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63
Computer Simulation Modeling to
Determine Trailhead Quotas for
Overnight Wilderness Visitor Use
Volume 32, Number 3
pp. 29–48
Journal of Park and Recreation Administration
Fall 2014
Robert Van Kirk
Steven Martin
Kai Ross
Mark Douglas
EXECUTIVE SUMMARY: Limits on overnight visitor use may be needed
when demand is very high and other management tools alone are inadequate to
protect resource and experiential conditions. In the wilderness, trailhead quotas
may be an effective management tool that allows for more visitor autonomy.
For trailhead quotas to be effective; however, managers must have a very good
understanding of the relationship between the trailhead origin of trips and
the resulting spatiotemporal distribution of users. Simulation modeling can
accurately determine this relationship, thus allowing managers to set informed
and appropriate trailhead quotas. This study showed how a simulation model
can be used to 1) monitor the distribution of overnight wilderness visitors in a
large wilderness area with a complex trails network and 2) achieve an informed
redistribution of overnight visitor use that reduces the number of areas that are
overcapacity while still accommodating the same overall amount and the same
temporal distribution of visitor use.
KEYWORDS: simulation model, trailhead quotas, wilderness use
AUTHORS: Robert Van Kirk is with the Henry’s Fork Foundation, Ashton ID,
83420, robert.vankirk@humboldt.edu. Steven Martin is with the Department of
Environmental Science & Management, Humboldt State University. Kai Ross
is with the Department of Quantitative Ecology and Resource Management,
University of Washington. Mark Douglas is with the Department of Society and
Conservation, University of Montana.
ACKNOWLEDGMENTS: The National Park Service, through a grant from the
Yosemite Conservancy, provided funding for this study. We wish to thank Bret
Meldrum, Mark Fincher, Paul Gallez, Mark Marschall, David Pettebone, Ken
Watson, Bill Kuhn, Jay Sammer, Martijn Ouborg, and Naomi Chakrin, along
with the wilderness permit distribution team and personnel at all park entrance/
exit stations for their assistance with the project. Surveys were administered
30
under Ofce of Management and Budget permit 1024-0224 NPS #09-014 and
National Park Service scientic research and collecting permit YOSE 2010 SCI
0048 Study ID 0041.
Over the past several decades, demand for wilderness recreation has challenged
managers of protected areas throughout the world to accommodate use while maintaining
both ecological integrity and the quality of the wilderness experience itself. With
the Wilderness Act of 1964, the U.S. Congress established the National Wilderness
Preservation System, protecting vast roadless areas with signicant recreational,
ecological, geological, scientic, educational, scenic or historical value. Although the
Wilderness Act served to establish the system, it did not establish specic management
practices for protecting the resources and values from use and overuse by the visitors for
whom it was, in part, created.
The Act directed the managing agencies to be responsible for preserving the
wilderness character of the area. Recreation visitor use, or overuse, may be a source of
impact to wilderness qualities and values such as naturalness and solitude (for detailed
reviews see Hammitt & Cole, 1998; Leung & Marion, 2000; Cole, 2009; Monz, Cole,
Leung, & Marion, 2010). In some wilderness areas, the spatiotemporal distribution of use
is such that visitors are heavily concentrated in popular locations. As Dawson and Hendee
(2009, p. 378) point out, some of these “popular locations . . . may be sensitive to physical
impacts from use and intrusions on solitude,” leading to any number of management
responses to minimize the negative effects of large numbers of visitors.
Visitor Management
Potential visitor management strategies and techniques generally fall into two broad
categories: 1) inuencing visitor access, such as daily trailhead quotas or purposely
making trail access more difcult, and 2) inuencing visitor behaviors and activities,
such as prohibiting campres or Leave No Trace education efforts. Within each of these
categories, specic actions fall along a continuum of direct to indirect management,
reecting the degree to which the management action restricts or preserves the behavioral
autonomy of the visitor. Direct visitor management is more restrictive and regulatory,
while indirect management relies on approaches such as information and education to
inuence decisions made by visitors, or on the presence or design of facilities in an area,
such as choosing whether or not to provide bridge access across a river (Manning & Lime,
2000). Generally, the more overt and regulatory the management presence in the visitor
experience, the more potential for adverse impact to that wilderness experience. Direct
management actions have greater potential to negatively impact a visitor’s wilderness
experience by detracting from “the sense of primitive and unconned recreation called for
in the Wilderness Act” and “diminishing the sense of experiencing wilderness and facing
challenges on one’s own” (Dawson & Hendee, 2009, p. 453).
One way to relieve some of what Dawson and Hendee call the “tension between
recreation and regulation” is to conduct as much of the regulatory management as possible
outside of the wilderness area, consequently maximizing visitor autonomy once inside the
wilderness. Trailhead quotas are one way of doing this. Although limiting and rationing
use to a wilderness by way of daily entry quotas may be a very direct and regulatory
approach to visitor management, it preserves a greater degree of visitor freedom once
in the wilderness (e.g. itinerary exibility, campsite choice). In heavily used wilderness
areas, where even the best and most carefully implemented indirect management tools
might still be ineffective in the absence of visitor use limits, trailhead quotas may be seen
as an effective frontcountry mechanism for achieving desired backcountry objectives such
as reduced ecological impacts and increased opportunities for solitude, while preserving
visitor freedom inside the wilderness. Managers of wilderness areas administered by the
31
National Park Service and the U.S. Forest Service throughout the Sierra Nevada mountains
of California commonly use daily trailhead quotas to limit use, thereby allowing visitors
greater autonomy and exibility to tailor their trip itinerary spontaneously once inside the
wilderness.
If daily trailhead quotas are to be used, the next question is, how are those quotas
determined? By way of tailored trailhead quotas, managers are attempting to achieve a
desired spatiotemporal distribution of visitor use. But the complexity of travel routes and
variability of visitors’ decisions make it extremely difcult for managers to be able to
predict with a reasonable degree of certainty the spatiotemporal distribution of visitors
from a given entry-point distribution. Furthermore, even when visitors are required to
specify a trip itinerary on their backcountry permit, it has long been known that visitors
frequently deviate from their intended itinerary (van Wagtendonk & Benedict, 1980;
Parsons, Stohlgren, & Kraushaar, 1982), so the relationship between trailhead-of-origin
and location of backcountry use determined from permit itineraries is not the actual
relationship realized on the ground. Accurately determining this relationship from trial-and-
error experimentation would be costly, time-consuming, and inuenced by uncontrolled
external factors (Dawson & Hendee, 2009, pp. 478–479).
