U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2015–1102

Evaluating Potential Overlap Between Pack Stock and Sierra 

Nevada Bighorn Sheep (Ovis canadensis sierrae) in Sequoia 

and Kings Canyon National Parks, California

Evaluating Potential Overlap Between Pack Stock and 

Sierra Nevada Bighorn Sheep (Ovis canadensis sierrae) in 

Sequoia and Kings Canyon National Parks, California

By Robert C. Klinger, Alexandra P. Few, Kathleen A. Knox, Brian E. Hatfield, Jonathan Clark, David W. German, 

and Thomas R. Stephenson

Open-File Report 2015–1102

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2015 

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Suggested citation:

Klinger, R.C., Few, A.P., Knox, K.A., Hatfield, B.E., Clark, J., German, D.W., and Stephenson, T.R., 2015, 

Evaluating potential overlap between pack stock and Sierra Nevada bighorn sheep (Ovis canadensis sierrae) in 

Sequoia and Kings Canyon National Parks, California: U.S. Geological Survey Open-File Report 2015-1102, 46 p., 

http://dx.doi.org/10.3133/ofr20151102. 

ISSN 2331-1258 (online)
iii

Contents

Abstract ...................................................................................................................................................................... 1

Introduction................................................................................................................................................................. 2

Methods...................................................................................................................................................................... 4

Study Area .............................................................................................................................................................. 4

Spatial Data Sources .............................................................................................................................................. 4

Association Analyses .............................................................................................................................................. 5

Number and Proportion of Area of Meadows Within Herd Home Ranges of Bighorn Sheep............................... 5

Bighorn Sheep Use and Availability of Meadows in Different Classes of Pack Stock Use .................................. 5

Meadow Community and Forage Analysis.............................................................................................................. 6

Sampling ............................................................................................................................................................. 7

Analysis............................................................................................................................................................... 7

Results...................................................................................................................................................................... 10

Association Analyses ............................................................................................................................................ 10

Meadow Community and Forage Analysis............................................................................................................ 28

Discussion ................................................................................................................................................................ 42

Acknowledgments..................................................................................................................................................... 43

References Cited...................................................................................................................................................... 44

Figures

Figure 1. Layout of plots used to sample meadow vegetation in four Sierra Nevada bighorn sheep/pack stock use 

classes in Sequoia and Kings Canyon National Parks, California, 2011–2012.......................................................... 8

Figure 2. Relationship between the estimated number of Sierra Nevada bighorn sheep locations and 

distance from escape terrain (a) and size of meadows (b) in Sequoia and Kings Canyon National Parks, 

California, 2011–2012.............................................................................................................................................. 11

Figure 3. Relationship of the distance a meadow was from Sierra Nevada bighorn sheep escape terrain and 

whether a meadow was ungrazed or grazed closed or open to pack stock grazing, respectively in Sequoia and 

Kings Canyon National Parks, California, 2011–2012 ............................................................................................. 13

Figure 4. Analysis of potential use-availability of meadows in four Sierra Nevada bighorn sheep and 

pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012 ............................... 14

Figure 5. Results of Monte Carlo simulations of potential use-availability of meadows in four 

Sierra Nevada bighorn sheep and pack stock use classes in Sequoia and Kings Canyon National Parks, 

California, 2011–2012.............................................................................................................................................. 16

Figure 6. Results of Monte Carlo simulations of potential use-availability of meadows in four 

Sierra Nevada bighorn sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, 

California, 2011–2012.............................................................................................................................................. 20

Figure 7. Results of Monte Carlo simulations of potential use-availability of meadows in four 

Sierra Nevada bighorn sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, 

California, 2011–2012.............................................................................................................................................. 24

Figure 8. Biplot of the results from a Distance-based Redundancy Analysis of species composition in meadows in 

four Sierra Nevada bighorn sheep and pack stock use classes in Sequoia and Kings Canyon National Parks, 

California, 2011–2012.............................................................................................................................................. 29
iv

Figure 9. Principal Components Analysis biplot of vegetation structure in meadows in four 

Sierra Nevada bighorn sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, 

California, 2011–2012.............................................................................................................................................. 32

Figure 10. Profiles of herbaceous species diversity for meadows in four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012 .................... 33

Figure 11. Simpson’s index of evenness (E1/d) in meadows in four Sierra Nevada bighorn sheep/pack 

stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012........................................ 34

Figure 12. Percentage (%) cover of herbaceous forage species for meadows in four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012 .................... 35

Figure 13. Profiles of herbaceous forage species diversity for meadows in four Sierra Nevada bighorn 

sheep and pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012 ............. 36

Figure 14. Simpson’s index of evenness (E1/d) in for herbaceous forage species in four Sierra Nevada 

bighorn sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012 ....... 37

Figure 15. Percentage (%) cover of bare ground for meadows in four Sierra Nevada bighorn sheep and 

pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012 ............................... 38

Figure 16. Pairwise similarity in herbaceous forage species composition among four Sierra Nevada 

bighorn sheep and pack stock use classes in Sequoia and Kings Canyon National Parks, California, 

2011–2012............................................................................................................................................................... 39

Figure 17. Pairwise similarity in herbaceous forage species composition among four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012 .................... 40

Figure 18. Pairwise similarity in herbaceous forage species composition among four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012 .................... 41

Tables

Table 1. Number of Sierra Nevada bighorn sheep locations collected from Global Positioning System and radio 

telemetry collars in five herd units within Sequoia and Kings Canyon National Parks, California .............................. 4

Table 2. Number of meadows, number of plots, and area in four combinations of use by Sierra Nevada bighorn 

sheep and pack stock within Sequoia and Kings Canyon National Parks, California, 2011–2012............................. 7

Table 3. Variables used in a Distance-based Redundancy Analysis (DbRDA) of species composition of meadow 

vegetation in Sequoia and Kings Canyon National Parks, California....................................................................... 10

Table 4. Number of meadows in two classes of use by pack stock and four classes of distance from Sierra 

Nevada bighorn sheep escape terrain in Sequoia and Kings Canyon National Parks, California, 2011–2012 ........ 12

Table 5. Statistics from a Distance-based Redundancy Analysis (DbRDA) of meadow vegetation species 

composition in Sequoia and Kings Canyon National Parks, California .................................................................... 30

Table 6. Tests of the importance of eight environmental variables in a Distance-based Redundancy 

Analysis (DbRDA) of turnover in meadow plant species composition in Sequoia and Kings Canyon 

National Parks, California ........................................................................................................................................ 31
v 

Conversion Factors

Inch/Pound to International System of Units

Multiply By To obtain

Area

acre 4,047 square meter (m2)

acre 0.4047 hectare (ha)

International System of Units to Inch/Pound

Multiply By To obtain

Length

meter (m) 3.281 foot (ft)

Area

square centimeter (cm2) 0.001076 square foot (ft2)

square meter (m2) 0.0002471 acre

square meter (m2) 10.76 square foot (ft2)

hectare (ha) 2,471 acre

Datums 

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88).

Elevation, as used in this report, refers to distance above the vertical datum.

Abbreviations

ANOVA analysis of variance

AICc Bias-corrected Akaike Information Criterion

DbRDA Distance-based Redundancy Analysis

GIS geographic information system

GPS Global Positioning System

GLMM Generalized Linear Mixed Model

NDVI Normalized Difference Vegetation Index

PCA Principal Components Analysis

r correlation coefficient

SEKI Sequoia and Kings Canyon National Parks 

SNBS Sierra Nevada bighorn sheep

USGS U.S. Geological Survey

wAICc AICc weights
vi 

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1 

Evaluating Potential Overlap Between Pack Stock and 

Sierra Nevada Bighorn Sheep (Ovis canadensis sierrae) in 

Sequoia and Kings Canyon National Parks, California

By Robert C. Klinger1, Alexandra P. Few2, Kathleen A. Knox2, Brian E. Hatfield1,2, Jonathan Clark1, David W. 

