, diversity within habi-
61
tats can be higher because more light-use strategies are possible. Diversity changes dramatically
through the course of mesic succession, with a
decrease in diversity among the dominant life
forms (cf. Fig. 6a, b) because the shade-intolerant
types that compete successfully in the high light
conditions of early succession are eventually
excluded by shade-tolerant types. However, there
may be an increase in total diversity as subordinate life forms such as vines, epiphytes, and
understory herbs with higher shade tolerance (but
reduced size and longevity) are added to the
community. Spatial patterns of diversity among
different patches or habitats are as likely to reflect
differences in successional age (e.g., Fig. 6a
vs. 6b) as they are to reflect differences in
response to water availability or the availability of
other resources that is not directly controlled by
the plants themselves.
Patterns of zonation change through time,
reflecting changes in resources, particularly light,
that are caused by the plants themselves. Fig. 6
illustrates the temporal changes in plant type distributions (i.e., zonation) between early (Fig. 6a)
and late succession (Fig. 6b) along a moisture
gradient. The principal changes are: (1)a decrease in the range of moisture conditions over
which a plant type is found, resulting primarily
from competition at the high resource end of the
gradient; and (2) a shift in the mode of the plant
distribution toward conditions of lower water
availability. In contrast to many models based on
niche theory that represent plant distributions
across resource gradients as Gaussian, the distributions produced by our model are not symmetrical. The distributions are skewed toward the
low resource end of the gradient, where they are
truncated by physiological limitations. A long tail
of the distribution persists under high resource
conditions where the plants can potentially survive, but are usually eliminated by competition.
This same pattern of skewness has been found in
many studies of plant distributions along resource
gradients (Austin 1987; Austin & Smith in press).
These patterns generated by the model for
moisture gradients (Fig. 6) are similar to the pattern documented by Werner & Platt (1976) for
goldenrods. There was higher goldenrod diversity
at most points along a moisture gradient and
greater overlap between species in an old field
(considered to represent an earlier stage of
herbaceous succession) than in a natural prairie.
Similar patterns of decreasing habitat breadth
through the course of succession have been
reported for other herbaceous communities
(Pineda et aL 1981 a and b) and forests (Auclair &
Goff 1971; Christensen & Peet 1984).
Shifting successional roles of functional types
When moisture availability is reduced, three
phenomena occur that influence successional
dynamics: (1) reduction in the number of possible
light-use strategies; (2)reduction in shade tolerance (i.e., whole plant light compensation levels
are increased); and (3) reduction in the maximum
potential growth rates of the functional types. The
first two phenomena have the effect of changing
the relative shade tolerances of functional types
(cf. Fig. 3), which allows a single functional type
to have different ecological roles (e.g., early successional vs. late successional) under different
conditions.
For example, functional types that dominate in
late succession under xeric conditions (e.g.,
type 10 in Fig. 5c) can also appear in the high light
conditions of early succession under mesic conditions, where shade tolerance is not critical (e.g.,
type 10 in Fig. 5d, e). However, as light at ground
level is reduced by increased leaf area during
mesic succession, shade tolerance becomes more
important. Therefore, the functional type that was
able to dominate in late succession under xeric
conditions, because it was the most shadetolerant type under those conditions, will be
replaced by more shade-tolerant mesophytic
types under mesic conditions (e.g., type 10 in
Fig. 5d, e). This trend continues as moisture
availability increases until eventually the xerophytic shade-intolerant types are eliminated even
in early succession by the faster growing mesophytic shade-intolerant types (Fig. 5t).
This shift in the ecological role of a functional
62
type is more easily visualized from Fig. 4, which
shows the changes in abundance of five functional
types over time as a function of moisture availability. Except for the type with the lowest tolerance to reduced moisture and greatest shade
tolerance (type 1), each functional type appears
initially as an early-successional transient under
conditions of high moisture availability and
becomes a late-successional dominant only in
communities with lower moisture availability.
