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Sustaining Rangelands: Application of
Ecological Models to Evaluate the Risks of
Alternative Grazing Systems
Mark E. Ritchie and Michael L. Wolfe 1
Abstract. - Sustaining natural ecosystems requires evaluating the
consequences of unpredictable environmental events, e.g. precipitation,
human disturbance. On North American rangelands, managers are
concern~d with sustaining plant communities in the face of grazing by
Iivestoc~ and wild herbivores and unpredictable precipitation. We present a
model for evaluating the probability that a given rangeland plant community
can be sustained over a specified time period while subject to grazing. The
model describes the population dynamics of herbivore and plant species in
terms of their mechanisms of resource acquisition, growth, and species
interactions. We then input randomly varying annual precipitation, a livestock
grazing strategy, and a wildlife harvest strategy to project the future
dynamics of herbivore and plant species. Iteration of model projections for
different random sequences of annual precipitation calculates the probability
that a particular grazing system will produce unacceptable consequences
(biological or political). As an example, we apply the model using data from
our current study of plant-herbivore interactions at Desert Land and
Livestock in northern Utah. We show that the modeling approach can
provide valuable insights for the management of herbivores to sustain
ecosystems.
INTRODUCTION
responses can be explored, and (3) the consequences of
alternative management plans can be compared. However,
modeling has a significant weakness: model predictions may not
reflect reality (Caswell 1975). One way to improve the match
between empirical data and modeling is to use "mechanistic"
ecological theory based on the known biology of the organisms
within ecosystems (Schoener 1986, Tilman 1980, 1987).
Mechanistic models can predict real dynamics of organisms, e.g.
population growth (Schoener 1973), competition (e.g. Tllman
1976, Rothhaupt 1988), and predation (Werner and Ha111988).
Consequently, simulation models of ecosystems that are based
on mechanistic models of population growth and species
interactions may be useful tools for evaluating ecological risks
in managing ecosystems. In this paper, we demonstrate how
such a modeling approach might wolk by considering a specific
management problem and constructing an example simulation
model.
A central problem in sustaining North American rangelands
is evaluating the impacts of grazing by livestock and wild
herbivores in the face of unpredictable annual precipitation
To sustain ecosystems, managers need to know how
ecosystems respond to manipulations (active management
practices) and unpredictable environmental events (e.g. weather,
human distuIbances). More specifically, managers need to
evaluate risks, or the probability of undesirable responses to their
management practices (Loucks 1985). Such evaluation is called
ecological risk assessment (Bartell et al. 1992). While empirical
responses of organisms have been used by toxicologists to assess
risk (e.g. Hendrix 1982, Suter et al. 1983), complexity and the
lack of good experimental data has discouraged such approaches
for whole ecosystems (Giesy 1980).
An alternative to using empirical responses to measure
ecological risk in ecosystems is to model (Bartell et al. 1992).
Modeling provides seveml powerful advantages: (1) complex
interactions among organisms can be considered, (2) long-teon
1 Mark E. Ritchie and Michael L. Wolfe are faculty members in
the Department of Fisheries and Wildlife, Utah State University,
Logan, UT 84322-5210.
328
for a given plant group i (e.g. grasses, forbs, shrubs) was
descnbed in tenns of the change in biomass Wi, glm2) from
one growing season to the next (time 1+1 - 1):
(Heitschmidt and Stuth 1991). On most rangeland, livestock
grazing is a major land use with important economic
implications. Livestock producers have traditionally perceived
competition for forage from wildlife as a threat to their
livelihood (Bastian et al. 1991). However, environmental groups
increasingly perceive livestock as a threat to sustaining
biodiversity on rangelands (Ferguson and Ferguson 1983). To
resolve this conflict, managers choose from different livestock
grazing strategies and wildlife harvest strategies to maintain
desired (acceptable) populations of plants and other animals.
Because animal and plant production is often highly variable,
making these choices depends on some type of risk assessment,
i.e. evaluating which grazing strategy is most likely to produce
the desired goal. Such evaluation from existing empirical
information is difficult because the interactions of multiple
species of rangeland plants and herbivores are not yet well
understood (Coughenour 1991). Risk assessment in this case
involves understanding complex ~ractions, long-term results,
and the consequences of many possible management
alternatives, so modeling may be the only reasonable way to
find a solution to the problem.