Thus, when dealing with wilderness recreation systems that involve both spatial
complexity and the uncertainties of visitor behavior, computer simulation has become
a standard tool that allows researchers and managers not only to better understand the
spatiotemporal distribution of visitors, but to “predict how distributions of visitor use
are likely to change in response to management actions” and to “test the feasibility and
effectiveness of management plan alternatives” (Cole, Cahill, & Hof, 2005). Different
management scenarios can be tested in a comprehensive, low-cost way, free of public
and political consequences, and managers can see what effects their various alternatives
would have in a variety of future use conditions (Cole & Daniel, 2003; Lawson, Manning,
Valliere, & Wang, 2003; Dawson & Hendee, 2009).
One of the rst models used for wilderness management was the Wilderness Use
Simulation Model (WUSM) developed by Smith and Krutilla (1976) and applied in many
different settings (Schecter & Lucas, 1978; van Wagtendonk, 1978; Potter & Manning,
1984). The WUSM simulated user behavior along trails or other travel routes, for the
primary purpose of quantifying encounters between parties (van Wagtendonk, 2003).
Applications of the WUSM focused on the effects of use on the recreational experience
of wilderness users themselves rather than on impacts to physical or biological resources.
Primary model inputs were denition of travel routes, estimated travel time over each route
segment, temporal and spatial distribution of parties entering the wilderness, and number of
users (Potter & Manning, 1984). Model inputs were usually derived from visitor registers,
permits, and interviews, which generally resulted in a relatively small set of xed travel
itineraries being used in the model. However, an application of the WUSM to boating on
the Colorado River employed computer simulation to generate trip itineraries, in order to
obtain an essentially limitless set of possible trips that could be taken (Underhill, Xaba, &
Borkan, 1986).
The next generation of recreational-use simulations models was implemented in
the software ExtendSim, an object-oriented, discrete-event, dynamic simulation package
(Imagine That, 2010). ExtendSim models have been used in many parks and wilderness
areas, including Acadia National Park (Wang & Manning, 1999), Arches National Park
(Lawson et al., 2003), Isle Royale National Park (Lawson, Kiely, & Manning, 2004),
and the John Muir Wilderness (Lawson, Itami, Gimblett, & Manning, 2006). Although
most of these applications still focused on “social carrying capacity” (Lawson et al.,
2003) rather than on natural-resource carrying capacity, the exibility of the ExtendSim
simulation environment and increased computational power allowed the model to track
and record data such as the number of visitors camping each night at a given location,
which could be used to assess effects of use on physical and biological resources. Higher
32
computational efciency also increased the number of random (“stochastic”) components
that could be included and allowed a larger number of independent stochastic replications
to be performed. This increased the number of different outcomes that could be generated
from a given set of inputs and increased statistical power in comparing model outputs to
actual observations. However, trip itineraries were still largely determined from interviews
or permits, again limiting the number of different itineraries included in the model and
the ability of the model to dynamically incorporate changes in visitor behavior once a
simulated party has entered the wilderness (Lawson et al., 2006).
These limitations have been addressed by development of agent-based models such
as RBSim, in which individual users interact dynamically with the physical environment
(Itami et al., 2003). Known as “individual-based” models in the ecology literature, agent-
based models have been widely applied to sh and wildlife management (e.g., Schumaker
et al. 2014). These “virtual reality” models (Bishop & Gimblett, 2000) use Geographic
Information Systems (GIS) to accurately simulate the physical environment encountered
by users and specify a set of behavioral rules that govern how simulated users react to their
environment. For example, the rules might specify that visitors are likely to stop at a scenic
viewpoint or avoid climbing a steep section of trail late in the day when they are tired
(Gimblett, Richards, & Itami, 2001). Agent-based models are limited only by the amount
of GIS data and complexity in the behavioral rules that are included in the model, but
increased realism comes at the cost of models that are difcult to parameterize, understand
and defend (Schumaker et al. 2014).
One of the earliest applications of trailhead quotas was in the wilderness of Yosemite
National Park. In response to overuse in the Yosemite wilderness, a mandatory permit system
was implemented in 1972. Subsequently, the wilderness was divided into 53 management
zones (Figure 1), and an overnight visitor use capacity was established for each zone in
1977 (van Wagtendonk, 1986). In order to minimize the probability that visitor use would
exceed zone capacities, without imposing excessive regulation on users once they enter the
wilderness, a trailhead quota system was implemented in 1977 (van Wagtendonk, 1981;
van Wagtendonk & Coho, 1986), and remains in effect today. All overnight visitors to the
Yosemite Wilderness are required to obtain a wilderness permit. When the permit is issued,
visitors indicate their intended trip itinerary, including number of nights and intended
campsite location for each night, at the resolution of the wilderness travel zone. Trailhead
quotas are enforced through the permit system, but visitors are not required to adhere to
their intended itinerary once in the wilderness; they may shorten or lengthen their trip, and
they may choose to camp in different locations than originally intended. Since wilderness
use estimates (both overall and by zone) are based on the intended trip itineraries contained
in the permit database, deviations from intended itineraries affect the accuracy of the
overall, and zone-by-zone, use estimates. Additionally, since many management actions
(trailhead quotas being probably the most obvious) are based on the spatial distribution
of visitors, spatial deviations from intended itineraries affect the efcacy of the trailhead
quotas and other spatially-based management actions.
The objectives of this study were to a) construct an overnight wilderness use simulation
model that uses dynamic rather than xed itineraries and incorporates visitor deviation
from intended itineraries, b) validate and apply the model to the Yosemite Wilderness to
predict visitor use and probabilities of overuse at the resolution of each wilderness zone
on each night of the season (“zone-night”), c) quantify the effect of itinerary deviation
on use estimates, d) determine the dependence of zone use on trailhead of origin, and e)
determine whether adjustment of trailhead quotas can reduce probability of overuse while
accommodating the current level and temporal distribution of visitor use. Although we
have applied the model to the Yosemite Wilderness, the model framework is applicable to
any management setting in which intended travel itineraries and deviation characteristics
are known.
33
Method
Study Area
The Yosemite Wilderness includes 281,855 ha, nearly 95% of the park, situated
on the western slope of the Sierra Nevada Mountains (Figure 1). Sixty-four trailheads
provide access to 1,112 km of trail. An additional 46 trailheads feed 669 km of trail on
adjacent U.S. Forest Service (USFS) wilderness lands. The Emigrant Wilderness borders
the Yosemite Wilderness to the north, as does the Hoover Wilderness to the east, and the
Ansel Adams Wilderness to the south. Two popular long distance hiking trails traverse
Yosemite’s wilderness; the John Muir Trail stretches from Yosemite Valley south to Mount
Whitney, and 80 km of the Pacic Crest National Scenic Trail (Fig. 1) are within the park
(van Wagtendonk, 2004). Peak use and the demands it places on the wilderness resource
necessitate use limits. Trailhead quotas are enforced through the wilderness permit system.
