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Theoretical Population Biology TB1327
Theoretical Population Biology 51, 165179 (1997)
Article No. TP971327
Herbivores, the Functional Diversity of Plants
Species, and the Cycling of
Nutrients in Ecosystems
John Pastor
National Resources Research Institute, University of Minnesota, Duluth, Minnesota 55811
and
Yosef Cohen
Department of Fisheries and Wildlife, University of Minnesota, St. Paul, Minnesota 55108
Received March 27, 1996
Numerous investigators have suggested that herbivores almost always increase rates of
nutrient and energy flow through terrestrial ecosystems by returning to the soil fecal
material and urine with faster turnover rate than shed plant litter. These previous theories
and models always treat the producer compartment as a homogenous pool. Essentially, they
assume that consumers feed through a pureed cream of vegetable soup. However, many field
observations and experiments have shown that consumers feed selectively (i.e., in a
cafeteria) and that consumer choice is made on the same chemical basis that determines
decomposition rates. Plants that are preferred food sources often have higher nutrient
content, higher growth rates, and faster decomposition rates. As consumption reduces
dominance of these species in favor of unpreferred species with slower decomposition, rates
of nutrient cycling and energy flow should therefore decline. We analyze a model in which
the consumer is given a choice among producers that vary in nutrient uptake rates, rates of
nutrient return to decomposers, and consumer preference, and which is parameterized for
plants and consumers characteristic of boreal regions. In this model, in an open, well-mixed
system with one consumer and two such producers, the nutrientenergy flow will not exceed
that of a system without the consumer. If the consumer has a choice between two such
producers, it must choose one plant over the other at a greater ratio than that between the
two plants in uptake and decay rates. In contrast, in a closed system the consumer must be
less selective to coexist with the two plants. The system behavior is determined by the level
of nutrient return through the consumer and the differences between the plants in nutrient
uptake rates and consumer preference. Species richness affects properties of this model
system to the extent that species are functionally distinct (i.e., have different rate
constants) in a multivariate space of life history traits (i.e., nutrient uptake and palatability).
We suggest that the biochemical variability of plant tissues that simultaneously determines
both consumer preference and decomposition rates is an essential feature of food webs that
cannot be ignored. Thus, ecosystem models should, at minimum, consider more than one
producer type with consumer preference. ] 1997 Academic Press
165
0040-580997 K25.00
Copyright ] 1997 by Academic Press
All rights of reproduction in any form reserved.
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Pastor and Cohen
INTRODUCTION
How herbivores alter ecosystem processes such as
nutrient cycling and energy flow has been the subject of
much research over the past several decades. Most of this
research stems from the seminal paper by Hairston et al.
(1960), which divided the world into homogeneous
trophic levels (decomposers, producers, consumers, and
predators). Hairston et al. (1960) postulated that ``the
world is green'' because predators limit the effect that
herbivores have on vegetation, which in turn is limited by
climate, water, or light (Fig. 1A). Hairston et al. (1960)
recognized that producers may compete for abiotic
resources but they did not recognize that the growth of
plants is often limited specifically by the release of
nutrients from litter by decomposers. They thereby
ignored the flow of nutrients through the system. In this
view, the decomposers are passive recipients of dead
organic matter and are not part of a feedback with higher
trophic levels. Therefore, the role of herbivores in an
ecosystem with feedback loops with decomposers was
not fully considered.
Further elaborations of the Hairston et al. hypothesis
were made by Oksanen and co-workers (Oksanen et al.
1981, Oksanen 1983, 1988). These papers considered
how trophic structure and energy flow might change
along gradients of productivity. They postulated that
only abiotic factors (mainly climate) control productivity. Nutrient availability in these papers was defined
as the size of a fixed inorganic nutrient pool, not as the
rate of cycling through the decomposer compartment.
Furthermore, variations in plant palatability to the herbivores and its consequences for nutrient and energy flow
were also not fully considered.
Subsequent advances along this line of reasoning were
made by Holt (1977) and Holt et al. (1994). Holt and
coworkers showed that for a closed ecosystem consisting
of one resource (a fixed soil nutrient pool), two plant
species, and one consumer (Fig. 1B), the presence of the
consumer can sometimes depress resource availability,
depending on ratios of the plant species and preference of
the consumer for one plant over another. They make the
simplifying assumption that nutrients are released instantaneously from plants or consumer biomass once they
are returned to the soil. There was no variability in the
rate of litter and nutrient return from plants or consumers. Decomposition and the decomposer trophic
level were not explicitly considered.
In the past 15 years or so, there has been increased
recognition of the need to explicitly consider interactions
between the food web and the cycling of limiting
nutrients through the decomposer level (reviewed in
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FIG. 1. Previous views of the role of consumers, plants, and
decomposers in the cycling of nutrients in ecosystems. (A) Litter is
returned to decomposers, but primary production is not controlled
by the recycling of nutrients through the decomposersoil organic
matter compartment (e.g., Hairston et al. 1960, Oksanen et al. 1981).
(B) Plants differ with respect to nutrient uptake and consumer
preference, but not in their effect on nutrient supply through the decomposers (e.g., Holt et al. 1994). (C) Nutrient feedback from consumers
and plants through decomposers determine net primary production,
but plants are homogeneous with respect to consumer preference,
nutrient uptake, and decomposition (e.g., Loreau 1995 with additional
examples reviewed in DeAngelis 1992).
DeAngelis 1992). Such studies typically include a decomposer compartment receiving nutrient inputs from plants
and consumers and releasing nutrients into an inorganic
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Herbivores and Nutrient Cycles in Ecosystems
pool, but they simplify the system to one plant producer
(Fig. 1C). They are an advance over previous studies
cited above in that the flows of nutrients through the
food web is explicitly considered. The common conclusion of these studies is that herbivores increase the rate of
nutrient cycling because the turnover rates of their bodies
and fecal material are faster than that of live plants and
their shed litter. This has become embedded in the
literature (e.g., Chew 1974, Mattson and Addy 1975,
Owen and Wiegert 1976, 1981, Petelle 1982). Loreau
(1995) recently proposed a model which is a generalization of the view that consumers almost always maximize
energy and nutrient flow through ecosystems given that
there is one plant producer and the consumer is not faced
with a choice.
There is reason to examine the consequences (to
nutrient flux in ecosystems) of the assumption that plants
are a homogeneous pool of material and that herbivores
do not discriminate among different plants or their parts.
No large herbivore lives in a system with only one plant,
and they do not forage indiscriminately among the
various plants they encounter. There is growing evidence
that herbivores discriminate among available foods on
the basis of their chemistry, particularly the concentrations of nutrients and carbon compounds that control
digestion rates (Jarman and Sinclair 1979, Mattson 1980,
Bryant and Kuropat 1980, Crawley 1983, Lindroth 1988,
Tahvanainen et al. 1991, Bryant et al. 1991, Hartley et al.
1995). These same carbon compounds, particularly the
lignin and cellulose that compose the cell walls, also
determine the rate of decay of plant litter and consequently the rate of release of limiting nutrients by decomposers (Melillo et al. 1982, Horner et al. 1988, Flanagan
and Van Cleve 1983, Wedin and Pastor 1993). This is
particularly true for nitrogen, which in turn limits plant
growth (Waring and Schlesinger 1985). Production of
secondary compounds in leaves and twigs also appears to
be inversely correlated with plant growth rates and
nutrient uptake rates, and positively correlated with
retention times of leaves on the individual plant (Coley et
al. 1985). Plant species that are palatable and easy to
digest are also easy to decompose for the simple reason
that soil decomposition and ruminant digestion are both
microbially mediated (after all, cell walls that are hard to
digest will be so for microorganisms both in the soil and
in an herbivore gut). This implies that plants which are
unpalatable to herbivores also have slower turnover
rates of nutrientsin live tissues because of slow growth
and evergreen habit, and in shed litter because of
recalcitrance to soil decomposers. Numerous examples
of the connections between plant tissue chemistry, herbivore preference, and decomposition rates have been
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reviewed elsewhere (Bryant and Kuropat 1980, Bryant
and Chapin 1985, Horner et al. 1988, Bryant et al. 1991,
Huntly 1991, Pastor and Naiman 1992).
