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Interaction Assessment: Predicting the
Impact of Alternate Range Management
Actions
John M. Emlen
D. Carl Freeman
J. M. Escos
C. L. Alados
costly experimentation to parameterize the model. Consequently, predictions may become available only well after
decisions have to be made. The bottom line, of course, is that
decisions must be made, even if extensive, reliable data are
not available. This does not, however, imply that decisions
must be made in a vacuum. What is needed is a rapid field
based approach for assessing the impacts of management
decisions and species interactions on the population growth
rates of all species in the community.
One promising candidate for such a method is Interaction
Assessment, or "INTASS" (Emlen and others 1989, 1993;
Freeman and Emlen 1995). INTASS is an analytic tool that
can be used quantitatively to describe the effects of species
interactions and local environmental variables on the percapita population growth parameter of any species of interest. Such expressions, derived for all major species in a
community, comprise a set ofsimultaneous equations which,
by subsuming the web of biotic-abiotic interactions, can be
utilized to predict how the impacts of various management
actions might ramify throughout the system. In this paper,
we present the rationale behind INTASS, then illustrate its
use in the context of a grazing management situation.
Abstract-Interaction Assessment, or "INTASS," is an analytic
tool used to quantitatively describe the effects of species interactions and local environmental variables on the per-capita population growth of a species, either plant or animal. Data from a farm on
the Iberian Peninsula in Spain was analyzed for 19 variables. Using
INTASS, the plant community dominated by Anthyllis was shown
to be most changed by grazing pressure. Work continues on developing user-friendly software for INTASS applications.
Good rangeland management requires that the likely
impacts of alternative management options be assessed on
both plants and animals, including livestock, before any
specific action is taken. Such assessments are not easily
made. Because grazers exhibit food preferences, different
plant species will be differentially affected by grazing. Some
plants may benefit from grazing, at least light grazing, while
others are harmed. Plant growth and reproductive output
may be impacted quite differently by grazing. Further, even
knowledge of grazing preferences and impacts on the individual species is insufficient to predict the response of the
plant community, for the temporal and spatial dynamics of
that community are affected also by competitive and facilitative interactions that occur among the plant species. To
make the picture still more complex, grazer consumptive
patterns and spatial distribution are likely to change with
shifts in plant community composition and grazer density.
Perhaps the most reliable means of assessing the likely
consequences of management options is to consult one of
those grizzled guru naturalists who somehow hold in their
heads a gestalt of all the system's complexities. Unfortunately, grizzled guru naturalists are a dying breed. Deprived
of this resource, we are destined to fall back on either
educated guesses, based on past experience, or on modelling.
The first option may work in some circumstances, but will
likely fail in many others, and must inevitably leave one
feeling a bit uncertain. Modeling may require lengthy and
Interaction Assessment
INTASS is based on the assertion that fitness (sensu the
number of individuals produced per individual per unit
time, such as an individual's contribution to the per-capita
population growth rate) is, on average, the same for individuals in all occupied microhabitats. Microhabitat is defined with respect to the values of all physical and biotic
variables affecting fitness in the immediate vicinity of the
individual in question; immediate vicinity is defined as that
area around an individual within which environmental
variables (soil features, slope and aspect, water availability,
facilitative or competitive effects of plants of all species,
grazers, etc.) are likely to effect the individual's growth,
survival and reproduction. The assertion is based on the
following lines of reasoning.
Regarding animals, a critical aspect of behavioral adaptation is that individuals have the ability to assess the impact
oftheirimmediate surroundings on their survival and health.
!ffood is in short supply, predators are leering from every
corner and cover is scarce (all local variables affecting
fitness), the adaptive response will be to leave the immediate
area. Where conditions are more benign, the animal should
In: Barrow, Jerry R.; McArthur, E. Durant; Sosebee, Ronald E.; Tausch,
Robin J., comps. 1996. Proceedings: shrubland ecosystem dynamics in
a changing environment; 1995 May 23-25; Las Cruces, NM. Gen. Tech. Rep.
INT-GTR-338. Ogden, UT: U.S. Department of Agriculture, Forest Service,
Intermountain Research Station.
John M. Emlen is with the Northwest Biological Science Center, National
Biological Service, Seattle WA. D. Carl Freeman is with the Department of
Biological Sciences, Wayne State University, Detroit, MI. J. M. Escos and C. L.
Alados are with the Instituto Pirenaico de Ecologia (CSIC), Zaragoza, Spain.
178
be more likely to remain. Whether the response to move or
stay results from guided search behavior or some sort of
kinesis is immaterial. The consequence is that individuals
will accumulate in patches of the "best" microhabitats until
the increased pressures of their density counteract the
microhabitat qualities. Net movement ceases when individuals can no longer increase their fitness by moving
somewhere else, resulting in equal average fitnesses across
the entire occupied habitat. Support for this assertion as it
applies to animals can be found in Emlen and others 1989.
