Final Report
Assessing five field sampling methods to
monitor Yellowstone National Park’s
northern ungulate winter range: the
advantages and disadvantages of
implementing a new sampling protocol
Pamela G. Sikkink1, Roy Renkin2, Geneva Chong3, and Art Sikkink4
What the study revealed
The five field sampling methods tested for this study differed in richness and Simpson’s
Index values calculated from the raw data. How much the methods differed, and which
ones were most similar to each other, depended on which diversity measure and which
type of data were used for comparisons. When the number of species (richness) was
used as a measure of similarity, the historic method captured significantly fewer species
than the Daubenmire, modified-Whittaker, or Forest Inventory and Analysis (FIA)
methods but similar numbers as the small-scale nested circular plot. When Simpson’s
Index was used to compare similarities, only the large-scale modified Whittaker method
showed significantly greater values than the small-scale nested circles; no differences
were observed among the other methods. If frequency data instead of cover data were
used to compare similarities among methods, the historical method had significantly
higher evenness, skewness, and kurtosis on average than all other methods. If a
correspondence measure based on diversity was used, the historic method was most
similar to the Daubenmire protocol.
Even though the plant communities across the northern range contained many species
and each appeared distinct during sampling, only the low elevation sites (n=3) in the
Gardiner Basin were significantly lower in community diversity; comparisons among the
other sample locations (n=16) were not significantly different. Because diversity
measures may be the same for very different communities, we used a statistical
ordination technique that placed similar communities near to each other in 3-D space.
The ordination shows which locations had different plant communities because it was
1
Research Ecologist, U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station,
Missoula Fire Sciences Laboratory, Missoula, MT and corresponding author (psikkink@fs.fed.us)
2
Vegetation Specialist, U.S. Department of Interior, National Park Service, Yellowstone National Park,WY
3
Research Ecologist, U.S. Department of Interior, U.S. Geological Survey, Northern Rocky Mountain Science
Center, Bozeman, MT
4
Volunteer (2009-2012), U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station,
Missoula Fire Sciences Laboratory, Missoula, MT
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based on the entire list of species at each location (and their frequency or percent cover
abundance) instead of a diversity value calculated from the species list and abundance.
Using ordination, the biota captured by the historic method was similar to the biota
captured by contemporary methods; the most difference between methods occurred in
areas where the historic transects were parallel to ecotones. Methods that sampled
larger areas than the historic method were able to capture diversity of the ecotone
areas. Ordination was also useful in capturing the variation in the cover of grass and
annual species from one sampling year to the next.
The difference in time and effort required to complete each method will be important
considerations that determine future monitoring directions in the park. We recommend
that historic methods continue to be employed alongside a contemporary method that
meets the park’s abilities to expend time, effort, and skills for monitoring. We also
recommend that efforts continue to find a relationship between data collected using
historic and contemporary methods. Finally, we recommend that an interdisciplinary
team of subject-matter experts be convened to assist the park in establishing explicit
goals, objectives, and procedures for implementing a long-term vegetation monitoring
program. The results of this study should inform such an effort.
Introduction
In 2002, the National Resource Council (NRC) recommended that Yellowstone National
Park (YNP) find a new, robust method for monitoring vegetation in its northern ungulate
winter range that could distinguish between several change factors affecting plant
community composition, including grazing, climate change, and natural and
anthropogenic disturbances (National Research Council 2002). To meet this challenge,
several small- and large-scale field sampling methods were installed between 2009 and
2012 to evaluate the ability of each method to capture 1) species composition and 2)
species coverage within diverse plant communities of the northern range. The methods
included a 100-ft line-intercept (Parker 1954), which was used almost exclusively in the
past, a 20 x 50 cm Daubenmire frame (Daubenmire 1959), a small circular nested plot
(Barnett et al. 2007), a modified Whittaker plot (Stohlgren et al. 1995), and a multi-circle
Forest Inventory and Analysis (FIA) Phase 3 plot design with 12 1-m2 quadrats
(http://www.fia.fs.fed.us/program-features/basic-forest-inventory/ ).
The goals for this study were similar to the goals that drove establishment of the
ungulate exclosures and permanently-marked transect lines in YNP in 1957; that is, to
find a sampling method that would best (1) describe the diversity in vegetation across
the northern winter range and (2) detect any change in vegetation composition and
structure between years and sample sites. The NRC recommendation in 2002 elevated
the emphasis on detecting the causes of change, whether they were climate-driven or
disturbance-driven, so the permanent transect lines and ungulate exclosures that were
established in the park in 1957 have become even more critical to identifying grazing
versus climatic factors in monitoring efforts. The importance of detecting cause and
effect has also become important to YNP to inform management decisions on herd sizes
(based on carrying capacity of the vegetation), invasive weed management, plant
restoration, and park response to climate change in the 21st century.
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The objectives of this study were:
1. To evaluate how each of the sampling methods captures species composition
and biodiversity in plant communities of the northern ungulate winter range.
2. To evaluate whether the historic vegetation sampling method is sensitive
and/or robust enough to use in interpreting vegetation-change factors in longterm data.
3. To determine the feasibility of developing a crosswalk between past and future
data.
4. To determine whether one sampling method is sufficient for capturing changes
in vegetation species and abundances throughout the entire northern ungulate
winter range.
5. To evaluate the tradeoffs of time, effort, knowledge, and financial costs
associated with each sampling method to monitor for vegetation change in the
future.
Background
In the early- to mid-1900s, Yellowstone National Park (YNP) was the center of heated
debates over whether its ungulate herds were exceeding the park’s capacity to support
them and whether the vegetation resource was being irreparably degraded for future
generations. To address public and neighboring rancher concerns, seasonal killings of
elk and bison within the park became common practice to keep the ungulate population
within predetermined limits (Barmore Jr. 2003; Yellowstone National Park 1997). The
“range war” that resulted for and against the culling of these animals, and for or against
natural regulation of herd sizes (Cole 1971; National Research Council 2002), led park
managers to design a natural experiment to determine if there really was scientific
evidence that would support the claim that the northern ungulate winter range was
being grazed beyond its carrying capacity.
In 1957, the new natural experiment included five range exclosures that were
constructed along the length of northern winter range (Fig. 1). Their sole purpose was
to attempt to answer the questions on grazing and carrying capacity of the northern
range vegetation (Edwards 1957). In 1962, three more exclosures were erected to
coincide with new herd-reduction measures. Inside and outside of the exclosures, park
managers installed permanently marked transect lines to monitor vegetation. The
historical sampling method used to evaluate vegetation change was the Parker 3-step
point-intercept method (Parker 1954; Parker and Harris 1958). The Parker 3-step was
rigorously tested in the mid-1950s to insure that it would adequately capture vegetation
change over the five years that park managers expected the experiment to run (Parker
and Harris 1958). Several transects were sampled prior to beginning the natural
experiment in 1957 using the Parker 3-step method. These transects were established
between 1954 and 1957 at six sites (Fig. 1) and were referred to as “free range”
transects because they were open to grazing.
More than 50 years after the natural experiment began, it is still running and the same
sampling method is in use to monitor the vegetation. Over the past 55 years, several
researchers have sampled the permanently marked transects associated with the large
ungulate exclosures to evaluate the effects of ungulate grazing on the park’s sagesteppe ecosystem (Barmore Jr. 2003; Denton 1958; Denton and Kittams 1958; Houston
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1982; Sikkink 2002; Sikkink and Alaback 2006). While the historical method is simple
and rapid to administer, it is perceived to lack robustness because of its minimal spatial
extent and opportunistic monitoring schedule. The monitoring schedule for the
northern winter range over the past 50 years has been intermittent, at best, and
conducted by students, volunteers, or park employees with varying knowledge of the
plants and minimal experience in vegetation monitoring. In 2002, the National Resource
Council recommended that a new monitoring method be found that would better assess
changes in vegetation due to climate change, grazing, or other disturbances that affect
vegetation in the park (National Research Council 2002).
Fig. 1. Sample sites across the northern winter ungulate range (red circles). Inset shows
location of 1998 winter range boundary (stippled) (courtesy of YNP Geospatial Center),
sample locations, and national forests surrounding the park that are also important for
ungulate winter range.
Today, there is a wealth of monitoring data for the northern range covering over 50
years. Numerous research projects exist that were based on the exclosures and
permanent transects; some used the historic sampling method and some did not.
Controversies still exist surrounding vegetation condition in the northern range because
of current densities and distributions of the bison, elk, pronghorn and other ungulate
herds in YNP (Buffalo Field Campaign 2012; Lundquist 2012). The new range wars
center on whether the depletion of willow, aspens, cottonwoods, native grasses, and
even sagebrush are due to changes in herd sizes. The answer to the question of
whether grazing or climate is central to current vegetation changes in the modern range
wars is more important than ever; and the historic exclosure data, along with a sampling
approach that provides comprehensive data on biodiversity and plant community
composition across the northern ungulate winter range, are critical to answering
questions on change. The question on whether the historic monitoring technique is
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effective at capturing those biodiversity changes and whether exclosures are effective
to determine the effects of grazing is still highly debated (Stohlgren et al. 1999). When
the NRC recommended using a more rigorous method to monitor vegetation change,
few studies were available that compared biodiversity captured by the historic method
with biodiversity captured by other sampling methods (Stohlgren et al. 1998).
Methods
Field data
Data were collected from sampling methods that included the historic Parker 3-step, a
small circular plot with nested quadrats (Barnett et al. 2007), 20 small Daubenmire
frames (Daubenmire 1959) , a modified Whittaker plot (Stohlgren et al. 1995), and a set
of four circular plots containing nested quadrats designed for the Forest Inventory and
Analysis (FIA) program (http://www.fia.fs.fed.us/program-features/basic-forestinventory/). Each method covered a different spatial scale, but all were centered on a
historic, permanently-marked transect so the methods covered the same area and could
be repeated in any future monitoring program (Fig. 2).