Permit reservations may be made up to 24 weeks in advance of the date of entry into the
wilderness. Daily, 60% of each trailhead quota is allocated to reservation, with 40% left for
rst-come rst-served access in person.
Description of Basic Model and Itinerary Simulation
Our goal was to develop a stochastic simulation model that incorporated the
advantages of agent-based models, in which users adjust their behavior dynamically once
32
Fig. 1. Map of Yosemite National Park, showing wilderness travel zones, trailheads, and trails,
including the Pacific Crest Trail (PCT).
Figure 1. Map of Yosemite National Park, showing wilderness travel zones,
trailheads, and trails, including the Pacic Crest Trail (PCT).
34
they begin their wilderness trip, while retaining the simplicity and statistical defensibility
of parameterizing the model with information based on visitor surveys and permits. We also
desired to use a platform that was familiar to managers and to incorporate only as much
spatio-temporal resolution as was necessary to inform management, which in Yosemite,
occurs at the level of trailheads, wilderness zones, and nights spent in the wilderness. Thus,
we built the model in ExtendSim and parameterized it with data from wilderness permits
and visitor interviews. However, we developed an innovative algorithm that simulated
individual travel itineraries dynamically based on probabilities of transitioning from a
particular trailhead to a wilderness zone on the rst day of the trip and then from zone to
zone or zone to exit on each subsequent day. Furthermore, we included a procedure that
allowed parties to deviate from their intended trip itinerary once in the wilderness. These
algorithms simulate a theoretically innite number of different itineraries from a very small
set of empirically determined probability distributions, balancing realism and simplicity.
Model details are given in Ross (2011); we provide a less detailed description here.
Distributions of party size, trailhead selection, and trip date were created empirically
from the Yosemite wilderness permit database, using information from all 14,497 parties
that started trips during the 153-day summer season (May 1 through September 30) in
2010 and intended to spend at least one night in the Yosemite wilderness. Trip date was
assigned deterministically in the model to match the observed temporal distribution of use;
all other characteristics were assigned or simulated randomly. Party size, trip date, and
trailhead-of-origin were assigned at the initiation of a simulated trip (Figure 2). Trailheads
were assigned randomly, according to observed probabilities of trailhead use. If random
selection of a trailhead from the empirical distribution resulted in assignment of a party
to a trailhead already at quota, that trailhead was removed from the empirical distribution,
and a new trailhead was randomly selected. On average, this had the effect of assigning
to the party the next most popular trailhead that was available. Once a party was assigned
a starting trailhead, an initial wilderness zone was randomly selected from the empirical
distribution of zones reachable from that trailhead, and the party spent its rst night in that
zone. For example, the permit database indicated that 95.1% of all parties starting trips
at trailhead 36 intended to spend their rst night in zone 75 (Figure 3), so in the model, a
party starting at trailhead 36 had a 0.951 probability of spending its rst night in zone 75.
Instead of creating a xed set of travel itineraries, travel route and trip duration for
each party were simulated dynamically according to a transition-probability matrix that
was created from all 14,497 intended itineraries in the permit database. The entries in
the matrix were the conditional probabilities of a party spending its next night in each of
the wilderness zones, given its current location. For example, entry [75,65] in this matrix
was 0.08349, indicating that if a party was currently in zone 75, it intended to spend
its next night in zone 65 with a probability of 0.08349 (Figure 3). Additional transition
matrices and user attribute distributions were created for Yosemite wilderness use that
originated at surrounding USFS trailheads, using permit data where available and visitor
survey responses (n = 147) otherwise. So that we did not have to preselect trip durations,
we included a state in the transition matrix that represented ending the trip. The model
multiplies the number of nights stayed in the zone by the size of the party to track how
many visitor nights are spent in each zone on each night.
Prior to accounting for itinerary deviation in the model, we used statistical verication
and validation to ensure that model algorithms were implemented correctly and model-
simulated intended-trip values matched observed intended-trip values. Based on behavior
of variance in model outputs, we used the results of 1,000 independent stochastic replicates
for verication and validation. We used a signicance level of α = 0.05 for verication and
validation tests, as well as for all other statistical analyses.
35
Deviation Data and Algorithm
We distributed a survey instrument to all parties that received a wilderness permit in
Yosemite on a stratied random sample of days during the 2010 summer season. Surveys
consisted of map diaries on which respondents marked their actual trip routes, from entry
trailhead to campsite(s) to exit trailhead, indicating each campsite’s location with a circled
number corresponding to the night of their trip (Douglas, 2011). We distributed the survey
to 2,755 overnight parties, of which 1,134 (41.2%) returned the survey. Of the returned
surveys, 1,123 could be compared to a complete, intended trip itinerary in the wilderness
permit database. These usable surveys represented 7.7% of all parties and 9.0% of all
visitor-nights. Potential non-response bias was evaluated by contacting a sample of parties
(n = 75) that obtained but did not return a survey. Statistical tests showed no evidence of
non-response bias (Douglas, 2011).
To evaluate the degree to which visitors deviated from their intended itinerary (as
detailed in the park’s permit database), we compared actual trip itineraries from returned
surveys to the corresponding intended trip itineraries from the park’s wilderness permit
database. Temporal deviations were dened as the difference between actual and intended
number of nights spent in the Yosemite Wilderness, including those resulting from parties
that obtained a permit but did actually enter the wilderness. A spatial deviation was dened
as any difference between the actual wilderness travel zone in which a party camped and
the zone in which the party intended to camp, including difference in order. For example,
a particular four-night itinerary in the permit database intended that the rst night was
33
YES
NO
YES
NO
YES
YES
NO
Create party and
assign party size.
Start season May 1.
Assign trailhead.
Above quota?
Assign zone.
Record
visitor nigh ts.
Draw transition.
To exit?
Season ends
New start date.
More parties?
30 September?
NO
Fig. 2. Flow diagram of simulation model. Italics indicate stochastic elements.
Figure 2. Flow Diagram of Simulation Model.
Italics indicate stochastic elements.