The assumption that plants are a homogeneous food
source to herbivores and decomposers alike therefore
appears to be untenable on biochemical grounds. Close
scrutiny therefore begs the question of whether, given
these observed correlations among plant traits, the
specific application of dung or urine can in fact increase
productivity or nutrient availability. While some have
found that fecal material from some consumers decomposes more quickly than that of plant material or soil
organic matter (Reuss and McNaughton 1987, Reuss et
al. 1988, Day and Detling 1990, Pastor et al. in press),
others have found that this is not always the case (Floate
1970, Pendeleton 1972, Pastor et al. 1993). The finding
that animal droppings sometimes have decreased
nutrient release compared with plant litter may be
because much of the nutrients in the plant material have
already been taken up by the animal during digestion.
Any potential manuring effect should also be evaluated
in the context of changes in the plant community and its
litterfall that might offset any locally and temporarily
increased nutrient availability. Herbivores ultimately
control ecosystem processes not only by what and how
much they eat, but also by what they don't eat.
Here, we explore the effect of herbivores on ecosystem
nutrient and energy flow, given the assumption that plant
species differ in herbivore preference, nutrient uptake
rates, and decomposition rates. We will show that if the
consumer selects a plant species based on the chemical
factors that simultaneously control both digestion and
decomposition, then over a very wide range of consumer
return of fecal material, the rates of energy and nutrient
flow through the system are less than that of a system
where the consumer is absent. Moreover, one of the
plants becomes extinct at high rates of consumption and
nutrient return in fecal material.
MODELING
Loreau (1995) presented a simplified ecosystem model
with decomposers, a producer, a consumer, and a
nutrient. Loreau's analysis of his model suggests that
consumers tend to increase the rate of energy flow
through the ecosystem when the producer compartment
is homogeneous and the rate of cycling of consumer
biomass and excretion through the decomposers is faster
than that of the producer. We wish to examine the consequences of relaxing the assumption of a homogeneous
168
producer compartment by introducing two plant
producers with different rates of consumption by the
herbivore and nutrient return to the decomposers. We
therefore present a model similar to that presented by
Loreau (1995). By similar we mean that the model equations remain unchanged; we remove (for simplicity) one
of the decomposer compartments, and add an additional
producer compartment (Fig. 2).
As in Loreau (1995), the ecosystem is modeled as
interacting compartments. Each compartment represents
a species, or a collection of functionally-related speciesnutrient pools or their energy equivalent, measured in
units of density (e.g., gm 2 ). The ecosystem is presumed
to be nutrient limited, and the identified compartments
(Fig. 2) are: a nutrient pool (N), two producers (x1 and x 2 ),
a consumer (C), and a decomposersoil organic matter
pool (D). We assume that the biomass in a compartment
is proportional to its nutrient density. The decomposer
receives a constant proportion of nutrients from each of
the producers and the consumer and returns a constant
proportion of its nutrients to the nutrient pool (N).
Flows from N to x 1 and x 2 , and from x 1 and x 2 to C are
assumed to be LotkaVolterra functions. The system is
open, with a constant input rate, Q, to the inorganic
FIG. 2. Model flow diagram (Eq. (1)). Nutrient flow through
ecosystems with two plants, one which has high nutrient uptake rates,
is preferred by the consumer, and decays rapidly (x 1 ) and one which is
not (x 2 ). The growth of the plants is determined by the supply of
nutrients through the inorganic pool and mediated by the rate of return
in litter and its decomposition.
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Pastor and Cohen
nutrient pool, and outputs from each compartment
regulated through linear functions with proportionality
parameters e i .
To make the model identical to that of Loreau (1995),
(i) remove one of the producer compartments, (ii) add a
decomposer compartment, and (iii) make all e i equal.
Our addition of another producer compartment (Fig. 2)
reflects the fact that the consumer has a choice of
two dietary items. Our elimination of one decomposer
compartment reflects the fact that litter, dung, urine, or
carcasses from both producers and the consumer enter
into a common soil organic matter pool and are subsequently decomposed by a single microbial community,
which eventually returns nutrients to the N compartment. Soil organic matter is composed almost entirely of
material that has been at least partially processed
through previous decomposers who decompose each
other in a complex food web (Moore and Hunt 1988);
therefore, D here represents the entire detrital-based
food web including partially decomposed plant litter and
microbial remains. In reality, the microbial community
is at least as complex as the plant community. Nonetheless, this simplifying assumption is equivalent to stating
that any differences in the distribution of microbial
species on different materials returned to the soil do not
effect the total release rate of nutrients to inorganic
pools. For a first approximation, this seems reasonable.
Finally, for simplicity we do not distinguish between
urine and fecal material in the returns of nutrients from
the consumer to the soil, treating them both together
with carcasses. While urine and fecal material release
nutrients at different rates (Schimel et al. 1986), we
are less concerned here with this difference than simply
with total flow of nutrients from the two producers,
through the consumer, back to the decomposers. Some
ammonium may also volatize from urine or fecal
material shortly after deposition (Schimel et al. 1986);
this ammonium volatilization is implicitly covered by
the export of nutrients from the consumer and decomposer pools. These assumptions merit further study,
which we do not undertake here.
We are interested first in determining the rates of
nutrient flow and the conditions for coexistence of a
consumer with two plants, a decomposer, and a finite
nutrient where the two plants compete for resources
because of differential uptake and return rates to the
soil nutrient pool (resource competition) and where
their relative abundance is also partly determined by
differential consumption by the herbivore (apparent
competition).
The equations that describe the ecosystem model in
Fig. 1 are
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Herbivores and Nutrient Cycles in Ecosystems
N4 =Q+d D D& f 1( } )& f 2( } )&e N N
x* 1 = f 1( } )& f 3( } )&b 1 x 1 &e 1 x 1
x* 2 = f 2( } )& f 4( } )&b 2 x 2 &e 2 x 2
(1)
C4 = f 3( } )+ f 4( } )&b C C&e C C
D4 =b 1 x 1 +b 2 x 2 +b C C&d D D&e D D.
Dots on compartment variables in Eq. [1] denote
derivatives with respect to time, andas in Loreau
(1995)dots in the functions f denote LotkaVolterra
forms:
f 1(N, x 1 )=a 1 Nx 1
f 2(N, x 2 )=a 2 Nx 2
(2)
f 3(x 1 , C)=c 1 x 1 C
f 4(x 2 , C)=c 2 x 2 C.
Saturating functional responses (e.g., handing time) may
give similar results but increase the probability of nonpoint attractors and are therefore not considered.
Furthermore, the forms of Eqs. (1) and (2) lead naturally
to calculations of mass balance of nutrients and energy.
The model (Eq. (1)) without the consumer and with
two producers reduces to
2
also small, and this seems for now to be a reasonable way
to proceed. We shall, however, return to this point later.
We first examine analytical solutions of Eqs. (1) and
(3) at equilibrium by simultaneously setting all the
differential equations in Eqs. (1)(3) to zero and solving
for each compartment. We sought analytical solutions
for both open systems (Q and e>0) and closed systems
(Q and e=0).