E. Forest Inventory and
Analysis Plot -shown 1/2
scale (12 microplots, 4
subplots)
D. Modified Whittaker Plot
(10 microplots, 3 subplots)
C. Daubenmire Plot
(20 frames = 20 microplots)
B. Nested Circular Plot
(3 microplots, 1 subplot)
A. Parker Cluster
(3 transect lines combined =
300 microplots; if 2
transects, microplots=200)
Fig. 2. Schematic layout of a Parker transect line (A) overlain by each contemporary
sampling method. The center rebar of the 100-ft (30.48 m) Parker transect line (lower
level) is used to center each method. The Parker method encompasses 0.03 m2
analyzed/transect. Contemporary methods include a nested circular plot (B)
encompassing 3 m2 analyzed/plot; a set of 20 Daubenmire frames (C) with 2 m2
analyzed/plot; a modified Whittaker plot (D) with 10 m2 analyzed/plot and a species list
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constructed with additional subplots and the entire plot area; and a Forest Inventory
and Analysis (FIA) plot (E) with 12 m2 analyzed/plot. Groups of one to three Parker
transect lines with similar grazing potential, slope, and aspect were designated as
“clusters” in 1958. Whittaker plots were centered on the center rebar of the Parker line
but rotated to align with the environmental gradient. FIA layer is diagrammed at ½ scale
to fit within the block.
Time to sample each location was recorded to gauge total time needed to monitor each
site using a particular method. Time to complete included (1) setup, (2) sampling and
(3) total effort (i.e., removal of tapes, flags, etc.). Hikes to and from sample locations
were not included in total efforts. Four of the methods were sampled almost exclusively
by one field crew from 2009 to 2012. A second crew sampled all of the small circular
plots with nested quadrats in 2009 and the two FIA plots at the Blacktail exclosure in
2010. 2010 and 2012 data for the small circular nested plots were pulled from the
center FIA circle sampled in those years. No samples were collected in 2011.
Historic Parker 3-step
The Parker 3-step (hereafter referred to as the Parker method, Parker transects, or
historic method) is the historic monitoring technique for the northern ungulate
winter range of Yellowstone National Park. It is a modified point-intercept method
devised to sample vegetation and substrate characteristics along a permanently
marked 100-ft line (30.48 m) (Parker 1954). Unlike strict point-intercept sampling, a
loop was used for each measurement instead of a point and the modification was an
attempt to add area to the sampling method.
Vegetation was sampled in the Parker method along a 100-ft line using a ¾ in. (1.9
cm) diameter loop. The loop was lowered to the ground at each foot mark along
the 100-ft line and plants whose basal portion fell within the loop were recorded as
“hits”. The “hits” could consist of shared species if plants are small and the basal
portions of both fell within the loop. If vegetation was not present within the loop,
the “hit” was recorded as substrate. Substrate elements included bare ground,
pavement (rocky hardpan surface), rock (>7.6 cm), moss and lichen combined, and
litter. Substrate elements were never recorded as a shared hit. Live elements (i.e.,
moss and lichen) took precedence over the non-living substrate elements when
recording. For the non-living substrate, the element that covered the most area
within the loop was recorded. If shrubs extended over the transect line at a foot
mark, the shrub species was recorded as “overstory.” Overstory was not a factor in
data analysis for the Parker transects in this study.
Each Parker transect was originally established as part of a “cluster” group (Fig. 2A).
Clusters had similar grazing potentials, slopes, and aspects. They existed inside and
outside of exclosures and were comprised of one to three transects per cluster
depending on location. For this study, all data for the Parker method were summed
and averaged by the cluster group. Clusters were also summed and averaged for
the “free-range” transects by combining the multiple transects for each sample
location.
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Parker transect data were most appropriate for calculating frequency or
percentages of species and substrate, although coverage calculations were possible.
In this study, frequency and cover data for the Parker method were equivalent.
Each loop was considered a “microplot” and no sub-plots existed. The total area
sampled along each Parker transect was 0.32 ft2 (0.03 m2).
Circular plot with nested quadrats
The small circular plot is 7.23 m in diameter and contained three 1 x 1 m sampling
frames (quadrats) within its circumference (Fig. 2B). Each of the 1 x 1 m sampling
frames within the circle were placed 4.57 m from the circle center at 30o, 150o, and
270o off due north (Fig. 2b). To sample the frames, visual estimates to the nearest
1% were made for all species and substrate elements. In addition to estimates of
cover within the sampling frames, visual estimates of cover were made to the
nearest 1% for each species within the entire circle. The full circle covered 168.2 m2
and was considered a subplot and used mainly for the species tallies in this study.
The 1x1 m quadrats sampling frames were considered “microplots” and used in all
data analyses. The total area sampled in microplots of the small circular plot was 3
m2.
Daubenmire small frame
This sampling method used a 0.20 x 0.50 m sampling frame placed along one side of
the historical transect (Daubenmire 1959). Frames were started at zero with the
long edge aligned along the 100-ft tape (Fig. 2C). Subsequent frames were placed
every five feet along the transect line for a total of 20 samples. Within each frame,
percent cover of all species and substrate elements were visually estimated using a
1-6 cover scale. Estimates of plant and substrate coverage often totaled more than
100% because species overlapped. Only the vegetation portion within the frame
was estimated if the base or foliage extended beyond the frame edge. In addition to
the substrate variables required by the historic method, the Daubenmire method
required cover estimates for persistent litter. All Daubenmire estimates were
converted to the mid-point of each of the six classes to establish the cover values
for all species and substrate elements. Each plot frame was considered as a
“microplot” for this study and there were no sub-plots. The total area sampled
along each Daubenmire transect was 2 m2.
Modified Whittaker plot
The modified Whittaker plot is a common contemporary sampling method covering
50 x 20 m (Stohlgren et al. 1995). It is comprised of 10 0.5 x 2 m, two 2 x 5 m, and
one 5 x 20 m subplot nested within the 20 x 50 m plot. Percent cover of all species
and substrate was visually estimated to the nearest 1% within the 0.5 x 2 m plots
(Fig. 2D). In addition to the substrate variables required by the historic method, the
modified Whittaker method required cover estimates for persistent litter. Only
presence/absence data were collected for plants within the 2 x 5 m subplot, the 5 x
20 m subplots, and the full 20 x 50 m plot, all of which were used for species counts
in this study. Each small 0.5 x 2 m subplot was considered a “microplot”; all of the
larger plots were considered sub-plots. The area sampled for the entire method
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was 1000 m2. The area sampled by the microplots and used in all statistical analyses
was 10 m2.
Forest Inventory and Analysis (FIA) plot
The FIA plot consists of four circular plots with nested quadrats (Fig. 2E). The
method is currently being used across the United States for inventory and
monitoring of forests, shrublands, and grasslands. FIA plots for this study were
established according to standard FIA methods for Phase 3 sampling
(http://www.fia.fs.fed.us/program-features/basic-forest-inventory/). Species and
substrate were visually estimated for the 1 x 1 m quadrats and the entire 7.28 m
diameter circles to the nearest 1% as described above. In addition to substrate
cover estimates required by the historic Parker 3-step method, cover estimates in
the FIA plots included dead wood and dung. The total area sampled for this method
was 672.7 m2. The full circles were considered subplots. The 12 1 x 1 m quadrats
were considered “microplots” for analysis in this study. FIA samples covered a total
area of 12 m2.
Data analysis
Analyses for this study were conducted on frequency data, percent cover data, and on
several biodiversity measures calculated from the frequency and cover data including
richness5, Simpson’s diversity index6, Shannon’s diversity index 7, and evenness8.
Statistical analyses used the microplot data; unique species analyses used the entire plot
area. Differences between methods primarily focused on richness (i.e., the number of
different species represented in a field sample or ecological community) and Simpson’s
diversity index (i.e., a measure of the likelihood that two randomly chosen plants from a
sample unit or ecologic community would be different species) (McCune and Grace
2002). Data sets included the following:
Frequency data of species and substrate were computed for each sample site
based on the number of times a species or substrate occurred in all of the
microplots that comprise a method.
Percent cover of each species or substrate was calculated as an average of all
cover estimates from the microplots that comprise a method.
5
The diversity measure general form is
, where D=diversity, p=proportion of
individuals belonging to species I, and s=number of species; if a=0, then D o = number of species in
a sample unit or richness. Therefore, richness is just a count of species.
6
If a=2 in the general diversity form, then
results in the diversity form of
Simpson’s index, which is the likelihood that two randomly chosen individuals from a sample
unit will be different species.
7
The Shannon-Wiener Index quantifies the uncertainty, or surprise, associated with correctly
predicting which species will be drawn next in a string of draws. It is calculated as
in PCOrd, which essentially is the log of the number of species of equal
abundance.
8
Evenness is a measure of the relative abundance of the different species making up the
richness of a sample unit. It quantifies how equal the species abundances are. As calculated in
PCOrd, evenness is Pielou’s J or
, where H’ is the Shannon-Wiener Index and S is the
average species richness.
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Biodiversity measures were calculated within PCOrd (McCune and Mefford
1999) from the frequency or cover species data obtained from microplots within
each method.
When locations were sampled in multiple years over the three sample years, diversity
measures were calculated separately for each sample year to incorporate year-to-year
changes within the data set. The five sampling methods, and their separation by year,
resulted in 147 distinct method/location/year records for each analysis. Data were
analyzed for species characteristics at each location and differences among methods,
locations, and plant communities9.
For all comparisons, the Parker transect data were analyzed by grouping individual
transects into their originally designated clusters of one to three transect lines. Species
and substrate frequency and cover values for the clusters were formed by averaging the
values from individual lines that formed each respective cluster.