German2, and Thomas R. Stephenson2 

Abstract

Pack stock (horses, mules, burros, llamas, and goats) are frequently assumed to have negative 

effects on public lands, but there is a general lack of data to be able to quantify the degree to which this 

is actually the case. Sequoia and Kings Canyon National Parks have received complaints that pack stock 

may affect Sierra Nevada bighorn sheep (Ovis canadensis sierrae; SNBS), a federally endangered 

subspecies that occurs in largely disjunct herds in the Sierra Nevada Range of California. The potential 

effects are thought to be displacement of SNBS from meadows on their summer range (altered habitat 

use) or, more indirectly, through changes in SNBS habitat or forage quality. Our goals were to conduct 

an association analysis to quantify the degree of potential spatial overlap in meadow use between SNBS 

and pack stock and to compare differences in vegetation community composition, structure, and 

diversity among meadows with different levels of use by bighorn sheep and pack stock. For the 

association analysis, we used two approaches: (1) we quantified the proportion of meadows that were

within the herd home ranges of bighorn sheep and were potentially open to pack stock, and, (2) we used 

Monte Carlo simulations and use-availability analyses to compare the proportion of meadows used by 

bighorn sheep relative to the proportional occurrence or area of meadows available to bighorn sheep that 

were used by pack stock. To evaluate potential effects of pack stock on meadow plant communities and 

SNBS forage, we sampled vegetation in 2011 and 2012 at 100 plots to generate data that allowed us to 

compare:

1. Herbaceous plant species composition, structure, and diversity in plots with different 

combinations of use by pack stock and SNBS; 

2. Cover of bare ground in plots with different combinations of use by pack stock and SNBS; 

and, 

3. Total cover, diversity, and species composition of SNBS forage species in plots with 

different combinations of use by pack stock and SNBS. 

1

U.S. Geological Survey.

2California Department of Fish and Wildlife, Sierra Nevada Bighorn Sheep Recovery Program.
2 

The association analyses indicated the potential for overlap between pack stock and SNBS was minimal; 

only 1 percent of the potential meadow area in the SNBS herd home ranges overlapped that of pack 

stock meadows. There were no systematic differences in overall vegetation structure or composition, or 

in diversity, cover, or composition of forage species, that indicated pack stock were altering SNBS 

habitat or affecting their nutrition. Variation in plant species composition was influenced primarily by 

random differences among meadows and environmental gradients, and there was little evidence that 

pack stock use contributed in meaningful ways to this variation. The few differences among meadows 

with different levels of use by bighorn sheep and pack stock either were minor or were not in a direction 

consistent with negative effects of pack stock on SNBS. We conclude that the current plan for managing 

pack stock grazing has been successful in minimizing significant negative effects on Sierra Nevada 

bighorn sheep at Sequoia and Kings Canyon National Parks. 

Introduction

Sierra Nevada bighorn sheep (Ovis canadensis sierrae; referred to hereon as “SNBS”) are a 

federally endangered subspecies that occurs in the Sierra Nevada Range of California. Although they 

feed on shrubs and subshrubs, SNBS are recognized primarily as grazers (Wehausen, 1980; Schroeder 

and others, 2010). Most of their diet is comprised of graminoids (grasses, sedges, and rushes) and forbs 

that provide adequate forage to meet their nutritional demands. During summer, SNBS primarily are 

present in steep, rocky areas characterized by a low density of vegetation, but they often move into 

meadows adjacent to rocky areas to feed. Meadows frequently have a relatively dense cover of highly 

nutritious herbaceous species (Wehausen, 1980). Thus, although SNBS spend most of their time in 

rocky areas, they likely get a disproportionate amount of their nutrition from the limited time they spend 

in meadows. 

Of the herd units identified in the Recovery Plan for Sierra Nevada bighorn sheep (U.S. Fish and 

Wildlife Service, 2007), 10 of 16 (62.5 percent) lie partially or wholly within Sequoia and Kings 

Canyon National Parks (SEKI). Therefore, maintaining the integrity of habitats within SEKI is essential 

for recovery of SNBS. However, the National Park Service has received complaints that pack stock 

(horses, mules, burros, llamas, and goats) use the same habitats as SNBS and may be having negative 

effects on SNBS recovery. Unlike in many other western national parks, pack stock are allowed to graze 

in many of the wilderness meadows of SEKI. Pack stock use in high-elevation habitats occurs near trail 

systems throughout much of SEKI (McClaren, 1989), and particular concern has been expressed about 

the effect of such use on meadows. These herbaceous-dominated communities often are focal areas for 

wildlife and human activities (McClaren and Cole, 1993; Ostoja and others,. 2014), but they are a 

limited resource in the Sierra Nevada; only an estimated 6–12 percent of the landscape in the alpine and 

subalpine zones of the Sierra Nevada is considered meadow (Robert C. Klinger, U.S. Geological 

Survey, unpub. data, 2012 ). Nevertheless, the importance of meadows to SNBS as well as other 

wildlife species greatly exceeds their land area (Allen, 1987). Currently, 219 meadows (totaling 753 

acres) are open to grazing, with additional meadows open to smaller pack animals such as llamas (Lama 

glama) and burros (Equus africanus). 
3 

Despite the potential for negative effects on SNBS (Papouchis and others, 2001; Ostoja and 

others, 2014), documented evidence of the degree to which pack stock or how pack stock might effect 

SNBS has been unavailable. Potential negative effects include disease transmission, habitat destruction 

or alteration, behavioral displacement, or excessive removal of forage. With the exception of goats 

(Capra aegagrus), pack stock are unlikely to pose a disease risk to SNBS. Experimental studies that 

examined the co-pasturing of bighorn sheep with llamas and horses (Equus ferus) did not identify any 

evidence of disease transmission or morbidity and mortality associated with such contact (Foreyt, 1994; 

Foreyt and Lagerquist, 1996). Conversely, domestic goats have been associated with negative effects of 

disease following contact with bighorn sheep (Jansen and others, 2006). The risk associated with the use 

of packing goats is recognized and has resulted in their exclusion from SEKI and much of SNBS range. 

In SEKI, potential effects by pack stock are most likely to be associated with influences on the 

foraging efficiency and forage supply for SNBS. Trampling by pack stock could have numerous effects 

on the structure of meadows through a combination of soil compaction, erosion, and destruction of 

vegetation (Cole and others, 2004). Additionally, grazing by pack stock could modify meadow structure 

because of excessive biomass removal (Ostoja and others, 2014). 

Pack stock also could have negative effects on SNBS through behavioral interactions. For 

example, Ostermann-Kelm and others (2008) observed that desert bighorn avoided water sources when 

horses were nearby, and Brown and others (2010) noted that bighorn sheep foraged less efficiently in 

the presence of livestock, specifically cattle. Shrestha and Wegge (2008) observed that grazing by 

livestock in areas overlapping with wild sheep habitat likely resulted in competition for forage.

Cole and others (2004) observed that horses and mules preferred graminoids, and consequently 

modified the species composition in Sierra Nevada meadows that were grazed. Although SNBS 

consume a combination of grasses, forbs, and shrubs, graminoids typically compose the largest 

proportion of the diet during summer (Wehausen, 1980) and winter (Schroeder and others, 2010). Thus, 

the potential exists for pack stock to compete with bighorn sheep for forage when using the same areas. 

However, grazing can have positive or negative effects on plant growth and production depending on 

the level of removal (McNaughton, 1983; Belsky, 1986). 

