Coefficients of Productivity for Yellowstone’s 

Grizzly Bear Habitat

By David J. Mattson,1 Kim Barber,2 Ralene Maw,3 and Roy Renkin4

1U.S. Geological Survey, Southwest Biological Science Center, Colorado 

Plateau Research Station, P.O. Box 5614, Northern Arizona University, Flagstaff, Arizona 86011-5614 2U.S. Forest Service, Shoshone National Forest, 808 Meadow Lane, Cody, 

Wyoming 82414 3U.S. Forest Service, Region 4, 324 25th Street, Ogden, Utah 84401 4National Park Service, P.O. Box 168, Yellowstone National Park, 

Wyoming 82190

Abstract

This report describes methods for calculating coefficients 

used to depict habitat productivity for grizzly bears in the Yellowstone ecosystem. Calculations based on these coefficients 

are used in the Yellowstone Grizzly Bear Cumulative Effects 

Model to map the distribution of habitat productivity and 

account for the impacts of human facilities. The coefficients 

of habitat productivity incorporate detailed information that 

was collected over a 20-year period (1977–96) on the foraging 

behavior of Yellowstone’s bears and include records of what 

bears were feeding on, when and where they fed, the extent 

of that feeding activity, and relative measures of the quantity 

consumed. The coefficients also incorporate information, 

collected primarily from 1986 to 1992, on the nutrient content 

of foods that were consumed, their digestibility, characteristic 

bite sizes, and the energy required to extract and handle each 

food. Coefficients were calculated for different time periods 

and different habitat types, specific to different parts of the 

Yellowstone ecosystem. Stratifications included four seasons 

of bear activity (spring, estrus, early hyperphagia, late hyperphagia), years when ungulate carrion and whitebark pine seed 

crops were abundant versus not, areas adjacent to (<100 m) 

or far away from forest/nonforest edges, and areas inside or 

outside of ungulate winter ranges. Densities of bear activity in 

each region, habitat type, and time period were incorporated 

into calculations, controlling for the effects of proximity to 

human facilities. The coefficients described in this report and 

associated estimates of grizzly bear habitat productivity are 

unique among many efforts to model the conditions of bear 

habitat because calculations include information on energetics 

derived from the observed behavior of radio-marked bears.

Introduction

The Yellowstone grizzly bear cumulative effects model 

(CEM) is used to assess the inherent productivity of grizzly 

bear habitat (see Appendix 1 for scientific names) and the 

impacts of human activities on bear use of that productivity 

potential (Weaver and others, 1986; Dixon, 1997). The CEM 

was developed by a team from the U.S. Forest Service and 

National Park Service in the mid-1980s in response to regulatory requirements that management agencies determine the 

cumulative effects of humans on grizzly bear populations 

listed under the U.S. Endangered Species Act (Dixon, 1997). 

Operations of the CEM can be characterized as those involved 

with data management, geographic information systems (GIS), 

and matrices of coefficients that are applied to map polygons 

on the basis of polygon attributes. One set of matrices is used 

to ascribe inherent habitat productivity to polygons, while 

another set of matrices is used to reduce that productivity 

depending on intersections of the habitat with “zones-ofinfluence” associated with human activities (see Appendix 

2). Coefficients of inherent habitat productivity vary with the 

season, habitat type (e.g., Steele and others, 1983), vegetation cover type (Despain, 1990), proximity to forest/nonforest 

edge, occurrence in an ungulate winter range, occurrence near 

cutthroat trout spawning streams, and occurrence near sites 

where army cutworm moths aggregate (see Mattson and others, 1986; Mattson and Knight, 1989).

Coefficients of habitat productivity that were previously 

used in operations of the Yellowstone grizzly bear CEM were 

developed in 1984, a time when relevant data were limited 

or even unavailable (Dixon, 1997). Because of limited data, 

it was understood that habitat coefficients were to be used 

primarily to assess and refine model performance. It was 

further assumed by those involved in developing the CEM that 

coefficients suitable for model applications would be developed at some later date when more of the requisite data were 

available, allowing not only for greater sample sizes but also 

for improvement in methods.

Much of the data that were missing or sparse in the mid1980s are currently available. Previous coefficients used in 

model operations were based on grizzly bear data collected 

from 1977 to 1983. Since then, the amount of relevant grizzly 
2 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

bear data has more than tripled. More important, information 

was collected from 1986 to 1996 with the intent of remedying 

deficiencies identified during the calculation of coefficients 

in 1984. Many of the parameters arrived at by professional 

judgement in 1984 can now be estimated empirically. Similarly, digital maps for estimating the aerial extent of different 

habitat strata were available only for the Yellowstone National 

Park portion of the ecosystem or, for some features, were not 

available at all. This situation has changed dramatically. Digital data for all relevant map features, for the full extent of the 

Yellowstone ecosystem, are now available.

New data and new analytical methods led to a directive 

from the Yellowstone ecosystem’s grizzly bear managers for 

researchers to recalculate matrices of coefficients used in the 

Yellowstone grizzly bear CEM for assessing inherent habitat 

productivity. This charge stemmed from a growing appreciation of the limits of historical coefficients and a desire to 

incorporate as much of the newer grizzly bear information as 

possible, using improved methods for calculations. The data 

and methods used to recalculate habitat coefficients for the 

Yellowstone ecosystem are described in this paper.

Objective

Our primary objective was to produce coefficients that 

can be (1) applied to currently mapped features of Yellowstone 

grizzly bear habitat and (2) used to calculate unit-area estimates of energy and nutrients derived by grizzly bears from 

specified map polygons. These estimates account for digestive efficiencies as well as certain energetic costs. The resulting map of relative unit-area net digested energy is roughly 

equivalent to a map of habitat capability or productivity. The 

“new” coefficients incorporate all of the available and relevant 

information from analyses of grizzly bear foraging activity 

conducted from 1977 to 1996 by the Interagency Grizzly Bear 

Study Team (IGBST). The IGBST was formed in 1973 and 

currently consists of the U.S. Geological Survey, National 

Park Service, U.S. Forest Service, and game management 

agencies from the States of Wyoming, Montana, and Idaho.

Other analyses of grizzly bear habitat use in the Yellowstone ecosystem have focused on estimating grizzly bear 

distribution with respect to explanatory features of their 

habitat, with an emphasis on the effects of human facilities 

(see Mattson and others, 1987, 1992; Mattson, 1997a). These 

analyses have not explicitly incorporated detailed information 

on grizzly bear foraging behavior and the associated gains or 

losses of energy and nutrients. The Yellowstone ecosystem is 

unique in having a large amount of this information available. 

Furthermore, the energetics of different activities, ranging 

from travel to consumption of high quality foods such as 

ungulate meat or seeds of whitebark pine, vary by orders of 

magnitude (Hamer and Herrero, 1987; Mattson, 1997a).

The primary response variable in this analysis is a timespecific index of net digested energy, rather than a timespecific probability of location. In this regard, other analyses 

have not focused on estimating the inherent “productivity” or 

“capability” of grizzly bear habitat, which is the primary aim 

of the approach described here. Although “productivity” is 

somewhat of an abstract parameter, it is foundational to operations of the CEM for grizzly bear habitat in the Yellowstone 

ecosystem. The CEM begins by calculating intrinsic habitat 

productivity and then reduces that value by varying degrees 

near human facilities or activities. In theory, this decrease in 

productivity value reflects reductions in “food availability” 

that are either a result of humans selectively killing bears that 

use human-influenced niches or of bears avoiding these same 

areas because they are wary of humans (Mattson and others, 1987, 1992, 1996; Pease and Mattson, 1999). Thus, the 

calculation of coefficients described here is tailored to grizzly 

bear habitat use and grizzly bear and human interactions as 

conceptualized in the Yellowstone CEM.

Methods

Field Methods

We obtained data from grizzly bears that were trapped 

and radio-marked in the Yellowstone ecosystem from 1975 to 

1996. We located these marked bears from fixed-wing aircraft 

by aerial telemetry once to twice a week. Although trapping 

was done in a way that attempted to represent different parts of 

the Yellowstone ecosystem, it was not randomized, especially 

with respect to distance from roads. Some Bear Management 

Units (BMUs) were also undersampled because of low bear 

densities and/or low levels of trapping effort. See Knight 

and Eberhardt (1985) and Blanchard and Knight (1991) for 

detailed descriptions of trapping and telemetry location 

methods.

Triplet grizzly bear cubs (third cub is behind cub on right) on the 

Two Ocean Plateau of Yellowstone National Park. Although most 

grizzly bear females have litters of two cubs, females with access 

to abundant whitebark pine seeds more often have triplets (photo 

by Bart Schleyer, Interagency Grizzly Bear Study Team).
 3

During 1977–96, field crews visited and sampled sites 

where radio-marked grizzly bears had been located by aerial 

telemetry. Feeding activity was not documented at many of 

these bear-specific locations, although bear signs were found 

at most sites (Mattson, 1997a). Field crews identified and 

analyzed additional grizzly bear activity sites while on the way 

to and from radio-telemetry locations selected for sampling. 

Feeding activity at these sites was not ascribed to a specific 

bear. Our subsampling of bear telemetry locations for visitation was representative and not random, primarily because of 

logistical constraints imposed by limited funding and limited 

helicopter access to the Yellowstone ecosystem area, which is 

mostly nonroaded (Mattson, 1997a). Approximately 88% of 

the primary study area was >500 m from a road of any type.

We classified all grizzly bear activity sites according 

to the habitat type and cover type used to map grizzly bear 

habitat in the Yellowstone ecosystem (Mueggler and Stewart, 

1980; Steele and others, 1983; Mattson and Despain, 1985). 