On the other hand, plants cannot move as animals do, but
they possess tremendous plasticity with respect to growth,
flowering, and seed set. Thus the number of viable seeds
produced by a plant reflects not only the size of the plant, but
also the local microhabitat of the plant and, thereby, indirectly (and loosely, depending on the distance of seed dispersal), the environment in which the seedlings will grow.
Now, because seedling survival falls with density feedback
(produced by competition from the parent plants and from
other seedlings), the number of seedlings that survive their
first year must rise and then fall with the number of seeds
produced per unit area by a parent plant. That is, there is an
optimal seed production for every plant in any given year,
which is a function of microenvironmental conditions, including cover of the parent plant and any other conspecifics
in the immediate vicinity. Ifwe presume that natural selection has shaped a plant's capacity to "do the right thing," we
should find seed production to be heavier (after correction for
size of parent plant) in microhabitats where each seed, on
average, is more likely to survive, and lighter in overcrowded
microhabitats where seedling survival is less likely. That is,
we expect an equilibrium to be approached in which the
average number of surviving seedlings per seed produced is
the same in all occupied microhabitats (Emlen and others
1989). Inasmuch as the vast proportion offitness variance in
plants is accounted for by early survival, the above implies,
to a good approximation, that average fitness of seeds will
converge across all occupied microhabitats.
If this equilibrium is reached only slowly, then the assertion of equal average fitness applies only loosely unless
population sizes are at equilibrium. There is good evidence,
however, that these adaptive changes in seed production
occur extraordinarily quickly. Palmblad (1968) conducted
experiments in which seeds from seven weed species were
sown in densities ranging from 55 to 11,000 seeds per square
meter. Despite the enormous discrepancy in density of seeds
sown, the number of seeds produced per unit area by the
resulting adults one year later varied by less than a factor of
2.0 in six of the seven species. Thus, within a single generation, the differential was reduced from 200 (11,000/55) to
less than 2.0. Harper (1977) cites another study in which a
300-fold seed sowing density range resulted in only a threefold difference in seed output per unit area for Digitalis
purpurea. In pure stands of Agrostemma githago, seed
output per unit area was nearly independent of seed input
(Harper and Gajic 1961). Finally, Bromus rubens, both in
pure stands and in mixtures with Lepidium densi/lorum,
exhibits similar behavior (Freeman, unpublished data). While
the above argument treats all seeds of a species as identical,
there is evidence also that suggests fitness is essentially
invariant with seed size (Stephenson and Winsor 1986).
Studies by Wulff (1986) indicate possible adaptive advantages to observed seed size variation. If, as an evolutionist
would suspect, this is generally true, seed size polymorphisms also suggest equal expected fitness contributions per
seed.
The per-capita population growth rate of any species can
be modelled as a function of local environmental variables,
including the densities of conspecifics and other interacting
species. Reasonable forms for such models can be gleaned
from the extensive literature on population dynamics; they
range from simple Lotka-Volterra type to any level of complexity desired. The difficulties of constructing and using
such models lie notin adequately approximating their forms,
but in assigning reasonable values to theIr various coefficients or parameters. Extremely detailed models are, of
course, the most reliable, but only if the parameter values
used are known to be accurate. Ifnot, errors may compound,
cascading through the calculations to generate utterly unreliable predictions. Sacrificing too much detail for exigency,
on the other hand, leads to inaccuracies for quite a different
reason; the models are too simplistic to reasonably describe
the system of interest. The INTASS methodology can, at
least in theory, be used to parameterize either model extreme, but too detailed models require unrealistically large
data sets (and may suffer from other statistical complications, for example, a multitude oflocal solutions). Models of
intermediate complexity, tailored to the local situation and
problem, are the most practical alternative.
Once a model (or a series of models , one for each species to
be analyzed) has been chosen, INTASS may be applied to
parameterize it as follows. Gather data on a quadrat-byquadrat basis on all environmental variables deemed pertinent to fitness of a species of interest. Quadrat size reflects
"immediate vicinity" which, in the case of plants , will generally be an area just slightly larger than the root mass/crown
of the species of concern. These quadrats are centered
around randomly chosen individuals of the species of interest. The data for all individuals are then entered into a
software routine that finds those model parameters/coefficients that most accurately reflect the assertion of equal
average fitness, for example, that result in minimal acrossmicrohabitat (across quadrat, in effect) variance in fitness.