36
spent in zone 75, the next two nights in zone 66, and the fourth night in zone 59 (Figure 3),
(i.e., the trip, 75,66,66,59). An actual trip of (75,66,59) would have a temporal deviation
of -1 days but no spatial deviation. The trip (75,66,59,66) would constitute a spatial but
not temporal deviation, and the trip (75,66) would deviation both spatially and temporally.
34
Fig. 3. Close-up view of zones and trailheads near the center of the park. Zone and trailhead
identification numbers correspond to those used in Figs. 4 and 5.
Figure 3. Close-up view of zones and trailheads near the center of the park.
Zone and trailhead identication numbers correspond to those used in Figures
4 and 5.
Temporal deviation was modeled by changing the probability of exiting the wilderness
in the transition matrix, without changing the relative transition probabilities among the
zones. The factor by which exit probabilities were adjusted was determined by requiring
mean trip duration produced by the model to match mean trip duration of actual parties,
when averaged over all parties over the entire season. This latter estimate was produced by
adjusting intended trip duration of all trips in the permit database by the temporal deviation
characteristics observed in the sample.
The distribution of spatial deviation probabilities across night of trip observed in
the sample was applied stochastically in the model. If a party was randomly selected to
be a spatial deviant, a new transition was selected from the transition matrix, without
replacement of the transition originally drawn. This algorithm forced the party to do
something other than what it originally intended, but it did so in a way that preserved
relative transition probabilities, so that the resulting “actual” itineraries were realistic.
Model Scenarios
We performed 1,000 independent, stochastic, season-long simulations under each of
ve scenarios: 1) validation, 2) current conditions, 3) current conditions including external
inuence, 4) maximum allowed use, and 5) a redistribution scenario that moved starting
locations of trips away from the most popular trailheads (Table 1). All scenarios were
parameterized with data from the 2010 summer season but differed from one another in
37
inclusion of itinerary deviation, inclusion of use originating at trailheads outside of the
park, and distribution of party start dates and trailheads of origin (Table 1). All scenarios
were run for 153 time-steps representing May 1 through September 30. The main output
for each scenario is a table containing the mean and standard deviation, across all stochastic
simulations, of visitor nights spent in each zone on each night across the entire season,
and a second table containing how many visitor nights each trailhead contributed to each
wilderness zone. Mean use for a given scenario was dened as the mean over the 1,000
simulations. The probability of use exceeding capacity in a given zone on a given night was
dened as the fraction of the 1,000 simulations in which the zone capacity was exceeded on
that night. The attributes of each party in each simulation were recorded so that we could
relate the number of visitors camping in each zone on each night to trailhead-of-origin.
34
Fig. 3. Close-up view of zones and trailheads near the center of the park. Zone and trailhead
identification numbers correspond to those used in Figs. 4 and 5.
31
Table 1. Summary of model scenario parameters and results.
Model scenario
Validation
Current
conditions
Current
conditions
(including
external
trailheads)
Maximum
allowable use
Redistribution
Itinerary deviation
NO
YES
YES
YES
YES
Use from trailheads
outside park
NO
NO
YES
NO
NO
No. of parties each
day
observed
observed
observed
Maximum
quota at each
trailhead
observed
Distribution of
starting trailheads
observed
observed
observed
Maximum
quota at each
trailhead
3,575 parties
moved from
high- to low-
use trailheads
Total season-long use
(mean visitor nights
over 1000
simulations)
103,941
89,997
100,007
345,780
89,997
Percentage of zone-
nights with at least
30% probability of
capacity exceedance
NA
1.6%
1.7%
27.6%
0.099%
Table 1
Summary of Model Scenario Parameters and Results
The validation model was parameterized directly from the permit database, without
accounting for itinerary deviation or use originating from outside of the park. The current
conditions scenario reected the best attempt at simulating actual overnight Yosemite
wilderness visitor use patterns, parameterized by trailhead of entry, entry date, party
size, trip length, and probabilistically simulated travel throughout the wilderness zones.
This scenario simulated actual Yosemite wilderness visitor use in 2010 from parties that
originated their trip at a trailhead in the park and served as a baseline scenario to which
the others could be compared. We calculated the effect of itinerary deviation by comparing
output of the current-condition scenario with that of the validation scenario. To quantify
the effect of external use, we performed a second version of the current-condition scenario
that included parties that originated their trip at a USFS trailhead outside of Yosemite.
38
The maximum-allowed-use scenario evaluated the effects of lling every trailhead
quota on every day of the season. Since the same number of visitors entered every day,
this scenario represented a stable equilibrium of wilderness visitation. To eliminate
confounding of the zone use-trailhead relationship by use originating at trailheads outside
of the park, we did not include these external trips in the maximum-allowed-use scenario.
This scenario had two objectives. The rst was to identify the total amount of overnight use
in each zone that could occur under the current trailhead quota system, if every trailhead
quota is lled on every night of the season. The second objective was to generate the
“true” dependence of zone use on trailhead of origin. The trailhead-zone use relationship
generated by the current-conditions scenario primarily reects trailhead popularity and
only secondarily reects trailhead quota, since the most popular trailheads are generally
lled to quota on most nights of the season, whereas many other trailhead quotas are either
lled only on the most busy weekends or are never lled at all. The maximum-allowed-use
scenario eliminates both temporal and spatial preference for trailhead selection and thus
generates a relationship between zone use and trailhead that is based only the quotas and
the accessibility of zones from trailheads.
The redistribution scenario involved 1) identifying trailheads that contributed most
to zone-capacity exceedance under current conditions, 2) using the model to determine
how many parties would need to be moved from these trailheads so that use in each zone
did not exceed capacity on any given night in more than 30% of all simulations, and 3)
redistributing the required number of parties from these high-use trailheads to low-use
trailheads. We reassigned parties that were turned away from the high-use trailheads by
using trailhead selection probabilities that were inversely proportional to those observed.
This had the effect of redistributing excess use from the most popular trailheads in the
park to the least popular trailheads. For consistency in comparison, we did not include use
originating from outside of the park in this scenario.
Results
Model Validation
There were no signicant differences in mean party size, trip duration, or itinerary
deviation rates between modeled and observed values (Ross, 2011). Discrepancies between
observed and simulated distribution of trailhead-of-origin were also small. For season-total
intended use across all zones, the modeled 95% prediction interval was 103,941 ±1,742
visitor nights, and the observed intended use from the park’s permit database was 105,515
visitor nights. Because the observed intended use fell within the prediction interval,
we concluded no signicant difference between modeled and observed values. For use
at the zone-night level, we performed the same type of analysis, adjusted for multiple
comparisons over all 8,109 zone-nights (53 zones x 153 nights). At 95% condence for
each zone-night, we expect observed zone-night use to fall outside the 95% prediction
interval in 5% of the zone-nights. Observed intended use fell outside of the modeled 95%
prediction interval in less than 1% of all zone-night combinations, indicating that there
was no signicant difference in zone-night use between the model and permit database.