Field crews also described the targeted food and the intensity 

of associated feeding. During 1986–96, the extent or intensity 

of feeding activity was quantified (Mattson, 1991; Mattson, 

1997a). For example, the volume of log, hill, or red squirrel midden debris excavated by bears foraging for ants or 

whitebark pine seeds was estimated (Mattson, 2001). Excavated whitebark pine cones were also counted (Mattson and 

Reinhart, 1997). The number of excavations for root foods 

and the number of roots obtained per individual excavation 

were estimated, as was the total volume of earth excavated in 

pursuit of rodents and the total number of rodent root caches 

or nests exploited (Mattson, 2004). Feces present at a feedsite 

were counted. Thus, for each activity site where feeding activity was found, grizzly bear activity was characterized by total 

volumes of excavations, as well as by total numbers of excavations, rodent nests, cones, and/or feces, in terms that could be 

compared among sites for a given feeding activity.

During 1986–96, field crews collected other data that 

pertained to the nutrient content of foods and the energetic 

costs of food extraction. A claw-o-meter (Holcroft and Herrero, 1984; Mattson, 1997c) was used to estimate how easy or 

difficult it was to excavate various substrates, including soils, 

logs, and anthill and squirrel midden debris. These measures 

provided a representation of energy expenditure (in maximum 

kilograms of resistance) that was comparable among sites and 

feeding activities. Samples of bear foods were also collected at 

feeding sites and analyzed for nutrient content (crude protein, 

crude fiber, total dietary fiber, starch, and ash). Other authors 

analyzed the nutrient content of foods for which we did not 

collect this information (e.g., whitebark pine seeds and army 

cutworm moths [Mattson and Reinhart, 1994; White, 1996]). 

In addition, we obtained seasonal estimates of ungulate carcass composition from Mitchell and others (1976), Anderson 

(1981), Bubenik (1982), Swift (1983), and Berger and Peacock 

(1988). Pond and Ramsay (1992) provided general allometric 

relations between adipose reserves and body mass. In combination with the work of Pritchard and Robbins (1990), these 

data allowed us to estimate amounts of digested energy and 

nutrients, comparable among foods and seasons.

We obtained estimates of volumes consumed per bite or 

other measured indicators of feeding activity at grizzly bear 

feedsites or derived this information from published research. 

Numbers of seeds were counted in whitebark pine cones. Bite 

sizes of foliage (in grams, dry weight per bite) were estimated 

by simulating grizzly bear grazing (Hudson and Frank, 1987) 

and were confirmed by comparison with published observations of grizzly bear bite sizes estimated under controlled conditions (Gross and others, 1993a, 1993b). Bite sizes of roots 

were estimated by weighing samples of excavated representative plants (Mattson, 1997c). Bite sizes of berries were derived 

from Welch and others (1997), assuming 1.5 berries per bite. 

Sizes of rodent root caches were estimated from excavated 

samples (Mattson, 2004) and were confirmed by comparison 

with estimates in Stuebe and Anderson (1985). Total mass 

consumed from ungulates was based on the species, gender, 

and age class, estimated amount of total edible biomass consumed by bears, and standardized tables of edible biomass for 

different carcass types (Mattson, 1997b). We obtained point 

estimates of ant, hornet, worm, and rodent biomass consumed 

per nest or unit volume of excavated material from the published literature (ants and hornets: Brian, 1978; Peakin and 

Josen, 1978; Akre and others, 1980; Redford and Dorea, 1984; 

Noyce and others, 1997; worms: Lawrence and Millar, 1945; 

Grant, 1955; Lee, 1985; rodents: Hansen and Bear, 1964; 

Pitts and Bullard, 1968; Hansen and Reid, 1973; Pinter, 1979; 

Anderson and MacMahon, 1981; Chase and others, 1982; 

Campbell and Dobson, 1992).

Field crews also collected bear feces while sampling 

grizzly bear activity sites from 1977 to 1996. During 1989–96, 

we also recorded the total volume of each collected feces. We 

used this information in conjunction with scat correction factors (milliliter of fecal volume to milligram of ingested mass; 

Hewitt and Robbins, 1996) and estimates of proportional fecal 

composition (Mattson and others, 1991a) to estimate ingested 

diet on a seasonal basis for 1989, 1991, and 1992, excluding 

feces that were known or suspected to be from black bears. 

Our analysis used these estimates of ingested diet for these 

3 years. We did not estimate seasonal ingested diet for 1990 

because some raw data were not available.

Analysis Methods

Our analysis methods were defined by three major tasks. 

First, we estimated relative net energy digested per gram of 

ingested food, by season where a difference was evident. 

Second, we estimated relative net gain of energy per feeding 

site by season and habitat type. Third, we estimated relative 

density of bear feeding activity by season, region, and habitat 

type, controlling for the effects of proximity to roads and other 

major human-related physical features (developments). We 

calculated final coefficients as the product of relative density 

of feeding activity times average relative net energy digested 

Methods
4 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

per feeding site (feedsite). The following sections describe the 

strata and methods that we used for each task. Table 1 lists and 

defines the variables that we used in calculations.

Stratifications

We calculated coefficients for several spatial and temporal stratifications. Spatial stratifications were by (1) habitat 

type, (2) ungulate winter range, (3) ecosystem region, and (4) 

forest and nonforest ecotone. Temporal stratifications were by 

(1) season and by type of year based on whether (2) whitebark 

pine seeds and/or ungulate carrion were heavily used or not. 

The following sections describe these stratifications in detail.

Spatial

Habitat Type

We stratified the study area into 18 forest/nonforest habitat types that were derived from previously mapped and 

identified mapping units (see Appendix 3 for a list of habitat 

types). Mapping units were described in previously published 

Table 1. Description of variables used in calculation of coefficients of productivity (coefjklmn) for grizzly bears, for habitat types in the 

Yellowstone ecosystem.

Variable Description Stratification

avefsjklm Average net digested energy per habitat type k by season j, year type l, and region m; does not differ by

edge type

cfctrij Factor for converting units of feeding activity to grams by season j; does not differ by habitat type, year type,

ingested for each food i, averaged over years h region, or edge type

denjklmn Total density of bear activity in habitat type k by season j, year type l, region m, and edge type n

eeij Relative energy expended per gram of food i by season j; does not differ by habitat type, region, year 

type, or edge type

fdjklmn Total density of feedsites in habitat type k by season j, year type l, region m, and edge type n

fslvijk Total units of feeding activity involving food i per feedsite by season j; does not differ by region, year type, or edge 

in habitat type k type

∑ fslvhij Total units of feeding activity involving food i summed does not differ by region, year type, or edge type 

over all habitat types for year h

fsneijk Net digested energy from food i per feedsite in habitat type k by season j; does not differ by region, year type, or edge 

type

fvolhij Total ingested grams of food i during year h (from fecal does not differ by region, year type, or edge type

analysis)

iexcij Mean volume (cubic decimeter) excavated per individual by season j; does not differ by habitat type, region, year 

excavation for food i type, or edge type

imassij Mean grams of food i ingested per feedsite by season j; does not differ by habitat type, region, year 

type, or edge type

neteij Relative net digested energy per gram of food i by season j; does not differ by habitat type, region, 

year type, or edge type

pactjkl Proportion of total activity in habitat type k that involved by season j and year type l; does not differ by region 

feeding of some type or edge type

pdeij Percent of total energy digested from food i by season j; does not differ by habitat type, region, 

year type, or edge type

propijklm Proportion of total feeding activity in habitat type k involving by season j, region m, and year type l; does not differ by 

food i edge type

resistij Kilogram of resistance per individual excavation for food i by season j; does not differ by habitat type, year type, 

region, or edge type

teij Total energy content per gram of food i by season j; does not differ by habitat type, year type, 

region, or edge type

vexcij Mean total volume (cubic decimeter) excavated per feedsite by season j; does not differ by habitat type, year type,

involving food i region, or edge type
Methods 5

cover type and habitat type classifications (see Pfister and 

others, 1977; Mueggler and Stewart, 1980; Steele and others, 

1983; Mattson and Despain, 1985). Habitat type maps were 

based on interpreting aerial photographs and field-classifying 

the delineated polygons (Mattson and Despain, 1985). We 

updated these maps to account for the effects of extensive fires 

that occurred during 1988 by analyzing satellite imagery. We 

used prefire and postfire maps in analyses, depending on the 

date that data were collected. We defined the 18 habitat types 

used in this study by clustering the previously mapped habitat 

types described in Appendix 3 on the basis of similarities of 

grizzly bear activities within each (tables 2 and 3). We used 

Euclidean distances and average linkages for the initial statistical clustering. We made subjective refinements to this clustering based on site and vegetation similarities of habitat types 

(tables 2 and 3). In particular, we reassigned nonforest habitat 

types characterized by few (n ≤ 5) samples of grizzly bear 

activity to the habitat categories of either mesic meadows and 

grasslands, wet meadows, or marshes and fens on the basis of 

site wetness and the related presence of indicative plant species (table 2). Small sample sizes caused unstable estimates 

of bear activity and made grouping of habitat types on the 

basis of other traits desirable for the purposes of mapping and 

description.

We lumped aggregate habitat types that were sparse 

(≤1% of the landscape) with other types that were more 

common based on similarities of site and vegetation features. 

Marshes and fens were uniformly rare and were combined 

with wet meadows for all analyses. High-water-table flux wetlands and clover patches were not mapped and were subsumed 

in areas identified as wet meadows. Miscellaneous other nonforest types (e.g., water and human features) were not included 

in the analyses.

Ungulate Winter Range

We stratified each region as being in bison winter range, 

in wapiti winter range, or in neither range. Bison winter range 

included areas used by wapiti and bison as well as areas used 

by bison alone. Wapiti winter range was not used by bison 

except incidentally. Ungulate winter ranges are a potentially 

important feature of grizzly bear habitat because grizzly bears 

in the Yellowstone ecosystem derive substantial energy from 

ungulates, principally from carrion on ungulate winter ranges 

(Mattson, 1997b). Furthermore, we distinguished between 

winter ranges with bison and those without because Yellowstone grizzly bears consume more meat from bison, per capita, 

than from any other ungulate species (Green and others, 1997; 

Mattson, 1997b).