In order for SNBS to be negatively affected by pack stock, there must be spatial overlap in 

habitat use that negatively affects habitat quality, habitat use, or forage acquisition by SNBS. Therefore, 

the study objectives were to:

1. Conduct an association analysis to quantify the degree of potential spatial overlap in 

meadow use between SNBS and pack stock; 

2. Analyze differences in vegetation community composition and structure among meadows 

with different levels of use by bighorn sheep and pack stock; and 

3. Compare cover, diversity, and species composition of summer forage with different levels 

of use by SNBS and pack stock. 
4 

Methods 

Study Area

The study focused on the Sawmill Canyon, Mount Baxter, Bubbs Creek, Mount Williamson, and 

Mount Langley herds. Situated within SEKI north to south along the Sierra Nevada escarpment, these 

five populations represent approximately 69 percent of all SNBS (Stephenson and others, 2012). SNBS 

spend summers in the alpine and subalpine zones, and winters either in the same summer habitats or on 

low-elevation winter ranges, typically east of the crest at the base of the escarpment (U.S. Fish and 

Wildlife Service, 2007). Pack animals are present in SNBS habitat in SEKI in the summer months, but 

are not present in the SNBS winter range. Therefore, we restricted our analysis to summer habitat for 

SNBS. 

Spatial Data Sources

The primary source of SNBS spatial data included 25,510 locations collected between 2005 and 

2012 in the five herd units within the boundaries of SEKI (table 1). SNBS locations were collected from 

Global Positioning System (GPS) and radio telemetry collars and digitized into geographic information 

system (GIS) shapefiles. 

Meadows were delineated from a GIS layer provided by SEKI. This layer included a field that 

identified whether a meadow was open or closed to use by pack stock. 

Table 1. Number of Sierra Nevada bighorn sheep locations collected from Global Positioning System and radio 

telemetry collars in five herd units within Sequoia and Kings Canyon National Parks, California. 

[Start year and End year are the years of first and last collection of data, respectively] 

Herd unit

Number of 

locations Start year End year

Mount Baxter 5,505 2008 2012

Bubbs Creek1 1,619 2010 2011

Mount Langley 8,224 2005 2012

Sawmill Creek 8,212 2005 2012

Mount Williamson1 1,950 2008 2012

1

These herd units did not encompass any meadows open to 

pack stock, so they were not included in any analyses.
5 

Association Analyses

Two approaches were used to quantify potential overlap in meadow use. The first approach was 

based on the proportion of meadows in the parks that was within the herd home ranges of bighorn sheep 

and that was potentially open to pack stock. In the second approach, we compared the proportion of 

meadows used by bighorn sheep relative to the proportional area of meadows available to bighorn sheep 

that were used by pack stock. The first approach allowed us to evaluate the potential for overlap of 

bighorn sheep and pack stock based on the number of meadows at the landscape scale, whereas the 

second approach allowed us to evaluate the potential for overlap after accounting for availability based 

on meadow area.

Number and Proportion of Area of Meadows Within Herd Home Ranges of Bighorn Sheep 

Pack stock are legally constrained to a subset of meadows within the parks, and bighorn sheep 

are biologically constrained to areas near escape terrain (defined as areas with slopes of 31°>x>70°). 

These constraints created four mutually exclusive meadow classes:

1. Not used by SNBS or pack stock, 

2. Used by SNBS but not pack stock, 

3. Used by pack stock but not SNBS, and, 

4. Used by SNBS and pack stock. 

We used GIS to generate minimum convex polygons from all locations within each herd unit, and then 

calculated the number of meadows that intersected or were within each herd unit polygon as well as the 

area (in hectares) of meadows within each of the herd unit polygons. Additionally, we calculated the 

number and area of the meadows open to pack stock grazing that were outside of the herd unit polygons. 

Bighorn Sheep Use and Availability of Meadows in Different Classes of Pack Stock Use

Although a meadow could be within a herd unit polygon, this did not necessarily mean it was 

available to bighorn sheep because of their strong tendency to be near escape terrain. Despite the large 

number of bighorn sheep locations, less than 2.5 percent (N=566) occurred within mapped meadows 

(N=92). Many other locations were near meadows, however, and it was reasonable to assume that 

SNBS were using many of those meadows. Moreover, more SNBS locations likely would be recorded 

in larger meadow polygons. Therefore, the first step was to establish a justifiable definition of meadow 

availability to SNBS. To do this, we used a Generalized Linear Mixed Model (GLMM) to analyze the 

relationship between the number of SNBS locations and distance from escape cover and meadow area. 

The model included a Poisson error structure and log link with herd unit as a random factor. The 

GLMM estimated potential availability; therefore, we classified the number of predicted SNBS

locations at distances from escape terrain of 50 m (a conservative estimate of availability), 100 m (a 

moderate estimate of availability), and 250 m (a liberal estimate of availability). We then calculated the 

percentiles of the predicted locations from the GLMM that occurred within each distance class.
6 

Two methods were used to compare potential use of meadows by SNBS relative to pack stock

use. The first method allowed us to account for potential use relative to availability after accounting for 

differences in meadow area. The second method allowed us to account for SNBS and pack stock not 

having equal probability of occurring in the meadows because of the distribution of the meadows within 

the herd units. The potential for overlap between pack stock and SNBS would be greatest if the number 

of meadows available to SNBS and open to grazing by pack stock was higher than would be expected 

based on their proportional area on the landscape. Meadows open to grazing by pack stock but not 

available for potential use by SNBS, meadows not open to pack stock but available for potential use by 

SNBS, and meadows not open to pack stock and not available for potential use by SNBS would provide 

reference levels relative to those meadows potentially used by both SNBS and pack stock. 

The first method consisted of a use-availability analysis where availability was based on the area 

(in hectares) of meadows in each of the four meadow use classes, and potential use by SNBS was based 

on the number of meadows in each of the use classes. A log-likelihood χ2 statistic first was used to 

evaluate evidence of overall differences in potential use among the classes. If the χ2 statistic was 

significant then simultaneous confidence intervals were constructed for each class; classes with 

confidence intervals not overlapping available area were considered to have the potential to be used 

more or less than their availability based on their proportional area (Manly and others, 2002). 

The second method consisted of a series of Monte Carlo simulations where we calculated the 

actual (“observed”) proportion of meadows within each of the three distance from escape terrain classes 

(determined from the GLMM). We then drew 10,000 random samples of meadows from within each of 

the three classes. To account for potential sample-size bias, we repeated this for samples based on 50, 

60, 70, and 80 percent of the total number of meadows within each of the three distance classes. We 

constructed frequency distributions of proportional use in each of the distance/sample size combinations 

(N=15), and then compared the actual proportion in each use class to the distribution of simulated 

values. If the actual proportion was less than the 5th percentile or greater than the 95th percentile, we 

considered this evidence of disproportionally lesser or greater chance of overlap, respectively, than 

expected by chance.

Meadow Community and Forage Analysis

Evidence of the potential for displacement of bighorn sheep by pack stock would represent a 

direct negative effect, but pack stock could have indirect negative effects due to habitat alteration or 

changes in forage quantity. By conducting an analysis of meadow vegetation composition and structure, 

we could infer the likelihood that potential indirect effects were occurring and, if so, how strong they 

were. Similarly, by analyzing forage cover, diversity, and species composition, we could infer the 

likelihood that pack stock were affecting SNBS nutrition. 
7 

Sampling

We used a GIS to randomly select 21 meadows within the herd home ranges of Mount Baxter, 

Mount Langley, and Sawmill Creek herd units. We randomly located 3–14 plots in each meadow 

(N=100 plots total) and classified each plot into one of the four SNBS/pack stock use classes (table 2). 

Each plot was 0.25 ha in area and consisted of four 25-m transects originating from a center point, with 

each transect oriented in one of the four cardinal directions. Ocular estimates of cover and 

measurements of height were made for all herbaceous species (forbs, grasses, and sedges) in five 

randomly selected 1-m2 quadrats along each transect (fig. 1). Cover and height of woody and 

herbaceous species and cover of rock were estimated with point-intercept sampling (points evenly 

spaced at 0.5-m intervals) along each transect. Woody plants were identified to species level, whereas 

herbaceous species were placed in one of three classes; forb, grass, or sedge. Woody density was 

estimated from species-specific counts in a 5-m belt transect (2.5 m on either side of each transect).

Herbaceous biomass (identified as forb, grass, or sedge) was collected from three 100-cm2 subplots on 

each transect. Data were collected from July through August in 2011 and 2012. 