Therefore, we concluded that the dynamic model accurately simulated intended visitor
behavior.
Deviation Satistics Obtained from the Visitor Survey
Based on the 1,123 usable visitor surveys, mean intended trip duration was 2.71 days
(SD = 1.69), whereas actual trip duration was 2.35 days (SD = 1.45). The surveyed parties
shortened trips by as many as 11 days and lengthened them by as many as 9 days. Among
the parties that deviated temporally, the mean temporal deviation was -1.02 days (SD =
1.45). Trips were shortened at a rate of 0.42 nights per night the party intended to spend in
the wilderness, and this rate was not signicantly different than the value of 0.33 estimated
in the 1970s (van Wagtendonk & Benedict, 1980).
39
Linear regression showed that actual trip duration did not depend signicantly on
trip start date (P = 0.786), but it increased signicantly with increasing party size (0.043
days per additional party member, P = 0.000276) and longer intended trip duration (0.695
days per additional day of intended duration, P < 0.001). That is, actual trip duration was
longer for larger parties and those that intended to take long trips to begin with. When
applied to the population of all parties in the permit database, the regression equation
predicted a mean actual trip length of 2.12 nights, signicantly lower than the intended
mean trip duration of 2.48 nights. Thus, in the temporal deviation algorithm, we increased
exit probabilities in the transition matrix so that the model produced a mean trip duration
of 2.12 nights.
In 2010, 36.2% of all parties deviated temporally from their intended itineraries,
and 54.4% deviated spatially; 25.2% of all parties deviated both spatially and temporally.
Spatial and temporal deviations were not independent of one another (χ2 = 70.9, df = 1, P
< 0.001). Parties had a tendency to either deviate both spatially and temporally or to not
deviate at all. Survey results showed that parties that deviated spatially were more likely
to deviate early in their trip than later; 30.6% of survey respondents spent their rst night
in a different zone than intended, 17.2% rst deviated from intended spatial distribution
on the second zone visited, and 6.5% rst deviated from intended spatial distribution after
their second zone transition.
Model-Predicted Effect of Itinerary Deviation
Prior to application of the deviation algorithm, model-predicted season-total use and
95% prediction interval from trips originating in Yosemite was 103,941 ± 1,742 visitor
nights (Table 1). Applying the effect of itinerary deviation in the model reduced predicted
season-total use to 89,997 ± 1,743, and this reduction was statistically signicant (t =
-163.66; df = 1947; P < 0.001). Use of the Yosemite Wilderness originating outside of the
park accounted for an average of 10,010 additional visitor nights per season and had very
little effect on capacity exceedance probabilities (Table 1).
Effect of Management Scenarios on Use Levels and Trailhead Relationships
Figure 4 displays zone capacity exceedance probabilities graphically; the shading
of each cell in the graphical array indicates the model-predicted probability that the
capacity of a particular zone will be exceeded on each night of the season. Darker shading
indicates a higher probability of capacity exceedance. Under the current-use scenario, high
probabilities of use exceeding capacity were limited to ve zones (63, 66, 67, 75, 81), as
indicated by the ve rows in the top panel of Figure 4 that contain the largest number of
dark cells. For example, predicted use in zone 75 (Figure 3) had a nonzero probability of
exceeding capacity on every night from June 13 to September 29 (Figure 4). Out of the
8109 zone-nights, there were 126 zone-nights, all in zones 66, 67, 75 and 81, that had
more than a 30% probability of exceeding capacity (Table 1). Use was predicted to exceed
capacity only rarely in the remainder of the 53 wilderness zones (top panel of Figure 4).
The relationship between trailhead-of-origin and zone use (Figure 5) is expressed as
the fraction of total use in each wilderness zone (row) that is due to parties that originate
their trip at a given trailhead (column). Darker cells indicate higher fractions of use
originating from the given trailhead. With the exception of only two zones (other than
three zones in which no camping is allowed), each wilderness zone received at least 20%
of its overnight use from one trailhead, under current conditions. Two of the four most
highly used zones received a majority of their use from one trailhead. For example, 54% of
the total visitor-nights in zone 75 received originated from trailhead 36 (Figures 3 and 5).
The maximum-allowed-use scenario produced a mean use level of 2,260 visitors per
night in the Yosemite wilderness. The nightly capacity of the 53 wilderness zones sums
to 4,200 visitors. Thus, even when all of the trailhead quotas are lled, total use is only
54% of the allowable wilderness zone capacity. However, even though trailhead use in this
scenario was given only by quota and not affected by visitor preference, spatial use was
not uniformly distributed across the zones, resulting in exceedance of zone capacity every
40
night in many zones (Figure 4). On the other hand, predominant travel patterns are such
that, despite maximum-use conditions as allowed by the trailhead quotas, simulated visitor
use in many zones rarely, if ever, exceeded capacity. For example, once the model reached
equilibrium (fourth day of the simulation), use in zone 75 (Figure 3) had over a 90% chance
of exceeding capacity every night, whereas the probability of use exceeding capacity in
zone 59 (Figure 3) was less than 0.2% on any given night.
The zone use-trailhead relationship generated by this scenario was somewhat
different than that under current conditions (Figure 5) because larger fractions of use in
the maximum-allowed-use scenario originated from trailheads that are currently lightly
used, resulting in a more uniform distribution of zone use across trailheads. However, the
similarities in the top two panels of Figure 5 show that that regardless of how heavily or
lightly used a trailhead is, certain trailheads are always the primary contributors to use in
certain zones, reecting the inherent geography of the wilderness and the behavior and
35
Date
Zone index
47
52
57
62
67
72
77
82
87
92
97
1 May 1 Jun 1 Jul 1 Aug 1 Sep
Trailhead Redistribut ion
47
52
57
62
67
72
77
82
87
92
97
Maximum Use
47
52
57
62
67
72
77
82
87
92
97
Current Conditions
0.0
0.2
0.4
0.6
0.8
1.0
Fig. 4. Mean probability of overnight wilderness visitor use exceeding capacity, based on 1,000
simulations, for current-condition, maximum-allowed-use, and redistribution scenarios. The
vertical axis refers to the 53 Yosemite wilderness zones, each of which is represented by a
horizontal bar. Each of the 53 horizontal bars contains 153 cells representing the 153 nights from
May 1 to Sept. 30. The darker the cell, the higher the probability that the zone exceeds its stated
visitor capacity for that night. No camping is allowed in zones 70, 73, and 82; hence those zones
received no use in simulations.