For spring only (see the subsection on season, p. 10), we 

calculated a coefficient that applied to all habitat types within 

and outside of ungulate winter ranges if an effect of winter 

range was evident statistically (see subsection on year type 

by bear use of ungulate carrion, p. 12). We did not investigate 

interactions between winter range and habitat type because of 

insufficient sample sizes. We usually did not detect an effect of 

ungulate winter range where winter range was closely associated with specific habitat types. In these cases, habitat type, as 

such, functioned as a surrogate for the distribution of winter 

ranges.

Ecosystem Region

We calculated coefficients for each habitat type for each 

of four regions within the Yellowstone ecosystem that were 

identified with existing BMUs (figs. 1 and 2). We had 

identified these regions for previous analyses and found them 

to be associated with differences in abundance of key bear 

foods and grizzly bear foraging behavior (Mattson, 1997a, 

1997b). Knight and others (1984) and Despain (1990) provide 

additional descriptions of these regions. We included the following BMUs in each of the four regions: in the north, Gallatin (#2), Washburn (#9), and Lamar (#5) BMUs; in the east, 

Crandall/Sunlight (#6) and Shoshone (#7) BMUs; in the west, 

Firehole/Hayden (#10) and Madison (#11) BMUs; and, in the 

south, Pelican/Clear (#8), Two Ocean/Lake (#14), Thorofare 

(#15), and Buffalo/Spread Creek (#17) BMUs. Some BMUs 

on the periphery of the Yellowstone ecosystem, known to be 

undersampled, were excluded from analysis (fig. 2; Hilgard 

[#1], Hellroaring/Bear [#3], Boulder/Slough [#4], Henry’s 

Lake [#12], Plateau [#13], South Absaroka [#16], and Bechler/

Teton [#18]). Coefficients calculated for regions containing 

BMUs #1, #3, #4, and #16 would apply in these areas. We 

have not yet determined appropriate sources of extrapolation 

for BMUs #12, #13, and #18.

We also stratified the south and west regions on the basis 

of BMUs that did and did not contain substantial numbers of 

bison year-round. Identification of BMUs with a “bison effect” 

Bull bison in central Yellowstone National Park. Bison are heavily 

scavenged by grizzly bears and provide the bears with more meat 

per carcass than any other type of scavenged ungulate (photo by 

Interagency Grizzly Bear Study Team).
6 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 2. Aggregate nonforest habitat types were defined by clustering constituent nonforest habitat types on the basis of grizzly bear 

activity in each type. Characteristic bear activities are shown as a percent of the total observations of bear activity within each type.

[Numeric designations are given for each type in parenthesis. Habitat types are further defined in Appendix 3. An asterisk (*) indicates a habitat type reallocated 

on the basis of similarity of site characteristics]

Aggregate and constituent nonforest habitat types (numeric designation) Characteristic activities in habitat type (percent)

Talus and scree (00007) Digging moths 85%

 Bedding 15%

Lithic ridges (00004) Digging biscuitroots 75%

Lithic alpine No feeding sign 14%

Geum rossii/Trifolium parryi Grazing clover 9%

Festuca idahoensis/Delphinium bicolor

F. idahoensis/Arenaria congesta

Lithic F. idahoensis

Lithic Artemisia tridentata

Lithic Poa spp.

Lithic Lomatium triternatum

Lithic forb

Dry meadows and grasslands (00002) No feeding sign 54%

Festuca idahoensis/Agropyron spicatum Grazing graminoids 17%

F. idahoensis/Stipa richardsonii Digging biscuitroots 15%

F. idahoensis/Agropyron caninum Digging pocket gophers 14%

F. idahoensis/Deschampsia caespitosa* Digging yampa 9%

Artemisia tridentata/F. idahoensis-F. idahoensis*

Potentilla fruticosa/F. idahoensis

Barren geothermal

Mesic geothermal

Mesic meadows and grasslands (00006) Digging yampa 28%

F. idahoensis/Agropyron caninum-Geranium viscosissimum Grazing graminoids 24%

Phleum alpinum/A. caninum-Carex microptera Digging pocket gophers 22%

Artemisia tridentata/F. idahoensis-Geranium viscosissimum Digging ants (anthills) 16%

Artemisia cana/F. idahoensis No feeding sign 11%

Lupinus argenteus/Fragaria virginiana

Clover patches (00001) Grazing clover 100%

 Grazing graminoids 33%

 Flipping rocks 33%

Wet meadows (00008) Grazing graminoids 41%

Salix geyeriana/Calamagrostis canadensis No feeding sign 31%

S. geyeriana/Fragaria virginiana Digging pocket gophers 12%

Salix wolfii/Carex aquatilis Browsing elk thistle 9%

S. wolfii/Fragaria virginiana Digging yampa 9%

Artemisia cana/Carex aquatilis Bedding 9%

A. cana/Fragaria virginiana

Potentilla fruticosa/Deschampsia caespitosa

Carex aquatilis/Pedicularis groenlandica

C. aquatilis/Deschampsia caespitosa

Calamagrostis canadensis/Deschampsia caespitosa

C. canadensis/Senecio triangularis*

Deschampsia caespitosa/Carex spp.*

D. caespitosa/Juncus balticus*

Phleum alpinum/Carex aquatilis

P. alpinum/C. microptera

Heracleum lanatum/Rudbeckia occidentalis

Marshes and fens (00005) No feeding sign 47%

Salix geyeriana/Carex rostrata Grazing graminoids 33%

Carex aquatilis/Salix phylicifolia Ungulates 22%

Carex rostrata/C. rostrata

Calamagrostis canadensis/C. canadensis

Scirpus olneyi/S. olneyi

High-water-table flux wetlands (00003) Digging pondweed 100%

Carex vesicaria/C. vesicaria Grazing graminoids 33%
 7

Table 3. Aggregate forest habitat types were defined by clustering constituent forest habitat types on the basis of grizzly bear activity 

in each type. Characteristic bear activities are also shown as a percent of the total observations of bear activity within each type. 

[Acronym and numeric designation are given for each type in parentheses. Habitat types are further defined in Appendix 3]

Aggregate and constituent forest habitat types (acronym and numeric designation) Characteristic activities in habitat type (percent)

Low elevation spruce-dominated sites (LPIEN, 10601) No feeding sign 54%

Picea engelmannii/Equisetum arvense Grazing graminoids 17%

P. engelmannii/Galium triflorum Grazing horsetail 17%

 Digging ants (logs) 14%

 Ungulates 9%

Low elevation lodgepole pine-dominated sites (LPICO, 10501) No feeding sign 49%

Abies lasiocarpa/Carex geyerii Digging ants (logs) 20%

Pinus contorta/Purshia tridentata Bedding 16%

P. contorta/Festuca idahoensis Ungulates 14%

P. contorta/Calamagrostis rubescens

P. contorta/Carex geyerii

P. contorta/Carex rossii

Mesic Douglas-fir-dominated sites (MPSME, 10801) Digging ants (logs) 44%

Pseudotsuga menziesii/Symphoricarpos albus No feeding sign 40%

P. menziesii/Calamagrostis rubescens Bedding 9%

P. menziesii/Spiraea betulifolia

Abies lasiocarpa/Vaccinium globulare-V. globulare

Populus tremuloides series

Mesic subalpine fir climax sites (MABLA, 10701) No feeding sign 51%

Abies lasiocarpa/Actaea rubra Digging ants (logs) 20%

A. lasiocarpa/Thalictrum occidentale Bedding 14%

A. lasiocarpa/Symphoricarpos albus Grazing 8%

A. lasiocarpa/Calamagrostis rubescens Ungulates 7%

A. lasiocarpa/Calamagrostis canadensis Digging sweet-cicely 6%

A. lasiocarpa/Osmorhiza chilensis

High elevation or dry Douglas-fir-dominated sites (HPSME, 10301) No feeding sign 71%

Pseudotsuga menziesii/Juniperus communis Bedding 15%

P. menziesii/Arnica cordifolia Digging ants (logs) 9%

P. menziesii/Symphoricarpos oreophilus Grazing graminoids 9%

P. menziesii/Berberis repens

Abies lasiocarpa/B. repens

High elevation subalpine fir climax sites (HABLA, 10101) No feeding sign 58%

Abies lasiocarpa/Vaccinium globulare-V. scoparium Digging ants (logs) 17%

A. lasiocarpa/Juniperus communis Bedding 11%

A. lasiocarpa/Arnica cordifolia Whitebark pine seeds 11%

Pinus albicaulis/Vaccinium scoparium

Sites dominated by grouse whortleberry (HVASC, 10401) No feeding sign 63%

Abies lasiocarpa/Vaccinium scoparium-Calamagrostis rubescens Digging ants (logs) 16%

A. lasiocarpa/Vaccinium scoparium-V. scoparium Bedding 12%

Pinus contorta/Vaccinium scoparium Whitebark pine seeds 9%

High elevation whitebark pine dominated sites (HPIAL, 10201) Whitebark pine seeds 45%

Abies lasiocarpa/Arnica latifolia No feeding sign 35%

A. lasiocarpa/Vaccinium scoparium-Pinus albicaulis Digging ants (logs) 11%

Pinus albicaulis/Festuca idahoensis Bedding 9%

Whitebark pine cover types on any habitat type

Dry forest openings created by timber harvest of fire (10100) No feeding sign 58%

Seedling-sapling cover type on LPICO, HVASC, HPSME, HABLA, Grazing graminoids 16%

 and HPIAL

 Bedding 11%

 Digging ants 11%

Mesic forest openings created by timber harvest or fire (10600) No feeding sign 44%

Seedling-sapling cover type on LPIEN, MPSME, and MABLA Grazing graminoids 24%

 Bedding 11%

 Digging ants 10%

Methods
8 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Figure 1. Map of the Yellowstone grizzly bear study area showing Yellowstone National Park (delineated by 

a dashed line) and the 18 numbered and named Bear Management Units that compose the Yellowstone grizzly 

bear recovery area.

was contingent on evidence that grizzly bears made substantial 

use of bison in these areas. In the south, the Pelican/Clear (#8) 

BMU and, in the west, the Firehole/Hayden (#10) and Madison (#11) BMUs were treated as containing year-round bison 

populations heavily used by bears; 84% of all grizzly bear use 

of bison during 1977–96 occurred in these three BMUs. We 

introduced this additional level of stratification because bison 

are so energetically important to bears (Mattson, 1997b) and 

because bison range in the Yellowstone ecosystem is highly 

circumscribed (Greater Yellowstone Coordinating Committee, 

1987).