Analysis

The cover data were used to derive Hill’s series of diversity numbers (Hill, 1973; Jost, 2006), as 

well as Simpson’s index of evenness (E1/d), for all herbaceous species and all herbaceous forage species. 

Hill’s series of diversity numbers is based on an order of mathematically related diversity indices. As 

the order of the series increases, the indices are less influenced by rare species (or, conversely, have 

increasing sensitivity to the dominant species in an assemblage). One of the most appealing 

characteristics of the series is that the numbers are interpreted as the effective number of species—that 

is, the number of species that would be expected if all had equal abundances (Chao and others, 2012, 

2014). We used three indices: N0 (species richness), N1 (eH, where H=Shannon’s diversity index), and 

N2 (1/d, where d=Simpson’s diversity index). Hill’s series and E1/d allowed us to measure diversity in 

the four bighorn sheep/pack stock use classes and then evaluate the degree to which they differed in the 

total number of species (N0), the effective number of more common species (N1 and N2), and relative 

abundance of the species (E1/d). 

Table 2. Number of meadows, number of plots, and area in four combinations of use by Sierra Nevada bighorn 

sheep and pack stock within Sequoia and Kings Canyon National Parks, California, 2011–2012.

Use class Meadows Plots

Area

(hectares)

No bighorn sheep and no pack stock 10 29 37

Bighorn sheep and no pack stock 8 46 39

Pack stock and no bighorn sheep 3 13 37

Bighorn sheep and pack stock 4 12 40
8 

25 m

4 m

Figure 1. Layout of plots used to sample meadow vegetation in four Sierra Nevada bighorn sheep/pack stock use 

classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use classes were (1) not used 

by Sierra Nevada bighorn sheep or pack stock; (2) used by Sierra Nevada bighorn sheep but not pack stock; (3) 

used by pack stock but not Sierra Nevada bighorn sheep; and (4) used by Sierra Nevada bighorn sheep and pack 

stock. The four solid center lines were used for point-intercept sampling of woody species cover. Counts of woody 

species were done in four 100-square-meter belts (outer dashed lines). Rectangles represent 1-square-meter

quadrats. See text (Subsection “Sampling” on page 6) for details on sampling protocols.
9 

We used GLMMs to analyze differences in diversity among the meadow use classes, with 

meadow as a random effect. The analysis for N0 had a Poisson error structure and log link, the analyses 

for N1 and N2 had a Gaussian error structure and identity link, and the analysis of E1/d had a binomial 

error structure and logit link. We used GLMMs with a binomial error structure and logit link to analyze 

differences in bare ground and total cover of forage species among the meadow use classes. Meadow 

was a random effect in the models. Forage species for SNBS on their summer range were based on 

Wehausen (1980). 

We derived two models for each GLMM—a model with a term for meadow use classes and a 

model without the meadow use class term (null model). We used the bias-corrected Akaike Information 

Criterion (AICc) and AICc weights (wAICc) to compare the models and to evaluate the relative level of 

support for each model (Burnham and Anderson, 2002). 

Principal Components Analysis (PCA) was used to derive gradients of vegetation structure from 

the total cover (summed across species) of forbs, grasses, sedges, bare ground, and litter. Analysis of 

variance (ANOVA) then was used to compare differences in vegetation structure (the PCA axes) among 

the meadow use classes. Meadow was coded as a block factor in the ANOVA.

We analyzed differences in species composition among the four meadow use classes with 

Distance-based Redundancy Analysis (DbRDA; Legendre and Anderson, 1999). DbRDA is a 

constrained version of PCA conducted on a distance matrix of dissimilarities. Continuous and 

categorical predictor variables can be included in the model, as can random effects. The importance of 

the predictor variables and ordination axes are evaluated from permutation tests, and the proportion of 

variance accounted for by the gradients can be calculated relative to the total variation in the model 

(“unconstrained variation”) or just the total variation accounted for by the predictor variables 

(“constrained variation”). We used a Hellinger transformation (Legendre and Gallagher, 2001) of the 

percent cover data to derive a Euclidean distance matrix among plots. We derived three models—the 

first model included eight environmental variables as well as the meadow use classes, the second model 

included only the eight environmental variables, and the third model included only the meadow use 

classes. In each model, we conditioned the permutation tests (N=1,000) on meadow (that is, meadow 

was a random factor). In combination, the three models allowed us to evaluate the proportion of 

variance in species composition that was explained by meadow use class relative to the environmental 

variables and the random effect of individual meadows. The environmental variables were divided into 

three classes—topography, vegetation, and climate (table 3). We started with 10 environmental 

variables, but highly correlated variables can lead to overestimates of the variation explained by 

DbRDA axes. Therefore we examined the pairwise correlations among the variables prior to running the 

analysis. We eliminated one of any pair with a correlation coefficient (r) >0.70. This resulted in 

retaining eight of the variables in the models (table 3). 

We analyzed differences in forage species composition among the four meadow use classes with 

pairwise similarity measures (Jost, 2007). The pairwise similarity analysis takes advantage of Hill’s 

numbers by calculating similarity indices based on N0 (Sorenson’s index), N1 (Horn’s index), and N2

(Morisita-Horn index). This approach permits an evaluation of similarity along a gradient of the indices 

sensitivity to dominant species. Estimates of the indices and their standard errors were derived from 

1,000 bootstrap samples. Differences in similarity among the four meadow use classes were evaluated 

by overlap in the error bars. 
10 

Table 3. Variables used in a Distance-based Redundancy Analysis (DbRDA) of species composition of meadow 

vegetation in Sequoia and Kings Canyon National Parks, California. 

[Vegetation data were collected July–August in 2011 and 2012. Model: Yes means the variable was included in the DbRDA; 

No means the variable had a strong correlation with another variable (r>0.70) and was not used in the DbRDA. Class: The 

general group into which variables were classified] 

Variable Abbreviation Model Class

Elevation Elevation No Topography

Slope Slope No Topography

Aspect (cosine transform) Aspectcos Yes Topography

Topographic Roughness Index TRI Yes Topography

Peak Normalized Difference Vegetation Index1 NDVIPeak Yes Vegetation

Photosynthetically Active Radiation PRR Yes Vegetation

Hillshade Index Hillshade Yes Vegetation

Annual Precipitation2 Precip Yes Climate

July Maximum Temperature3 Tmax07 Yes Climate

January Minimum Temperature3 Tmin01 Yes Climate

Meadow use class Occurcode Yes Pack stock

1 Mean peak NDVI from June through September 1990 through 2010. 

2 Mean total annual precipitation from 1950 through 2000. 

3 Climate layer source: Alvarez and others (2013).

Results

Association Analyses

A total of 5,892 meadows have been mapped within the borders of SEKI. Of those, 2,780 (47.2 

percent) are open to pack stock grazing. However, only 621 meadows (10.5 percent of all meadows, 

22.3 percent of grazed meadows) occur in the five occupied bighorn sheep herd unit polygons that are 

within the boundaries of the parks (table 1). Moreover, the Bubbs Creek and Mount Williamson herds 

do not have any meadows open to grazing. Thus, meadows (N=57) in these herd units were not included 

in any of the analyses.

The five herd units within the boundaries of the parks comprise 58,378 ha, and the herd unit 

polygons comprised 40,415 ha. The total area of the 621 meadows within the herd units was 660 ha (1.1 

percent of the herd unit area and 1.6 percent of the herd unit polygon area). Thus, even before further 

filtering for distance from escape terrain, this was a strong indication that there is very little overlap at 

the landscape scale between bighorn sheep and pack stock. 

There was a strong negative relationship between the number of bighorn sheep locations and 

distance of the meadow from escape terrain (fig. 2a). The 50-m distance from escape terrain class 

represented the 76th percentile of predicted locations, whereas the 100-m and 250-m distance classes 

represented the 89th and 97th percentiles, respectively. The number of bighorn sheep locations was 

highest for meadows ranging in area from 7 to 17 ha (fig. 2b). 
11 

0 200 400 600 800

0 50 100 150 200

(a)

Distance (m)

Expected number of locations

0 5 10 15 20

0 50 100 150 200

(b)

Meadow area (ha)

Expected number of locations

Figure 2. Relationship between the estimated number of Sierra Nevada bighorn sheep locations and distance from 

escape terrain (a) and size of meadows (b) in Sequoia and Kings Canyon National Parks, California, 2011–2012. 