In this paper, we develop, validate, and explore a simple
simulation model to address the implications of different
livestock grazing and wildlife harvest strategies on rangeland
ecosystem sustainability. The model uses simple equations that
describe the population dynamics of herbivores and plants,
where herbivores are limited by plant abundance and plant
production is limited by water availability. Our goal was to
describe these dynamics as simply as poSSIble with the fewest
data inputs, since managers are unlikely to ever have extensive,
detailed data sets with which to model. In addition, we made
the model as general as possible, but left room for site-specific
inputs of herbivore and plant species as well as precipitation
We tried to take typical manager's viewpoint of having a vexing
problem but scarce resources, little time, and few data with
which to address the problem
n
x
Nut1 - Mu
i=l
= CJ It! [<St!I$ Nu)
j=l
- MJ] - $
lMNW Jl.~
(1).
Q is the IUltrient-use efficiency of plant group i (g tissue
produced per g nutrient). Mi is the maintenance nutrient
requirement for plant group i per unit above-ground biomass
during its growing season. SN is the supply rate of nutrient
(g/season). The function b.i{NjJ) is the consumption rate
(gIseason) of plant group i by an individual of herbivore gJOup
j as a function of plant biomass. H.u is the density (#/m2) of
herbivore group j during time 1. The variable n is the number
of plant groups and x is the number of herbivore groups. Thus,
plant dynamics depend on IUltrient availability, their efficiency
at utilizing nutrients, and the intensity of herbivory. Note that
the plant groups compete exploitatively for the limiting resource.
The population growth of each herbivore species j was
descnbed as a function of the species' dry-matter intake of each
plant group, its ability to utilize that intake, and its rate of
harvest:
n
(2).
OJ is the conversion efficiency of energy into new offspring
for herbivore group j (offspringlkJ). 14 is the dry-matter
digestible energy content of plant group i (kJ/g). &i is the energy
requirement (kJ/season) of herbivore group j. Finally, ~j is the
proportion of herbivore group j halVested each seasQn (a
different harvest function could easily be used). Other
parameters and functions are the same as in Eqn 1. Herbivore
groups compete exploitatively by indirectly reducing the
biomass of plant groups.
Consumption of each plant group by a given herbivore group
is a complex function that depends on plant biomass, Time
available for foraging, proportion of the plant group in the diet,
herbivore bite size and herbivore movement rate (Spalinger and
Hobbs 1992).
MODELS OF POPULATION DYNAMICS
To describe the dynamics of plants and hetbivores, we used
simple, previously established mechanistic population growth
models from the ecological literature (Schoener 1973, TIlman
1980). In doing so, we made several simplifying assumptions.
First, we assumed that herbivores and plants were resource
limited, i.e. hetbivores were limited by plant abundance and
plants were limited by a single resource (e.g. water, nitrogen,
light). Second, we assumed that populations had no age or size
structure. Third, we assumed that there was no physical
distutbance to the community, e.g. fire, soil disturbance, etc.
Fourth, we assumed that dynamics could be descnbed with
difference equations, i.e. population changes occurred in discrete
intelVals or "pulses". We made these assumptions to keep the
model simple and data inputs to a minimum Population growth
I aj Qi Ni.t
m(NLt) =
1 +. 14 ($ giN!.!)
(3).
I
I is the time the forager spends fornging (min/season). The
variable Qi is the product of the diet proportion and aboveground
biomass proportion of the plant group i . The variable iij reflects
the herbivore group's search capability (arealmin). The variable
hi reflects the herbivore group's handling cost (area/g), and
reflects the time required to bite all the food items encountered
per unit area. This variable is a function of bite size and search
capability (Spalinger and Hobbs 1992).
329
EXAMPLE SIMULATION
Table 1. - Average plant characteristics used in the
population dynamics equations for plants and herbivores
In the simulation model.
Characteristic
Grasses
Forbs
Shrubs
These population dynamics models are useful to managers
only when parameter values, nutrient inputs, and initial
conditions are specified. To demonstrate how these models can
be used, we will perform an example simulation using specific
data from a field study site, Desert Land and Livestock (DL&L),
a 911 km2 ranch in northern Utah (elevation 1900 - 2600 m).