Forest/nonforest Ecotone

We further stratified habitat types by whether they were 

within or beyond 100 m of forest/nonforest edge; 100 m was 

roughly the extent of this ecotone’s effect on grizzly bear 

foraging activity (Graham, 1978; Blanchard, 1983; Mattson, 

1997c). We calculated coefficients for forest/nonforest edge 

by region and season but only in instances where an effect of 

edge was statistically evident. We did not investigate interactions between ecotone and habitat type because of insufficient 

sample sizes. We also did not estimate differences in the 

proportional occurrence of feeding activities by habitat type 
Methods 9

Figure 2. Map of the Yellowstone grizzly bear recovery area showing delineations of regions (north, east, south, and west). Bear 

Management Units (BMUs) from which data were used for development of cumulative effects model coefficients are colored 

green, purple, or brown. BMUs with year-round bison populations used heavily by grizzly bears are identified by number (BMUs 

#8, #10, and #11). The boundary of Yellowstone National Park is shown as a dashed line. Arrows indicate the source of coefficients 

applied to BMUs (colored yellow) that were not used in calculations.
10 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

for areas within and beyond ecotones, again because of limited 

sample sizes.

Temporal

Season

We calculated coefficients for each spatial stratification 

(habitat type, ungulate winter range, ecosystem region, and 

forest/nonforest ecotone) for each of four seasons of bear 

activity—spring, estrus, early hyperphagia, and late hyperphagia (table 4). Early hyperphagia was of shorter duration than 

the other seasons.

Year Type by Bear Use of Whitebark Pine Seeds

We calculated coefficients for each spatial stratification, 

for early and late hyperphagia only, distinguishing between 

years for which consumption of whitebark pine seeds by grizzly bears was a major feeding activity and years for which it 

was not. We based determinations of year type on the level 

of use of pine seeds by bears, which was evident in feces 

collected at feedsites and examined during field sampling of 

grizzly bear radio-telemetry locations (tables 5–7). Heavy use 

roughly corresponded to years when mean cone production on 

whitebark pine trees at permanent transects exceeded 20 cones 

per tree, compared to years when production was <20 cones 

per tree (Mattson and Reinhart, 1994).

Table 4. Definition of seasons for analyzing Yellowstone grizzly bear data.

Spring—den emergence through 15 May

Approximately corresponds to hypophagia (sensu Nelson and others, 1983) and the period during which ungulate carrion is available to and used by grizzly bears on ungulate winter ranges (Mattson, 1997b; Green and others, 1997).

Estrus—16 May through 15 July

Approximately corresponds to the mating season and the period of female estrus (Schleyer, 1983; Craighead and others, 1995); this 

period also begins with the advent of predation on wapiti calves (Gunther and Renkin, 1990) and coincides with the period during 

which the majority of fishing for spawning cutthroat trout occurs (Reinhart and Mattson, 1990; Mattson and Reinhart, 1995).

Early hyperphagia—16 July through 30 August

Approximately corresponds to the early part of hyperphagia (sensu Nelson and others, 1983), as indicated by an escalation in feeding activity (Mattson and others, 1991a; Mattson, 1997a). This period is distinguished by the unavailability of whitebark pine seeds 

from the current year’s crop (Mattson and others, 1994), by the advent of foraging in alpine cirques for army cutworm moths (Mattson and others, 1991b; French and others, 1994), and by an increase in excavations for roots of biscuitroot and yampa (Mattson and 

others, 1991a).

Late hyperphagia—1 September through advent of denning

Approximately corresponds to the later part of hyperphagia (sensu Nelson and others, 1983), as indicated by continued high levels 

of feeding activity (Mattson and others, 1991a; Mattson, 1997a). This period is distinguished by the excavation of red squirrel middens for whitebark pine seeds from the current year’s crop, during years when seed crops are relatively large (Mattson and others, 

1994). This period also corresponds to an escalation in consumption of ungulates related to rutting activity and post-rut mortality of 

bull bison, wapiti, and moose (Mattson, 1997b), and the availability of carcass remains from ungulates killed by hunters.

Whitebark pine tree on Mount Washburn in Yellowstone National 

Park. The whitebark pine produces cones with large fat-rich 

seeds that are a major food of especially female grizzly bears 

(photo by David Mattson, U.S. Geological Survey).
Methods 1

1

Table 5. Frequency of feeding activity and percent volume in feces related to grizzly bear use of ungulates in the spring and whitebark pine seeds during estrus and hyperphagia in the Yellowstone ecosystem, 1973-96. Counts of carcasses from transects in the Firehole/Hayden winter range and of cones from whitebark pine transects are also given. [Numbers in bold meet criteria for a “use” year (Y) either for ungulates or whitebark pine seeds, while numbers in parentheses are based on small (≤20) samples]

Spring ungulate use Early season (estrus early hyperphagia) Late hyperphagia

Whitebark pine seed use Whitebark pine seed use

Year Ungulate Volume in Carcass Pine seed Volume in Pine seed Volume in Cone

feedsites May feces counts feedsites feces feedsites September feces counts

Percent n Percent n n Percent n Percent n Percent n Percent n n

73 (32)eh (25)eh74 (8)eh (99)eh75 (4%, n = 68)f (5%, n = 37)g76 (45%, n = 23)f (73%, n = 29)g77 4 76 38 37 0 44 2 212 (0) 13 0 2778 24 55 (29) 11 2 174 3 364 (33) 12 60 9279 13 47 11 61 12 162 51 579 51 82 74 11180 35 40 (37) 20 2 45 8 240 51 39 (25) 12 2681 9 23 3 26 6 51 5 161 (0) 6 (0) 5 1382 (Heavy winter kill) (40) 20 6 99 8 24 2 39 1783 (80)a 15 (15) 15 (0) 17 1 190 (0) 1 (0) 6 1784 -- 0 (18) 11 (0) 1 2 343 -- 0 (50) 8 685 4 53 (5) 20 51 (0) 7 10 355 27 26 72 43 2786 (17) 12 17 32 74 17 209 18 324 2 82 9 109 187 11 56 2 42 16 14 280 23 292 40 104 64 78 288 16 74 18 27 47 2 323 1 215 0 79 0 61 289 52 56 33 85 325 5 288 5 366 75 61 62 133 4990 2 53 5 33 6 10 264 25 401 15 40 13 74 291 (0) 11 24 44 2 235 4 248 58 64 77 70 1692 13 90 6 31 (32)c 1 189 2 153 48 54 53 41 1593 27 22 (18)b (59)b (21)c 0 99 (0)d (150)d (0) 20 (15)h (33)h 1094 (0) 14 (9)b (64)b (6)c 0 99 (0)d (119)d 0 33 (2)h (32)h 295 (12) 17 (6)b (50)b (24)c 1 83 (0)d (54)d (0) 4 (0)h (7)h 396 (20) 4 (2)b (20)b (35)c 7 60 (12)d (39)d 86 29 (75)h (47)h 25

aDuring 1983 crews oversampled sites where bears fed on ungulates.

bThese values were obtained from IGBST annual reports and are for the period March-June. Raw data for these years were not available for analysis.cThese counts were obtained using a different protocol compared to 1985-90.dThese values were obtained from IGBST annual reports and are for the period July-August. Raw data for these years were not available for analysis.eThese values were obtained from summaries in Mealey (1975). Raw data for these years are unavailable.fThese values were obtained from the 1976 IGBST annual report and are for the entire year. Raw data for these years are unavailable.gThese values were obtained from summaries in Blanchard (1978) and are for the entire year. Raw data for these years are unavailable.hThese values were obtained either from IGBST annual reports or Mealey (1975) and are for the period September-October. Raw data were unavailable for analysis.
12 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 6. Rule set for classifying years as either being a heavy (Y = yes) or light (N = no [not heavy]) year for Yellowstone grizzly bear 

use of ungulate carrion and whitebark pine seeds. 

[Determinations for each year are given in table 7]

Spring use of ungulate carrion1

If either percent ungulate feedsites ≥ 20 (and n > 20) or percent ungulate volume in May feces ≥ 20 (and n > 20), then UNG2 = Y.

If n ≤ 20 for feedsites and feces then UNG = Y if percent ungulate feedsites ≥ 20 and percent ungulate volume in May feces ≥ 20.

Late hyperphagia use of whitebark pine seeds3

If either percent whitebark pine feedsites ≥ 20 (and n > 20) or percent whitebark pine seed volume in September feces ≥ 20 (and n > 20), then

WBP(L)4 = Y.

If n ≤ 20 for feedsites and feces then WBP(L) = Y if percent whitebark pine feedsites ≥ 20 and percent whitebark pine seed volume in 

September feces ≥ 20.

If information on feedsites and feces is missing, then WBP(L) = Y if mean cone count/tree ≥ 20.