Dashed lines are 95-percent confidence intervals. Locations are from Global Positioning System and radio 

telemetry fixes collected between 2005 and 2012 (N=25,510).
12 

A total of 407 meadows in the Mount Langley, Mount Baxter, and Sawmill Creek herd units 

were not open to pack stock (referred to hereon as “ungrazed”; table 4). A total of 157 meadows within 

these herd units were open to pack stock (referred to hereon as “grazed”; table 4). Most grazed meadows

generally were nearly 400 m from escape terrain, whereas ungrazed meadows were within 225 m from 

escape terrain (fig. 3). There were few grazed meadows in the 50 and 100-m distance classes (N=1 and 

4, respectively), whereas 42 grazed meadows were in the 250-m distance class and potentially were 

used by SNBS (table 4). In contrast, 24 and 61 ungrazed meadows were in the 50 and 100-m distance 

classes, whereas 265 ungrazed meadows were in the 250-m distance class. 

The analysis of use-availability based on meadow area indicated that grazed meadows available 

to SNBS occurred in proportion to their area on the landscape regardless of their distance from escape 

terrain (fig. 4). Proportional availability and potential use by SNBS was lowest for this use class on the 

landscape. Ungrazed meadows not available to SNBS comprised the greatest area of the landscape for 

the 50-m and 100-m distance classes; the number of meadows was proportional to meadow area in these 

distance classes (fig. 4). In contrast, ungrazed meadows not available to SNBS comprised less landscape 

area in the 250-m distance class, and the number of meadows in this class was significantly less than 

expected relative to their area (fig. 4). This was because there was a greater number and area of 

ungrazed meadows available to SNBS in the 250-m distance class (fig. 4); the number of meadows was 

significantly higher than expected in this class relative to their area. In the 50-m and 100-m distance 

classes, however, the proportion of ungrazed meadows available to SNBS sheep was less than 0.1 of the 

total landscape area and the number of meadows was proportional to their area on the landscape (fig. 4). 

Regardless of the distance class, the number of grazed meadows not available to SNBS was 

disproportionally lower than the area they comprised on the landscape (fig. 4).

Table 4. Number of meadows in two classes of use by pack stock and four classes of distance from Sierra Nevada 

bighorn sheep escape terrain in Sequoia and Kings Canyon National Parks, California, 2011–2012.

Distance class

Use class

50-

meters

100-

meters

250-

meters

>250-

meters

Closed to pack stock (ungrazed) 24 61 265 57

Open to pack stock (grazed) 1 4 42 110
13 

Distance (m)

Ungrazed Grazed

0 100 200 300 400 500

Figure 3. Relationship of the distance a meadow was from Sierra Nevada bighorn sheep escape terrain and 

whether a meadow was ungrazed or grazed closed or open to pack stock grazing, respectively in Sequoia and

Kings Canyon National Parks, California, 2011–2012. Error bars are 95-percent confidence intervals.
14 

Escape Terrain < 50 m

Use

Proportion

Bighorn Both Neither Pack Stock

0.0 0.2 0.4 0.6 0.8 1.0

Av ailable

Used

Escape Terrain < 100 m

Use

Proportion

Bighorn Both Neither Pack Stoc

0.0 0.2 0.4 0.6 0.8 1.0

Av ailable

Used

Escape Terrain < 250 m

Use

Proportion

Bighorn Both Neither Pack Stock

0.0 0.2 0.4 0.6 0.8 1.0

Av ailable

Used

Figure 4. Analysis of potential use-availability of meadows in four Sierra Nevada bighorn sheep and pack stock use 

classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. Use and availability were defined as 

meadows within 50, 100, and 250 m of bighorn sheep escape terrain. Error bars are 95-percent confidence 

intervals.
15 

Results from the Monte Carlo simulations were similar to those of the analyses of potential use 

and availability based on area of the meadows (figs. 5–7). When a conservative estimate of availability 

was used (50 m), the estimate of availability was well within the 2.5 and 97.5 percentiles regardless of 

how large of a sample (that is, 50, 60, 70, and 80 percent) of the meadows was used in the simulations 

(fig. 5). When a moderate estimate of availability was used (100 m), the estimate of availability was

well within the 2.5 and 97.5 percentiles for all classes except ungrazed meadows available to SNBS; 

more meadows occurred in that class than expected based on the random samples of their distribution on 

the landscape (fig. 6). When a liberal estimate of availability was used (250 m), the estimate of 

availability was well outside the 2.5 and 97.5 percentiles for all use classes (fig. 7). A greater proportion 

of grazed meadows was available to SNBS than expected based on random samples of their distribution 

on the landscape; however, this use class comprised less than 4 percent of the meadows on the 

landscape. A much greater proportion of ungrazed meadows available to SNBS occurred on the 

landscape than expected based on random samples of their distribution. This use class comprised more 

than 30 percent of the meadows on the landscape (fig. 7). Ungrazed meadows not available to SNBS as 

well as grazed meadows not available to SNBS occurred less than expected on the landscape (fig. 7). 

These two classes comprised 31–35 percent and 23–24 percent of the landscape area, respectively.
16 

Both

50% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5 6

0 1000 2000 3000 4000

Bighorn Only

50% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 2000 3000 4000

Neither

50% of Data

Occurrence (%)

Frequency

35 40 45 50 55

0 1000 2000 3000 4000

Pack Stock Only

50% of Data

Occurrence (%)

Frequency

20 25 30 35 40

0 1000 2000 3000 4000

A. 50 percent of the meadows within 50 meters of bighorn sheep escape terrain. 

Figure 5. Results of Monte Carlo simulations of potential use-availability of meadows in four Sierra Nevada bighorn 

sheep and pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012.

Randomizations were conducted for 50, 60, 70, and 80 percent (%) of the meadows within 50 meters of bighorn 

sheep escape terrain. Vertical dashed lines are the actual proportion in each use class. 
17 

Both

60% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5

0 1000 2000 3000 4000

Bighorn Only

60% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 2000 3000 4000

Neither

60% of Data

Occurrence (%)

Frequency

40 45 50 55

0 1000 2000 3000 4000

Pack Stock Only

60% of Data

Occurrence (%)

Frequency

25 30 35

0 1000 2000 3000 4000

B. 60 percent of the meadows within 50 meters of bighorn sheep escape terrain.

Figure 5.—Continued. 
18 

Both

70% of Data

Occurrence (%)

Frequency

0 1 2 3 4

0 500 1500 2500

Bighorn Only

70% of Data

Occurrence (%)

Frequency

15 20 25 30

0 500 1500 2500

Neither

70% of Data

Occurrence (%)

Frequency

40 45 50 55

0 500 1500 2500

Pack Stock Only

70% of Data

Occurrence (%)

Frequency

25 30 35

0 500 1500 2500

C. 70 percent of the meadows within 50 meters of bighorn sheep escape terrain.

Figure 5.—Continued. 
19 

Both

80% of Data

Occurrence (%)

Frequency

1 2 3 4

0 1000 3000 5000

Bighorn Only

80% of Data

Occurrence (%)

Frequency

16 18 20 22 24 26 28

0 1000 3000 5000

Neither

80% of Data

Occurrence (%)

Frequency

40 45 50

0 1000 3000 5000

Pack Stock Only

80% of Data

Occurrence (%)

Frequency

25 30 35

0 1000 3000 5000

D. 80 percent of the meadows within 50 meters of bighorn sheep escape terrain.

Figure 5.—Continued. 
20 

Both

50% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5

0 1000 2000 3000 4000

Bighorn Only

50% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 2000 3000 4000

Neither

50% of Data

Occurrence (%)

Frequency

35 40 45 50 55

0 1000 2000 3000 4000

Pack Stock Only

50% of Data

Occurrence (%)

Frequency

20 25 30 35 40

0 1000 2000 3000 4000

A. 50 percent of the meadows within 100 meters of bighorn sheep escape terrain.

Figure 6. Results of Monte Carlo simulations of potential use-availability of meadows in four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012.