We are interested only in the single solution that
allowed coexistence of the consumer with both producers
and the decomposer and a positive nutrient pool. Solutions in which one or more of these compartments is zero
represent simpler cases discussed by others (Fig. 1). For
the system with finite values for all compartments, the
solutions for all compartments were unwieldy except for
the expression for the consumer. For an open system
with a consumer, two producers, a decomposed, and a
positive nutrient pool,
C*=
a 1(b 2 +e)&a 2(b 1 +e)
.
a 2 c 1 &a 1 c 2
(4)
For C*>0, the following conditions must be satisfied:
b 1 +e a 1 c 1
< < ;
b 2 +e a 2 c 2
(5a)
b 2 +e a 2 c 2
< < .
b 1 +e a 1 c 1
(5b)
or alternatively,
N4 =Q+d D D&N : a i x i &e N N
i=1
x* i =a i Nx i &b i x i &e i x i ,
i=1, 2
(3)
2
D4 = : b i x i &d D D&e D D.
i=1
This system cannot have a stable equilibrium with
both producers present except under extremely unlikely
balancing of the parameters (Armstrong and McGehee
1980) or unless resource supply to the two producers is
spatially segregated (Huston and DeAngelis 1994). We
will demonstrate this further below.
To simplify the analysis for the sake of obtaining an
analytical solution, we assume with Loreau (1995) that
e N =e 1 =e 2 =e C =e D =e. This is equivalent to saying
that some constant fraction (e) of the total nutrient pool
of the ecosystem (N+x 1 +x 2 +C+D) is lost each year
without specifying the exact mechanism of loss (i.e.,
leaching, migration, volatilization, etc.), and that the
same fraction is lost from each of the compartments.
Because export of nutrients is small in most ecosystems
near equilibrium (Waring and Schlesinger 1985), differences between compartments in the rate of export are
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These ratios indicate the relative preference of the consumer for one plant over the other (e.g., c 1 c 2 ), the difference in nutrient uptake rates of the two plants (e.g.,
a 1 a 2 ) and the differences in their decay rates (e.g., b 1 b 2 ).
These conditions are satisfied whether producer 1 or
producer 2 is the preferred plant so long as b 1 <a 1 <c 1
(producer 1 is preferred and cycles nutrients faster) or
b 2 <a 2 <c 2 (producer 2 is preferred and cycles nutrients
faster). This is because there is nothing in the equations
that specifies one producer over the other with respect
to nutrient cycling and consumption, except in their
parameterization. Therefore, the conditions hold regardless of which plant is preferred by the producer and cycles
nutrients at the faster rate, so long as the correlations
among the traits hold. We have reviewed the experimental evidence for these correlations among plant traits previously in the Introduction. For simplicity, we shall
therefore proceed for the remainder of the paper with the
assumption that producer 1 is the preferred plant with
170
Pastor and Cohen
greater uptake and decay rates. In this regard, it is easiest
to examine the conditions required for coexistence at
equilibrium from Eq. (5a) with the preferred plant in the
numerator.
For an open system at equilibrium, the consumer must
select producer 1 over producer 2 to a greater extent than
the ratios in relative uptake rates of the two plants
(c 1 c 2 >a 1 a 2 ). Furthermore, the plants must show
greater differences in uptake rates than in decay
a 1 a 2 >b 1 b 2 ). These inequalities determine a region in
the plane of a 1 and a 2 within which the two plants can
coexist in the presence of the consumer (Fig. 3). This
region can be plotted by multiplying through the above
inequalities by a 2 , yielding
c1
b 1 +e
a 2 <a 1 < a 2 .
b 2 +e
c2
(6)
The ratios (b 1 +e)(b 2 +e) and c 1 c 2 are the slopes of the
limiting relations between a 1 and a 2 and determine the
region of coexistence of the two producers (Fig. 3).
We can now ask, assuming the correlations among
plant traits discussed previously, What are the broadest
range of conditions from Eq. (6) that would allow
coexistence given that b 1 >b 2 , a 1 >a 2 , and c 1 >c 2 ? This
would happen if: (i) the consumer increases preference
for producer 1 over producer 2; (ii) the plants differ less
in decay rates than in consumer preference; (iii) export
from the ecosystem increases because lim e (b 1 +e)
(b 2 +e)=1 and so increasing e would minimize this
ratio and hence widen the range of application of the
constraint. However, if export from the ecosystem is
high, then all compartments will tend to zero and will
go extinct when e(N+x 1 +x 2 +C+D)>Q. Therefore,
the widest possible range of conditions that allow
coexistence of the consumer with two plants that differ in
decay, uptake, and consumption rates will be in an
ecosystem with consumer preference for the producer
with high rates of nutrient cycling and with some (but
not high) loss of the nutrient.
The importance of the export term in this inequality
that defines the region of coexistence of two plants of
different cycling rates is surprising and not intuitive from
a simple inspection of the equations. We have made the
assumption that all e i s are equal in order to achieve an
analytical solution. Because export of nutrients is small
in ecosystems near equilibrium, differences in export
rates are probably minor. Nevertheless, it would be interesting to determine whether export from one compartment is more important in determining coexistence of the
two producers than export from others. For example,
does export of nutrients by consumer migration (e C )
have a greater effect than export by leaching (e N )?
A relaxation of this assumption of uniform export rates
bears further examination, which we do not undertake
here.
For a closed system, a solution that allows coexistence
of all compartments at equilibrium requires the consumer biomass to be
C*=
a 2 b 1 &a 1 b 2
,
a 1 c 2 &a 2 c 1
(7)
for which the following conditions must hold:
b1 a1 c1
> > .
b2 a2 c2
FIG. 3. Relationships between the uptake rates of the preferred
(a 1 ) and unpreferred (a 2 ) producer in an open system with a consumer
at equilibrium. Slopes of the relationships define the limiting conditions
that the plants must satisfy for coexistence with the consumer. The
shaded area is the region of possible coexistence identified by the
inequalities in Eq. (5)
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(8)
(Again, we remind the reader that we proceed by assuming
that producer 1 in the numerator is the preferred plant
with faster cycling rates and that similar conditions exist
were producer 2 to be the preferred plant.) These are
171
Herbivores and Nutrient Cycles in Ecosystems
exactly the opposite conditions of the open systems (5a).
In this case, the consumer must decrease its preference
for one plant over the other relative to the differences
between the plants in nutrient uptake and decay rates.
Therefore, a consumer must be more selective for the
producer with faster nutrient cycling in an open system
and less selective in a closed system.
We are now interested in comparing the nutrient flow
through the system at equilibrium, with and without the
consumer, and with the consumer returning nutrients to
the system (through D) at ever increasing rates. As an
index of nutrient flow, we compute the material flow
from N to x 1 and x 2 ; i.e.,
s
F=N : a i x i ,
(9)
i=1
where s ( =2 in the example here) denotes the number
of producer compartments (i.e., species or a group of
functionally related species). We are interested in
the behavior of stable equilibria only. To convert
from nutrient to energy (i.e., carbon) flow, one need only
multiply the a i x i in Eq. (9) by a suitable CN ratio.
Because the analytical solutions of this model were
unwieldy for the other compartments, we proceed
instead to examine model behavior with and without a
consumer with numerical solutions. Because its simplicity matches that of the model here, we will use the
boreal forest as a real world analogue.
To proceed, we choose the following realistic values for
the parameters for boreal forests that maintain the
inequalities for the open system found analytically:
a 1 =1.5,
c 1 =1,
a 2 =1.0,
c 2 =0.1,
b 1 =11,
e=1,
b 2 =10,
Q=30, d D =1.