Early season (estrus − early hyperphagia) use of whitebark pine seeds

If either % whitebark pine feedsites ≥ 10 (and n > 20) or percent whitebark pine seed volume in feces ≥ 15 (and n > 20), then WBP(E)5 = Y.

If n ≤ 20 for feedsites and feces then WBP(E) = Y if percent whitebark pine feedsites ≥ 10 and percent whitebark pine seed volume in feces 

≥ 15.

Year-long use of whitebark pine seeds

If either WBP(E) or WBP(L) = Y then WBP(year-long) = Y.

1

May feces were used for determining spring levels of ungulate use because of the greater sample sizes collected during this month and because fecal volumes 

at this time are more sensitive to the abundance of carrion, given the greater number of foraging options available. 2

“UNG” is the variable name used in our calculations to denote whether grizzly bears made heavy (Y) or light (N) use of ungulates during spring of that year. 

3

September feces were used for determining levels of whitebark pine seed use during late hyperphagia because of the relatively consistent sample sizes collected during this month, in contrast to the considerable variation in sample sizes or absence of data collected during October. 4

“WBP(L)” is the variable name used in our calculations to denote whether grizzly bears made heavy (Y) or light (N) use of whitebark pine seeds during late 

hyperphagia of that year. 5

“WBP(E)” is the variable name used in our calculations to denote whether grizzly bears made heavy (Y) or light (N) use of whitebark pine seeds during early 

hyperphagia of that year.

Year Type by Bear Use of Ungulate Carrion

We calculated coefficients for each spatial stratification, for spring only, distinguishing between years for which 

consumption of carrion by grizzly bears was a major feeding 

activity and years for which it was not. We based determinations of year type on the level of ungulate use by bears evident 

in feces collected and at feedsites examined during field sampling of grizzly bear radio-telemetry locations (tables 5–7). 

Heavy use of carrion roughly corresponded to years when 

the number of carcasses found on ungulate carcass transects 

exceeded 40 carcasses compared to years when this count was 

lower (Green and others, 1997).

Net Energy Digested per Gram of Ingested Food

We calculated a relative measure of the net energy 

digested per gram of dry weight ingested food (neteij) for feeding activity i and season j as the product of total energy (teij) 

times percent energy digested (pdeij) minus an index of energy 

expended (eeij): neteij = [(teij × pdeij) − eeij] + 0.1. We calculated seasonal values only where a seasonal effect was evident 

(α = 0.1) by analysis-of-variance for some parameter included 

in the calculation. All values were log-transformed for these 

tests to meet the assumptions of normality and homogeneity 

of variance. This measure only accounted for expenditures 

immediately associated with extracting the food from its 

enclosing matrix or shearing it from supporting tissue and did 

not account for costs of search and movement, either within or 

between sites.

Total energy content. — We calculated total energy content (teij, in kilocalories) as a function of the energy contained 

in each nutrient and the dry weight nutrient composition of the 

ingested fraction of the food. This calculation excluded, for 

example, skeleton and viscera of ungulates (Green and others, 1997; Mattson, 1997b) and structural parts of whitebark 

pine cones (Mattson and Jonkel, 1990; Mattson and Reinhart, 

1994). The calculation was: teij = (crude protein × 4.3) + (ether 

extract × 9.4) + (starch × 4.2) + (sugar × 3.8) + (ash × 0) + 

(remainder [carbohydrate] × 4.2), where each nutrient was 

expressed as a proportion of total dry weight (fig. 3). Remaining carbohydrate was calculated by subtraction. We obtained 

energy contents from Robbins (1983) and Schmidt-Nielson 

(1990). We took nutrient contents of some foods from published research, most notably sugar and ether extract from 

Craighead and others (1982).

Percent digested energy. — We obtained estimates of 

percent digested energy (pdeij) directly from Pritchard and 
 13

Robbins (1990) or from relationships that they presented. 

Unmodified values were used for ungulate meat (mule deer), 

cutthroat trout, rodents (ground squirrels), and whitebark 

pine seeds (pinyon pine). We estimated other digestibilities 

from their relationship to total dietary fiber (tdf): pdeij = 101.3 

− (1.39 × tdf). We obtained an estimate of digestibility for 

army cutworm moths from O’Brien and Lindzey (1994), who 

also referenced Pritchard and Robbins (1990). Total digested 

energy (denij) was the product of pdeij times teij.

We related tdf to crude fiber (cf), ash (ash), and starch 

(strch) based on paired analyses of nutrients from a single 

sample, as follows:

tdf = 6.63 + (1.54 × cf) + (3.84 × lnash); R2 = 0.88, F = 192.2, 

df = 2, 51

tdf = 15.1 + (1.56 × cf); r2 = 0.87, F = 341.6, df = 1, 52

tdf = e (3.85 [0.024 × strch]); r2 = 0.50, F = 22.1, df = 1, 22.

Because most analyses of nutrient content in this study did not 

include tdf, we based estimates of digestibility on these subsidiary relationships between tdf and cf or tdf and strch. We did 

not commonly analyze total dietary fiber because the use of tdf

for estimating digestibility was not established until late in our 

study. We used simple relationships between tdf and cf or tdf

and strch in a few cases because cf and ash were not analyzed 

for all samples. We did not analyze the joint effects of strch

and cf because of high multicollinearity, which potentially 

resulted in unstable coefficients.

Relative energy expenditure. — We prorated relative 

energy expenditure to grams ingested and scaled the final 

calculation to derive as meaningful an index of net energy 

gain as possible (fig. 4). We obtained estimates of grams 

ingested (imassij) per feedsite from field samples and previously published research. We divided this value by volume 

(in cubic decimeters) of excavated material (vexcij) to obtain 

grams ingested per cubic decimeter of excavated material. 

We similarly divided kilograms of resistance (resistij) by 

mean volume of individual digs (iexcij) to obtain kilograms of 

resistance per cubic decimeter excavated. We then calculated 

kilograms of resistance per gram of food by dividing grams 

per cubic decimeter of excavated material into kilograms of 

resistance per cubic decimeter. We scaled this value assuming 

that grizzly bears obtained some net energetic reward from all 

feeding activities. The excavation of ants from logs provided 

the least energetic gain (digested kilocalories per gram) per 

unit of energy expended (kilograms of resistance per gram). 

We multiplied relative energy expenditure by a factor (sfactor) 

that produced a result equal to digested energy for excavation 

of ants from logs. We then multiplied energy expenditure for 

all other feeding activities by sfactor, which was the same 

for all foods and seasons, so as to standardize relative energy 

expenditure across all activity types. The calculation of eeij

reduced to:

eeij = [(resistij × vexcij) / (imassij × iexcij)] × sfactor.

Prior to standardization (i.e., while still working in units 

of kilograms of resistance), we used expert judgement to 

assign relative energy expenditures to some activities, such as 

grazing and use of carcasses, that could not be simulated using 

the claw-o-meter. We ascribed costs to these activities by comparing visual observations of bears engaged in activities for 

which we had estimated energetic expenditure using the clawo-meter with visual observations of bears engaged in activities for which we did not have direct estimates. On this basis, 

we ascribed a greater cost to use of bison and moose carrion 

compared to use of wapiti carrion because of differences in 

resistance of hide, viscera, and skeleton (Green and others, 

1997). We also ascribed a greater cost to use of ungulates during early and late hyperphagia compared to use of ungulates 

during spring because predation was more frequent during the 

later seasons (Mattson, 1997b).

Final values of relative net digested energy (neteij) 

included the addition of 0.1 (see the first paragraph under 

Methods

Table 7. Classification of years according to whether grizzly 

bear use of ungulate carrion was heavy during the spring (Y) or 

not (N), whether use of whitebark pine seeds was heavy during 

some time of the year (Y) or not (N), and whether whitebark pine 

seed use was heavy during late hyperphagia (Y) or not (N) in the 

Yellowstone ecosystem during 1973–96. 

[Determinations were made based on information presented in tables 5 and 6]

Year Classification Classification Classification

 by ungulate by whitebark by whitebark 

 use pine seed use pine seed use

 (spring) (year-long) (late hyperphagia)

73 Y Y

74 N N

75 N N

76 Y Y

77 Y N N

78 Y Y Y

79 N Y Y

80 Y Y Y

81 N N N

82 Y N N

83 no data N N

84 N N N

85 N Y Y

86 N Y N

87 N Y Y

88 N N N

89 Y Y Y

90 N Y N

91 Y Y Y

92 N Y Y

93 Y N N

94 N N N

95 N N N

96 N Y Y
14 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

subsection “Net Energy Digested per Gram of Ingested Food,” 

p. 12). We made this adjustment so that the excavation of ants 

from logs would contribute some value to the estimated aggregate productivity of habitat types. Without this addition, the 

excavation of ants from logs would have made no contribution 

and would have been assumed to be of no energetic benefit to 

bears. Because grizzly bears so commonly excavated logs, we 

judged this assumption to be untenable (see Noyce and others, 

1997; Mattson, 2001).

Net Energy Digested per Feeding Site

We calculated a relative measure of net energy digested 

per feeding site (fsneijk) as the product of per gram net digested 

energy (neteij) times a conversion factor (cfctrij) that related 

grams ingested to units of feeding activity, times the mean 

level of feeding activity at a feeding site (fslvijk) in units unique 

to each activity: fsneijk = neteij × cfctrij × fslvijk (fig. 5). Variation in fsneijk among habitat types was due only to variation in 

mean level of feeding activity (fslvijk); per gram net digested 

energy and conversion factors did not differ among habitat 

types. We estimated net digested energy for each food i, 

specific to each season j, only where some season effect was 

evident (see first paragraph under subsection “Net Energy 

Digested per Gram of Food,” p. 12). Where possible, we 

estimated conversion factors for each food and season. We 

estimated mean per feedsite level of feeding activity for all 

combinations of food, season, and habitat type k.