Data distribution, tests for normality, homogeneity of variance, and significance tests
among groups were tested within SAS 9.3 (SAS Institute Inc. 2008) using non-parametric
analyses. Tests for normal distribution were conducted within SAS on groups of unequal
size using the Shapiro-Wilk test (Shapiro and Wilk 1965). Homogeneity of variance was
tested with Brown and Forsythe’s test (Brown and Forsythe 1974), because it is more
robust for non-normal distributed data (SAS Institute Inc. 2008) than either Levene
(Levene 1960) or Bartlett tests (Bartlett 1937; Snedecor and Cochran 1989). KruskalWallis Rank Sum tests (Kruskal and Wallis 1952) were conducted within SAS to
determine if groups were significantly different. Groups that tested positive for
significant differences in their means with Kruskal-Wallis tests were further examined
with Dunn’s Pairwise Multiple Comparison tests (Dunn 1961) in SAS (Elliot and Hynan
2011) to determine which groups within the methods and location tests were different.
All statistical analyses were considered significant if p<0.05.
Descriptions of species characteristics
The difference between the number of species captured in the microplots and the
number of species captured by an entire method was described using tallies of
unique species. The tallies gave a better picture of the ability of a method to assess
species richness on the landscape because the sub-plot data from each method,
which were comprised of presence-absence data or estimates of species cover for
whole plots, was ignored in all PCOrd calculations of biodiversity. Therefore, the
actual number of species captured by each sampling method was under
represented in most statistical analyses.
Sample data and information on species names and phenologic characteristics were
stored in linked tables and queries within an Access database (Microsoft
Corporation 2010). Filters were used to output information on species
9
A plant community is an assemblage or association of populations of two or more different
species occupying the same geographical area.
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characteristics by location, method, or both. The information on species
characteristics by method and locations was summarized in tables and bar charts.
Tests for differences among methods
To compare how the five sampling methods detected values of biodiversity, the
diversity calculations were analyzed separately by location and sample year. A
Skillings-Mack statistic for non-parametric, unbalanced, incomplete (i.e., missing
data) block sample designs was used to test for differences among the methods.
The statistic was run within SAS using procedures by Cunningham (2010). Tests
were run on the 2009 sample methods as a group; and on the 2010-2012 methods
as a group. Within each statistical test, a weighted sum of centered ranks was
calculated that indicated the rank order of observations, such as which had the
highest richness or Simpson’s Index values and which methods were ranked closest
to each other for each test. Box plots were constructed to visually show the range
and differences in means among the five methods.
Diversity measures were also compared among the historic method and
contemporary methods using graphical correspondence measures. Plot diversity
measures obtained from the Parker method were plotted against the same diversity
obtained from a contemporary method on a scatterplot where a perfect fit between
Parker diversity measures and a contemporary method was marked by a 1:1
correspondence line. The plots were analyzed for the amount of scatter and the
distance from the correspondence line to determine similarity of method results.
The correspondence line was also compared to a linear regression line through the
data points for each method to determine whether there was a relationship that
might be exploited to relate historic and contemporary methods.
Tests for differences among locations
Only Parker 3-Step samples were used to test whether there were differences in
diversity between the inside and outside of exclosures or the free range areas. The
Parker transects were sampled each year of the study, both inside and outside of
exclosures, and by the same crew; therefore, the variation in the plots was
theoretically due mainly to year-to-year differences in vegetation that could be
detected with this method. Parker transect data were coded by location (inside
exclosures, outside exclosures, free range, etc.) and processed together using
Kruskal-Wallis tests to detect differences in group means. 1958 and 1962 exclosures
were combined for the inside samples at each respective location.
Tests for differences among communities
Because plant communities can have similar numbers of species in various locations
but very different community compositions, diversity measures alone can be
inadequate to show the variation in species that would need to be monitored across
the northern ungulate winter range. To determine whether the biota of the
northern winter range divided into distinct biotic communities and whether
different sampling methods captured the community composition similarly, an
ordination was conducted using the percent cover data for the biota. Ordinations
use a distance measurement to calculate how similar samples are in n-dimensional
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space. Samples that plot close together in n-dimensional space are more similar in
composition than those that are separated by great distance (McCune and Grace
2002). For this analysis, a non-metric multidimensional scaling (NMS) ordination
was chosen (Kruskal 1964; Mather 1976). A number of combinations of species data
(from all methods, locations, and years) and substrate data (using all Parker 3-step
categories, slope, elevation, and aspect) were tested for the NMS, but the best
representation of the biotic community was obtained when the ordination was run
with only species data. The relationships of the substrate and the environmental
variables with the species assemblages were explored with correlation analysis.
NMS was run within PCOrd using Sorensen (Bray-Curtis) distance and the built-in
automated process (see McCune and Grace (2002) for a full description of the
automated process). One analysis incorporated cover data from all locations, all
methods, and all years. A second analysis incorporated just Parker transect data
from all locations and all years to show how one method could vary from one
sampling year to the next. The data set for all methods consisted of 147 records
with 205 species; the data set for the Parker clusters consisted of 125 records with
113 species. Prior to running each ordination, the raw frequency or percent cover
data were transformed with a simple logarithmic transformation that put the data
on similar relative scales but still preserved rank orders.
Results
During the three years of sampling, data were collected from 125 individual Parker
transect lines that were grouped into 44 individual clusters, 36 nested circular plots, 32
Daubenmire plots, 8 modified Whittaker plots, and 6 FIA plots. We summarized the
sampling results in several ways. First, we described the general characteristics of plant
communities for the northern winter range as a whole. Second, we grouped and
summarized biodiversity data by sample method to examine how well each sampling
method detected the variety of species present in the winter range. Third, we grouped
all data to summarize species presence and abundance inside and outside of exclosures
and for the free range areas. Finally, we used ordination graphs for individual plots to
summarize similarities in species composition and abundance within the plant
communities and their changes over time.
Statistical summaries for each group of data sets are available in Appendix A (Tables A1A4). Regardless of how the data were grouped, distribution analyses, Shapiro-Wilk, and
Brown-Forsythe tests showed that most of the diversity measures for each group were
normally distributed and that they had distinct differences in group variances (Appendix
A, Table A5-A6). Within each data set, however, one or two elements were found to
have non-normally distributed data or equitable variances, which resulted in a decision
to use non-parametric tests to determine if group differences were statistically
significant. The groups that were not normally distributed or had equitable variances
are discussed in their applicable sections below.
General characteristics of the northern winter range biota
The total number of species captured by all microplots and sub-plots for all sample
methods during the three-year study was 205. This tally of species was not intended to
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be a comprehensive list of flora present within the park or the northern winter range. It
only includes the biota encountered during three years of sampling in a restricted
number of locations. Of the number of unique species tallied at each sample location,
forbs comprised 55 - 65%. Grasses comprised about 20% of the total numbers. The
proportions of grasses, forbs, and shrubs were fairly consistent across all locations.
Although mosses and lichens were an important component to ecological function in all
sample areas, they were not individually identified for this study; rather they were
grouped together as a moss/lichen entity during sampling and there is not a true
measure of their diversity within the sampled areas.
Differences among methods
Sampling time
The five methods explored in this study took significantly different times to complete
(p<0.05). The average times for set up and sampling for each method were:
Historic method (clusters):
Nested circular plot:
Daubenmire (20 frames):
Modified Whittaker:
Full FIA (4 circular plots):
<1.5 hr
2 hr
3 hr
5 hr
7 hr
None of the sample times included hiking to the locations, finding the permanent
markers used as center points for each method, or identifying unknown plants during
the cover estimation process. All unknowns were given descriptions, collected, and
identified in an office after sampling was complete. A two-person crew was used for all
methods. One crew had 6 years’ of experience working with plants of the northern
range and two of the sampling methods; the second had no previous experience with
the local vegetation but extensive experience using the nested circular plot method in
other geographic areas including sage-steppe.
Species list
The total number of species captured by each sample method is shown in Table 1. The
methods that covered large spatial scales (i.e., the Whittaker and FIA plots) captured at
least 50% more species than either the Parker clusters or the nested circle but they also
occasionally sampled vegetation that was very different from what was intended to be
monitored by the historic method. Lamar In and Junction Butte In (In=inside exclosure)
were prime examples of this problem. Because of the angles and distance off center
that the circular plots were placed, two of the FIA circles were situated in forested
communities or shrub areas that were very different in composition than the areas
sampled by the other two FIA circles or than areas sampled by the other methods used
in this study. As a result, the number of unique species captured at these two locations
appears very high and contains species that are uncharacteristic for these particular
grass and shrub communities (Table 3).
Each method captured approximately the same numbers of species of shrubs, grasses,
and moss/lichen lifeform species (Table 2). The nested circle and Daubenmire captured
the highest number of unique species using similar numbers of plots. The Parker
method captured a similar number of species but with 50% more plots. Forbs were
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Table 1. Total number of unique species captured by each of the five sampling methods across the
northern winter range separated by location and sample year. Where double exclosures exist, “IN”
includes species numbers from inside the 1958 and 1962 exclosures combined. “Out” are matching
locations to IN found outside the exclures. “Free” indicates free-range plots not associated with an
exclosure. Totals include basal and overstory species from each method’s entire area. Sample years
include 2009 (09), 2010 (10), and 2012 (12).