The results of this analysis should be viewed as an example of
how modeling can be used to address management problems,
rather than as a general statement about plant-hetbivore
interactions.
Rangelands at DL&L consist of two types, winter range
(sagebrush grassland) and sl1lIll!ler range (montane meadows
interspersed with timber). Mule deer (Odocoileus hemionus), elk
(Cervus e/aphus) and cattle are the major livestock species on
the ranch. Competition among wildlife and cattle for spring and
summer range is often most controversial (Bastian et al. 1991.
Consequently, we analyzed ~ effects of different grazing
strategies and wildlife harvest rales on the long-term impacts of
elk, deer, and cattle on summer range vegetation To simplify
the model, vegetation was grouped as grasses, foms, and shrubs.
For the intermountain West, water is the nutrient most likely to
limit plant production, even on summer range (MacMahon and
Schimpf 1991). Consequently, we used water as the nutrient
limiting plant growth in our simulation
Our simulation attempted to capture the natural timing and
use of summer and winter range by these hetbivores. We divided
each year into two seasons: summer (150 days) and winter (210
days), and calculated changes in plant biomass and hemivore
densities in each season We assumed that cattle density changed
only with stocking rate. Elk and deer densities were assumed to
change with plant biomass, with summer range biomass
affecting reproduction and winter range biomass affecting
mortality. Consequently we modeled the dynamics of plants on
both summer and winter range as well as the dynamics of deer
and elk.
For plants, we obtained average parameters for each plant
group from the literature (Table 1), including water-use
efficiency and seasonal water requirements. For each plant
group, average dIy-matter digestible energy content for deer and
elk as well as diet proportions for cattle, deer, and elk were also
obtained from the literature (Table 1). Proportions of
above-ground biomass were OJ for grasses, 0.5 for foms, and
0.25 for shrubs (MacMahon and Schimpf 1981). For hemivores,
we estimated average energy conversion efficiency, maintenance
energy requirements, search ability, and handling costs from
hemivore body mass using allometric relationships (peters 1983,
Calder 1984) (Table 2). Daily feeding time was approximately
300 min/day for all three hemivores (Belovsky and Slade 1986).
Except for cattle densities, initial conditions were kept
constant in all simulation runs. For winter range, initial
biomasses (gIm2) of plants were: grasses, 25; fOlbs, 10; shrubs,
Water-Use Efficiency
(g tissue/g H2O) 1
Summer Range
Wnter Range
0.0018
0.0023
0.0020
0.0031
0.0028
0.0040
Water Requirements
(g H2O-g tissue'1 . season'1)2
Summer Range
Wnter Range
68.7
53.8
100.4
64.8
77.7
54.4
7.02
12.2
NA
13.1
4.38
8.77
5.2
9.1
15.9
7.89
10.5
1.00
0
0
0.60
0.40
0
0.35
0.40
0.25
0
0.12
0
0.46
1.00
0.42
Dry-Matter Digestible
Energy Content
(kJ/g dry mass)3
Elk
Wnter
Summer
Deer
Wnter
Summer
Diet Proportions4
Cattle
Elk
Winter
Summer
Deer
Wnter
Summer
NA
1 During growing season, Refs: Miller 1988, Romo and
Haferkamp 1989, Wame et a/. 1990, Singh et a/. 1991.
2 During growing season, Refs: Detling et a/. 1979, Atkinson
1986, lIVing and Silsbury 1987, Miller 1988.
3 Refs: Robbins 1992, Frank and Kam 1988.
4 Refs: Mackie 1970, Be/ovksy 1986.
Table 2. - Allometric body mass relationships used in the
population dynamics equations for herbivores in the
simulation model1•
Parameter
Energy Requirements
KJ/season
Conversion Efficiency
offspr/KJ
Search Ability
M2/min)
Handling Cost
(area/g)
Equation 2
0.000153 M- 1.33
0.1 MO. 54
1.3 M-O· 37
1 Refs: Peter 1983, Calder 1984.
2 M
body mass in kg.
=
100. For summer range, biomasses (gIm2) were: grasses, l00~
foms, 10; shrubs, 300. Deer and elk densities each began at
101km2.
330
Because water was assumed to be the major limiting nutrient
for plants, we used precipitation to measure water availability.