We estimated level of feeding activity (fslvijk) by the various measures of feeding intensity described under the section 

on “Field Methods,” including, for example, total number 

of excavations, total volume of excavations, total kilograms 

of ingested meat, and total number of feces (+1, so that sites 

with no feces would receive some value). These measures 

were comparable among seasons and habitat types for a given 

feeding activity but were not comparable among activity types. 

In other words, total volumetric consumption of a given food 

associated with a given feeding activity would be apportioned 

among habitat types proportional to the intensity of that feeding activity. However, because units of measure for intensity 

differed among activity types it was not self-evident how, for 

example, number of root excavations compared to number of 

feces counted at a grazing site.

We used conversion factors (cfctrij) to translate the various units of measure for feeding intensity into common units 

Figure 3. Schematic for the calculation of per gram net digested energy (neteij) for food i during season j, for foods used by grizzly 

bears in the Yellowstone ecosystem.

Percent crude 

protein
 15

of grams ingested. We estimated conversion factors by dividing the total mass (in grams) of different foods ingested during 

a given year h (1989, 1991, or 1992; see “Field methods”) and 

season j (fvolhij) by the summations of feeding activity units for 

the corresponding feeding activity and time period 

(Σ fslvhij): cfctrhij = fvolhij / Σ fslvhij. We used a mean among 

years, by season (cfctrij), in final calculations. We estimated 

total ingested mass from contents of feces, converting milliliters of fecal volume to grams of ingested mass by factors given 

in Hewitt and Robbins (1996). We did not calculate conversion 

factors by habitat type because it was difficult to ascribe the 

contents of specific feces to specific sites and because of insufficient sample sizes.

Average Net Energy Digested per Feedsite by 

Habitat Type

We calculated the relative net energy digested per feeding 

site within a given habitat type k for season j, year type l, and 

region m (avefsjklm) as the average of the net digested energy 

(fsneijk) of all feeding activities occurring in that time and 

place, weighted by their proportional frequencies 

(propijklm): avefsjklm = [Σ (propijklm × fsneijk)] over all foods i (fig. 

6). We attributed variation in avefsjklm among year types and 

regions only to variation in proportions of feeding activities; 

net digested energy per feedsite of a given type did not differ 

among these strata. We used all activity sites, whether ascribed 

to radio-marked bears or not, to estimate proportional frequencies of feeding activities. This approach approximately doubled sample sizes and was deemed defensible given that the 

greatest discrepancy between results from radio-marked bears 

and other bears was in the occurrence of nonfeeding activity 

that did not leave sign. In calculations where the occurrence 

of nonfeeding activity was judged to be consequential (see 

“Density of Feeding Activity,” below), only activity sites from 

radio-marked bears were used.

Density of Feeding Activity

We calculated density of feeding activity (fdjklmn) as the 

product of total density of bear activity (denjklmn) times the 

proportion of that activity (pactjkl) that was associated with 

feeding: fdjklmn = denjklmn × pactjkl; for season j, habitat type 

Figure 4. Schematic for calculation of the index of energy expended per gram (eeij) of food i ingested during season j, for foods used 

by grizzly bears in the Yellowstone ecosystem.

Methods
16 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

k, year type l, region m, and edge type n (fig. 6). Variation in 

fdjklmn among regions and edge types was due only to variation in density of total activity (denjklmn); feeding activity as a 

proportion of total activity did not differ among these strata.

Density of grizzly bear locations. — We used radiotelemetry locations of marked bears directly to estimate total density 

of bear activity in each habitat type by season, year type, edge 

type, and area, controlling for the effects of proximity to roads 

and major human facilities. We used data from 1976 to 1992.

We calculated relative density of total activity (denjklmn) as 

the quotient of estimated proportional use of different spatial 

strata by radio-marked bears (ujklmn) divided by the 

proportional area of each stratum (akmn): denjklmn = ujklmn / akmn. 

We calculated proportional use, by season and year type, as: 

ujklmn = [akmn / (1 − pjklmn)] − akmn, where pjklmn was the probability that a location would be that of a telemetered radio-marked 

bear versus a random point. This expression is equivalent to 

the odds that a location would occur in a given stratum. Probabilities (pjklmn) were back-calculated from logits (p = elogit / (1 

− elogit)) that were modeled as dependent responses in analysisof-covariance on categories (Demaris, 1992).

We considered the effects of habitat type, forest/nonforest 

edge, distance to the nearest road, distance to the nearest 

major human development, and, for spring only, winter range 

in the development of statistical models. Habitat type, edge 

(≤100 m versus >100 m), and winter range (bison, wapiti, and 

neither) were categorical variables. Distances to nearest road 

and human development were covariates. We used roads of 

all types specified in the Yellowstone grizzly bear cumulative effects model database, whereas we defined major human 

developments as any concentration of human activity that 

included ≥30 facilities (e.g., houses) or the capacity for ≥100 

persons to overnight within a 1-km-radius circular area. In 

most models these human-related effects were expressed as 

second- and third-order polynomials. We calculated logittransformed probabilites of bear activity, used to calculate 

densities, from models where human-related effects were set 

to zero. We developed different models for each season, year 

type, and region, as well as different models for areas within 

regions that were with and without substantial year-round 

bison populations heavily used by grizzly bears. We selected 

models on the basis of minimizing Akaike’s Information Criterion (AIC) (Sakamoto, 1991; Burnham and Anderson, 1998), 

except that we constrained all models to include habitat type.

We weighted frequencies of random points so that they 

summed to the total of bear locations used in each model 

(Manly and others, 1992). The resulting beta coefficients 

approximately equaled zero when modeled frequency of bear 

use equaled the frequency of random points in a given stratum. 

A coefficient ≈ 0 corresponded to p ≈ 0.5 and den ≈ 1 (i.e., the 

odds that a location would have been from a telemetered bear 

equaled the odds that it would have been a random point). This 

Figure 5. Schematic for the calculation of total digested energy per feedsite k from food i for season j (fsneijk), for foods and habitat 

types used by Yellowstone grizzly bears.
 17

structure allowed us to easily compare results among models, 

but it also implicitly assumed that density of bear use was 

equal among seasons, year types, and regions. This assumption 

is reasonable when comparing seasons and year types within 

regions but questionable when comparing among regions. 

Densities of grizzly bears probably differed among regions 

in the Yellowstone ecosystem as a function of differences in 

overall habitat productivity (Mattson, 1987; Blanchard and 

others, 1992).

We subsumed changes in proportional areas of habitat types and forest/nonforest edge that were attributable to 

the 1988 fires in procedures for calculating akmn. Prefire and 

postfire habitat type and edge identifications were assigned to 

random points proportional to the bear sample that was preand postburn in each ecosystem region. This was done by generating a random variable with a uniform distribution ranging 

from 0 to 1. Random points with values greater than or equal 

to the proportion of bear locations obtained after the 1988 

fires were assigned a postfire coefficient. Random points with 

values less than the proportion of bear locations prefire were 

assigned prefire coefficients. This procedure allowed us to 

use prefire and postfire bear data without separate prefire and 

postfire models for each temporal and spatial stratum. Sample 

sizes of bear locations were too small to support what would 

otherwise have been an additional permutation of models.

Proportion of bear locations with feeding activity. — We 

estimated the proportion of bear locations at which feeding 

activity occurred (pactjkl) for each season j, habitat type k, 

and year type l. We used only observations that were obtained 

from locations of radio-marked bears. This approach reduced 

sample sizes by approximately one-half compared to our analysis of the proportional distribution of feeding activities (see 

“Average Net Energy Digested per Feedsite by Habitat Type,” 

p. 15). These small sample sizes prevented us from estimating 

proportional levels of feeding activity for each region and edge 

type. We also combined year types within seasons for this 

calculation when sample sizes for both year type categories 

were too small.

Methods

Figure 6. Schematic for the final calculation of productivity for habitat type k (coefjklmn), for Yellowstone grizzly bears.
18 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

We adjusted total density to reflect the proportional 

occurrence of feeding activity because our analysis focused 

on the extraction of energy from different landscape units by 

Yellowstone grizzly bears rather than on density of bear activity. Many telemetry locations were associated with bears either 

traveling or resting (Mattson, 1997a). These types of activities 

undoubtedly engendered energetic costs and benefits. Such 

gains or losses are difficult to quantify, however, and are likely 

to be a small fraction of a grizzly bear’s energetic budget during the active season (Fancy and White, 1985).

Coefficients

We calculated coefficients (coefjklmn) for assessing the 

productivity of Yellowstone’s grizzly bear habitat for each 

temporal and spatial stratum as the product of density of 

feeding activity (fdjklmn) times net energy digested per feeding 

site (avefsjklm): coefjklmn = fdjklmn × avefsjklm (fig. 6). Variation 

in coefjklmn between edge types was due only to variation in 

density of feedsites; net digested energy per feedsite did not 

differ for this stratification. These coefficients of productivity directly reflect the net energy that bears derive from an 

area, accounting for the energetic benefits of foods that were 

consumed and the energetic costs of extracting those foods 

once found. They do not reflect the energetic costs of search 

and travel or the energetic benefits of favorable microclimates. 

Coefficients are in units that have temporal and spatial specificity so that they can be summed over units of time and space. 

However, coefficient values are still indicative rather than 

absolute measures of net energetic gain, primarily because the 

measure of energy expenditure is an index and also because 

there are not explicit estimates of the total food derived from a 

given type at a given time. Coefficients have additional value 

in that the fraction of energy gained from different feeding 

activities or foods can be specified for each stratum and for 

areas to which the coefficients are applied so that judgements 

can be made regarding the relative importance of different 

feeding activities or foods.