Parker
Year 0
9
1
0
1
2
Nested
Circle
09 10 1
2
Daubenmire
Whittaker
09
09
12
12
FIA
10
Blacktail In
25
23
34
44
14
1
38
36
34
Blacktail Out
24
28
30
40
211
39
36
37
Gardiner In
25
20
29
42
34
36
Gardiner Out
15
21
25
28
Junction Butte In
22
29
29
Junction Butte Out
18
23
30
Lamar In
30
34
39
Lamar Out
15
18
25
24
Mammoth In
27
29
49
42
Mammoth Out
20
18
34
35
Geode Creek Free
31
28
37
36
Blacktail Hill Free
24
24
27
29
Landslide Creek Free
12
18
18
27
23
Game Ranch Free
20
14
17
29
23
27
30
Lamar Horseshoe
Free
Specimen Ridge Free
22
22
20
19
21
33
34
24
--
21
36
31
27
27
28
12
33
2
30
53
45
35
59
632
29
35
42
1
Nested plot data from 2010 and 2012 were constructed by using data from the center circle of each FIA plot. The FIA plots were
measured by different personnel than measured the nested plots in 2009. For 2010 and 2012, only one center circle for inside and outside
locations were measured, whereas four center circles were measured inside the Blacktail exclosure in 2009 and two were measur ed
outside, which explains the large discrepancy in species numbers between 2009 and 2010.
2
Samples include forest and ecotone communities in part.
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Table 2. Unique species captured by each of the five sampling methods identified by lifeform. Sample
locations include only those areas where both the Parker method and a contemporary method were
sampled in the same year. Data includes all basal and overstory species captured within each method’s
entire area. Sample years include 2009, 2010, and 2012.
Method
Parker
Clusters
n
44
Nested Circle
30
Nested Circle
(FIA centers)
6
Daubenmire
32
Whittaker
8
FIA
6
Conifer
Tree
Deciduous
tree
1
1
Evergreen
Shrub
Deciduous
Shrub
Grass
Forb
Lichen
Total
Species
2
8
26
73
1
110
3
14
28
89
1
136
6
15
45
1
67
2
11
28
93
1
1
136
1
13
24
67
1
2
108
2
10
24
68
2
107
Total
205
Moss
captured best by the Daubenmire method; although Whittaker and FIA methods would
probably have been much higher than any of the methods if their sample numbers (n)
were equivalent.
The numbers of unique native and non-native species captured by each method had the
same general relationships among methods as the lifeforms had (Table 3). Daubenmire
and nested circle captured slightly more species in both the non-native and native types
than the other methods. The nested plot extracted from the FIA center had the lowest
number of unique species. In some cases, the low number of species for the extracted
method was because the plots were done in areas of low diversity (e.g., Game Ranch
and Landslide Creek); but in other areas, it may simply relate to the low sample number
overall compared to the nested circles done in 2009. For the Whittaker and FIA plots,
lower than expected total species for these large plots probably reflects the low number
of total field samples completed for this method compared to the small-scale samples.
The total number of non-native species encountered during sampling was 17. Nonnative species were found only within the grass and forb lifeforms; and they utilized a
full range of lifecycles. The highest numbers of non-native species were found on the
mudflats and disturbed areas near Gardiner; however, they were also found at every
other location to varying degrees. The most commonly encountered perennial nonnatives included Bromus inermus (smooth brome), Camelina microcarpa (littlepod false
flax), and Taraxacum officinale (common dandelion). The non-native grasses Bromus
tectorum (cheatgrass), B. japonicus (Japanese brome), and Agropyron triticeum (annual
wheatgrass) were concentrated mainly in the Gardiner sites. However, isolated pockets
of Bromus tectorum and Bromus inermus were also found at Lamar Horseshoe along
with the small annual mustard, Alyssum desertorum (desert madwort). Distribution and
spread of three non-native, invasive species across the northern winter range (i.e.,
Bromus tectorum, Alyssum desertorum, Alyssum alyssoides, and Agropyron triticeum are
covered in a separate report by Chong et al. (2011).
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Table 3. Unique species captured by each of five sampling methods identified by origin.
Data includes all basal and overstory species captured within each method’s entire area.
Sample years include 2009, 2010, and 2012.
Method
n
Number of
locations
sampled
Parker Clusters
44
16
12
90
8
110
Nested Circle
30
16
14
117
5
136
Nested Circle (FIA
centers)
6
4
6
57
4
67
Daubenmire
32
16
13
109
14
136
Whittaker
8
4
10
93
5
108
FIA
6
4
12
87
8
107
Total
205
Non-native
species
Native
species
Unknown
1
origin
Total
unique
species
1
Unknown origin includes species identified to Genus only or plant specimens that were not identifiable in
either the field or lab because of deterioration.
Diversity comparisons
Within the cover data, richness varied from a mean of 15.5 species in the nested circle
plots to 30.7 species in the large FIA plots; mean Simpson’s Index values ranged from
0.76 in the nested circles to 0.84 in the Whittaker plots (see summary statistics for all
the diversity measures using cover data in Appendix A (Table A-1)) . Simpson’s Index
represents a combination of richness and evenness that indicates how evenly individuals
and species are distributed among samples; higher Simpson’s index values indicate both
greater richness and evenness. Richness values were lowest in the Parker clusters and
nested circles (Fig. 3A), but Parker clusters had the greatest spread and highest
Simpson’s Index values (0.46-0.92; see Fig. 3B).
Distribution of all richness data was normal except for the nested circle method
(Shapiro-Wilk p=0.004) (Appendix A Table A-5). Whittaker, and FIA plot data were
normally distributed for the Simpson’s Diversity Index; Parker cluster, nested circles, and
Daubenmire plots were not.
The only analyses that had distinct differences in variance for the five methods was
Simpson’s Index using cover data (Brown-Forsythe homogeneity of variance p=0.335).
All others did not have significant differences in variance, which indicated that the
variances within each method were no different than would be expected from random
samples drawn from a population (Appendix A Table A-6).
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A.
B.
Fig. 3. Box plots showing range of values for A) richness and B) Simpson’s Index for each sampling
method using only cover data. Data encompasses multiple locations across the northern ungulate
winter range and multiple sample years for each method. Boxes show the 25th percentile (lower
line), median (middle line), and 75th percentile (upper line), and the whiskers show the limits for
1.5 times the interquartile range.
The Skillings-Mack non-parametric tests showed significant differences between the
three sampling methods used in 2009 (see Appendix A Table A-7). The weighted sum
values from the Skillings-Mack tests on richness and Simpson’s Index indicate that (1)
the Parker and nested plots are most similar and (2) the Daubenmire method captured
the most richness but had the lowest Simpson’s Index (Table 4). For all five methods
tested between 2010 and 2012, richness was significantly different for all of the
methods but Simpson’s Index was not. The weighted sums again showed that the
Parker and nested were similar and Daubenmire was quite different. They also showed
that the large-scale plots were similar to each other and that they captured the most
richness.
Table 4. Weighted sum of center-ranked values from Skillings-Mack tests to determine
how groups differ among methods using only cover data. All test statistics were
significant except 2010-2012 Simpson’s Index. p-values <0.05 were considered
significant.
Weighted Sums
Response
Parker
Nested
Daubenmire
Whittaker
FIA
Richness
2009
-18.19
-31.31
49.5
-
-
Simpson's Index
2009
17.32
-25.25
7.91
-
-
-12.3
-10.57
0
13.21
6.51
-7.21
-1.41
2.51
9.66
0.41
Richness
Simpson's Index
16
Year
20102012
20102012
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Correspondence between the historic and contemporary methods
With the Parker cluster showing statistically significant differences with the
Daubenmire, Whittaker, and FIA methods, scatterplots were constructed to see how far
off of a 1:1 correspondence line with contemporary methods the Parker cluster plots
were. The scatterplots showed that all methods except the nested circle plotted
consistently above the 1:1 correspondence line using richness measures (Fig. 4); but,
when plotted using Simpson’s Index data, the plots fall on both sides of the
correspondence line in an unpredictable pattern (Fig. 5). Most of the plots were quite
highly scattered, except when there were very few samples (i.e., Whittaker or FIA plots).
When linear regression lines were plotted, most of the regression lines were very
different from the correspondence line. The exception was for Daubenmire richness. It
plotted nearly parallel to the 1:1 line but offset above it (Fig. 4). All other regression
lines were quite different than the correspondence line.
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A.
B.
C.
D.
Fig. 4. Correspondence of historic method (Parker clusters) and four contemporary sampling methods
using the richness diversity measure and cover data. Pairings include: A) Parker cluster vs. nested circle;
B) Parker cluster vs. Daubenmire; C) Parker cluster vs. Whittaker; and D) Parker cluster vs. FIA. The solid
black line is the 1:1 correspondence line. The colored dashed line shows the linear regression through
each data set; and the colored dotted line shows the area of 95% prediction. Regression line r2 values
equaled A) 0.403; B) 0.704; C) 0.182; and D) 0.246.
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A.
B.
C.
D.
Fig. 5. Correspondence of historic method (Parker clusters) and four contemporary sampling methods
using the Simpson’s Index diversity measure and cover data. Pairings include: A) Parker cluster vs.
nested circle; B) Parker cluster vs. Daubenmire; C) Parker cluster vs. Whittaker; and D) Parker cluster vs.
FIA. The solid black line is the 1:1 correspondence line. The colored dashed line shows the linear
regression through each data set; and the colored dotted line shows the area of 95% prediction.
Regression line r2 values equaled A) 0.236; B) 0.527; C) 0.913; and D) 0.083. NOTE: The clumping of a
small number of points for the regression in “C” results in a 95% prediction line that is perpendicular to
the 1:1 line, resulting in a deceptively high r2.
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Differences among locations
Richness and Simpson’s Index measures on Parker transect cover data were highly
variable at each location. The mean number of species for the Parker Cluster cover data
ranged from a low of 12 species in plots outside of the Gardiner exclosures to a high of
29 species at Geode Creek (GO and Y6 in Appendix A, Table A-4). The greatest variability
in richness occurred in the transect lines outside of the Blacktail exclosure (Fig. 6);
whereas the most variability in Simpson’s Index measures occurred in two free range
plots, Y3 and Y4, located near Gardiner (Fig. 7).