In the case of plants, there is no contribution to fitness by
individuals that produce no seeds; indeed, the contribution
is proportional to seed number. Thus, for plants, the routine
is applied over all seeds rather than over individual parent
plants.
If a linear model is utilized, confidence intervals on the
derived parameter values are calculated as in standard
multiple regressions (see Emlen and others 1989, 1993).
Where nonlinear models are used, confidence intervals can
be found with the use ofthe inverted Hessian matrix (matrix
of second derivatives of the variance with respect to all
parameters).
Methods _ _ _ _ _ _ _ __
Data were collected during the summers of 1993 and 1994
on the Pajares Livestock Farm in the Filabres Mountains
(elevation 850 m) in Almeria Province, Iberian Peninsula, in
Spain. The plant community there is shrub-steppe, with
179
600 mm annual rainfall, dominated by Anthyllis. cytisoides,
Artemisia tridentata,Retama spaerocarpa, Stipa tenacissima,
and various other grasses. Grazing (by goats) is light or
absent over much of the area, heavier on the rest. Variables
measured in each quadrat included:
Poe
.
Finally,
p =~exp{-~10X18}
a+Q 2
.
Parameter values (a,{on were found using a minimization
routine where the objective function was mean (logP-IogF')2,
with p* the true early survival. The latter was estimated for
each quadrat from the ratio "seedlings in 1994/seeds in
1993."
The study for which these data were gathered was conceived for purposes other than those discussed in this paper.
Only Anthyllis was considered from the perspective of
INTASS. While this, unfortunately, precludes a full analysis
ofpotential grazing management effects, the followinganalysis nevertheless provides a partial illustration ofhow INTASS
can be used for assessing such effects. Suppose, for example,
that grazing were to be doubled. What would such a change
do to the plant community, and ultimately to the well being
of the grazers and to the consequent economic costs and
benefits?
To address this question, we make use of the variable
values gathered from random quadrats, but double the
number of grazers in each quadrat. Then, using the derived
parameter values for all plant species and a computer
routine to figuratively add or subtract plant cover for all
plant species, quadrat-by-quadrat, in such manner as to
maintain minimum variance in fitness (keeping with the
basic INTASS assertion) until average fitness returns to a
value indicating population equilibrium (this will be the p*
value used in the analysis in most cases). Of course a
doubling in grazer number will not necessarily result in a
doubling ofgrazers, equally, in all quadrats; the grazers may
shift their dispersion pattern as a function of social factors
and/or increased competition for food. Certainly grazer dispersion will change as plant dispersion and codispersion
change consequent to the increased grazing pressure. Thus,
once a new, first estimate for plant abundance and distribution pattern has been calculated, the INTASS expression
derived for the grazer must be used to calculate a next
estimate for grazer dispersion pattern. This, in turn, is used
to calculate a second estimate for plant dispersion and
codispersion. The process is continued until convergence
occurs in the values obtained.
In the present instance, we have an INTASS expression
for Anthyllis only, so the full process cannot be demonstrated. Suppose, however, purely for the purposes of illustration, that we suppose the grazers don't redistribute themselves as their density changes and as plant distributions
change, and that plant interactions have minimal effect on
the response of Anthyllis to grazing. Then we can at least
calculate the impact of a change in grazing intensity on the
cover of Anthyllis. To do so we applied the model with the
parameter values in table 1 (we used those for P* = 0.03),
incrementing or decrementing Anthyllis cover in each quadrat individually in such manner as to minimize Var(logPlogP*) until mean of 10gP equalled 10gP·.
1. Age of plant
2. Plant canopy area
3. Plant volume
4. Area occupied by other conspecifics within the quadrat
5. Total number of seeds on each sampled plant (in 1993)
6. Mean seed weight for each sampled plant
7 . Number of seedlings under each plant in 1994
8. Percent cover of Artemisia
9. Percent cover of Stipa
10. Percent cover of Retama
11. Percent cover of other grasses
12. Slope (level ground = 1, slight = 2, high = 3)
13. Soil stone structure (few or no mid-sized stones = 1,
intermediate = 2, high = 3)
14. Soil pH
15. Soil conductivity
16. Soil organic content
17. Soil texture (percent soil consisting of particles greater
than 2 mm diameter)
18. Grazing (no = 1, yes = 2)
19. Soil moisture at 10 cm depth
Preliminary analyses included regressions of Anthyllis
cover values on the various measured variables (8 through
19), and plots of estimated fitness (no. seedlings in 1994/no.
seeds in 1993) against these variables. On the basis of the
results, the final INTASS analysis was simplified by deleting variable 13. In addition, we reasoned that the soil
moisture measure would be highly variable over time and
might, therefore, be misleading as a reflection of effective
moisture availability to Anthyllis. Rather, it seemed likely
that available moisture would be a global variable modified
by the other variables. Consequently, variable 19 also was
deleted from the final analysis.