Randomizations were conducted for 50, 60, 70, and 80 percent (%) of the meadows within 100 meters of bighorn 

sheep escape terrain. Vertical dashed lines are the actual proportion in each use class..
21 

Both

60% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5

0 1000 2000 3000 4000

Bighorn Only

60% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 2000 3000 4000

Neither

60% of Data

Occurrence (%)

Frequency

40 45 50 55

0 1000 2000 3000 4000

Pack Stock Only

60% of Data

Occurrence (%)

Frequency

20 25 30 35 40

0 1000 2000 3000 4000

B. 60 percent of the meadows within 100 meters of bighorn sheep escape terrain.

Figure 6.—Continued. 
22 

Both

70% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5

0 500 1500 2500

Bighorn Only

70% of Data

Occurrence (%)

Frequency

16 18 20 22 24 26 28 30

0 500 1500 2500

Neither

70% of Data

Occurrence (%)

Frequency

40 45 50 55

0 500 1500 2500

Pack Stock Only

70% of Data

Occurrence (%)

Frequency

25 30 35

0 500 1500 2500

C. 70 percent of the meadows within 100 meters of bighorn sheep escape terrain.

Figure 6.—Continued. 
23 

Both

80% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5

0 1000 3000 5000

Bighorn Only

80% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 3000 5000

Neither

80% of Data

Occurrence (%)

Frequency

40 45 50 55

0 1000 3000 5000

Pack Stock Only

80% of Data

Occurrence (%)

Frequency

25 30 35

0 1000 3000 5000

D. 80 percent of the meadows within 100 meters of bighorn sheep escape terrain.

Figure 6.—Continued. 
24 

Both

50% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5 6

0 1000 2000 3000 4000

Bighorn Only

50% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 2000 3000 4000

Neither

50% of Data

Occurrence (%)

Frequency

35 40 45 50 55

0 1000 2000 3000 4000

Pack Stock Only

50% of Data

Occurrence (%)

Frequency

20 25 30 35 40

0 1000 2000 3000 4000

A. 50 percent of the meadows within 250 meters of bighorn sheep escape terrain. 

Figure 7. Results of Monte Carlo simulations of potential use-availability of meadows in four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012.

Randomizations were conducted for 50, 60, 70, and 80 percent (%) of the meadows within 250 meters of bighorn 

sheep escape terrain. Vertical dashed lines are the actual proportion in each use class. 
25 

Both

60% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5

0 1000 2000 3000

Bighorn Only

60% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 2000 3000

Neither

60% of Data

Occurrence (%)

Frequency

40 45 50 55

0 1000 2000 3000

Pack Stock Only

60% of Data

Occurrence (%)

Frequency

25 30 35 40

0 1000 2000 3000

B. 60 percent of the meadows within 250 meters of bighorn sheep escape terrain. 

Figure7.—Continued. 
26 

Both

70% of Data

Occurrence (%)

Frequency

0 1 2 3 4 5

0 1000 2000 3000

Bighorn Only

70% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 2000 3000

Neither

70% of Data

Occurrence (%)

Frequency

40 45 50

0 1000 2000 3000

Pack Stock Only

70% of Data

Occurrence (%)

Frequency

25 30 35

0 1000 2000 3000

C. 70 percent of the meadows within 250 meters of bighorn sheep escape terrain.

Figure 7.—Continued. 
27 

Both

80% of Data

Occurrence (%)

Frequency

0 1 2 3 4

0 1000 3000 5000

Bighorn Only

80% of Data

Occurrence (%)

Frequency

15 20 25 30

0 1000 3000 5000

Neither

80% of Data

Occurrence (%)

Frequency

40 45 50

0 1000 3000 5000

Pack Stock Only

80% of Data

Occurrence (%)

Frequency

25 30 35

0 1000 3000 5000

D. 80 percent of the meadows within 250 meters of bighorn sheep escape terrain.

Figure 7.—Continued. 
28 

Meadow Community and Forage Analysis

The DbRDA indicated that differences in species composition in the plots were primarily due to 

random effects within the meadows and environmental gradients (fig. 8). Relative to the amount of 

unconstrained variation, the predictor variables in the model that included the eight environmental 

variables and the meadow use classes accounted for 17.5 percent of the variation in species composition 

(table 5), whereas the variation in the models with just the eight environmental variables and just the 

meadow use classes was 15.0 and 3.9 percent, respectively. The variation explained by random effects 

within meadows was 22.1 percent. The first three constrained axes in the model with the eight 

environmental variables and the meadow use classes had meaningful contributions to variation in 

species composition (P <0.01). The first axis primarily was a topographic roughness and 

photosynthetically active radiation gradient (38.0 percent variation explained). The second axis was a 

gradient characterized by peak NDVI and the amount of shading in a plot (27.7 explained), and the third 

axis was a gradient of peak NDVI and meadow use class (10.9 percent explained). Compared to the 

environmental gradients, however, there was very little turnover in species composition among the 

meadow use classes, with the centroids of the four classes all clustered near the origin of the ordination 

space (fig. 8). Moreover, the permutation tests indicated only marginal support for meaningful levels of 

variation in species composition among the meadow use classes (P=0.071; table 6). Finally, plots in 

ungrazed and grazed meadows not used by SNBS were very similar in species composition (fig. 8).
29 

Aspectcos

PRR

Hillshade

TRI

NDVIPeak

Precip

Tmax07

Tmin01

-1 1

1

-1

Meadow 

Neither

Bighorn

Both

Pack Stock

Figure 8. Biplot of the results from a Distance-based Redundancy Analysis of species composition in meadows in 

four Sierra Nevada bighorn sheep and pack stock use classes in Sequoia and Kings Canyon National Parks, 

California, 2011–2012. The use classes were (1) not used by bighorn sheep or pack stock (Neither), (2) used by 

bighorn sheep but not pack stock (Bighorn), (3) used by bighorn sheep and pack stock (Both), and (4) used by 

pack stock but not bighorn sheep (Packstock). Circles represent the centroids of the use classes, and crosses 

represent position of the species in ordination space.
30 

Table 5. Statistics from a Distance-based Redundancy Analysis (DbRDA) of meadow vegetation species 

composition in Sequoia and Kings Canyon National Parks, California. 

[Vegetation data were collected July–August in 2011 and 2012. λ = Variation. See table 3 for definitions of variables] 

Source of variation λ Percent

Environmental 0.6250 17.5

Meadow (random) 0.7903 22.1

Unexplained 2.1600 60.4

Total 3.5753 100.0

Variable Axis 1 Axis 2 Axis 3

Bighorn only1 0.2567 -0.4620 -0.0266

Pack stock only1 -0.1558 0.0430 0.0376

Bighorn and pack stock1 0.1253 0.1579 -0.6084

Aspectcos 0.2830 -0.6581 -0.1332

PRR -0.3943 0.0490 -0.0229

Hillshade -0.0886 -0.4499 -0.2718

TRI 0.3991 -0.0896 0.1378

NDVIPeak 0.0924 0.5579 -0.6325

Precip 0.0934 0.0449 -0.0053

Tmax07 -0.1873 0.2736 0.0324

Tmin01 -0.1485 0.2786 0.0312

Variation explained

Unconstrained (percent) 8.5 6.2 2.4

Constrained (percent) 38.0 27.7 10.9

Meadow Use Centroids

Class Axis 1 Axis 2 Axis 3

No use by bighorn sheep or pack stock -0.1739 0.2460 0.2966

Bighorn sheep only 0.1206 -0.2171 -0.0125

Pack stock only -0.1748 0.0482 0.0422

Bighorn sheep and pack stock 0.1472 0.1855 -0.7146

1

Meadow use class.
31 

Table 6. Tests of the importance of eight environmental variables in a Distance-based Redundancy Analysis 

(DbRDA) of turnover in meadow plant species composition in Sequoia and Kings Canyon National Parks, 

California. 