All richness data were normally distributed except for the data set from Landslide Creek
(Y3) (Shapiro-Wilk p<0.0001 in Appendix A, Table A-5). All Simpson’s Index data were
normally distributed except for the plots inside the Blacktail exclosure (Shapiro-Wilk
p=0.02). Each group had distinct differences in variance for both richness and
Simpson’s Index (Brown-Forsythe Homogeneity of variance p=.318 and 0.685,
respectively). Numbers of samples at each location ranged from two to 10 (Appendix A
Table A-4).
Fig. 6. Richness results by location using only the Parker 3-step data. Boxes show the 25th
percentile (lower line), median (middle line), and 75th percentile (upper line), and the whiskers
show the limits for 1.5 times the interquartile range. BI=Blacktail Inside Exclosures; BO=Blacktail
Outside Exclosures; GI=Gardiner Inside Exclosures; GO=Gardiner Outside Exclosures; JI=Junction
Butte Inside Exclosure; JO=Junction Butte Outside Exclosures; LI=Lamar Inside Exclosures; LO=
Lamar Outside Exclosures. Y-Series = free-range plots pre-construction of 1957 exclosures
(Y1=Geode Creek, Y2=Blacktail Hill, Y3=Landslide Creek, Y4=Game Ranch, Y5=Lamar Horseshoe,
Y6=Specimen Ridge).
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Fig. 7. Simpson’s Diversity Index results by location using only the Parker 3-step data. Boxes
show the 25th percentile (lower line), median (middle line), and 75th percentile (upper line), and
the whiskers show the limits for 1.5 times the interquartile range. BI=Blacktail Inside Exclosures;
BO=Blacktail Outside Exclosures; GI=Gardiner Inside Exclosures; GO=Gardiner Outside
Exclosures; JI=Junction Butte Inside Exclosure; JO=Junction Butte Outside Exclosures; LI=Lamar
Inside Exclosures; LO= Lamar Outside Exclosures. Y-Series = free-range plots pre-construction of
1957 exclosures (Y1=Geode Creek, Y2=Blacktail Hill, Y3=Landslide Creek, Y4=Game Ranch,
Y5=Lamar Horseshoe, Y6=Specimen Ridge).
Groupings on location were significantly different in both richness (Kruskal-Wallis
p=0.0025) and Simpson’s Index (Kruskal-Wallis p= 0.0001) (Appendix A, Table A-8).
However, the differences were significant only between the Gardiner Out location and
Geode Creek free range using richness values; and Geode Creek and Landslide Creek
locations using Simpson’s Index values. There were no statistical differences between
any of the exclosures and their outside plots, or among the individual free range plots,
using the data collected between 2009 and 2012.
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Differences among communities
Ordination using all data
The ordination diagram formed by using data from all methods and all years showed
four important results. First, the diagram showed that methods were intermixed
throughout ordination space (Fig. 8), indicating that sample method was secondary to
community composition in placing plots across the ordination. Second, for most of the
samples, Parker transects were in the same area of the diagram as the contemporary
methods. The most variation in sample-methods positions was for Mammoth, Lamar,
and Geode Creek, which were all locations of high species diversity. Third, even though
the diversity analyses had only two locations significantly different from each other
using cover data, several sample locations plotted at extreme edges of 3-D ordination
space. This indicated that the locations were actually quite different in community
composition, which better reflected the impressions formed during field sampling than
the results obtained by reducing community data to richness or Simpson’s Index.
Finally, plots sampled inside and outside of exclosures were not greatly separated in
ordination space, indicating they were more similar to each other than they were to
other locations.
The most important species separating plots in the NMS included Festuca idahoensis
(Idaho fescue), Artemisia tridentata (big sagebrush), Poa secunda (Sandberg’s
bluegrass), Phlox hoodii (Hood’s phlox), Antennaria microphylla (Rosy Pussytoes), and
Erigeron corymbosus (Foothill Daisy). The first separation of plots was based on the
presence or absence of Festuca idahoensis. F. idahoensis was present to some extent in
all areas except Gardiner, so Gardiner In and Out, Landslide Creek, and Game Ranch
separated from all other sample locations mainly on the absence of this particular
perennial grass. Gardiner plant communities were also separated from other areas
based on their unique shrubs, Krascheninnikovia lanata (winterfat), and Atriplex
nuttallii (saltbrush), and abundant non-native annuals. Artemisia tridentata was quite
important in dividing the ordination space. In the Parker transects, however, A.
tridentata and other shrubs were considered as overstory species and overstory species
were not included in microplot analyses. Unlike the other methods which reflected
shrub presence, the Parker microplots only registered shrubs if there was a direct hit on
the base of the shrub or a seedling that fell within the loop that could be counted as a
hit.
The factors that appear to be driving each of the NMS axes in Fig. 8 were the same
factors that are important to many rangelands. Axis NMS 1, which explained 44% of the
variation in the ordination, appeared to be driven mostly by evapotranspiration. From
the low elevation areas near Gardiner to areas located in the shadows of hills or
adjacent to coniferous forest stands for cooling effects, NMS 1 ranged from dry, hot, low
elevation conditions on the left to moister, more shaded, and usually higher elevation
areas on the right. Using the species associations along the axis, the lowest NMS1
values (i.e., the Gardiner area plots) consisted of plots with cactus, annual grasses and
forbs with shallow root systems, and shrubs that were common in very dry
environments. Most other areas consisted of plants that needed more moisture, such
as Idaho fescue and large perennial forbs. Evapotranspiration integrates the
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Fig. 8. 3-dimensional NMS diagram showing all samples from all years and methods. The plots were separated by Free Range and Exclosure
areas for clarity. Both diagrams use exactly the same axes and increments so samples are in the same positions they would be in if all were
plotted on the same diagram. Note that the plots are mostly separated by location, not method, in both diagrams; and that the historic
Parker clusters are not widely separated from most other methods. NMS Axis 1 r2=0.44; NMS Axis 2 r2=0.28; NMS Axis 3 r2=0.17 (Total
variance in the data explained = 89%). Possible drivers for distribution along the axes are given in the text.
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temperature, precipitation, rocky soil, and elevation conditions into a single entity that
appeared to explain the locations of plots along NMS1 fairly well. NMS 2 explained 28%
of the variation in the ordination and plot distribution could also be attributed to a
common driver in rangelands. Plots along NMS2 appeared to be driven by soil
conditions, specifically texture and depth. At the lower end of NMS2 were thin, young,
rocky soils characterized by the plots at Specimen Ridge. Soil map layers obtained from
Yellowstone National Park’s Spatial Analysis Center showed the soils to be mollisols and
bedrock. At the upper end of this axis were plots from Geode Creek. Geode Creek had
more developed mollisols than Specimen Ridge; they were less rocky texture, moister,
and supportive of several species indicative of a productive site. The fine-grained,
mudflow deposits (inceptisols) near Gardiner differed from areas on either end of NMS
2 that were located on mollisols or mollisols/bedrock. Because soils were not
specifically sampled and characterized in this study, their direct effects on the
ordination could not be fully evaluated but vegetation was distinct on each type. NMS 3
explained 17% of the variation in the ordination. It appeared to be some effect
associated with the exclosures themselves. Free-range plots and plots outside of the
exclosures were mainly located at the lower end of the axis. Plots inside the exclosures
were, in general, located at the upper end. These effects were not obvious in the field.
Visually, most of the exclosures looked like they had about the same types of vegetation
and cover on the inside as out. The effects may be due to cover reductions from
grazing, less plant vigor due to lack of grazing, soil compaction on the outside of
exclosures that affected plant growth or soil moisture retention, soil enrichment of
nutrients due to animal droppings, or a number of other effects that cannot be
determined from the substrate or environmental characteristics collected for this study.
The distribution of inside vs. outside plots was, however, distinctive so more study
needs to be conducted to more clearly determine cause(s).
Ordination using Parker transect data
The NMS was fairly sensitive to changes in composition and/or abundance from year to
year. Using Parker data only, plots that were sampled in 2010 and 2012 experienced
minimal changes in community characteristics so the NMS plots for those locations
moved very small distances in the NMS space. When locations were sampled in 2009
and not again until 2012, the distances that the samples moved in NMS space were
greater than those with the shorter sampling schedule (Fig. 9). A few of the sites with
longer movements also had different numbers of transects sampled by the Parker
method each year but, for the most part, the ordination highlights variations in biota
not variations in sample numbers.
The ordination using only the Parker Clusters distributes plots similarly to the ordination
that uses all plots and all methods shown in Fig. 8. Because each axis from the two
ordinations is derived from independent analyses, however, the drivers for each should
not be interpreted as identical. Using only the Parker samples, NMS Axis 1 has hot, dry,
low elevation plots on the right; and cooler, moister, more shaded, and higher elevation
plots on the left (Fig. 9). NMS2 is distributed along the same soil gradient as described
for Fig. 8. A third axis was not created during the ordination process using only Parker
data. This should not be interpreted as Parker transects not exhibiting exclosure effects.
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They may be integrated within axes NMS1 and/or NMS2 because of the limited number
of samples in the three- year dataset.
Fig. 9. NMS derived from Parker Cluster samples only. Arrows show changes in plant
composition and/or abundance between sample years for the same locations. Samples
were taken in 2009, 2010, and 2012. NMS Axis 1 r2= 0.55; NMS Axis 2 r2=0.32.
The movement of the same clusters of plots within the ordination in Fig. 9 appeared to
be caused mainly by variations in the year-to-year frequencies of the different grass and
sedge species, but variations in the frequency of annuals (particularly Alyssum
desertorum), and the timing of sampling in relation to vegetation development (i.e.
some years we were on site when Lewisia rediviva was visible and other years we were
not) were also important. There were no major plots where major influxes of new
invasive species explained movements along each axis.