Coefficients for Army Cutworm Moth and 

Cutthroat Trout Feeding Sites

Grizzly bear use of aggregated army cutworm moths 

and spawning cutthroat trout was singular with regards to our 

research sampling efforts in the Yellowstone ecosystem. These 

activities were undersampled in the ecosystem-wide effort 

because they were, to a unique extent, highly localized around 

highly productive sites (Mattson and others, 1991b; Mattson and Reinhart, 1995). For this reason, we took a tailored 

approach to estimating coefficients for these activities and 

others associated with habitat complexes around moth aggregation sites and trout spawning streams. These coefficients 

supercede all other coefficients within specified zones-ofinfluence (ZOIs).

Our rationale for calculating moth and trout ZOI coefficients was the same as described in preceding sections, except 

that some data were different. Calculations of net digested 

energy were the same. Overall density of grizzly bear activity was analyzed for composite ranges of bears known to use 

these two foods. We treated the ratio of observed to expected 

levels of use for ZOIs within these composite ranges as the 

analogue of relative density (Mattson and others, 1991b; 

Mattson and Reinhart, 1995). In fact, this treatment is directly 

comparable to densities calculated, as described above, with 

random locations weighted to total the number of bear locations used in each model. We defined the extent of zonesof-influence as the point where levels of proportional use 

first equaled levels of proportional availability within 500-m 

intervals successively farther away from aggregation sites 

or streams (Mattson and others, 1987; Mattson and others, 

1991b; Mattson and Reinhart, 1995). No moth sites were 

located near enough to roads or major human developments 

to be affected by bears avoiding these features (Mattson and 

others, 1991b; O’Brien and Lindzey, 1994). Some spawning 

streams were located near human facilities (Reinhart and Mattson, 1990), but we assumed that the effect of bears underusing streams near humans would be offset by bears overusing 

more remote streams when considering the entire spectrum 

of streams around Yellowstone Lake (Reinhart and Mattson, 

1990).

We reduced densities of bear locations near moth sites or 

spawning streams to reflect only feeding activity. We based 

this on the proportion of time bears were observed to be feeding by direct visual observation (French and French, 1990; 

O’Brien and Lindzey, 1994; Mattson and Reinhart, 1995; 

White, 1996). We calculated average feedsite values using the 

proportions of food items in the diets of bears that used habitat 

complexes associated with these two foods. We estimated 

these diets from analyses of feces collected within each habitat 

Cutthroat trout (left) and army 

cutworm moths (above) are major 

grizzly bear foods in certain regions 

of the Yellowstone ecosystem. Bears 

consume cutthroat trout in spawning streams tributary to Yellowstone 

Lake and army cutworm moths at high 

elevations in the Absaroka Mountains 

to the east (trout photo by Daniel 

Reinhart, National Park Service; moth 

photo by Jeff Henry, Roche Jaune 

Pictures).
Results 19

complex (Mattson and others, 1991b; Mattson and Reinhart, 

1995) and corrected to account for detection- and digestionrelated biases (Hewitt and Robbins, 1996).

Results

Net Energy Digested per Gram of Ingested Food

Nutrient content of foods consumed by Yellowstone grizzly bears varied considerably within and among seasons (table 

8). Percent crude protein content varied 20 times between 

stems of flowering elk thistles and the tissue of ungulates 

during spring. Protein content of clovers and graminoids 

consumed by bears declined with progression of the growing 

season, and for graminoids, protein content averaged one-half 

of spring values during late hyperphagia. In general, crude 

protein content was much higher for animal foods than for 

plant foods. Among plant foods, crude fiber content varied by 

six times and was lowest in roots and highest in graminoids, 

horsetail, and elk thistle. Ash content was high in horsetail 

because of its high silica content (Cody and Wagner, 1981), 

and also high in pondweed roots, mushrooms, and pocket 

gopher root caches. Fat content was singularly high in army 

cutworm moths, followed by late season ungulate tissue, ants, 

and whitebark pine seeds.

Estimated mean percent digestibility of energy in foods 

consumed by Yellowstone grizzly bears was nearly as variable 

as nutrient contents (table 9). Digestibility varied five- to sevenfold, from a low of 19% for elk thistle and 13% for late season graminoids to a high of 95% for cutthroat trout (Pritchard 

and Robbins, 1990). In general, the energy in vertebrates was 

most digestible, followed by energy in invertebrates and roots. 

Of foliage grazed by bears, energy contained in clover, spring 

beauty, dandelions, and fireweed was most available to bears.

As would be expected, the average dry weight of foods 

varied depending on the units that were used to measure consumption by grizzly bears (tables 10–12). Among foods where 

consumption was calculated in terms of bite size, volumes of 

graminoid and clover increased commensurate to plant growth 

during the active season and reached a maximum with horsetail and late season consumption of clover. These maximum 

bite sizes (0.54 g for horsetail and 0.44 g for clover) were 

similar to the asymptotic bite size estimated for grizzly bears 

consuming fresh alfalfa (0.64 g) (Gross and others, 1993b). 

Conversely, bite sizes of spring beauty were quite small 

because of the dispersed nature and small size of spring beauty 

stems. Excluding spring beauty, bite sizes of fruits (0.15 g−0.60 g) 

were similar to those of grazed foods (0.12 g−0.54 g). Among 

root foods, individual roots of biscuitroots were larger, on 

average, than individual roots of yampa or sweet-cicely. 

However, judged on the basis of cubic decimeters of excavation, differences were minimal between yampa and biscuitroot 

because, on average, more than one yampa root was excavated 

per dig. On a per cubic decimeter basis, bears obtained more 

of yampa and biscuitroot than sweet-cicely or pondweed roots. 

Finally, invertebrates were the smallest units of food: all were 

<0.1 g per individual.

Mean resistances (kilograms) of matrix material to 

excavation varied sixfold depending on the season and type of 

matrix (table 13). On average, resistance was least for dirt and 

debris hills constructed by ants and was greatest late in the 

growing season for soils enclosing yampa roots. Even so, difficulty of excavation was quite similar for a number of activities, including the excavation of roots early in the growing 

season, the excavation of cones from middens, the excavation 

of ants from logs, and the excavation of mushrooms from forest floor debris.

Relative net energy digested per gram of ingested food 

accounted for digestive efficiencies and the energetic costs 

of extracting a bite from a surrounding matrix or shearing it 

from contiguous tissue such as leaf or stem (Appendix 4). This 

measure did not account for metabolic efficiencies or costs of 

search among and within sites. This measure also reflects the 

energetics of a subset of sites and foods that were selected out 

of all of those available for exploitation by bears. For example, 

the net digested energy associated with grazing clover during 

late hyperphagia only applies to those few patches of clover 

Biscuitroots excavated from a grizzly bear feeding site in northern 

Yellowstone National Park. Biscuitroots are frequently consumed 

by grizzly bears, especially on wind swept ridges in northern and 

eastern parts of the Yellowstone ecosystem (photo by David Mattson, U.S. Geological Survey).
20 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 8. Mean percent moisture-free nutrient content of foods consumed by grizzly bears in the Yellowstone ecosystem, 1987-92.

[(-) denotes a situation where SD could not be calculated because n=1]

Food Percent crude protein Percent crude fiber Percent ash Percent starch

(SD) n (SD) n (SD) n (SD) n

 Graminoids 

 Spring 20.7 (4.8) 24 21.2 (3.9) 24 10.2 (2.0) 16

 Estrus 20.1 (5.4) 36 23.0 (4.6) 37 9.1 (1.6) 28

 Early hyperphagia 15.0 (3.1) 5 29.4 (5.9) 5 7.8 (1.2) 4

 Late hyperphagia 9.0 (5.8) 4 31.2 (4.0) 4 9.4 (2.5) 4

Clover 

 Spring 25.7 (2.0) 4 12.6 (1.3) 4 10.1 (2.1) 2

 Estrus 21.5 (2.7) 8 16.7 (6.1) 8 15.4 (5.0) 6

 Early hyperphagia 20.3 (3.3) 7 19.2 (4.2) 7 9.8 (2.2) 4

Dandelion 19.2 (6.7) 2 14.0 (5.2) 2 17.4 (7.2) 2 

Fireweed 

 Estrus 15.8 (-) 1 17.1 (-) 1 8.4 (-) 1

 Early hyperphagia 23.0 (4.5) 3 10.7 (2.0) 3 9.2 (1.0) 3

Horsetail 13.3 (5.6) 26 20.8 (4.8) 27 21.7 (4.7) 24

Spring beauty 25.4 (5.8) 11 13.7 (3.3) 12 14.2 (2.2) 10

Elk thistle 4.1 (1.6) 16 27.8 (4.5) 16 15.2 (3.2) 16

Mushroom 17.8 (5.1) 4 12.6 (2.8) 4 18.0 (9.6) 4

Pocket gopher cache 8.6 (2.9) 8 10.8 (3.6) 8 18.3 (8.2) 8 5.0 (3.0) 10

Vole cache 5.1 (-) 1 5.2 (-) 1 4.9 (-) 1 8.3 (-) 1

Pondweed root 8.7 (0.6) 2 6.4 (0.7) 2 25.9 (7.5) 2 28.5 (11.8) 5

Yampa root 5.9 (1.7) 26 6.5 (2.7) 27 6.6 (4.4) 23 36.3 (11.0) 57

Sweet-cicely root 7.8 (1.5) 4 13.2 (5.0) 4 7.8 (7.8) 4 27.8 (20.9) 11

Biscuitroot root 5.2 (1.4) 34 9.5 (2.5) 34 11.4 (6.4) 34 31.7 (11.1) 69

 Percent fat

Ant 36.8 (-) 1 18.3e 6.1e 32.5e

Wapitia

 Spring and Estrus 80 4 18

 Early hyperphagia 62 4 36

 Late hyperphagia 45 4 53

Bison and moosea

 Spring and Estrus 81 2 15

 Early hyperphagia 67 2 29

 Late hyperphagia 53 2 43

Cutthroat troutb 69.6 9.3 17.5

Army cutworm mothsc 34.2 64.0

Whitebark pine seedd 12.8 34.8 2.2 27.1

a

From information in Mitchell and others, 1976; Anderson, 1981; Bubenik, 1982; Robbins, 1983; Berger and Peacock, 1988; Pritchard and Robbins, 1990; 

Pond and Ramsay, 1992; Mattson, 1997b. b

From Pritchard and Robbins, 1990.

c

From O’Brien and Lindzey, 1994; White, 1996.

d

From Mattson and Reinhart, 1994.

e

From Ogborn, 1990; Noyce and others, 1997.
Results 21

Table 9. Estimated mean percent digestibility of energy in foods consumed by grizzly bears in the Yellowstone ecosystem, 1987-92.