(10)
These choices of parameter values reflect the facts that
compared to a unit of biomass density of x 2 , the first
producer (x 1 ): extracts nutrients from N at a faster rate
(a 1 >a 2 ), and its nutrients move at a faster rate to both
D(b 1 >b 2 ) and to C(c 1 >c 2 ). The rates of return of
nutrients from the plants to the decomposers incorporate
both the differences between the species in turnover rates
of live vegetation (litterfall) as well as the differences in
rates of incorporation of shed litter into decomposer
biomass (decomposition). Because boreal evergreens
produce litter that decays slowly while deciduous species
produce litter that decomposes more quickly, the rate of
litter return from these species is correlated with their
decay rates and the two processes can be subsumed into
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one rate return parameter for each species (b 1 and b 2 ).
Because the two producer species differ in energy
nutrient flow to the consumer, from the consumer ``perspective'' it is more efficient to feed on x 1 than on x 2 .
With our choice of parameters, the producer x 1 is ten
times more preferred than the producer x 2 , responds
500 faster to nutrient availability, and decays 100
faster. These measured differences in parameter values
reflect the inequalities between the plants in decay,
uptake, and consumer preference from the analytical
solution of the model (Eq. (5)).
These parameter values are similar to measured differences between quaking aspen (Populus tremuloides),
which serves as a surrogate for x 1 , and either white
spruce (Picea glauca) or balsam fir (Abies balsamea),
which can serve as surrogates for x 2 (Weetman 1968,
Lousier and Parkinson 1978, MacLean and Wein 1978,
Van Cleve and Oliver 1982, Van Cleve et al. 1983,
Flanagan and Van Cleve 1983, Moore 1984,
Tahvanainen et al. 1991, McInnes et al. 1992, Pastor et
al. 1993). Moose (Alces alces) or snowshoe hare (Lepus
americanus) are the most important mammalian herbivores in systems composed of these tree species (Bryant
et al. 1991). Thus, this choice of parameters makes our
model system analogous to the boreal forest although
with suitable parameter choices it can apply to other
systems. We will present evidence for this conclusion, as
well as a special case where these conclusions do not
apply, later in the Discussion.
We wish to determine the sensitivity of modelled
nutrient cycling rate to the return of nutrients from C to
D and to differences in the plant species in uptake rates
(a 1 and a 2 ) and consumer preference (c 1 and c 2 ). To do
this, we change the values of b C , and the ratios a 2 a 1 and
c 2 c 1 . Increases in b C reflect increased deposition of
urinefecal materialcarcasses to the soil and increased
decomposition of these materials. We choose to examine
the ratios a 2 a 1 and c 2 c 1 rather than their inverses as
examined in the analytical solutions because this allows
us to bound the relative differences between the plant
between values of 0.0 and 1.0. To change these ratios, we
hold the values for the preferred producer in the
denominator constant (a 1=1.5 and c 1=1.0) and increase
those for the unpreferred producer in the numerator from
0.0 to a 1 or c 1 . Thus the sum of the uptake rates (a 1 +a 2 )
and consumption rates (c 1 +c 2 ) is not constant but also
increases from a 1 or c 1 to 2a 1 and 2c 1 . As both ratios
approach 1.0, the difference between the two producer
species declines, and we converge on one plant species
with the biomass equal to the sum of the two species
taking up nutrients and being consumed at the rate of
species x 1 , i.e., a 1 N(x 1 +x 2 ) and c 1 N(x 1 +x 2 ). The
172
discrimination of the consumer for the two plant species
increases as the ratio c 2 c 1 approaches zero. As the two
ratios both approach 0, the flow of nutrients and energy
through producer x 2 declines and we converge on one
plant species, x 1 .
Pastor and Cohen
We then calculate the stable equilibrium values of each
compartment and total nutrientenergy flow for each of
ten values of a 2 a 1 (from 0.0 to 1.0) and b C (from
0.0 to 2.5), and for c 2 c 1 =0.1 (high discrimination by
the consumer) and c 2 c 1 =0.9 (low discrimination by the
FIG. 4. Energy flow and compartment sizes in the ecosystem (Fig. 2 and Eqs. (1) and (2)) at stable equilibria for varying values of b C , a 2 a 1 ,
and c 2 c 1 , and the remaining parameter values given in Eq. (10). (A) Total nutrient flow through the two producers at c 2 c 1 =0.1, c 2 c 1 =0.9, and
for a system with no consumers (Eq. (3). (B) The decomposersoil organic matter compartment. (C) The preferred producer (x 1 ). (D) The unpreferred
producer (x 2 ). (E) The consumer. (F) The inorganic nitrogen pool. For all pairs of surfaces, corresponding surfaces (not shown) for
c 2 c 1 =0.2, 0.3, ..., 0.8 are sandwiched between those for c 2 c 1 =0.1 and c 2 c 1 =0.9.
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Herbivores and Nutrient Cycles in Ecosystems
consumer). We also calculated the stable equilibrium
values of these compartments and nutrient flow for a
system without any consumers. Local stability was determined numerically using standard linearization methods
(e.g., May 1975) by computing the eigenvalues of the
linearized system (Eqs. (1) and (2)) at the equilibrium
values. The choice of 0b C 2.5 reflects the fact that for
bC >2.5 the model becomes unstable (positive real part of
eigenvalues) for all values of the remaining parameters and
one of the species goes extinct. As this represents the case of
a simpler system represented by one of the diagrams in
Fig. 1, our model reduces to that of others in such cases.
These other cases (Fig. 1) are then particular instances of
this model. We therefore only discuss the parameter space
that allow coexistence of the consumer with both
producers, the decomposer, and a finite nutrient pool.
This is a somewhat different approach of analyzing
model behavior than that of Loreau (1995), who
adjusted the effect of herbivory by increasing total consumption of one plant. Here, we increase rate of nutrient
return from the consumer to the soil to simulate the
manuring effect and adjust the ratios of consumption of
the two plants to simulate selective foraging on
producers with different rates of nutrient uptake and
litter decay. Total consumption of the two producers is
affected through this ratio rather than being adjusted
directly as in Loreau (1995). However, in both our case
and that of Loreau (1995), total nutrient flow through
the ecosystem is calculated according to the same equation (Eq. (9)).
The responses of nutrient flow (Eq. (9)) and each of
the compartments to variation in b C , a 2 a 1 , and c 2 c 1
are shown in Fig. 4. Each point on the surfaces in
Figs. 4A4F represents a stable equilibrium solution of
Eqs. (1)(3) and (9). In all cases simulated, there was a
single stable equilibrium (i.e., a single equation solution
for which the real parts of the eigenvalues were all
negative). The numerical simulations indicate that, in a
system with consumers and with parameters as above, as
b C increases from zero to 2.5, the nutrient flow through
the plants (Eq. (9)) at stable equilibrium increases
steadily. At first glance, this would appear to support the
contention of Loreau (1995) and others (Chew 1974,
Mattson and Addy 1975, Owen and Wiegert 1976, 1981,
Petelle 1982) that herbivores do increase the rate of
nutrient cycling. However, note that the equilibrium rate
of nutrient cycling remains below that of a system
without any consumers (Fig. 4A). We wish to emphasize
that, although our choice of parameters is realistic for
boreal forests, it is not the specific parameter values that
are important, but rather the qualitative results that
these values reflect.
As b C increases above 2.5, the unpreferred plant with
slower nutrient uptake rates becomes extinct as the
FIG. 4Continued
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174
output from this plant through the consumer increases
above the input to the plant from the nutrient pool. Note
that the total nutrient flow through the producers
remains below that of a system without consumers in this
stable region of parameter values, and that the system
without the consumer is also stable throughout this
region. Thus, there appears to be a limit on how fast
nutrients can be recycled through the consumer without
causing extinctions in this model system. In this case, the
producer trophic level collapses to that assumed by
Loreau (1995), and the model becomes Eq. (3) without
one of the producers. Since b C <b 1 , we necessarily reach
the same conclusions as Loreau (1995), namely that consumers will decrease the rate of nutrient cycling when
they return nutrients at a slower rate than the producer.