This shift in roles is most pronounced in the
functional types with the lowest shade tolerance
and highest tolerance to low moisture conditions
(e.g. types 10, 13, and 15).
Although these early-successional transients,
which are shade-intolerant but tolerant to low
water availability, do not persist when water
availability is higher, they may achieve much
greater sizes and higher growth rates on an individual basis under moister conditions than they
do under the drier conditions where they dominate the community. For example, Acacia karoo
shows this pattern in southern Africa; it is a tall,
fast-growing early-successional tree on the
coastal sand dunes (Weisser & Marques 1979),
but it is a slower-growing tree of smaller stature
in the semi-arid savannas where it is the dominant
species over extensive areas (Acocks 1975).
Several pine species show this same role shift in
southeastern North America, where they are
early-successional
transients
replaced
by
hardwoods on favorable sites but they persist and
dominate exposed dry sites (Oosting 1942). Likewise, as Peet & Loucks (1977) observed, communities of Quercus macrocarpa and Q. velutina
persist on xeric sites, although both species are
typical of early-successional stages on more productive mesic sites.
Discussion
Resource variability and the ecological classification
of plants
Just as the successional role of a plant functional
type can change in response to conditions such as
water availability, so can other plant roles that
have been used to classify plants. For example,
whether a particular plant is a 'gap' or a 'forest'
species or where in a gap it occurs is not a constant, but a consequence of the plant's particular
resource-use strategy (functional type) and the
environment in which it occurs. Thus, a plant can
have different roles, depending on environmental
conditions such as the degree of water or nutrient
availability. Because traits such as successional
roles, characteristic spatial position, and other
aspects of a plant's interactions with its environment are variable, they cannot be the sole basis for
a functional classification of plants. Inherent
physiological and life history characteristics,
which determine how the plant responds to varying environmental conditions, are a more appropriate basis for an explanatory classification of
plant strategies.
The correlation between environmental conditions and plant distributions has been the basis of
most previous classification of plant strategies or
vegetation types, including r, K, and adversity
strategies (MacArthur
& Wilson
1967;
Southwood 1977; Greenslade 1983); early and
late successional types (Budowski 1965, 1970;
Whittaker 1975; Bazzaz 1979; Finegan 1984;
Swaine & Whitmore 1988); exploitative and conservative responses (Bormann & Likens 1979);
ruderal, stress tolerant, and competitive strategies
(Grime 1977, 1979); gap and non-gap species
(Hartshorn 1978; Brokaw 1985a, b); structural
characteristics (Raunkiaer 1934; Hall6 1974;
Hall6 & Oldeman 1975; Webb et al. 1970; Walker
et al. 1981). Most of these schemes are based on
plant responses to a particular set of environmental conditions, such as resource availability
and disturbance regime, rather than on inherent
properties of the plants themselves.
Our system of classifying plant functional types
differs from most previous classifications in that
it is not based on plant distributions or patterns of
environmental conditions (e.g., the habitat templet (Southwood 1977)). Rather it is based on
biological constraints imposed on individual organisms by processes at lower levels of system
organization (e.g., physics, chemistry, physiology). These biological constraints interact with
63
environmental conditions at higher levels of system organization (e.g., climate, geology), which
can be defined independently of the response of
the plants themselves. The vital attributes model
of Noble & Slatyer (1980) is also based on the
interaction of plant properties with environmental
conditions.
The complexity of interactions between different environmental factors was studied by
Shelford (1951 a, b), who developed three-dimensional surfaces of population responses to levels
of two physical factors (generally precipitation
and temperature presented as thermohydrograms). Shelford specifically focused on environmental conditions during periods that are critical
to reproductive success. His work was a significant contribution to understanding the effect of
interacting factors on population dynamics.
However, his work was on animal responses, and
did not consider plant responses to interacting
conditions.