Figure 4. Mean probability of overnight wilderness visitor use exceeding
capacity, based on 1,000 simulations, for current-condition, maximum-allowed-
use, and redistribution scenarios. The vertical axis refers to the 53 Yosemite
wilderness zones, each of which is represented by a horizontal bar. Each of the
53 horizontal bars contains 153 cells representing the 153 nights from May 1
to Sept. 30. The darker the cell, the higher the probability that the zone exceeds
its stated visitor capacity for that night. No camping is allowed in zones 70, 73,
and 82; hence those zones received no use in simulations.
41
physical abilities of users. For example, under current conditions, 54% of the total use in
zone 75 was from parties that originated their trip at trailhead 36, and this fraction remained
unchanged under the maximum-allowed-use scenario. This is due to the proximity of zone
75 to trailhead 36 (Figure 3), regardless of whether use of trailhead 36 is given by current
visitor preference or is articially lled to quota every day.
36
Trailhead index
Zone index
47
52
57
62
67
72
77
82
87
92
97
510 15 20 25 30 35 40 45 50 55 60
Trailhead Redistribut ion
47
52
57
62
67
72
77
82
87
92
97
Maximum Use
47
52
57
62
67
72
77
82
87
92
97
Current Conditions
0.0
0.2
0.4
0.6
0.8
1.0
Fig. 5. Individual trailhead contribution to wilderness zone overnight visitor use for current-
condition, maximum-allowed-use, and redistribution scenarios. The vertical axis refers to the 53
Yosemite wilderness zones, and the horizontal axis refers to the 64 Yosemite Park trailheads.
Shading indicates the fraction of season-total use in each zone originating at each trailhead. No
camping is allowed in zones 70, 73, and 82; hence those zones received no use in simulations.
Figure 5. Individual trailhead contribution to wilderness zone overnight visitor use
for current-condition, maximum-allowed-use, and redistribution scenarios. The
vertical axis refers to the 53 Yosemite wilderness zones, and the horizontal axis
refers to the 64 Yosemite Park trailheads. Shading indicates the fraction of season-
total use in each zone originating at each trailhead. No camping is allowed in zones
70, 73, and 82; hence those zones received no use in simulations.
The redistribution scenario was successful in lowering probabilities of capacity
exceedance in the most heavily used zones, while accommodating the current level and
temporal distribution of use (Figure 4). Under the redistribution scenario, mean visitor
use exceeded capacity on zero nights, and use on only eight out of 8,109 possible zone-
nights had more than a 30% probability of exceeding capacity (Table 1). For example,
under current conditions, use in zone 75 (Figure 3) had at least a 30% chance of exceeding
capacity on 15 nights during the season, whereas under the redistribution scenario, there
were no nights on which the probability of use exceeding capacity in zone 75 was greater
than 30%. To achieve these results, 3,575 parties per year, on average, were redistributed
to less heavily used parts of the park. This represented spatial redistribution of over 22,000
visitor nights (about 25% of total use originating in Yosemite) from heavy- to low-use
42
areas. This redistribution increased the probability of capacity exceedance in zones that
are currently lightly used, although the probabilities of exceedance in these zones on any
given night were generally less than 10% (Figure 4). For example, use in zone 98 had no
probability of exceeding capacity on any night under current conditions, whereas under
the redistribution scenario, there was a nonzero probability of use exceeding capacity on
88 different nights. However, the maximum probability of capacity exceedance across all
of these nights was 9.6%. The zone use-trailhead relationship for this scenario was very
similar to that for the maximum-use scenario (Figure 5), providing more evidence that
the dependence of zone use on trailhead-of-origin is determined primarily by the park’s
geography and not by how parties are distributed among the trailheads. For example, under
both current conditions and maximum allowed use, zone 75 received 54% of its total use
from parties that originated at trailhead 36 (Figure 3). Under the redistribution scenario,
this fraction was reduced only slightly, to 53%, again reecting the fact that zone 75 is
adjacent to trailhead 36.
Discussion
Model Characteristics and Performance
We created and validated a model of wilderness use that reproduced observed use
characteristics at the zone-night resolution with a minimal set of assumptions. Validation
showed that averaged over many simulations, the model produced the same intended
wilderness trip characteristics as those observed. This result indicated the efcacy of our
approach to modeling trip duration dynamically with transition probabilities rather than by
predetermining trip duration for each party at the beginning of its trip. The transition matrix
approach also avoided having to limit itineraries to a nite set. Observed, intended use
calculated from the permit database did not differ statistically from that predicted by the
model at either the season-total or zone-night level, indicating that any small differences
in trip characteristics that may exist between the simulation model and the permit database
did not affect the spatiotemporal distribution of wilderness use.
We emphasize the dynamic nature of trip simulations in our model. The only trip
characteristics that are statically assigned to a simulated party at the beginning of its trip
are start date, party size, and trailhead, all according to the actual distributions of those
attributes from the permit database. Trailhead assignment was somewhat dynamic in the
sense that if a party’s selected trailhead was at quota on that day, a new trailhead was
selected from the remaining trailheads available on that day. The end user of the model can
easily adjust the trailhead quotas and the number of parties that start on each day of the
season to investigate other scenarios and examine the effects of increasing or decreasing
particular trailhead quotas on use. Itinerary and trip duration were determined dynamically
as the party traveled, based on probabilities of state transition and effects of spatial and
temporal deviation. Thus, camping locations and trip duration of each simulated party
were not known until the party completed its simulated trip.
By using probabilistic travel zone transition matrices we neither specied trip
durations at the start of a trip nor limited the possible routes taken by parties. This means
that any feasible trip that can occur in Yosemite has a possibility of occurring in the model.
Since Yosemite is such a large and interconnected area, creating “typical” itineraries would
be difcult and would not accurately reect the full picture of use in the park.
The model accounts for spatial deviation dynamically. Unlike temporal deviation,
spatial deviation is dened categorically, so there is no way to measure its effects by an
average of some quantity. Accounting for spatial deviation in the model allows simulation
of crucial information that is not available otherwise. Standard statistical analysis may tell
us how many parties deviate, but not what effect it has on overall wilderness visitor use.
The only way to see the effects of spatial deviation in the park is to simulate it. By not
using preselected routes or durations, we were able to dynamically alter routes to represent
deviation.