Our results differ from that of Loreau in that this is the
only region of parameter space that the two producers
can coexist, at least in boreal regions. We have previously
shown that nutrient release rates of fecal material from
moose, an important boreal herbivore, is less than that
from plant litter and bulk soil organic matter (Pastor et
al. 1993), which lends empirical support to these conclusions. Loreau (1995) showed that in a system with one
producer, a consumer will increase the rate of nutrient
cycling only when it returns nutrients the decomposer (or
the returned material decays faster) than that from the
producer. Our results suggest that this cannot happen in
the presence of two producers of the different uptake,
decay, and consumption rates used here and when those
rates are correlated as found in numerous experiments in
boreal forests (see citations in Introduction). It may be
possible for two plants of different uptake and consumption rates (e.g., one plant with even higher rates than
those of producer 1) to coexist with the consumer at
higher rates of b C . However, in this case this third plant
would be preferred plant and the inequality in Eq. (5a)
must still be satisfied. Nutrient flow in such a system may
be greater than that here. Elsewhere, we show that such
a system satisfies the conditions of evolutionary stable
strategies (Cohen and Pastor in press), whereas here we
are concerned only with ecological stability.
The discrimination of the consumer for the two plants
(c 2 c 1 ) had no effect on both the nutrientenergy flow
through the plants and the size of the decomposersoil
organic matter compartment until the ratio a 2 a 1
reached 0.5 (Figs. 4A and 4B). At this point, there is an
apparent bifurcation in the system behavior. Above this
ratio, the two plants increasingly take up nutrients at the
same rate (a 2 a 1 approaches 1.0). It is in this region of
parameter space that the discrimination of the consumer
for the two plants begins to affect the system. When the
consumer strongly discriminates between the two plants
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(c 2 c 1 =0.1), both the total nutrientenergy flow and the
size of the decomposersoil organic matter compartment
increase. When the consumer does not strongly discriminate (c 2 c 1 =0.9), both the nutrientenergy flow
and the decomposersoil organic matter compartment
decrease as a 2 a 1 approaches 1.0. As a 2 a 1 increases
further, the system becomes unstable (i.e., appearance of
positive real parts of eigenvalues) because the inequality
in the constraint on the analytical solution of this system
(Eq. (5)) is violated. Recall that b 1 =11, b 2 =10, a 1 =1.5,
and b 1 b 2 <a 1 a 2 for coexistence of all compartments.
Therefore, when a 2 >1.3636. . . this inequality is violated.
The surfaces of both the decomposer compartment and
the energy flow resemble that of the unpreferred plant
when the consumer strongly discriminates among the
two plants, but resembles that of the preferred plant
when the consumer does not discriminate (compare
Figs. 4A and 4B with Figs. 4C and 4D). Thus, the effect
of differences in uptake rates of the plants is to control
how much the consumer affects the system, and the
degree of discrimination of the consumer determines
whether the preferred or unpreferred plant controls the
energy flow and the size of the decomposer compartment.
When nutrient uptake rates are both high, the
unpreferred plant controls the system dynamics at equilibrium to the extent that the consumer discriminates
against it: not being eaten, it contributes a greater
proportion of nutrients to the decomposersoil organic
matter compartment from which they are recycled for
further uptake.
The equilibrium size of the decomposersoil organic
matter compartment mirrors that of the energy flow
through the producers throughout the parameter space.
This symmetry reflects the fact that the signs of the of the
corresponding terms in the equation for D are the
opposite for those of x 1 and x 2 . For example, the decomposer equation includes the terms b 1 x 1 and b 2 x 2 as
inputs while in the producer equations these identical
terms are negative because they are outputs. Similarly,
the output from producers to the consumer is negative
with coefficients c 1 x 1 and c 2 x 2 while the input from the
consumer to the decomposer is positive with coefficient
b C , with all three flows being proportional to C. The
symmetry of the surfaces also reflects the fact that at equilibrium the flow of nutrients through the plants to the
consumer has to be balanced by the return of nutrient
from the consumer through the decomposer back to the
inorganic N pool.
Similarly, the surfaces for the consumer qualitatively
mirror those of the nutrient pool throughout the
parameter space (Figs. 4E and 4F), except for scaling
effects determined by the products a 1 c 1 and a 2 c 2 .
Herbivores and Nutrient Cycles in Ecosystems
Increases in b C cause declines in bothfor the consumer
because output is greater and for the nutrient pool
because of corresponding increases in the size of the
nutrient uptake through the plant compartments
(Fig. 4A). This effect of b C is uniform throughout the
range of the ratios a 2 a 1 and c 2 c 1 . As above, there is
a bifurcation in the compartment behaviors when
a 2 a 1 >0.5 where the degree of discrimination of the consumer has an effect. In this region the more discriminatory the consumer is (c 2 c 1 =0.1), the greater its
biomass; less discrimination (c 2 c 1 =0.9) decreases consumer biomass. Thus the consumer biomass is maximized when the consumer discriminates against the plant
with low nutrient return rates to the soil and low nutrient
uptake rates.
Therefore, for both preferred and unpreferred
producers to coexist with a consumer in a stable open
ecosystem characteristic of boreal regions, nutrient flow
through the consumer must operate in a domain where
total nutrient flow through the ecosystem is reduced,
which is exactly the pattern we have seen on Isle Royale
(McInnes et al. 1992, Pastor et al. 1993).
DISCUSSION
The example here is simple. It captures two essential
facts not included in the model analyzed by Loreau
(1995): (i) the consumer has a choice; (ii) one of the
dietary items is of higher nutritional value than the other,
and this item returns nutrients to the decomposer compartment and draws nutrients from the inorganic
nutrient pool at a faster rate (a common situation in
boreal and conifer dominated ecosystemssee Coley et
al. 1985, Horner et al. 1988, Bryant and Chapin 1985,
Bryant et al. 1991). With these two facts, we show that at
equilibrium in an open system: (i) the consumer must
choose the faster growing plant over the slower growing
plant in greater proportion than the ratios of the plants
in uptake and decay ratesi.e., the consumer must be
selective; (ii) the presence of a consumer in such a system
reduces the rate of nutrientenergy flow below that of a
system without consumers; and (iii) both producers must
be present and must be dissimilar in uptake rates and
consumer preference for the system to be stable in the
presence of the consumer. In other words, even a slight
change in the number of species and their traits at one
level leads to conclusions the opposite from those
reached by others (Chew 1974, Mattson and Addy 1975,
Owen and Wiegert 1976, 1981, Petelle 1982). This is
in accordance with the conclusions of Abrams (1993),
who showed that heterogeneity of trophic levels with
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175
respect to their kinetics can lead to different conclusions
regarding bottom-up control of ecosystem energy and
nutrient flows and species abundances. Thus, the analysis
here indicates that, at a minimum, nutrient cycling
models with trophic levels should include consumer
preferences and differences among producers with respect
to nutrient or energy flow rates.
This conclusion bears some resemblance to that
obtained from a one consumer-two producer model
analyzed by Abrams and Shen (1989), although their
model does not include nutrient cycling as we do here.
Abrams and Shen (1989) concluded that if the consumption rates of the two producers are negatively related (i.e.,
in our terms they differ in consumer preference), then the
consumer maintains a constant, optimal ratio of consumption between the two producers to maximize
individual fitness. It would be interesting to learn if this
optimal ratio in the Abrams and Shen model satisfies the
constraint on this ratio in our model (Eq. (5)). We
explore other consequences of our model for evolutionary stable strategies in a separate paper (Cohen and
Pastor in press).