[Vegetation data were collected July–August in 2011 and 2012. See table 3 for definitions of variables. DF = degrees of 

freedom, F = F-ratio, p = probability based on 1000 Monte Carlo simulations] 

Variable DF Variance F P

Meadow Use Class1 3 0.1414 1.877 0.071

Aspectcos 1 0.0925 3.681 0.011

PRR 1 0.0664 2.645 0.022

Hillshade 1 0.0973 3.873 0.010

TRI 1 0.0503 2.003 0.029

NDVIPeak 1 0.0630 2.509 0.031

Precip 1 0.0501 1.997 0.113

Tmax07 1 0.0224 0.890 0.415

Tmin01 1 0.0417 1.659 0.109

1

Meadow use classes: not used by pack stock or Sierra Nevada bighorn sheep, 

used by bighorn sheep but not pack stock, used by pack stock but not bighorn 

sheep, and used by both

The PCA indicated a high degree of overlap in vegetation structure among the four use classes 

(fig. 9). Meadows open to grazing by pack stock and meadows open to grazing by pack stock and 

available to SNBS had greater cover of grasses and sedges than the other two use classes. The ANOVA 

of the PCA scores indicated that the only significant difference in structure was between grazed 

meadows available to SNBS and ungrazed meadows available to SNBS (P=0.029), primarily because of 

greater sedge cover in grazed meadows and available to SNBS (fig. 9). 
32 

-6 -4 -2 0 2

-4 -2

0

2

4

PC1

PC2

Bare

Litter

Forbcv r

Grasscv r

Sedgecv r

Meadow Use

Neither

Pack Stock

Bighorn

Both

Figure 9. Principal Components Analysis biplot of vegetation structure in meadows in four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use 

classes were (1) not used by bighorn sheep or pack stock (Neither), (2) used by pack stock but not bighorn sheep 

(Packstock), (3) used by bighorn sheep but not pack stock (Bighorn), and (4) used by bighorn sheep and pack 

stock (Both).
33 

There was virtually no evidence of differences in N0 (ΔAICc=6.27; wAICc =0.96) or N1

(ΔAICc=2.69; wAICc=0.79) for herbaceous species diversity among the meadow use classes. The null 

model for N2 also had the greatest support, but the evidence was weaker (ΔAICc=1.04; wAICc=0.63). 

The diversity profiles clearly showed, however, that any differences among the use classes were 

ecologically trivial (fig. 10). Evenness was low in all meadow use classes, but there was overwhelming 

evidence that E1/d differed among them (ΔAICc=9.67; wAICc=0.99). This was because of relatively 

higher values of E1/d in plots used just by SNBS (fig. 11), but the differences were small and probably 

biologically irrelevant. There was no evidence of meaningful differences in E1/d among the other use 

classes (fig. 11). 

Herbaceous Species

Hill number (N)

Value

0 1 2

0

5 10 15 20 25

Meadow U

Neither

Bighorn

Both

Pack Stock

Figure 10. Profiles of herbaceous species diversity for meadows in four Sierra Nevada bighorn sheep/pack stock 

use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use classes were (1) not 

used by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock (Bighorn), (3) used by 

bighorn sheep and pack stock (Both), and (4) used by pack stock but not bighorn sheep (Packstock). N0 = species 

richness, N1 = the exponentiation of Shannon’s index, and N2 = the inverse of Simpson’s index. Error bars are 95-

percent confidence intervals.
34 

Use class

E1 d

Neither Bighorn Pack Stock Both

0.0 0.1 0.2 0.3 0.4 0.5

Figure 11. Simpson’s index of evenness (E1/d) in meadows in four Sierra Nevada bighorn sheep/pack stock use 

classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use classes were (1) not used 

by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock (Bighorn), (3) used by pack 

stock but not bighorn sheep (Packstock), and (4) used by bighorn sheep and pack stock (Both). Error bars are 95-

percent confidence intervals. 
35 

Wehausen (1980) described 54 herbaceous forage species used by SNBS. Of these, 27 (50 

percent) were recorded in our plots. There was overwhelming evidence that total cover of these forage 

species differed among the meadow use classes (ΔAICc=176.6; wAICc=1.00). Cover was 

approximately two times greater in plots used just by pack stock than in plots used just by SNBS or 

those not used by pack stock or SNBS, and it was approximately three times greater than in plots used 

by both (fig. 12). 

Use class

Cover of forage species (%)

Neither Bighorn Pack Stock Both

0

5 10 15 20 25 30 35

Figure 12. Percentage (%) cover of herbaceous forage species for meadows in four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use 

classes were (1) not used by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock 

(Bighorn), (3) used by pack stock but not bighorn sheep (Packstock), and (4) used by bighorn sheep and pack 

stock (Both). Error bars are 95-percent confidence intervals.
36 

There was virtually no evidence of differences in N0 (ΔAICc=6.02; wAICc=0.95), N1

(ΔAICc=4.88; wAICc=0.92), or N2 (ΔAICc = 4.94; wAICc = 0.92) for forage species diversity among 

the meadow use classes (fig. 13). Evenness was moderate in all meadow use classes, but there was 

overwhelming evidence that E1/d differed among them (ΔAICc=28.24; wAICc=1.00). This was because 

of relatively higher values of E1/d in plots used just by both pack stock and SNBS (fig. 14). The 

differences in E1/d among the four classes were small, however, and probably biologically irrelevant. 

Forage Species

Diversity order (Q)

Value

0 1 2

0 1 2

3

4

5

6

7

Meadow U

Neither

Bighorn

Pack Stock

Both

Figure 13. Profiles of herbaceous forage species diversity for meadows in four Sierra Nevada bighorn sheep and 

pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use classes were 

(1) not used by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock (Bighorn), (3) 

used by bighorn sheep and pack stock (Both), and (4) used by pack stock but not bighorn sheep (Packstock) . N0 = 

species richness, N1 = the exponentiation of Shannon’s index, and N2 = the inverse of Simpson’s index. Error bars 

are 95-percent confidence intervals.
37 

Use class

E(1/d)

Neither Bighorn Pack Stock Both

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Figure 14. Simpson’s index of evenness (E1/d) in for herbaceous forage species in four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use 

classes were (1) not used by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock 

(Bighorn), (3) used by pack stock but not bighorn sheep (Packstock), and (4) used by bighorn sheep and pack 

stock (Both). Error bars are 95-percent confidence intervals. 
38 

There was overwhelming evidence that bare ground was 10–11 percent greater in grazed plots 

not available to SNBS and ungrazed plots available to SNBS compared to plots not used by either or 

plots used by both (ΔAICc=24.88; wAICc=1.00). There was no evidence that bare ground differed in 

any ecologically meaningful way among plots not used by either pack stock or SNBS or plots used by 

both pack stock and SNBS (fig. 15). 

Use class

Bare ground (%)

Neither Bighorn Pack Stock Both

0

5 10 15 20 25 30 35 40

Figure 15. Percentage (%) cover of bare ground for meadows in four Sierra Nevada bighorn sheep and pack stock 

use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use classes were (1) not 

used by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock (Bighorn), (3) used by 

pack stock but not bighorn sheep (Packstock), and, (4) used by bighorn sheep and pack stock (Both). Bare ground 

was defined as exposed soil other than rock. Error bars are 95-percent confidence intervals.
39 

There was little evidence of differences in forage species composition among the meadow use 

classes (figs. 16–18). Similarity generally was high to moderately high regardless of the index, and the 

error bars generated from the bootstrap samples overlapped among all classes.