Annual and even seasonal precipitation in the intennountain
West is unpredictable, so we treated it as a random variable. We
used crop-year (April - September) precipitation measured for
1950-1990 at the two closest weather stations to DL&L (summer
range: Monte Cristo ranger station, Utah; winter range:
Woodruff, Utah). To generate a random sequence of annual
water availability, we picked random values from the distribution
of crop-year precipitation at each weather station TIrus, each
year of a simulation run differed in precipitation, and each run
differed in its sequence of ammal pmcipitation To estimate the
actual water available during the growing season, crop-year
precipitation was then multiplied by. 0.29 to account for run-off,
evaporation, and percolation below the rooting zone (Johnson
and Gordon 1988).
To measure effects of management strategies, we simulated
the population dynamics resulting from each strategy for twenty
years (a typical tatget time frame for management decisions).
Management strategies were imp'lemented in the fonn of
different cattle stocking rates (grazing strategies) and different
harvest proportions (harvest strategies). Effects of strategies on
biomass of each plant group and hetbivore densities were
estimated from the mean biomass in year 20, based on 50 runs.
The probability that a plant group would go extinct was
calculated as the frequency of 1000 runs in which that plant
group was reduced to zero biomass.
cattle stocking rates with elk densities obselVed in summer range
pastures stocked with different cattle densities. We chose this
test because predicted hetbivore densities are most likely to
reflect compounded errors or incorrect assumptions in the
population dynamics equations (Caswell 1975). Ken Clegg
(unpubl. data) provided ground counts of elk and cattle using
different 5-10 km2 drainages within 400 km2 of summer range
at DL&L in 1992.
Elk densities declined negatively and non-linearly with cattle
densities (Fig. 1). Using the obselVed cattle densities as inputs,
we predicted elk densities with our model (Fig. 1). The predicted
densities tend to ~restimate observed elk densities, but the
same negative, non-linear relationship with cattle densities is
predicted. Predicted (P) and obselVed (0) elk densities are also
positively correlated (1' = 0.66, 0 = 9.6 + 1.45 P, P < 0.(01)
and the slope of the relationship is not different from one (t =
0.92, df = 9, P = 0.36). These results suggest that our model
may be useful for describing the qualitative relationships among
hetbivores and, by inference, the ~ffects of these hetbivores on
plant biomass. From this comparison, we argue that the
simulation model can provide some insights into the effects of
potential management strategies at DL&L.
MODEL PREDICTIONS
We predicted sustainability of plant groups in two ways: (1)
mean biomass, and (2) the probability of extinction Greater
biomass is often used (directly or indirectly) as a measure of
land "health" or "condition" (Heitschmidt and Stuth 1991).
Probability of extinction is the chance that the density of a group
or species is reduced to zero within a specified time. In variable
ecosystems, this probability is always greater than zero, since
there is always some chance, however small, that a population
will go extinct (Goodman 1987).
For these measures, we addressed three important questions
about hetbivores and ecosystem sustainability.
(1) What is the effect of increasing hetbivore density on
plant production and biomass?
(2) Does a mixture of livestock and wildlife have less
impact on plant biomass and diversity than
livestock alone?
(3) At what densities do herbivores begin to reduce
biodive~ity or degrade land?
We used our model to provide answers about the DL&L
system; the results may apply to other systems as well, but such
generality awaits future tests.
Different hetbivore densities were produced by altering cattle
stocking densities and wildlife harvest rates. We simulated the
effects of grazing strategies by stocking 0-100 cattlelkm2, while
allowing wildlife to attain unharvested denc;ities. The typical
pattern for summer range in northern Utah is a 2 or 3 pasture
rotation, i.e. cattle are moved at a density of 20-30/km2 through
three pastures during the course of the summer and each pasture
is grazed only once (Heitschmidt and Stuth 1991). Thus, a
MODEL VALIDATION
Any simulation model requires validation to be useful. As a
preliminaty validation of the model presented here, we chose to
compare the densities of elk predicted by the model for different
-E
C\I
.lI.
Model Validation
150
"=It 100
•
RA2 = 0.59,
P < 0.001
•
•
Observed
Predicted
•
100
200
300
Cattle Density (#/kmA2)
Figure 1. - The relationship between elk density vs. cattle density
observed in different watersheds on Desert Land and
Livestock summer range in 1992 (closed Circles).