Plant responses to interacting environmental
factors have also been considered in some
resource-based models of plant growth. The graphical model of plant responses to changing
amounts and ratios of two different resources
developed by Heady et al. (1955), quantifies the
multidimensional response of several crop species
to different ratios and amounts of nitrogen and
phosphorus. In this approach, different pairs of
resources may be classified as essential, complementary, substitutable, etc. for a particular plant;
furthermore, different plant species can be characterized by their growth isoclines for two limiting
resources (Heady et al. 1955). This approach has
been used to look at competition for resources
between two or more different species (Leon &
Tumpson 1975; Tilman 1980, 1982). Our major
criticisms of this approach to plant responses to
resources are (1) it is based on competitive equilibrium, which is unlikely to be relevant in most
ecological situations (DeAngelis & Waterhouse
1987); and (2) it inappropriately aggregates many
different components of competitive ability for a
particular resource by creating an a priori definition of competitive ability (see discussion in
Huston & Smith 1987).
A recently published model of vegetation
dynamics (Tilman 1988) is based on the consequences of root-shoot tradeoffs on competition
for nitrogen and light. This model is similar in its
essential details to other individual-based plant
competition models (e.g., Botkin et al. 1972), and
is an example of one aspect of the tradeoffs we
address in our theory.
Vegetation pattern, resources, and disturbance
The scale of vegetation pattern is determined by
the scale of resource variation. For example,
because the vertical distribution of light is under
the control of the plants themselves, the horizontal
scale of variation in light availability is determined
by scale of the dominant plants in the environment. Light gaps, which provide much of the horizontal variability in light, are formed by the death
of one or a few large individuals. Although large
light gaps can be formed by the death of many
trees during large-scale disturbances, the minimum scale of horizontal light variation is on the
order of individual plants.
Significant variation in water availability can
occur on a much larger spatial scale than variation
in light. The spatial scales of variation in water
availability can explain both small-scale vegetation patterns ranging form moisture gradients on
hillslopes or around individual shrubs in arid
regions to large-scale patterns along continental
moisture gradients. The temporal scale of water
availability is also much different than that of
light. On a scale of days or weeks (but not hours,
minutes, or seconds) variation in total light availability is relatively homogeneous and predictable.
In contrast, water availability is extremely variable and unpredictable on the scale of days or
weeks, although it is more predictable on both an
hourly or a yearly basis. Plants have little control
over water availability. Although root uptake and
transpiration can reduce water locally (Ehleringer
1984), water availability is primarily an allogenic
consequence of climate, weather, soils, and topography.
To the extent that the effect of disturbances
64
upon resource availability can be determined, the
response of vegetation to disturbance can be
predicted by a model based on plant functional
responses to resources. The level of one critical
resource can determine the extent to which a given
type of disturbance will influence other critical
resources and thus affect plant community structure. For example, disturbances that remove vegetation and increase light availability will have little
impact on diversity within or between habitats in
xeric environments, where only one or a few lightuse strategies are possible. However, the restructuring of vertical and horizontal light availability
in mesic areas can have a major impact on the
diversity of functional types. The role of gap formation, in particular, is known to play a critical
role in structuring both tropical and temperate
forests (Hartshorn 1978; Runkle 1981, 1982;
Runkle & Yetter 1987; Brokaw 1985a, b).
Thus, disturbances can have very different
effects at different points along a resource
gradient. Some disturbances are limited to certain
portions of a gradient, whereas other disturbances
have a large effect only under particular resource
conditions. Most disturbances, whether autogenic or allogenic, tend to occur with a characteristic frequency and intensity in different regions
of a landscape. This periodicity of disturbances
allows the establishment of a dynamic equilibrium
between the rate of vegetation change (i.e., succession) and the extent to which disturbances
slow or prevent succession or reinitiate succession from some earlier stage. This dynamic
equilibrium in turn strongly influences species
diversity (Huston 1979, 1985) and can also
influence a wide variety of other community and
ecosystem properties (Pastor & Post 1986;
Huston & Smith 1987).
Relation to results of gradient experiments
Our computer simulation experiments are analogous to the field and laboratory experiments of
Ellenberg (1953, 1954), Austin & Austin (1980),
and Austin et al. (1985). The fact that the simulation results closely match the experimental
results suggests that our simple model incorporates the underlying processes that produce the
consistent patterns of plant distributions found in
these experiments.