Summary
A major finding of this study is that the historic Parker transect sampling method, if
grouped as clusters, is as effective at capturing species richness and abundance as the
small-scale contemporary methods tested in this study. The Parker clusters are most
effective in areas where the vegetation communities are fairly homogeneous; and even
the large-scale plot methods have results similar to the historic Parker clusters if the
samples come from homogeneous landscapes. Alternately, if the landscape is
composed of several different types of plant communities and/or ecotones that are
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located within short distances of the historic transects, there was much more variation
between results of the contemporary and historic methods. Examples of such highly
varied landscapes were found at the Mammoth, Lamar, and Junction Butte exclosures
where the methods covering large spatial-scales, and even the smaller-scale nested
circles, included data from ecotones that spanned grasslands and forests or shrublands
and forests, which were not normally described using a line transect or microplot along
a line. If a large-scale method is chosen for future monitoring effort in these diverse
areas, there will be little correlation with historic data because they sample different
vegetation communities. To meet some monitoring objectives for the park, however,
these ecotones might be important for some purposes and large-scale methods would
be justified.
A second important finding of this study is that diversity calculations were ineffective at
making connections between any historic and contemporary data sets. Too many sites
have the same calculated richness and/or Simpson’s index values even though they are
derived from very unique communities. The results gave statistically insignificant
differences in sample data between locations when they were, in fact, quite different.
The uniqueness of each site, and the ability of each method to capture its
characteristics, was lost unless the full complement of species and their abundances
were used to describe the sampled communities.
Monitoring goals for YNP will be critical to make decisions on which monitoring method
is most appropriate for future needs. The broad, long-term goals of the park are to
monitor for vegetation change and to partition change among biotic and abiotic factors.
The NRC directives are to find a method that can detail trends in biodiversity, plant
spatial distribution, or both, in enough detail to determine cause and effect. Capturing
species numbers and/or rare plants over time and defining their change mechanisms is a
very different objective than discerning changes in forage species or cover for the
ungulate herds and their underlying causes. Finding a single, cost-effective monitoring
method to do both objectives will be difficult. More specific objectives will need to be
formulated before any sampling method (or methods) can be recommended for a new
monitoring program. In the meantime, each sampling method does have specific
advantages and disadvantages to its use.
The Parker historic method is easy to learn and takes the least amount of time to do. It
requires little equipment to implement. It is as effective as the contemporary methods
if used in homogeneous landscapes but does not capture species composition and
abundance from ecotones or other diverse landscapes as well. The ordination of the
Parker data showed little difference in the plant communities inside and outside of the
exclosures, but the ordination encompassed only three years of data and all samples
were collected under drought conditions when vegetation was stressed. The Parker
method is also backed by 55 years of historic data, which is a very important legacy for
correlations with climate change. No other method has this legacy data.
The nested circular plot covers more spatial area than the Parker transects, but takes
25% longer to do. Estimating percentages to 1% accuracy for the entire 168.2 m2 circle
is difficult without abundant experience, although this accuracy is not a normal
component for data collection using this method. The mean richness and Simpson’s
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Index values calculated from the microplots were the lowest of any method; but, using
species tallies from both the microplots and entire circle, it did capture 40-50% more
species than the historic method. Although there were no statistically significant
differences between it and the Parker cluster data, correspondence and linear
regression lines between it and the historic method were very low, indicating that it
might not be appropriate for cross-walk correlations between it and the historic data.
The Daubenmire method using 20 microplots improves on the historic method because
it captures percent cover values for biota and substrate and it creates a more extensive
species list to track changes in species over time. It is the most time intensive of the
small-scale methods with low setup times but long times for estimating cover of all
species and substrate elements in the 20 microplots. The method requires little
equipment, and consistent estimates of cover percent for each species are easily made.
It samples more area than the Parker transects, but much less than any other
contemporary method. Richness measures using cover data correlated very closely with
the historic method as did an offset linear regression line. In most areas, Daubenmire
samples correlated closely with the historic method using full biotic composition and
abundance (i.e., they plotted close together on the NMS diagrams), probably because
both methods stayed on or adjacent to the historic line. There was also no significant
difference between the Daubenmire and large spatial scale plots (Whittaker and FIA). It
captured as many species as the Whittaker plots did using the entire 20 x 50 m area,
which might make it a good compromise between small- and large-scale methods to
monitor for changes in cover and changes in richness over time. Daubenmire legacy
data exists on the historical transects only for 1994 (Prather and Prather 1994; Utley and
Stringfield 1994) and minimally for 2002 (Sikkink 2002), but neither of these data sets
are probably comprehensive enough to correlating variations in vegetation with climate
change or grazing.
The Whittaker method is time intensive for both set-up and percent-cover estimations
of species and substrate elements. Because species and substrate cover estimates are
made within rectangular portions, however, it is like working a huge Daubenmire plot
with half as many microplots. Unlike the Daubenmire plots where cover is estimated
more quickly within broad cover classes, cover within the Whittaker plots is estimated
to within the nearest 1% so the method captures highly detailed data for species and
substrate variables. It did not capture the highest number of species for this study, but
this is probably a reflection of the limited number of plots that could be established by
one crew. One problem with using the full modified-Whittaker method is that, even
though presence-absence data are easy to collect from the sub-plots, they are in such a
different format than the microplot data that it is difficult to tie both together in data
analyses.
Because this method was not statistically different than either the Daubenmire or FIA
methods, the decision to make it a preferred monitoring method will depend on
whether the highest priority for monitoring is large spatial coverage or limited sample
times. The large spatial area covered by this method is an asset if changes in cover are
the priority because movement or disappearance of communities would have more
probability of being captured using a larger plot. However, the reality of sampling
27
Assessing Sampling Methods YNP 2013
Final Report
numerous Whittaker plots during a season, or even staggered over many seasons, may
be unfeasible with limited personnel or budgets.
The FIA method is the most time consuming of the methods. It captures the most
species; and, because of its large size, it sometimes samples completely different
vegetation communities in forests or ecotones. Like the nested circle, estimating cover
to 1% accuracy for the full circles (four in total) was difficult without a wealth of
experience. The method did not capture any more species than the Whittaker plot for
the extra time it took to implement nor did it correlate with the historic method using
correlation analysis or linear regression. It is also likely that the differences in
vegetation communities affected the ordination analysis, and this influence will be
examined in future analysis. Because of the long times necessary to complete this
method, personnel might also be exposed to safety issues during the sampling process
(i.e., bison, bears, and wolves), especially in the free range areas and areas outside of
exclosures.
Recommendations
The analyses presented here clearly demonstrate that no single method of vegetation
sampling maximizes inferences that are desired from the data. Each method has its own
strengths and constraints, depending on the specific question or metric being analyzed.
The analysis, however, does offer two options for consideration. The first option is for
maintaining the long-term integrity of the database and the historic experimental
design, including retaining the established exclosures. The second option is for
developing a long-term, broad-scale vegetation monitoring protocol for the park. These
options result in the following recommendations:
1) Retain the sites and historic methods currently employed to monitor vegetation in
YNP, and further explore the reported correlation between species richness/abundance
(Parker clusters vs. Daubenmire) and the temporal trends of species cover among and
within sites. Within this report, we state that plant frequency is identical to percent
cover using the Parker methodology, and that a linear, additive relationship appears to
exist with Daubenmire cover richness. Exploring this relationship further and subjecting
the Parker and Daubenmire cover data to a time series analysis would allow for an
assessment of temporal changes in species cover among and within sites, including the
effect of exclosure. Even though Daubenmire cover data is categorical, analysis using
the mid-points of the cover classes should be sufficiently robust to allow for detection of
real and significant changes in cover richness. The analysis would further reveal, for
example, the arrival/presence of any non-native species that contribute to temporal
changes in vegetation community structure.
The outcome of the analysis identified above would further support a recommendation
to retain the long-term ungulate exclosures and the sampling protocols that were
established at the time of their construction. The historical experimental design is
useful to monitor for vegetation trends and inform management of the ungulate
influences; but, with more than 50 years of protection from grazing/browsing, it also
adds power to detect any climate-induced changes in vegetation that are anticipated
under future scenarios of global climate change. Even if broad-scale inference is
28
Assessing Sampling Methods YNP 2013
Final Report
constrained by the existing experimental design (see below), “manipulation” by means
of exclosures is the only rigorous means of determining cause-and-effect relationships
between vegetation change, grazing, and climatic trends.
A secondary recommendation, which goes along with the recommendation to retain the
ungulate exclosures and historic sampling protocols, would be to continue to explore
the correlations between historic and new sampling protocols. The correlations
explored in this study, and in past studies, are based on sample sizes that are too small
to construct convincing equations and/or relationships for a “bridge” or crosswalk
between historic and current data. For this reason, the need to continue sampling with
the historic sampling method is ongoing. With several more years of data collection
using the historic method alongside a contemporary sampling method, AND collecting
data under a variety of climatic conditions, building a crosswalk between past and
present may become more feasible. The nature of the Parker data focuses change
detection on common species. Shrubs are rarely included, even though they may be
common in the community. Rare species are usually not factored at all as are nonnative species early in their establishment. In other words, sampling only common
species inside and outside of exclosures may not be able to discern changes beyond
those expected by background variation in moisture (Coughenour et al. 1994).
However, the ordination of recent Parker data presented here (Figure 9) suggests a way
that the different methods may be compared and the long-term data set re-analyzed to
look for magnitude and direction of change between pairs of sampling years. So, our
“bridge” may just be a recommendation to re-analyze historic and contemporary data
using ordination techniques.