Regression line is y = 120.4 - 12.7 log (x). Elk densities
predicted with the simulation model for the same cattle
densities are also shown (solid squares).
331
typical stocking mte produces an overall density of 7-10
cowslkm2 . However, cattle densities in preferred-use areas (e.g.
riparian areas, wet meadows) may greatly exceed the overall
mte. To simulate wildlife harvest stmtegies, we used harvest
mtes ranging from 0-0.5 of the density of deer or elk, while
holding cattle densities at 9/km2. The typical harvest mte for
these species rnnges from 0.05-0.15 (Utah Division of Wtldlife
Resources harvest books). A harvest mte of 0.5 approximates a
maximum sustained yield harvest (Getz and Haight 1989).
Grasses
200
"'""
N
<
E
........
C)
"-" 1 00
en
en
('0
E
Herbivore Effects on Plant Biomass
0
a
al
Because we input randomly vatying precipitation, simulation
runs with the same initial conditions produced different results.
Consequently, we analyzed effects of grazing and harvest
stmtegies on the mean response. of plants and hemivores and
tested the statistical significance of differences in responses with
standard analysis of variance.
Increased cattle densities significantly reduced gmss biomass
but increased shrub biomass (Fig. 2). Intermediate cattle
densities significantly increased fom biomass. Increased wildlife
harvest mtes had less dramatic effects (Fig. 3). Gmss biomass
decreased significantly at intermediate harvest levels, while fom
biomass increased significantly at only the highest harvest level.
Harvest rates had no significant effects on shrub biomass. These
results suggest that plant biomass is more sensitive to cattle
stocking mtes than to wildlife harvest rates. The results also
suggest that indirect effects can be as important as direct
consumptive effects. For example, increased cattle densities led
to increased shrub biomass because cattle grazing reduced
competition between gmsses and shrubs, thereby increasing
shrub vigor.
4XRR
No Cows
2XRR
Seasonal
Grazing Strategy
Forbs
12
"'""
N
A.
<
E
*
9
........
C)
"-"
en
en
6
('0
E
0
3
al
o
No Cows
4XRR
2XRR
Seasonal
Grazing Strategy
Shrubs
600~------------------------~
*
""'"
N
<
*
E
....... 400
Effects of Single vs. Multiple Herbivores
-
C)
en
en
co 200
We tested whether wildlife species could affect the impact of
cattle grazing on ecosystems. Specifically, we compared gmss
biomass predicted for three different cattle densities under two
types of simulations (Fig. 4). First, we kept wildlife density at
zero (No Wildlife). Second, we began with 10/km2 each of deer
and elk and allowed them to undergo simulated dynamics with
no harvest (With Wildlife). With no cattle stocked, adding
wildlife did not affect gmss biomass. As cattle density increased,
however, adding wildlife increased gmss biomass, and the
magnitude of increase grew with increasing cattle density. This
pattern was due to indirect effects, namely wildlife reducing
shrub biomass and competitive effects on gmsses, thereby
increasing gmss vigor. These results suggest that multiple
hemivore species, which are likely to consume a variety of plant
groups or species, may improve ecosystem sustainability.
E
o
al
O~~~~~~~~~~~~~~~
No Cows
4XRR
2XRR
Seasonal
Grazing Strategy
Figure 2. - Predicted effects of different cattle grazing strategies
on standing crop biomass of three principal plant groups
from the simulation model. The four grazing strategies
tested were. in increasing order of grazing intenSity. no
cattle. 4 pasture rest-rotation (4XRR) (9/km2 ). 2 pasture
rotation (2XRR) (18/km 2 ). and seasonal (cattle stocked in a
single pasture for 180 days. 36/km2 ). Asterisks indicate
significant differences from the no cattle treatment.
332
200~--------------------------'
.......
II
E::l
N
E
.......
Grasses
C')
....... 200
- 100
en
en
(\J
E
.......
ctJ
-
E
C)
o
en 100
en
co
[C
E
0
[C
0
None
Male Only
80th Sex
*
12
-
8
ctJ
4
We addressed the possibility that management strategies
might result in the extinction of plant groups or species, and
thus fail to sustain the original ecosystem (Fig. 5). We calculated
probabilities of extinction within twenty years for grasses, foms,
and shrubs. We estimated two types of extinction: (I) probability
of diversity loss (one or more plant groups going extinct), and
(2) probability of land degradation (grasses going extinct).