The Model
exp{~lOx18}
------------------------------
In this semi-desert habitat, moisture is likely to be the
primary factor limiting plant fitness. Other variables, nevertheless, might be important in their own right, as well as
mediators of local differences in moisture availability. Consequently, we constructed an extremely general function to
describe "environmental quality per unit plant cover," Q,
and presumed that the probability of early plant survival (P)
would rise and then asymptote with Q:
Poe ~: Q = (X161iIX141i2X121i3X151i4x171i5)/(N+&;xs+B,X9+8gXlO+agXU)
a+Q2
The subscripts on {x} refer to the list of variables, above;
Alpha and {~} are the model parameters to be found by fitting
the model to observed data.
Survival must fall off (roughly) exponentially with grazing rate. Thus, also:
180
Table 1-Derived parameter values for the Anthyl/is model, with
95% confidence range for the case of P* = 0.03.
B~alue
Parameter
P* = 0.01
0.03
0.10
Soil organics
0.027
0.029
0.027
Soil pH
1.044
1.075
1.074
Conductivity
-0.221
-0.179
-0.235
-0.103
Texture
-0.070
-0.079
-0.057
Slope
-0.058
-0.058
Grazing
0.162
0.187
0.181
Anthyl/is cover
1.0000 by definition
0.113
Artemisia cover
0.113
0.113
0.432
Stipa cover
0.432
0.432
0.902
Retama cover
0.902
0.902
0.824
Other grasses
0.824
0.824
0.032
<X
0.354
0.107
Discussion and Conclusions ---Accurate and exhaustive data, gathered over time to
reflect seasonal and annual variation in climate, form the
most reliable basis for predictive models for resource management. The number of factors that must be considered,
however, make prediction a risky practice because of the
tendency for cascading errors in complex models. In addition, the time required to obtain parameter values sufficiently accurate to guard against such output errors is often
much longer than managers have before management decisions have to be made. The INTASS approach, used to
parameterize models of intermediate complexity, using
rapidly and inexpensively acquired quadrat-type data, represents a practical compromise between simplistic approaches and unreliably unrealistic insistence on completeness. It represents a viable approach to addressing
management problems where time and money are limited.
Work continues on protocols for modeling and on the
development of user-friendly software for INTASS applications. We are still in a fairly early stage of our work, but would
be delighted to share our ideas and existing software with
interested parties. In particular, we welcome input, suggestions, research collaborations, questions from those who
might start their own investigations into this methodology.
95%
confidence range
for P*= 0.03
0.012 to 0.048
1.064 to 1.081
-0.210 to -0.264
-0.035 to -0.132
-0.045 to -0.071
0.147to 0.216
---------
0.061 to
0.252 to
0.010 to
0.734 to
0.088 to
0.165
1.116
1.794
0.914
0.127
0= (organics)027(pH)1.o44(slope)-o58(conduct)--17l1(texture)--o7o
(Anthyllis)+.113(Artemisia)+.432( Stipa)+.902(Retama)+.824(grasses)
p=
0 2 exp {-.181 (grazing)}
.107+02
Results
-----------------------------------
Early survival based on data from 1993 and 1994 (number
of seedlings in 1994/number of seeds in 1993) is about 0.03.
Of course, this can be expected to vary year-to-year. Accordingly, analyses were run for p* values ranging from 0.01 to
0.10. Except for the value of (x, results varied only slightly
(table 1). Confidence intervals, based on the inverted Hessian matrix approach were calculated using a p* value of
0.03.
The impact of various putative management schemes
(doubling grazing pressure, eliminating grazing pressure,
raising soil organic content by 20%, doubling soil organic
content, raising pH by 0.1) are given in table 2. As might be
expected in a situation where moisture, primarily a global,
not locally varying variable, is undoubtedly the major factor
influencing fitness, the only variable that appears to make
much difference to Anthyllis is grazing pressure. Furthermore, even the effect of grazing is modest, a fifty percent
change in grazing intensity resulting in a change inAnthyllis
cover of only about 14 to 15%.
Acknowledgment _ _ _ _ __
This manuscript benefited from assistance from the Intermountain Research Station, Shrubland Biology and Restoration Research Work Unit, Provo, UT.
References
Table 2-lmpact on Anthy/lis cover of various habitat alterations.
Management action
Double number of grazers
Eliminate grazers
Raise soil organic content by 20%
Double soil organic content
Raise pH by 0.1
-------------------------------
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453-458.
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Change in Anthyllis cover
Percent
-13.4
+15.4
+0.5
+2.0
+1.4
181