Coexistence of the two plants was not possible in any
solution of both open and closed systems without a consumer: the biomass of one plant always went to zero at
equilibrium. This implies that the consumer is needed for
coexistence of the two plant species. However, this conclusion may also be due to the assumption of this model
that the nutrient pool is well mixed and that there is no
spatial segregation of the nutrient transport to the two
producers. With this assumption relaxed, Huston and
DeAngelis (1994) have shown that two producers can
coexist without a consumer. The effect of spatial segregation of resource supply and uptake on the behavior of the
current model requires further examination, but is
beyond our current objectives.
These results also have interesting implications for the
relationship between biodiversity and ecosystem processes. The system without a consumer but with competitive interactions between the two plants has only one
producer species at equilibrium, the other having been
driven to extinction through competition. Stability of the
numerical solutions of our model for boreal regions
requires at least two functionally distinct producer
species in the presence of a consumer. These results
suggest that, through selective foraging, consumers
in boreal regions not only reduce the rate of nutrient
cycling, they also increase diversity of food sources by
providing conditions that allow coexistence. In the equations for plant growth, this arises by apportioning the
loss of biomass to the consumer among both plants in
the ratio c 2 c 1 . The maintenance of consumer choice is
176
essential in some common situations in real ecosystems:
One of the plants an herbivore consumes may contain an
essential nutrient, and thus is crucial for the survival of
the herbivore, andor the availabilities of different plant
species varies seasonally (not simultaneously) during the
year. The latter is the case of moose in a boreal forest,
for example. The moose relies on deciduous plant tissue
during spring and summer (``x 1'' e.g., P. tremuloides,
Corylus cornuta), and more so on less digestible (``x 2''
e.g., A. balsamea) during winter. These plants, the
analogues of x 1 and x 2 in our model, decay at different
rates, and supply the herbivore with nutrients (and
energy) at different rates (Bryant and Kuropat 1980,
Flanagan and Van Cleve 1983, Moore 1984, Brandner et
al. 1990, McInnes et al. 1992, Pastor et al. 1993).
The ratios a 2 a 1 and c 2 c 1 are measures of functional
distinctiveness in nutrient uptake and herbivore
preference, and hence functional diversity as opposed to
taxonomic diversity. Note that it is this functional diversity rather than richness per se that affects the equilibrium level of ecosystem functioning, in contrast to
recent hypotheses (e.g., Tilman et al. 1996). What determines the system behavior at a given level of nutrient
return through the consumer (b C ) are the functional contrasts between the plants in nutrient uptake rates (a 2 a 1 )
and consumer preference (c 2 c 1 ), not simply the number
of species, which remain constant in the parameter space
with stable solutions. Species richness affects properties
of this model system only to the extent that species are
functionally distinct (i.e., have different rate constants) in
a multivariate space of life history traits (i.e., nutrient
uptake and palatability).
The parameter values used here in the numerical solutions reflect those of boreal species and the model
behavior is consistent with observed effects of herbivores
in those regions. In boreal regions, herbivory appears to
depress nutrient cycling rates through its effect on vegetation composition and litterfall rather than through fecal
material because the total flow through fecal material is
very small (Pastor et al. 1993, Pastor et al. in press).
Increased dominance by unbrowsed, highly defended,
slow-growing evergreens and depression of soil nitrogen
availability appears to be the common response of plant
communities to browsers and grazers in the boreal
forests of North America (Bryant et al. 1983, Bryant and
Chapin 1985, Pastor et al. 1993). These long-term
changes in the plant community appear to override the
potential and local short-term stimulation of nutrient
availability by deposition of fecal materials (Pastor et al.
1993). These community and ecosystem responses to
browsing are not coincidental, but are entirely consistent
with the discrimination of defended plants by herbivores,
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the constraints imposed on the carbon-nutrient balance
of these plants by the energetically costly metabolism of
lignin, cellulose, and secondary compound production,
and the constraints imposed on the decomposer community by these same compounds (Bryant et al. 1983,
Bryant and Chapin 1986, Bryant et al. 1991, Pastor and
Naiman 1992, Pastor et al. 1993). Thus the assumption of
plants being a homogeneous food source for herbivores
could lead to erroneous conclusions regarding the direction of change imposed by herbivores on nutrient and
energy cycling rates at least in boreal ecosystems.
The analytical solutions suggest that the qualitative
behavior of the model represents that of any ecosystem
that has qualitative characteristics similar to those
analyzed here (consumer choice and differences between
plant species in decomposition and uptake rates): the
presence of a consumer reduces energy and nutrient flow
through the system at equilibrium compared to an
ecosystem without the consumer.
Others have suggested that the large herds of
ungulates in the Serengeti and American grasslands
increase rates of nutrient cycling (McNaughton 1979,
Holland et al. 1992). While the deposition of fecal
material in these ecosystems might temporarily increase
local nutrient availability (Reuss and McNaughton 1987,
Day and Detling 1990; but see Floate 1970, Pendeleton
1972), it is also significant that Frank and McNaughton
(1993) found no correlation between annual dung
deposition and annual aboveground net primary production in Yellowstone grasslands. It should also be noted
that invasion by unpalatable woody shrubswith slower
nutrient turnover ratesis the longer term fate of both
the Yellowstone and Serengeti grasslands (Houston 1982,
Norton-Griffiths 1979). It is the frequent recurrence of
fire, rather than grazing, that maintains the dominance of
the grasses preferred by these ungulates (Houston 1982,
Norton-Griffiths 1979) and presumably the high rates of
nutrient cycling. It has been shown that aboveground
production and nutrient uptake in these systems
increases with grazing (McNaughton 1985, Frank and
McNaughton 1993); this is consistent with increased
nutrient flow through our model system with increases in
b C . However, it is not consistent with the conclusion that
consumers increase nutrient cycling rates over systems
where they are absent (i.e., compare surfaces in Fig. 4A).
The same correlation between forage nutrient content
and litter quality that we find determines nutrient cycling
rates in boreal forests may be operating in grasslands as
well. Recent research suggests that different grasses can
have substantially different effects on soil nitrogen
availability in as few as four years because of different
nitrogen and lignin contents (Wedin and Pastor 1993).
177
Herbivores and Nutrient Cycles in Ecosystems
At least in the Serengeti, there is strong evidence that
ungulates discriminate among grasses and even plant
parts on the basis of nitrogen and lignin contents (Jarman
and Sinclair 1979). Furthermore, in the Serengeti grasslands, impala (Aepyceros melampus), topi (Damaliscus
korrigum), buffalo (Syncerus caffer), and other ungulates
all show seasonal reliance on more than one plant species
(Jarman and Sinclair 1979), which is consistent with our
findings that the consumer must maintain the presence of
both plant species for the system to be stable. Finally, du
Toit (1991) found a decline in soil nitrogen availability
with increased herbivory in South African savannas that
supports the extension of our conclusions for boreal
forests into at least some graminoid systems. The correlation between foraging pressure and nutrient content of
aboveground production in these systems (McNaughton
1988, 1990) could reflect foraging strategy rather than
nutrient feedback from herbivores to decomposers. We
suggest that ungulate-plant community-nutrient interactions in these grassland ecosystems might profitably bear
further scrutiny.
We know of only one example where a herbivorecaused increase in nutrient cycling rate has been shown
unequivocally rather than through inference. This is
the case of large flocks of lesser snow geese (Chen
caerulescens) in salt marshes of Hudson Bay (Jefferies
1988, 1989, Hik and Jefferies 1990). Here, the large flocks
of geese consume virtually all aboveground productionessentially treating the food source as homogeneous and
rapidly pass the food through their guts, returning it to
the soil where it has a rapid decay rate and is an energy
source for nitrogen fixing bacteria (Bazeley and Jefferies
1985, Reuss et al. 1989). The digestive tract of birds
differs from that of ruminants in that food in the gut of
birds has a short residence time, allowing them to extract
only the most labile forms of nutrients from their food
(Gill 1995). In contrast, a ruminant has a long residence
time of food, extracting as much of the nutrient content
of food as possible. Ruminant digestion therefore has a
greater potential to decrease rates of nutrient cycling
compared with avian digestion. This makes the one
unequivocal example of a herbivore actually increasing
rates of nutrient cycling extremely interesting because of
the high throughput through the consumer and because
of the simplicity of this system. However, it should be
noted that recent research in the goose-salt marsh
ecosystem (Jefferies and Bryant 1995) indicates that it is
becoming unstable with increased population densities of
geese (and consequently increased consumption of forage
plants) due to reduced mortality on their winter range.