Diversity loss occurred primarily but not always from foms
going extinct.
Without cattle and at maximum wildlife harvest rate,
probabilities of diversity loss and land degradation in twenty
years were less than I x 10.6. With zero wildlife harvest but no
cattle the chance of diversity loss increased to 27%. Stocking
cattle with unharvested wildlife further increased the chances of
diversity loss. 'JYpical cattle stocking densities with unharvested
wildlife produced a 30-40% chance of diversity loss. With no
cattle, the probability of diversity loss declined rapidly with
increasing wildlife harvest. Overall, wildlife harvest rates had a
larger impact on reducing diversity loss than stocking fewer
cattle. This result is due to wildlife feeding preferentially on the
rarest plant group, foms.
The chance of land degradation changed only with increased
cattle density; it was unaffected by wildlife harvest rate. 'JYpical
cattle stocking densities produced a low chance of degradation
« 0.5%). Chances of degradation increased rapidly, however,
for cattle densities in the range of 50-1 OO1km2. Such densities
are typically obselVed in riparian areas (Ferguson and FelWISon
1983). At low cattle densities, grasses are able to sustain a large
enough biomass to avoid extinction in low precipitation years.
There appears to be a threshold, however, where cattle reduce
grasses to a level where they are vulnerable to extinction by
drought.
0
[C
0
None
Male Only
80th Sex
MSY
Harvest Strategy
Shrubs
......
600
N
<
E
.......
-
400
C)
en
en 200
ctJ
E
0
[C
o.s
Herbivore Effects on Extinction
C)
E
0.18
16
(\J
en
en
b
Figure 4. - Predicted effects of the presence of wildlife on the
impact of cattle on grass biomass. Predictions are shown
for three different cattle stocking densities (0, 18, and 60
cows/km 2) and for no wildlife vs. wildlife occurring at
densities predicted for each cattle stocking density (no
harvest). Asterisks indicate significant differences for a
given cattle density.
MSY
Forbs
E
.......
o
Cattle Density (#/ha)
Harvest Strategy
.......
Wildlife
No Wildlife
0
None
Male Only
80th Sex
MSY
Harvest Strategy
Figure 3. - Predicted effects of different wildlife harvest
strategies on standing crop biomass of three principal plant
groups from the simulation model. The strategies tested
were, in increasing order of harvest intensity, no harvest,
all-male harvest (10% of density), harvest of both sexes
(20%) and maximum sustained yield (60%). Asterisks
indicate significant differences from the no harvest
treatment.
333
For our example system at DL&L, the simulations suggest
that different management stmtegies should be used for different
types "Of sustainability goals. If the management goal is to
produce cattle but also maximize "condition" or grass biomass,
then wildlife should be either unharvested or harvested at a low
rate and cattle should be stocked in a rotational grazing scheme.
If the management goal is to maximize plant diversity, then
wildlife should be harvested at a high rate and cattle should not
be stocked. On the other hand, if the management goal is to
maximize wildlife density (as in a camera patk), then cattle
should definitely not be stocked and some plant diversity should
be expected to be lost.
I
DL&L has a goal of maintaining range "condition" and
avoiding land degradation, while simultaneously making some
economic profit. Interestingly, their management strategies are
to use an extensive rest-rotation cattle grazing system and
harvest 5-10% of wildlife density each year. These would be
the management stmtegies predicted to be " best" for the
management goal by our simulation model. DL&L uses
extensive, long-term, empirical data collected at the ranch to
make their decisions; it is reassuring that our model predictions,
which actually use no data from the ranch, make similar
recommendations as the ranch managers.
The modeling results predict that some management strategies
may be mutually exclusive, or trade-off. For example,
maximizing plant diversity is best achieved by heavy harvesting
of wildlife, which may risk population crashes or extinction of
herbivores. Thus, improving plant diversity is likely to be
incompatible with sustaining large hemivore populations.