2) Develop a broad-scale vegetation monitoring program. The free-ranging transects (n
= 15 transects in clusters of 2-3 at 6 sites) and exclosures still in existence today (n = 8 at
5 locations) were established to be coincident with planned elk herd reductions (195758, which did not occur, and 1961-62, which did occur) and not as part of a larger goal
to maximize the spatial inferences to be drawn. Sites were deliberately selected to
represent a variety of vegetation types and topo-edaphic conditions, and many
transects within sites were purposely placed on ridgetops or upper slopes where harsh
conditions and exposure to grazing was maximized (D. Houston, 1978 letter to files
N1433). Standard methods of vegetation measurement (Parker transects for
herbaceous strata, sagebrush, aspen, and willow belts, etc.) and analysis from that era
were employed in an attempt to describe vegetation change. These early transects
were established to detect vegetation changes between two permanently marked
points due to grazing – not to describe the vegetation community of the site as a whole
(Canfield 1941). Barmore Jr. (2003) reiterates this philosophy when he says that “the
[Parker] method is not appropriate as an index or estimate of absolute measures of
vegetation… but more appropriate for detecting vegetation differences over time and
between sites.” He goes on to say that accuracy for the method can be increased by
using more transects and grouping species. Because the early range studies used
transects primarily to detect vegetation change due to grazing, little consideration was
given to powerful and unbiased quantitative measures – balanced experimental design,
stratification and replication, explicit hypothesis-driven field sampling, and statistical
analyses- that would determine the exact information being pursued and the optimal
methods to acquire and analyze the data. Today, the experimental design employed to
29
Assessing Sampling Methods YNP 2013
Final Report
monitor for long-term vegetation change would encompass these modern
requirements. Recognizing these potential biases and shortcomings, it is desirable to
develop a broad-based vegetation monitoring program, not only for the sagebrushsteppe system of the park referenced here, but to encompass all major vegetation zones
within the park. Therefore, it is recommended that an interdisciplinary team of subjectmatter experts be convened to assist the park in establishing explicit goals, objectives,
and procedures for implementing a long-term vegetation monitoring program. The
information and analyses provided in this report on sampling protocols, cost-benefit,
and site conditions would inform such an effort. For reasons identified above, it is
expected that historic vegetation monitoring sites/methods would be retained as part of
a long-term vegetation monitoring program, and that basic and applied research
objectives would be a component of the vegetation monitoring program to provide
further insight into cause-and-effect relationships for vegetation change.
Acknowledgements
This study was conducted under Research Joint Venture Agreements between
Yellowstone National Park, the U.S. Forest Service (09-IA-11221637-252) and the U.S.
Geological Survey (1580090009). We sincerely thank the Yellowstone National Park
Foundation for providing a portion of the funding that made this project possible. We
also thank Kathi Irvine (statistician, USGS) and Scott Baggett (statistician, RMRS Forest
Service), for valuable statistical discussions and guidance; Jared Woolsey, Ben Chemel,
and Rebecca Saunders for field sampling the nested circle plots and two FIA plots; and
Christie Hendrix, Stacy Gunther, and John Klaptowski for logistics and assistance during
field sampling.
30
Assessing Sampling Methods YNP 2013
Final Report
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Appendix A: Analysis Results
Section 1.1 Summary statistics
Table A-1a. Summary statistics for diversity measures by sample methods using cover
data. S=Richness; E=Evenness; D’= Simpson’s Diversity Index.
Method
Variable
Mean
Std Dev
Minimum
Maximum
n
Parker 3-Step
Cover
S
17.32
5.00
6.00
31.00
65
E
0.77
0.11
0.43
0.93
65
D`
0.81
0.10
0.46
0.92
65
Skewness
6.35
1.73
3.71
10.29
65
Kurtosis
47.48
25.70
14.45
108.50
65
S
15.47
4.26
9.00
29.00
36
E
0.70
0.12
0.42
0.88
36
D`
0.76
0.12
0.48
0.90
36
Skewness
7.21
2.28
3.46
11.04
36
Kurtosis
61.60
35.59
13.22
125.65
36
S
24.22
6.12
14.00
36.00
32
E
0.66
0.10
0.37
0.83
32
D`
0.80
0.10
0.49
0.90
32
Skewness
7.08
1.81
4.40
10.91
32
Kurtosis
58.15
29.03
18.89
123.20
32
S
29.88
8.11
22.00
43.00
8
E
0.69
0.04
0.64
0.75
8
D`
0.84
0.03
0.80
0.89
8
Skewness
5.90
0.98
4.67
7.51
8
Kurtosis
38.93
14.08
23.07
64.22
8
S
30.67
9.83
22.00
49.00
6
E
0.65
0.07
0.50
0.70
6
D`
0.82
0.09
0.65
0.90
6
Skewness
6.02
1.37
4.31
8.49
6
40.90
19.08
19.75
76.79
6
Nested Circle
Cover
Daubenmire
Cover
Whittaker
Cover
FIA
Cover
Kurtosis
34
Assessing Sampling Methods YNP 2013
Final Report
Table A-1b. Summary statistics for diversity measures by sample methods using
frequency data. S=Richness; E=Evenness; D’= Simpson’s Diversity Index.
Method
Variable
Mean
Std Dev
Minimum
Maximum
N
Parker 3-step
Freq
S
17.32
5.00
6.00
31.00
65
E
0.76
0.10
0.45
0.93
65
Nested Circle
Freq
Daubenmire
Freq
Whittaker Freq
FIA Freq
35
D`
0.81
0.09
0.48
0.92
65
Skewness
6.29
1.67
3.58
10.23
65
Kurtosis
46.52
24.75
13.27
107.69
65
S
15.47
4.25
9.00
29.00
36
E
0.96
0.00
0.94
0.98
36
D`
0.91
0.02
0.86
0.95
36
Skewness
3.20
0.91
1.09
4.67
36
Kurtosis
10.62
6.21
-0.07
23.29
36
S
24.21
6.11
14.00
36.00
32
E
0.89
0.02
0.81
0.94
32
D`
0.92
0.02
0.87
0.95
32
Skewness
3.48
0.69
2.36
4.97
32
Kurtosis
12.45
5.76
4.65
25.53
32
S
29.87
8.11
22.00
43.00
8
E
0.92
0.02
0.88
0.95
8
D`
0.94
0.01
0.93
0.96
8
Skewness
2.39
0.50
1.62
3.16
8
Kurtosis
5.13
2.71
1.82
9.46
8
S
30.66
9.83
22.00
49.00
6
E
0.91
0.02
0.89
0.95
6
D`
0.94
0.01
0.92
0.97
6
Skewness
2.51
0.76
1.36
3.55
6
Kurtosis
6.39
4.54
0.95
13.57
6
Assessing Sampling Methods YNP 2013
Final Report
Table A-2. Summary Statistics for locations within the northern ungulate winter range using richness cover data.
Richness
Parker Cover
Location
Blacktail Inside
BI
Blacktail Outside
Gardiner Inside
Gardiner Outside
Junction Butte Inside
Junction Butte Outside
Lamar Inside
Lamar Outside
Mammoth Inside
Mammoth Outside
Free: Geode Creek
Free: Blacktail Hill
Free: Landslide Creek
Free: Game Ranch
Free: Lamar Horseshoe
Free: Specimen Ridge
BO
GI
GO
JI
JO
LI
LO
MI
MO
Y1
Y2
Y3
Y4
Y5
Y6
36
Mean
15.7
Std
Dev
4.4
n
9
18.8
14.5
12.2
16.6
15.6
22.5
15.0
25.0
18.0
29.0
22.5
16.0
16.0
20.7
22.5
7.3
3.6
2.9
2.7
2.4
1.3
1.4
1.4
1.4
2.8
0.7
3.5
3.0
1.5
2.1
5
10
6
5
5
4
2
2
2
2
2
3
3
3
2
Assessing Sampling Methods YNP 2013
Nested Cover
Std
Mean
Dev n
2.7 5
12.4
16.3
12.6
11.5
17.0
15.5
19.7
15.0
18.0
14.0
21.0
17.0
14.0
16.0
17.0
22.0
6.4
2.1
3.5
3.5
0.7
8.1
.
4.2
1.4
.
.
.
4.2.
4.2.
.
3
5
2
3
2
3
1
2
2
1
1
1
2
2
1
Daubenmire Cover
Std
Mean
Dev n
3.6 4
18.8
22.5
18.4
17.0
25.3
24.0
32.7
24.0
31.5
28.5
36.0
29.0
23.0
23.0
21.0
31.0
6.4
2.1
0.0
4.5
0.0
2.5
.
2.1
4.9
.
.
.
.
.
.
2
5
2
3
2
3
1
2
2
1
1
1
1
1
1
Whitaker Cover
Std
Mean
Dev n
. 1
30
FIA Cover
Std
Mean
Dev
.
24
n
1
30
27
22
41
.
.
.
.
1
1
1
1
30
.
1
33
.
1
43
.
1
49
.
1
23
23
.
.
1
1
22
26
.
.
1
1
Final Report
Table A-3. Summary statistics for areas within the northern ungulate winter range using Simpson’s Diversity Index cover data.
Location
Blacktail Inside
Blacktail Outside
Gardiner Inside
Gardiner Outside
Junction Butte Inside
Junction Butte
Outside
Lamar Inside
BI
BO
GI
GO
JI
JO
LI
Parker Cover
Std
Mean
Dev
n
0.06
0.79
9
0.09
0.82
5
0.05 10
0.83
0.07
0.76
6
0.06
0.84
5
0.02
0.87
5
0.90
0.01
Simpson's Diversity Index
Nested Cover
Daubenmire Cover
Std
Std
Mean
Dev n Mean
Dev n
0.14 5
0.10 4
0.69
0.77
0.17 3
0.04 2
0.79
0.85
0.17 5
0.12 5
0.77
0.73
0.02 2
0.02 2
0.80
0.76
0.07 3
0.01 3
0.79
0.84
0.05 2
0.05 2
0.80
0.85
0.80
0.02
2
2
2
2
0.63
0.68
0.77
0.85
.
0.08
0.00
.