43
We also emphasize that the model is not a “black box” simulation containing numerous
parameters whose values have been chosen through a calibration procedure to minimize
differences between model-predicted and observed use. The parameter governing increase
in exit probability was the only model parameter whose value was determined through a
calibration procedure, and it was calibrated by matching simulated and observed mean trip
duration. No parameterization was performed by attempting to match model-predicted and
observed wilderness use; instead, model validation was used to show that our modeling approach
yields use values consistent with those observed. Thus, our model framework is not specic to
Yosemite but has broad applicability.
Itinerary Deviation and Effects on Use Patterns
As expected, visitors deviated both spatially and temporally from intended trip itineraries.
Based on the survey sample, 66% of parties deviated from their intended itinerary, compared
with 62% reported for Yosemite wilderness users in the 1970s (van Wagtendonk & Benedict,
1980), and this difference was not signicant (z = 1.71, P = 0.087). However, the distribution
of deviation types differed signicantly between the 1970s and the current study (χ2 = 28.7, df =
3, P < 0.001); a smaller proportion of parties reported some sort of temporal deviation in 2010
(35.5% versus 41.5%), and a larger proportion of parties reported some sort of spatial deviation
in 2010 (56.4% versus 49.2%). Mean temporal deviation in this study was -1.02 days, compared
with values observed in the 1970s of -0.58 days in Yosemite (van Wagtendonk & Benedict,
1980) and -0.60 days in Sequoia and Kings Canyon national parks further south in the Sierra
Nevada (Parsons et al., 1982).
Our model predicted that season-total use would be overestimated by about 15% without
accounting for the difference between intended and actual trip duration (Table 1), compared
with 23% estimated for Sequoia and Kings Canyon by Parsons et al. (1982). Itinerary deviations
resulted in a lower fractional discrepancy between intended and actual use in our study because
mean party size was smaller (2.9 versus 3.3 visitors per party), mean actual trip duration was
smaller (2.1 nights versus 4.5 nights), and the fraction of parties reporting temporal deviation
was smaller (35.5% versus 44.7%) in our study than in that of Parsons et al. (1982). Similarly,
mean party size and trip duration of Yosemite wilderness parties in the 1970s were smaller than
we observed by 0.34 visitors per party and 0.46 nights per trip, respectively (van Wagtendonk &
Benedict, 1980). In general, smaller party sizes, shorter intended trip durations, and decreased
probability of temporal deviation decrease the relative difference between use estimates made
from intended trip itineraries and those made from actual itineraries, but the 15% discrepancy
we estimate in overall use is still substantial from a management standpoint.
Visitor management systems that use trailhead quotas rather than wilderness zone or
campsite-specic quotas are designed, in part, to allow visitors the freedom to roam and to
give visitors the right to alter their plans serendipitously. Such systems can maximize freedom
to visitors once inside the wilderness, consistent with wilderness experience and resource
constraints (van Wagtendonk & Coho, 1986). This may increase the potential of a wilderness
to provide visitors with a sense of inspiration, escape, and/or autonomy. This study conrmed
that visitors are altering their trips (i.e., deviating from their intended trip itineraries) in both
time and space, thereby demonstrating both the necessity for managers to allow, and proof
of visitors exercising those rights to, itinerary freedom. However, the frequency with which
wilderness zone use exceeded nightly capacity was much lower when the effects of deviation
were incorporated. Thus management actions to lower visitor use of certain zones, if informed
by permit data without accounting for itinerary deviations, are likely to be overly conservative.
Although shorter trip durations do not necessarily lead to zone capacities being exceeded,
they do lead to a greater fraction of total use in zones that are readily accessible from trailheads.
Three such travel zones that are among the eight most heavily used zones today were not in
the top eight in the 1970s, providing some evidence that a preference for shorter trips may be
leading to increased use in zones close to trailheads. Redistributing some of these shorter trips
to parts of the park that receive less use could lower the probability of exceeding zone capacities
under current use levels and trip characteristics.
44
Use Scenarios and Zone-trailhead Relationships
The current-use scenario demonstrates the model’s use as a tool to monitor current
conditions. This scenario accounts for itinerary deviation and can also include USFS
trailhead contribution to produce our best estimate of actual spatiotemporal distribution of
wilderness visitor use in 2010. The redistribution scenario showed how the model can be
used as a predictive tool to test various management scenarios. Our redistribution trailhead
quota solution illustrates just one of many ways in which current use can be redistributed
to lower-use areas in the park to achieve substantially lower probabilities of exceeding
zone capacities, without changing overall amount of use, temporal distribution of use, or
any other party or trip attribute. By lowering trailhead quotas at nine of the most popular
trailheads, and redistributing an average of 3,575 parties annually from those trailheads
to less popular trailheads, we simulated a condition in which the current level of use is
still accommodated, but the probability that use would exceed zone capacities was greater
than 30% in only eight out of 8,109 possible zone-nights, compared with 126 zone-nights
under current conditions. This suggests that trailhead quotas can be a viable approach to
managing visitor use in wilderness.
The maximum-allowed-use scenario shows the model can be used in a more
experimental sense, testing conditions that may not be truly feasible but that still may
provide insight into the system. It allowed us to calculate the system’s inherent zone use-
trailhead relationship, unconfounded by visitor preference for particular trailheads. Had we
selected trip itineraries from a xed set, no matter how large, the model would not have
retained the full complexity of this relationship.
We found that on some nights, some wilderness zones likely receive a level of use
that exceeds their stated overnight capacities. We produced a tool that allows managers
to accurately determine trailhead quotas that bring visitor use levels in overused zones
back down to capacity, while still accommodating the same overall amount of wilderness
visitor use. It is ultimately up to managers to decide how best to use the modeling tool
provided, but it may be worth noting that a previous study using stated-choice modeling
found Yosemite visitors would be willing to accept a lower chance of receiving a permit in
order to gain improvements in other conditions, such as having fewer encounters with other
visitors during their trips (Newman, Manning, Dennis, & McKonly, 2005).
Under current visitor use levels and spatiotemporal distribution, most wilderness
travel zones receive the majority of their use from only a few trailheads; 18 of the 53
zones receive over 50% of their use from one trailhead. Only a relatively small part of
this observed zone use-trailhead relationship is determined by visitor preference in time
and space. The similarity in the relationship between zone use and trailhead of origin
across the three scenarios (Figure 5) shows that there is an inherent relationship between
zone use and trailhead of origin that is determined by the geography of the park, and the
physical capabilities and behaviors of wilderness users in selecting routes and camping
locations. The simulations showed that even after removing the effect of visitor preference
for trailheads or redistributing visitors to less popular trailheads, certain trailheads are still
the primary source of use in particular zones.