This is consistent with the unstable behavior of the model
presented here as b C increases, although it should be
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admitted that at present it is yet to be determined
whether the instability of the real ecosystem arises for the
same mechanisms noted in our model ecosystem.
We suggest that the inherent variability in plant chemical composition that simultaneously determines both
consumer preference and decomposition rates is an
essential feature of food webs that cannot be ignored.
Models of energy and nutrient flows through trophic
levels should include at a minimum two producers that
differ in uptake, palatability, and decomposition, and
consumer preference for one producer over the other.
ACKNOWLEDGMENTS
This research was funded by a grant from the National Science Foundation's Ecosystem Studies Program, whose continued support is
greatly appreciated. We thank Lauri Oksanen, Dick Wiegert, Ron
Moen, Brad Dewey, Mac Post, Peter Abrams, Jim Grover, and Dave
Wedin for helpful comments on previous versions of the manuscript.
REFERENCES
Abrams, P. A. 1993. Effect of increased productivity on the abundances
of trophic levels, Amer. Nat. 141, 351371.
Abrams, P. A., and Shen, L. 1989. Population dynamics of systems with
consumers that maintain a constant ratio of intake rates of two
resources, Theor. Popul. Biol. 35, 5189.
Armstrong, R. A., and McGehee, R. 1980. Competitive exclusion, Am.
Nat. 115, 151170.
Bazeley, D. R., and Jefferies, R. L. 1985. Goose faeces: A source of
nitrogen for plant growth in a grazed salt marsh, J. Appl. Ecol. 22,
693703.
Brandner, T. A., Peterson, R. O., and Risenhoover, K. L. 1990. Balsam
fir on Isle Royale: Effects of moose herbivory and population
density, Ecology 71, 155164.
Bryant, J. P., and Chapin, F. S., III 1986. Browsing-woody plant
interactions during boreal forest plant succession, in ``Forest
Ecosystems in the Alaskan Taiga'' (K. Van Cleve, F. S. Chapin, III,
P. W. Flanagan, L. A. Viereck, and C. T. Dyrness, Eds.),
pp. 213225, Springer-Verlag, New York.
Bryant, J. P., and Kuropat, P. J. 1980. Selection of winter forage by subarctic browsing vertebrates: The role of plant chemistry, Ann. Ecol.
Systematics 11, 261285.
Bryant, J. P., Chapin, F. S., III, and Klein, D. R. 1983. Carbonnutrient
balance of boreal plants in relation to vertebrate herbivory, Oikos
40, 357368.
Bryant, J. P., Provenza, F. D., Pastor, J., Reichardt, P. B., Clausen,
T. P., and du Toit, J. T. 1991. Interactions between woody plants and
browsing mammals mediated by secondary metabolites, Ann. Rev.
Ecol. Systematics 22, 431446.
Chew, R. M. 1974. Consumers as regulators of ecosystems: An alternative view, Ohio 74, 359370.
Cohen, Y., and Pastor, J. 1991. The responses of a forest model to serial
correlations of global warming, Ecology 72, 11611165.
178
Cohen, Y., and Pastor, J. 1997. Nutrient cycling in evolutionary stable
ecosystems, submitted for publication.
Coley, P. D., Bryant, J. P., and Chapin, F. S., III. 1985. Resource
availability and plant herbivore defense, Science 230, 895899.
Crawley, M. J. 1983. ``Herbivory,'' Blackwell, Oxford.
Day, T. A., and Detling, J. K. 1990. Grassland patch dynamics and
herbivore grazing preference following urine deposition, Ecology 71,
180188.
DeAngelis, D. L. 1992. ``Dynamics of Nutrient Cycling and Food
Webs,'' Chapman 6 Hall, London.
du Toit, J. T. 1991. Introduction of artificial waterpoints: Potential
impacts on nutrient cycling, in ``Management of the Hwange
Ecosystem'' (M. Jones, and R. Martin, Eds.), USAID: Zimbabwe
Department of National Parks and Wildlife Management, Harare,
Zimbabwe.
Flanagan, P. W., and Van Cleve, K. 1983. Nutrient cycling in relation
to decomposition and organic matter quality in taiga ecosystems,
Can. J. Forest Res. 13, 795817.
Floate, M. J. S. 1970. Decomposition of organic materials from hill soils
and pastures. II. Comparative studies on the mineralization of
carbon, nitrogen, and phosphorus from plant materials and sheep
faeces, Soil Biol. Biochem. 2, 173185.
Frank, D. A., and McNaughton, S. J. 1993. The ecology of plants, large
mammalian herbivores, and drought in Yellowstone Nation Park,
Ecology 73, 20432058.
Gill, F. B. 1995. ``Ornithology,'' 2nd ed., Freeman, New York.
Hairston, N. G., Smith, F. E., and Slobodkin, L. B. 1960. Community
structure, population control, and competition, Am. Nat. 94,
421425.
Hartley, S. E., Nelson, K., and Gorman, M. 1995. The effect of fertiliser
and shading on plant chemical composition and palatability to
Orkney voles, Microtus arvalis orcadensis, Oikos 72, 7987.
Hik, D. S., and Jefferies, R. L. 1990. Increases in the net above-ground
primary production of a salt-marsh forage grass: A test of the predictions of the herbivore-optimization model, Ecol. 78, 180195.
Holland, E. A., Parton, W. J., Detling, J. K., and Coppock, D. L. 1992.
Physiological responses of plant populations to herbivory and
their consequences for ecosystem nutrient flow, Am. Nat. 140,
685706.
Holt, R. D. 1977. Predation, apparent competition, and the structure of
prey communities, Theor. Popul. Biol. 12, 197229.
Holt, R. D., Grover, J., and Tilman, D. 1994. Simple rules for
interspecific dominance in systems with exploitive and apparent
competition, Am. Nat. 144, 741771.
Horner, J. D., Gosz, J. R., and Cates, R. G. 1988. The role of carbonbased secondary plant metabolites in decomposition in terrestrial
ecosystems, Am. Nat. 132, 869883.
Houston, D. B. 1982. ``The Northern Yellowstone Elk: Ecology and
Management,'' Macmillan, New York.
Huntly, N. 1991. Herbivores and the dynamics of communities and
ecosystems, Ann. Rev. Ecol. Systematics 22, 477504.
Huston, M. A., and DeAngelis, D. L. 1994. Competition and
coexistence: The effect of resource transport and supply rates, Am.
Nat. 144, 954977.
Jarman, P. J., and Sinclair, A. R. E. 1979. Feeding strategy and the
pattern of resource-partitioning in ungulates, in ``Serengeti: The
Dynamics of an Ecosystem'' (A. R. E. Sinclair and M. NortonGriffiths, Eds.), pp. 130163, Univ. Chicago Press, Chicago.
Jefferies, R. L. 1988. Vegetational mosaics, plant-animal interactions,
and resources for plant growth, in ``Plant Evolutionary Biology,''
L. D. Gottlieb and S. K. Jain, Eds.), pp. 341369, Chapman 6 Hall,
London.