4
0.87
0.03
3
1
2
2
1
0.76
0.83
0.85
0.87
.
0.04
0.02
.
1
2
2
1
3
Whitaker Cover
Std
Mean
Dev
.
0.83
.
0.89
.
0.80
.
0.80
n
1
1
1
1
FIA Cover
Std
Mean
Dev
.
0.81
.
0.84
n
1
1
0.86
.
1
0.85
.
1
0.85
.
1
0.90
.
1
Lamar Outside
Mammoth Inside
Mammoth Outside
Free: Geode Creek
LO
MI
MO
Y1
0.84
0.84
0.86
0.91
0.00
0.02
0.01
0.00
Free: Blacktail Hill
Free: Landslide
Creek
Free: Game Ranch
Y2
Y3
0.87
0.56
0.01
0.10
2
3
0.87
0.48
.
.
1
1
0.86
0.49
.
.
1
1
Y4
0.62
0.11
3
0.77
0.10
2
0.69
.
1
0.87
.
1
0.65
.
1
Free: Lamar
Horseshoe
Free: Specimen
Ridge
Y5
0.87
0.01
3
0.79
0.08
2
0.88
.
1
0.85
.
1
0.85
.
1
Y6
0.90
0.02
2
0.90
.
1
0.90
.
1
37
Assessing Sampling Methods YNP 2013
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Table A-4: Summary statistics for locations sampled by Parker 3-step only.
BI=Blacktail Inside Exclosures; BO=Blacktail Outside Exclosures; GI=Gardiner Inside
Exclosures; GO=Gardiner Outside Exclosures; JI=Junction Butte Inside Exclosure;
JO=Junction Butte Outside Exclosures; LI=Lamar Inside Exclosures; LO= Lamar Outside
Exclosures. Y-Series = free-range plots pre-construction of 1957 exclosures (Y1=Geode
Creek, Y2=Blacktail Hill, Y3=Landslide Creek, Y4=Game Ranch, Y5=Lamar Horseshoe,
Y6=Specimen Ridge).
Location
BI
BO
GI
GO
JI
JO
LI
LO
MI
38
Variable
Mean
StdDev
Minimum
Maximum
n
S
15.67
4.39
10.00
22.00
9
E
0.74
0.06
0.64
0.83
9
H
2.01
0.18
1.70
2.23
9
D`
0.79
0.06
0.67
0.84
9
S
18.80
7.26
11.00
27.00
5
E
0.76
0.10
0.60
0.89
5
H
2.18
0.43
1.59
2.52
5
D`
0.82
0.09
0.67
0.89
5
S
14.50
3.63
6.00
20.00
10
E
0.81
0.07
0.70
0.93
10
H
2.12
0.25
1.67
2.41
10
D`
0.83
0.05
0.74
0.89
10
S
12.17
2.93
7.00
16.00
6
E
0.74
0.08
0.66
0.88
6
H
1.82
0.29
1.47
2.20
6
D`
0.76
0.07
0.70
0.87
6
S
16.60
2.70
14.00
20.00
5
E
0.78
0.08
0.68
0.87
5
H
2.18
0.23
1.85
2.47
5
D`
0.84
0.06
0.73
0.89
5
S
15.60
2.41
13.00
19.00
5
E
0.85
0.04
0.82
0.91
5
H
2.33
0.13
2.17
2.46
5
D`
0.87
0.02
0.85
0.89
5
S
22.50
1.29
21.00
24.00
4
E
0.86
0.04
0.82
0.90
4
H
2.67
0.07
2.61
2.74
4
D`
0.90
0.01
0.89
0.92
4
S
15.00
1.41
14.00
16.00
2
E
0.80
0.00
0.80
0.80
2
H
2.16
0.07
2.11
2.21
2
D`
0.84
0.00
0.83
0.84
2
S
25.00
1.41
24.00
26.00
2
Assessing Sampling Methods YNP 2013
Final Report
MO
Y1
Y2
Y3
Y4
Y5
Y6
39
E
0.76
0.04
0.73
0.79
2
H
2.45
0.09
2.38
2.52
2
D`
0.84
0.02
0.83
0.85
2
S
18.00
1.41
17.00
19.00
2
E
0.82
0.02
0.80
0.83
2
H
2.36
0.12
2.27
2.45
2
D`
0.86
0.01
0.85
0.87
2
S
29.00
2.83
27.00
31.00
2
E
0.82
0.02
0.80
0.83
2
H
2.75
0.02
2.73
2.76
2
D`
0.91
0.00
0.91
0.91
2
S
22.50
0.71
22.00
23.00
2
E
0.78
0.00
0.78
0.78
2
H
2.43
0.03
2.40
2.45
2
D`
0.87
0.01
0.87
0.88
2
S
16.00
3.46
12.00
18.00
3
E
0.50
0.07
0.43
0.57
3
H
1.39
0.29
1.08
1.65
3
D`
0.56
0.10
0.46
0.66
3
S
16.00
3.00
13.00
19.00
3
E
0.54
0.12
0.47
0.68
3
H
1.48
0.22
1.34
1.74
3
D`
0.62
0.11
0.55
0.75
3
S
20.67
1.53
19.00
22.00
3
E
0.79
0.04
0.76
0.83
3
H
2.40
0.07
2.31
2.45
3
D`
0.87
0.01
0.86
0.88
3
S
22.50
2.12
21.00
24.00
2
E
0.85
0.04
0.82
0.88
2
H
2.65
0.19
2.51
2.78
2
D`
0.90
0.02
0.89
0.92
2
Assessing Sampling Methods YNP 2013
Final Report
Section 1.2 Tests for distribution and variance within data
Table A-5. Shapiro-Wilk p-values from tests for normality. Data were diversity
calculations based on frequency and percent cover analyses from five sampling methods
from locations throughout the northern ungulate winter range. Table is divided by (1)
method (upper portion), where data was grouped solely on method and could include
several locations and years; (2) location (middle portion), where each location may have
been sampled by several different methods and in multiple years; and (3) Parker
locations only (lower portion). Red = data not normally distributed (i.e., if p-values
<0.05, reject the null hypothesis that a sample came from a normally distributed
population). BI=Blacktail Inside Exclosures; BO=Blacktail Outside Exclosures;
GI=Gardiner Inside Exclosures; GO=Gardiner Outside Exclosures; JI=Junction Butte Inside
Exclosure; JO=Junction Butte Outside Exclosures; LI=Lamar Inside Exclosures; LO= Lamar
Outside Exclosures. Y-Series = free-range plots pre-construction of 1957 exclosures
(Y1=Geode Creek, Y2=Blacktail Hill, Y3=Landslide Creek, Y4=Game Ranch, Y5=Lamar
Horseshoe, Y6=Specimen Ridge).
By
Location
Richness
(Cover)
Simpson’s
Index
(Cover)
By Method
Richness
(Frequency)
Simpson’s
Index
(Frequency)
Richness
(Cover)
Simpson’s
Index
(Cover)
Parker
0.23
Nested
0.004
Daubenmire
0.17
Whittaker
0.10
FIA
0.15
<0.001
0.0032
0.08
0.63
0.60
0.23
0.00
0.17
0.10
0.15
<0.0001
0.00
0.00
0.66
0.06
BI
BO
GI
GO
JI
JO
LI
LO
MI
MO
Y1
Y2
Y3
Y4
Y5
Y6
0.36
0.26
0.10
0.29
0.17
0.78
0.97
1.00
1.00
1.00
1.00
1.00
<0.0001
1.00
0.64
1.00
0.02
0.10
0.37
0.06
0.16
0.24
0.07
1.00
1.00
1.00
1.00
1.00
0.82
0.17
0.21
1.00
Table A-6. Brown-Forsythe test results for homogeneity of variance
By Method
Richness
(Frequency)
Simpson’s
Index
(Frequency)
Richness
(Cover)
Simpson’s
Index
(Cover)
40
F-value
2.95
n
147
p-value
0.0223
8.36
147
<0.0001
2.95
147
0.0223
1.15
147
0.3353
Assessing Sampling Methods YNP 2013
Final Report
By Location
Richness
(Frequency)
Simpson’s
(Frequency)
Richness
(Cover)
Simpson’s Index
(Cover)
F-value
N
p-value
0.3186
1.20
65
-----
65
------
1.20
65
0.3186
.72
65
0.6853
Section 1.3 Statistical tests for differences among groups
Table A-7. Skillings-Mack results for differences among methods using cover data. Block
= site, treatment = method, and response = richness or Simpson’s Index. The weighted
sum of centered ranks shows which methods have the higher or lower ranked
observations. P-values are considered significant if p<0.05.
Weighted Sums
Year
SkillingsMack value
Response
Scale
Richness
Simpson's
Index
Small
2009
42.388
Small
2009
11.356
Richness
Simpson's
Index
Mixed
Mixed
20102012
20102012
p-value
Parker
Nested
Daubenmire
Whittaker
FIA
6.25 E-10
-18.19
-31.31
49.5
-
-
0.003
17.32
-25.25
7.91
-
-
18.762
0.0009
-12.3
-10.57
0
13.21
4.07
0.397
6.51
-7.21
-1.41
2.51
9.66
0.41
Table A-8. Kruskal-Wallis results for richness and Simpson’s Index using frequency and
cover data from Parker data only. Parker 1958 and 1962 exclosures insides were
combined for location analyses (n=15). P-values considered significant if p<0.05.
Differences
By (Parker)
Location
41
Variable
Richness
Data Type
Frequency
N
65
Chi-square
34.9802
DF Pr>Chi Square
15 0.0025
Simpson’s Index
Richness
Simpson’s Index
Frequency
Cover
Cover
65
65
65
43.0360
34.9802
43.6033
15
15
15
Assessing Sampling Methods YNP 2013
0.0002
0.0025
0.0001