Filling every trailhead’s quota on every day under the maximum allowed use scenario
resulted in visitor use that totaled only 54% of the sum total of the wilderness zone
capacities. This might suggest a disconnect between the trailhead quotas and the wilderness
capacity, calling into question the trailhead quotas as a viable basis for managing visitor use
of the wilderness. However, allowing visitors the freedom and autonomy to decide where
to camp makes it impossible to perfectly match these two measures. Most of the unused
capacity is in remote areas of the park that receive little use. The quotas for the trailheads
that serve those zones could be increased, but that would not translate into higher use in
those “underused” portions of the park; it likely would only create additional overcapacity
issues in the zones closer to those trailheads.
Requiring overnight users to camp in designated campsites or in predetermined
wilderness travel zones, and/or to adhere to xed itineraries without the freedom or
45
exibility to modify their trip spatially or temporally to adapt to changing conditions
or desires, would achieve a more predictable spatiotemporal use distribution across the
wilderness landscape. This could help reduce use impacts at popular locations, maximizing
the naturalness and undeveloped values of wilderness called for in the Wilderness Act.
The trade-off, however, is a diminished sense of the “outstanding opportunities for
solitude or a primitive and unconned recreation” also called for by the Wilderness Act.
Although trailhead quotas are a regulatory action, they are applied to visitors prior to
entering the wilderness, thus preserving to a greater degree the autonomy and “unconned
recreation” many wilderness visitors seek. The increased understanding and predictability
of visitor use patterns afforded by a computer simulation model may make trailhead
quotas an effective and reasonable compromise between the sometimes competing values
of regulation to maximize resource protection on the one hand, and preserving visitor
freedom and autonomy on the other.
Management Implications
We conclude that the inherent relationship between wilderness travel zone use and
trailhead use has changed very little since the inception of the quota system in Yosemite,
given that this relationship is based primarily on geography, behavior and physical
capabilities of wilderness users, and the quotas themselves. Thus, the original quota system
remains a viable basis from which to determine future management. More importantly,
our redistribution scenario illustrates that some portion of the current visitor use could be
redistributed to less popular areas in the park to achieve substantially lower probabilities of
exceeding zone capacities, without changing overall amount of use, temporal distribution
of use, or any other party or trip attribute.
However, it is difcult to condently predict how visitors seeking permits would
react to reduced permit availability at popular trailheads. Quotas could be increased at
other trailheads to allow for the same total amount of wilderness access, but those other
trailheads are clearly not as popular with visitors. Would visitors accept a less preferred
trailhead, one that likely would not lead to their desired destination? Would they decline
to take a wilderness trip at all if they could not gain access via their preferred trailhead?
On the other hand, this is not fundamentally different than the system that is now in
place. Visitor use currently is being redistributed, relative to spatial demand, by way of
the trailhead quotas. The most popular trailheads in Yosemite have daily quotas that are
certainly lower than the demand for permits for those trailheads. Wilderness visitors very
commonly end up choosing trailheads that are not their rst choice when they see the
“Trailhead Full” sign on the list of trailheads in the Wilderness Centers where they obtain
their permits. In this sense, our redistribution scenario is simply an extension of the current
management strategy.
Another possible outcome of signicantly reducing use at some popular trailheads is
that visitor use could increase in other portions of the wilderness that are currently more
lightly used. This could increase visitor use impacts to resources in those more pristine
portions of the wilderness, as well as decrease opportunities for solitude, and in the long
term could narrow the range of conditions and opportunities available in the wilderness
(Cole, 2001). Before any attempt is made to redistribute use, managers would want to think
very carefully about which low-use portions of a wilderness are truly underused, in the
sense that they could accommodate more visitor use without unacceptable consequences,
and which portions are low-use by design (i.e. by management objective) and should
remain as low-use areas.
A product of simulation modeling such as ours is that managers have a more
accurate, and more quantitative, understanding of existing conditions. The vastness of the
wilderness, and its many access points, limits the ability of managers to precisely monitor
visitor use conditions, particularly the number of visitors camped overnight in any given
wilderness zone. A simulation model can generate reliable estimates of these hard-to-
measure variables, providing managers information about current use conditions to inform
establishment of a baseline of wilderness character. The spatiotemporal model outputs
46
allow managers to identify the place and time that use occurs, especially when and where
there is concern that concentrated use could lead to conicts among different user types
or impacts to fragile ecological resources or wildlife habitat (Lawson et al., 2006). Other
model scenarios can provide sideboards to facilitate the prescriptive process of selecting
management alternatives. With such a model, managers can evaluate the effectiveness of
alternative management strategies (e.g. alternative trailhead quotas) more efciently and
with less risk than with trial and error, and can evaluate potential increased or decreased
visitor use demands and develop informed plans to prepare for those potential conditions
(Lawson et al., 2006).
Limits on visitor use may be needed when demand is very high and other management
tools alone are inadequate to protect resource and experiential conditions. Trailhead quotas
may be an effective externally-applied management tool that allows for more visitor
autonomy once in the wilderness. For trailhead quotas to be effective, however, managers
must have a very good understanding of the relationship between the trailhead of origin
of trips, and the resulting spatiotemporal distribution of users. By incorporating novel
approaches to simulating visitor itineraries dynamically and modeling observed tendencies
for visitors to deviate from intended itineraries, we have developed a simulation model
capable of quantifying the dependence of wilderness zone use on trailhead of origin, which
is the key piece of information necessary for managers to successfully apply a trailhead
quota system. Simulation results show that in a large, complex, and heavily used wilderness
such as Yosemite, adjustment of trailhead quotas can be a frontcountry management tool
that is effective in achieving backcountry management objectives. In any wilderness setting,
there will always be certain destinations that are more popular than others; our modeling
approach allows managers to quantify the degree to which management objectives can be
met by redistributing use away from popular areas and towards less heavily used areas.
However, to enhance the utility of any model, it is advisable that managers seek more
information about how visitors select trailheads and how they respond to full quotas. While
our model simulates how visitors behave once assigned to a trailhead, it would be improved
if we learned more about why visitors choose certain trailheads and travel itineraries. With
such information, managers could make more informed choices when evaluating different
visitor use scenarios to simulate with the model, and could improve their own decision-
making processes when choosing between education or regulation strategies for wilderness
management.
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