File: 653J 132714 . By:DS . Date:30:06:97 . Time:07:13 LOP8M. V8.0. Page 01:01
Codes: 17542 Signs: 6951 . Length: 54 pic 0 pts, 227 mm
Pastor and Cohen
Jefferies, R. L. 1989. Pattern and process in arctic coastal vegetation in
response to foraging by lesser snow geese, in ``Plant Form and
Vegetation Structure, Adaptation, Plasticity and Relation to
Herbivory'' (M. J. A. Werger, Ed.), pp. 120, SPB Academic, The
Hague.
Jefferies, R. L., and Bryant, J. P. 1995. The plant-vertebrate herbivore
interface in arctic ecosystems, in ``Arctic and Alpine Biodiversity''
(F. S. Chapin, III and C. Korner, Eds.), pp. 271282, Ecological
Studies, Vol. 113, Springer-Verlag, New York.
Krefting, L. W. 1974. ``The Ecology of the Isle Royale Moose,'' University of Minnesota Agricultural Experiment Station, Technical
Bulletin 297, Forestry Series 15, St. Paul, MN.
Lindroth, R. L. 1988. Adaptation of mammalian herbivores to plant
chemical defenses, in ``Chemical Mediation of Coevolution''
(K. C. Spencer, Ed.), pp. 415445, Academic Press, New York.
Loreau, M. 1995. Consumers as maximizers of matter and energy flow
in ecosystems, Am. Nat. 145, 2242.
Lousier, J. D., and Parkinson, D. 1978. Chemical element dynamics in
decomposing leaf litter, Can. J. Botany 56, 29752812.
MacClean, D. A., and Wein, R. W. 1978. Weight loss and nutrient
changes in decomposing forest floor material in New Brunswick
forest stands, Can. J. Botany 56, 27302749.
Mattson, W. J., and Addy, N. D. 1975. Phytophagous insects as
regulators of forest primary production, Science 190, 515522.
Mattson, W. J. 1980. Herbivory in relation to plant nitrogen content,
Ann. Rev. Ecol. Systematics 11, 119161.
May, R. M. 1974. ``Stability and Complexity in Model Ecosystems,''
Monographs in Population Biology, No. 6, Princeton Univ. Press,
Princeton, NJ.
McInnes, P. F., Naiman, R. J., Pastor, J., and Cohen, Y. 1992. Effects
of moose browsing on vegetation and litterfall of the boreal forests
of Isle Royale, Michigan, U.S.A., Ecology 73, 20592075.
McNaughton, S. J. 1985. Ecology of a grazing ecosystem: The
Serengeti, Ecol. Monogr. 55, 259294.
McNaughton, S. J. 1986. On plants and herbivores, Am. Nat. 128,
765770.
McNaughton, S. J. 1988. Mineral nutrition and spatial concentrations
of African ungulates, Nature 334, 343353.
McNaughton, S. J. 1990. Mineral nutrition and seasonal movement of
African migratory ungulates, Nature 345, 613615.
Melillo, J. M., Aber, J. D., and Muratore, R. F. 1982. Nitrogen and
lignin control of hardwood leaf litter decomposition dynamics,
Ecology 63, 621626.
Moore, J. C., and Hunt, H. W. 1988. Resource compartmentation and
the stability of ecosystems, Nature 333, 261263.
Moore, T. R. 1984. Litter decomposition in a subarctic sprucelichen
woodland, eastern Canada, Ecology 65, 299308.
Norton-Griffiths, M. 1979. The influence of grazing, browsing, and fire
on the vegetation dynamics of the Serengeti, in ``Serengeti: The
Dynamics of and Ecosystem'' (A. R. E. Sinclair and M. NortonGriffiths, Eds.), pp. 310352, Univ. of Chicago Press, Chicago.
Oksanen, L. 1983. Trophic exploitation and arctic phytomass patterns,
Am. Nat. 122, 4552.
Oksanen, L. 1988. Ecosystem organization: Mutualism and cybernetics
or plain Darwinian struggle for existence?, Am. Nat. 118, 240261.
Oksanen, L., Fretwell, S. D., Aruda, J., and Niemela, P. 1981. Exploitation ecosystems in gradients of primary productivity, Am. Nat. 131,
424444.
Owen, D. F., and Wiegert, R. G. 1976. Do consumers maximize plant
fitness?, Oikos 27, 488492.
Owen, D. F., and Wiegert, R. G. 1981. Mutualism between grasses and
grazers: An evolutionary hypothesis, Oikos 36, 376378.
Herbivores and Nutrient Cycles in Ecosystems
Pastor, J., and Post, W. M. 1986. Influence of climate, soil moisture,
and succession on forest carbon and nitrogen cycles, Biogeochemistry 2, 327.
Pastor, J., and Naiman, R. J. 1992. Selective foraging and ecosystem
processes in boreal forests, Am. Nat. 139, 690705.
Pastor, J., Dewey, B., Naiman, R. J., McInnes, P. F., and Cohen, Y.
1993. Moose browsing and soil fertility in the boreal forests of Isle
Royale National Park, Ecology 74, 467480.
Pastor, J., Dewey, B., and Christian, D. P. in press. Carbon and
nutrient mineralization and fungal spore composition of fecal pellets
from voles in Minnesota, Ecography.
Pendleton, D. F. 1973. ``Degradation of Grassland Plants,'' Ph.D.
dissertation, Colorado State University, Ft. Collins, CO.
Petelle, M. 1982. More mutualism between consumers and plants,
Oikos 38, 125127.
Ruess, R. W., and McNaughton, S. J. 1987. Grazing and the dynamics
of nutrient and energy regulated microbial processes in the Serengeti
grasslands, Oikos 49, 101110.
Ruess, R. W., Hik, D. S., and Jefferies, R. L. 1989. The role of lesser
snow geese as nitrogen processors in a sub-arctic salt marsh,
Oecologia 79, 2329.
Schimel, D. S., Parton, W. J., Adamsen, F. J. Woodmansee, R. G.,
Senft, R. L., and Stillwell, M. A. 1986. The role of cattle in the
File: 653J 132715 . By:DS . Date:30:06:97 . Time:07:13 LOP8M. V8.0. Page 01:01
Codes: 7038 Signs: 2608 . Length: 54 pic 0 pts, 227 mm
179
volatile loses of nitrogen from a shortgrass steppe, Biogeochemistry
2, 3952.
Tahvanainen, J., Niemela, P., and Hentonnen, H. 1991. Chemical
aspects of herbivory in boreal forests: Feeding by small rodents,
hares, and cervids, in ``Plant Defenses against Mammalian
Herbivory'' (R. T. Palo and C. T. Robbins, Eds.), pp. 115132, CRC
Press, Boca Raton, FL.
Tilman, D., Wedin, D., and Knops, J. 1996. Productivity and
sustainability influenced by biodiversity in grassland ecosystems,
Nature 379, 718720.
Van Cleve, K., and Oliver, L. K. 1982. Growth response of postfire
quaking aspen (Populus tremuloides) to N, P, and K fertilization,
Can. J. Forest Res. 6, 145152.
Van Cleve, K., Oliver, L. K., Schlentner, R., Viereck, L. A., and
Dyrness, C. T. 1983. Productivity and nutrient cycling in taiga forest
ecosystems, Can. J. Forest Res. 13, 747766.
Waring, R. H., and Schlesinger, W. H. 1985. ``Forest Ecosystems:
Concepts and Management,'' Academic Press, New York.
Wedin, D. A., and Pastor, J. 1993. Nitrogen mineralization dynamics in
grass monocultures, Oecologia 96, 186192.
Weetman, G. F. 1968. ``The Nitrogen Fertilization of Three Black
Spruce Stands,'' Pulp and Paper Research Institute of Canada,
Quebec. [Woodlands Paper No. 6.]