The simulation results illustrate the difference
between the 'physiological optimum' (Fig. 7a) and
the 'ecological optimum' of a species (Fig. 7b)
(Salisbury 1929; Walter 1971; Ellenberg 1953,
1954; Mueller-Dombois & Ellenberg 1974;
Rorison 1968; Austin 1982). Each functional type
(with the exception of the two extreme types)
shows declining total biomass both with increased
and with decreased moisture availability when
they are grown together with all other functional
types (Figs 4, 7b). The decline in relative biomass
of most types as moisture availability is increased
results from competition for light, since each type
has its maximum potential growth under high
resource conditions (Fig. 7a). As moisture decreases, most functional types decline in total
biomass as a consequence of both competition
and physiological limitations. (Fig. 7b).
As a general rule, all plants grow best with
abundant light and water (as well as mineral
nutrients and CO2), but plants are rarely most
abundant in natural communities under their
physiologically optimum conditions because of
competition from other species. Many studies
have found a great similarity in the physiological
optima of most species when they are grown in
monocultures along experimental gradients of
nutrients (Bradshaw et al. 1964; Austin & Austin
1980) and moisture (Ellenberg 1953, 1954;
Mueller-Dombois & Sims 1966). However, there
is much less overlap in the resource conditions
under which plants actually achieve their highest
biomas s in natural multispecies communities (i.e.,
the ecological optimum Ellenberg 1953, 1954;
Walter 1971; Austin 1982). In addition, the position of the ecological optima of many plant
species along a resource gradient can be very
different from the position of their physiological
optima (Mueller-Dombois & Sims 1966; Austin
1982; Austin et al. 1985).
As a result, there is much more variation in the
conditions under which plants are actually found
than in the conditions under which they grow best
65
in the absence of competition. Competition displaces species toward environmental conditions
that they are able to tolerate, but which the species
that outcompete them under optimal conditions
cannot tolerate (cf. Connell 1972). Thus, for many
species, the ecological optimum is closer to their
physiological limit than to their physiological
optimum.
The inevitable result of adaptive tradeoffs is
that no organism can be dominant over the entire
range of conditions under which it can survive (cf.
Darwin 1859; Clements 1916; Clements etal.
1929). Plant types adapted to low resource conditions are at a competitive disadvantage under high
resource conditions because competitors adapted
to only high resource conditions have none of the
constraints associated with adaptations required
to survive at low resource levels. Likewise,
functional types adapted to high resource levels
are at disadvantage under conditions of low
resource availability (resource levels that are near
or below the minimum requirements of those
types). Therefore, as resource levels change
across either space or time, the distribution of
plant functional types will also change. This
theory explains the spatial and temporal patterns
of plant distributions across the range of environmental conditions on a landscape as the ecological consequence of evolutionary adaptations
to a specific set of environmental conditions.
Acknowledgements
This work was supported by a Eugene P. Wigner
Fellowship, the Walker Branch Watershed Project of the Office of Health and Environmental
Research, U.S. Department of Energy, under
contract DE-ACO5-84OR21400 with Martin
Marietta Energy Systems, Inc., and by National
Science Foundation (NSF) grant BSR-8315185.
We thank many friends and reviewers who have
given us invaluable suggestions as we tried to
clearly express these ideas, including M . P .
Austin, D.L. DeAngelis, K.T. DeLong, B. E.
Kimmel, G. M. Logsdon, L. M. McCain, S.B.
McLaughlin, R.J. Norby, J.J. Pastor, W.M.
Post, H. H. Shugart, A. J. Stewart, G. E. Taylor,
D.L. Urban and A. B. Wellington. This work
was first presented in a Symposium on the Ecosystem and Community Implications of Population Models at the 1986 meeting of the Ecological
Society of America. This is Publication Number
3306 of the Environmental Sciences Division of
Oak Ridge National Laboratory.
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