Likewise, improving range condition may be incompatible with
increasing or sustaining plant diversity. For example, cattle
densities might be increased without reducing diversity if
wildlife harvest rates are also increased, but this is likely to lead
to reduced grass biomass and poorer range "condition". Such
trade-offs in the consequences of different management
stmtegies are often the source of intense controversies in natural
resources management (e.g. Wagner 1978, Singer and Schullery
1989). These trade-offs require the use of optimization
techniques to decide which combinations of management
stmtegies will achieve biologically or politically acceptable
criteria (Bastian et al. 1991, Loomis et al. 1991). Perhaps the
use of models based on ecological theOly may help managers
to understand and solve these conflicts better.
The model predictions are driven mainly by two assumptions:
(l) plants compete, and (2) wild hetbivores reduce the biomass
of both the dominant plant group (shrubs) and the rare poorly
competitive plant group (forbs). The ill'St assumption is likely
to be true, as plants have been shown to compete in most
environments (Grace and Tilman 1990). The validity of the
second assumption depends upon the relationship between plant
competitive ability and its palatability to herbivores (pacala and
Crawley 1992). In the model, the most palatable plants to
wildlife, forbs, are the poorest competitors, the rarest, and the
most vulnerable to extinction. Consequently, increased wildlife
densities increase the chance of fom extinction
Cattle Grazing
1.0
>. 0.8
....,
0.6
.c
CtJ
.c 0.4
0
L-
a..
Diversity
Degradation
0.2
0.0
3
2
1
0
Cattle Density (#/ha)
Wildlife
Harvest
0.4
--0--
>...
....,
___
Diversitv
Degradation
0.3
.c
ro
.c
o
L-
a..
0.1
O.O--~~~~~----~~--~~--r-~~
U.O
0.1
0.2
0.3
0.4
0.5
0.6
Harvest
Figure 5. - Predicted effects of cattle stocking and wildlife
harvest on the sustainability of a grasslforb/shrub
ecosystem. We calculated the probability that diversity
would fail to be sustained, i.e. at least one functional group
(grasses, forbs, or shrubs) would go extinct in twenty years
(open circles). We also calculated the probability that land
degradation would occur (grasses would go extinct) (solid
squares). Probabilities of extinction were calculated by
repeating simulations 1000 times, each time with a different
random sequence of annual preCipitation, and calculating
the proportion of runs resulting in extinction.
DISCUSSION
The example simulation model we present illustmtes how
models can be used to evaluate alternative management
decisions for ecosystems. Specifically, we show that basic
ecological theory can be put into practice with a four step
process: (1) consider mechanisms of population growth and
species interactions, (2) :find data for these mechanisms for the
appropriate species at a given site, (3) validate the model, and
(4) apply different management stmtegies by altering model
inputs. Such an approach does not produce a single, general
model that "will wotk anywhere" ~ rather the approach defines
an Olganized way to synthesize information and make better
guesses about how the ecosystem of interest wotks.
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Competition among plants produces indirect effects among
hetbivores and plants, such as positive interactions between
hetbivores and non-forage plants and between hetbivores (Grace
and Ttlman 1990). Such indirect effects have been documented
in the literature (e.g. Urness 1975, Reiner and Urness 1982,
Brown and Heske 1990). Indirect effects were crucial in
detennining sustainability in our model system. For example
they explain why the presence of wildlife increases grass
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with the idea of "holistic" management (Savory 1988), in that
sustainable ecosystems incorporate many interacting processes
and managers must maintain a "bahmce" of these processes or
risk a break-down of the system. A model, such as ours, can
provide valuable clues as to how to maintain such an ecosystem
The model predictions also indicate that considering
variability is crucial in detennining sustainability. For example,
the effects of hetbivores on mean biomass of different plant
groups suggested that increasing wildlife density should improve
sustainability (in teons of bio~s) (Figs. 3, 4). However,
calculating probabilities of extinction, which incorporated
variability in precipitation and wildlife density, revealed the
opposite prediction: increasing wildlife density should decrease
sustainability (in tenns of diversity). Thus, risks of undesirable
outcomes to management may be independent of the mean
outcome. Too often, land managers and ecologists have
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management strategies (Chesson 1985). Risk management
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to traditional problem-solving management techniques that may
prove invaluable for sustaining ecosystems. The consequences
of variability and risk can usually only be evaluated with many
repetitions of experiments or calculations (Goodman 1987,
Belovsky 1987); models may be indispensable for such analyses.
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