Forage Species

Meadow use

Sorenson's index

Bighorn Pack Stock Both

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Meadow Use

Neither

Bighorn

Pack Stock

Figure 16. Pairwise similarity in herbaceous forage species composition among four Sierra Nevada bighorn sheep

and pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use classes 

were (1) not used by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock 

(Bighorn); (3) used by pack stock but not bighorn sheep (Packstock), and (4) used by bighorn sheep and pack 

stock (Both). Error bars are standard errors generated from 1,000 bootstrap samples. 
40 

Forage Species

Meadow use

Horn's index

Bighorn Pack Stock Both

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Meadow Use

Neither

Bighorn

Pack Stock

Figure 17. Pairwise similarity in herbaceous forage species composition among four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use 

classes were (1) not used by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock 

(Bighorn), (3) used by pack stock but not bighorn sheep (Packstock), and (4) used by bighorn sheep and pack 

stock (Both). Error bars are standard errors generated from 1,000 bootstrap samples. 
41 

Forage Species

Meadow use

Morisita-Horn index

Bighorn Pack Stock Both

0.0 0.2 0.4 0.6 0.8 1.0

Meadow Use

Neither

Bighorn

Pack Stock

Figure 18. Pairwise similarity in herbaceous forage species composition among four Sierra Nevada bighorn 

sheep/pack stock use classes in Sequoia and Kings Canyon National Parks, California, 2011–2012. The use 

classes were (1) not used by bighorn sheep or pack stock (Neither), (2) used by bighorn sheep but not pack stock 

(Bighorn), (3) used by pack stock but not bighorn sheep (Packstock), and, (4) used by bighorn sheep and pack 

stock (Both). Error bars are standard errors generated from 1,000 bootstrap samples. 
42 

Discussion

Overall, the study indicated that there is little overlap in spatial use of meadows by SNBS and 

pack stock at SEKI. Meadows open to pack stock grazing generally were at large distances from SNBS 

escape terrain, and those relatively near SNBS escape terrain generally were not open to grazing by 

pack stock. Even when we used a very liberal definition of availability (250 m from escape terrain) a 

large proportion of meadows were closed to pack stock use. Furthermore, meadows open to grazing by 

pack stock and available to SNBS represented a very small proportion of all meadows on the landscape. 

These patterns were consistent regardless of whether availability was based on meadow area or 

distribution of meadows on the landscape. They were influenced minimally by sample sizes used in the 

analyses and simulations, and virtually all patterns were the opposite of patterns one would expect if 

pack stock were having negative effects on SNBS. Finally, relatively few meadows that were open to 

grazing by pack stock occurred within the herd unit polygons. However, the analyses for the 50 and 

100-m distance classes in the use-availability and Monte Carlo simulations need to be interpreted with 

some caution because of the small number of meadows available to SNBS and open to grazing by pack 

stock. This largely reflected the reality of the use class designation. However, it also could be an artifact 

of SNBS frequently using small alpine meadows that typically are smaller than the mapping resolution 

used in this study. If this was the case, however, it would only increase the level of separation between 

SNBS and pack stock because these small meadows are not open to pack stock grazing.

Cole and others (2004) reported that horses and mules preferred graminoids and altered species 

composition in herbaceous assemblages in a field experiment conducted in Yosemite National Park. 

However, the grazing intensity in their study was artificially high and likely not representative of pack 

stock grazing regimes in SEKI. There was little evidence in our study indicating that pack stock grazing 

was having a consistent effect on plant community structure or species composition in meadows. 

Differences in species composition were most related to abiotic (topographic complexity and solar 

radiation) and biotic (vegetation production) factors. Variation in species composition among the 

meadow use classes was small compared to random variation among meadows and the influence of 

environmental variables. Structure did not vary among the use classes in a direction that would be 

expected if pack stock were having a significant effect on the relative abundance of forbs or graminoids. 

For instance, total cover of SNBS forage species was greatest in plots that were open to grazing by pack 

stock and not SNBS, and sedges, which are a favored diet item of pack stock and SNBS, were most 

common in plots open to pack stock and SNBS. The amount of bare ground was similar among plots not 

used by pack stock or SNBS and those potentially used by both, and it was almost twice as high in plots 

used just by pack stock or potentially just by SNBS compared to the other two classes. Moreover, there 

was no evidence that plant diversity was lower in meadows open to grazing by pack stock than in 

meadows not open to grazing. This was the case for overall herbaceous plant diversity and forage 

species alike. Finally there were no consistent differences in species identity or relative abundance of 

the SNBS forage assemblage suggesting negative effects by pack stock.
43

These patterns underscore two very important points that Ostoja and others (2014) made in their 

review of potential pack stock effects in meadows in the Sierra Nevada. First, meadows in the Sierra 

Nevada are heterogeneous; therefore, it is likely that such relatively fine-grained variation will override 

effects from low and moderate levels of grazing. This point is consistent with our finding that the 

greatest amount of variation in herbaceous species composition was explained by random effects of the 

meadows, as well as a lack of any consistent patterns of low plant cover, more bare ground, or low 

diversity in areas open to grazing by pack stock. Second, grazing by pack stock in the Sierra Nevada 

tends to be relatively intermittent and of low intensity. This also is the case with SNBS, which occur at 

low densities, seldom stay in an area for periods of time exceeding several hours, and spend the 

overwhelming amount of their time in rocky habitats. Thus, it is possible that such a grazing regime in 

meadows in the Sierra Nevada, by either pack stock or SNBS, may either increase herbaceous plant 

species diversity or at least have a neutral effect, as has been observed in other grazing systems 

(McNaughton, 1983; Belsky, 1986).

Our findings indicate that the current plan for managing pack stock grazing at SEKI (National 

Park Service, 1986) has been successful at minimizing the likelihood of significant negative effects on 

SNBS. A critical piece of information in evaluating potential effects of pack stock on SNBS is that there 

has been no observed decrease in population size of SNBS that could be attributed to interactions with 

pack stock. On the contrary, the population of bighorn sheep in the Sierra Nevada has increased since 

being listed as federally endangered in 1999 (Stephenson and others, 2012), and in particular the herds 

in this study have all had strong positive rates of population change since then (Runcie and others,

2014).

In conclusion, we stress that these analyses provided only an indirect measure of potential, not 

actual, overlap or impacts. Direct measurement of displacement of SNBS by pack stock would require 

an intensive observational study or a manipulative experiment, both of which likely would be timeconsuming and costly. Instead of investing in such a costly study, our analyses allowed us to first assess 

how great the potential for displacement of SNBS by pack stock actually was and (or) if there was 

evidence of pack stock having a negative effect on SNBS forage. If our results indicated that the 

potential for these negative effects was high, then an investment in a more costly study would be 

justified. However, our results suggest that such an investment likely is not warranted.

Acknowledgments

Numerous personnel contributed to recovery efforts and data collection, including Steven 

Anderson, Bridgett Benedict, Todd Calfee, Jennifer Chase, Michael Cleaver, Vicki Davis, Jonathan 

Fusaro, Sarah Hoff, Stacey Huskins, Dennis Jensen, Drew Maraglia, Carli Morgan, Julia Runcie, Derek 

Spitz, Lindsay Swinger, Laurel Triatik, and Lacey Greene. We thank Landell’s Aviation, Quicksilver 

Air, and Leading Edge Aviation for their assistance in capturing and handling Sierra Nevada bighorn 

sheep. We express special thanks to Sylvia Haultain and Erik Frenzel of Sequoia and Kings Canyon 

National Parks for facilitating logistics and providing the spatial data on pack stock use. Matt Brooks, 

Susan Jones, and Danny Gammons provided helpful comments on the manuscript. The California 

Department of Fish and Wildlife, the National Park Service (Interagency Agreement P11PG80136), and 

the U.S. Geological Survey Wildlife Program funded this project.
44

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Klinger and others—Evaluating Potential Overlap Between Pack Stock and Sierra Nevada Bighorn Sheep, Sequoa and Kings Canyon Parks, California—Open-File Report 2015–1102

ISSN 2331-1258 (online)

http://dx.doi.org/10.3133/ofr20151102