Food Year-round Spring Estrus Early hyperphagia Late hyperphagia

(SD) n (SD) n (SD) n (SD) n (SD) n

Stems Graminoids 33.9 (8.1) 24 31.4 (9.1) 37 17.5 (12.4) 5 13.0 (8.0) 4

 foliagea

 Clover 52.8 (3.5) 4 42.7 (12.0) 8 38.6 (8.4) 7 46.8 (8.9) 2

 foliagea

 Dandelion 45.6 (5.8) 46

 foliage and 

 flower 

 Fireweed 43.6 (-) 1 56.9 (4.6) 3

 foliagea 

 Horsetail stem 32.0 (8.6) 27 

 Spring beauty 48.7 (7.4) 12

 foliage and 

 flower 

 Elk thistle stem 18.8 (11.2) 16 

Mushroom 51.1 (4.5) 4

 basidiocarp 

Roots 

 Pocket gopher 47.9 (18.6) 10

 root cache 

 Vole root cache 71.5 (-) 1 

 Pondweed root 68.4 (8.6) 5 

 Yampa rootb 71.8 (8.0) 57 

 Sweet-cicely 63.6 (14.2) 11

 root 

 Biscuitroot 63.3 (8.7) 69

 rootb 

Whitebark 49.4

 pine seedsd 

Ant adults 57.2 (-) 1 

Army cutworm 75

 mothsc 

Ungulatesd

 Wapiti 90 90 92 93 

 Bison & moose 92 92 94 96 

Cutthroat troutd 94.5 

a

Means differed (α = 0.10) by season and between bear feeding sites and monitoring plots. Only samples from feeding sites were used.

b

Means differed between bear feeding sites and random plots. Only samples from feeding sites were used.

c

From O’Brien and Lindzey, 1994.

d

From Pritchard and Robbins, 1990.

used by bears, presumably because of desirable nutritional 

characteristics. Digested energy was typically highest for 

ungulates followed by insects, fruits, seeds, roots, and grazed 

foods. Considering the costs of extraction, ungulates remained 

the energetically most valuable food. A large number of 

root, fruit, and seed foods clustered together at intermediate 

values, followed by most grazed foods, insects (excluding 

army cutworm moths), rodents, and rodent food caches. The 

net energetic value of insects dropped dramatically from that 

associated only with digestive efficiencies because of the often 

high costs of extraction coupled with the small size of rewards. 

Exceptions to these generalities included ants from dirt and 

debris hills, which exhibited a high value because of typically large colony sizes and ease of excavation; voles during 

spring and estrus, because of the preponderance of meat in the 

reward; and fireweed during hyperphagia.

Coefficients of Habitat Productivity

The factors given in Appendix 5 were used to convert 

units of activity observed at grizzly bear activity sites to units 

of mass (grams) that could be compared among different 

seasons and types of feeding activity. These values reflect not 

only the amount of food obtained per unit activity but also 
22 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

more common in most types during early and late hyperphagia compared to spring and estrus. This escalation was to be 

expected since early and late hyperphagic seasons were defined 

on the basis of previously documented increases in feeding 

activity (see table 4). Feeding activity was also proportionally 

more common during all seasons in nonforest types compared 

to forest types. This prevalence of feeding versus other activities was especially evident for lithic ridges (habitat type 4), 

mesic grasslands and meadows (habitat type 6), marshes, fens, 

and wet meadows (habitat types 5 and 8).

Relative density of feeding activity (Appendix 9) was 

multiplied times the mean energetic value of a feedsite 

(Appendix 10) to obtain coefficients of habitat productivity 

(Appendix 11) for each habitat type, year type, season, and 

region. Examined separately, relative density and mean 

feedsite value provide insight into the seasonal foraging 

environment of different habitat types. For example, density of 

feeding activity was typically high but mean energetic value of 

feedsites was low in mesic grasslands and meadows (habitat 

type 6). This example characterizes a foraging environment 

with numerous predictable low to moderate quality feeding 

opportunities that attract considerable bear use. By contrast, 

some habitat types such as mesic subalpine fir forests (habitat 

type 10701) were characterized by relatively low densities of 

different probabilities of detection associated with different 

foraging behaviors. For example, the very low values associated with yampa and biscuitroot reflect not only the small 

reward per dig (i.e., roughly one root) but also the likelihood 

that root excavations are more often documented in comparison to activities such as grazing because of the prominence 

and durability of the associated sign. By contrast, the large 

values for grazed foods reflect the many bites represented 

by a single feces (the unit of activity for grazing), as well as 

the lower probabilities of detection associated with grazing, 

which is a relatively cryptic behavior. These conversion factors therefore contain information pertaining to the behavior 

of bears and the characteristics of their foods as well as the 

biases introduced during the sampling process. Mean levels 

of activity specific to each food and type (Appendix 6) were 

multiplied by the conversion factors to obtain mean relative 

net energy per feedsite (fsneijk) (Appendix 7). Because this 

calculation controlled for sampling bias, values in Appendix 

7 should be interpreted as conveying information about the 

energy obtained per feedsite and as correcting for biases introduced during sampling.

The proportion of grizzly bear locations where feeding 

signs were observed varied considerably among habitat types 

and seasons (Appendix 8). Feeding activity was proportionally 

Table 10. Basis for estimates of nutrient content for ungulates and army cutworm moths and of digestibility for ungulates used in 

calculation of coefficients of habitat productivity for Yellowstone grizzly bears.

Assumption or calculation Reference or source

Wapiti during late hyperphagia were ascribed the protein and fat composition Pritchard and Robbins, 1990

of deer.

Bison and moose during late hyperphagia were ascribed the protein and fat Pritchard and Robbins, 1990

composition of cattle.

Edible fractions of the carcass (ebw) were calculated as: ebw = live weight Mattson, 1997b

(lw) − skeletal weight − rumen weight − water weight. 

Differences between fall and spring or late winter ebw (ebwfall and 

ebwspring, respectively) were attributed to loss of body fat.

Change in ebw from fall to spring (∆ ebw) was standardized as: Mitchell and others, 1976; Anderson, 1981; Bubenik, 1982; 

∆ ebw = (ebwfall − ebwspring)/ebwfall; where ebwspring was recalculated based Berger and Peacock, 1988

on percent or absolute changes in lw from fall to spring obtained from the 

listed references.

Percent ebwspring protein (proteinspring) was calculated as: proteinspring = 

100 × (proteinfall/[100 − % ash − ∆ ebw])

Percent ebwspring fat (fatspring) was calculated as: fatspring = (100% - ash) - 

proteinspring

Nutrient fractions of moths were calculated as the average of two O’Brien and Lindzey, 1994; White, 1996

studies, using the average for each study of values obtained 

after August 1.

Animal fat was assumed to be ca. 99% digestible, ash and total Pritchard and Robbins, 1990

dietary fiber not digestible, and protein (dprot) digestible according 

to percent of protein (protein) in the carcass as: dprot = 3.82 + 

1.01 protein.
Results 23

Table 11. Average dry weight (in grams) obtained by grizzly bears per feeding unit (e.g., bite, root, excavation, food cache, stem) at 

feeding sites in the Yellowstone ecosystem, 1986-92. 

[Samples size (n) denotes number of sites; within-site sample sizes varied from 5 to >100, depending on the food]

Food Year-round Spring Estrus Early hyperphagia Late hyperphagia

(SD) n (SD) n (SD) n (SD) n (SD) n

Graminoids

(per bite)a 0.14 (0.04) 18 0.20 (0.11) 14 0.30 (0.16) 5 

Clover (per bite)a 0.21 (0.07) 5 0.22 (0.13) 9 0.44 (0.26) 17

Dandelion 0.33 (0.34) 11

(per bite) 

Fireweed 0.28 (-) 1

(per bite) 

Alpine clover 0.12 (0.04) 3

(per bite) 

Horsetail 0.54 (-) 1

(per bite) 

Spring beauty 0.03 (0.01) 9 (assuming 1.5 stems per bite, bite size = 0.05)

(per stem) 

Elk thistle 4.9 (2.1) 14

(per stem) 

Mushrooms 7.6 (5.0) 3

(per basidiocarp) 

Rodent root 37.8 (32.5) 12

cache (per 

cache) 

Earthworms 1.1 (-) 1

(per excavated 

cubic decimeter) 

Pondweed 0.25 (0.12) 6

root (per 

excavated 

cubic decimeter) 

Yampa 

 (per root)a 0.21 (0.05) 3 0.57 (0.28) 14 0.49 (0.17) 54 0.54 (0.10) 5

 (roots per 1.6 (0.52) 96

excavation) 

(cubic 2.0 (1.0) 20

decimeters 

per excavation) 

Sweet-cicely 

 (per root) 0.60 (0.38) 14 

 (roots per 3.3 (4.8) 12

excavation) 

(cubic 9.2 (16.6) 12

decimeters per 

excavation) 

Biscuitroot 

 (per root) 0.89 (0.41) 104 

 (cubic 2.3 (2.4) 28

decimeters per 

excavation) 

a

Means differed (α = 0.10) by season.
24 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

feeding activity, with high average feedsite value, especially 

during spring. This pattern suggests a patchy and unpredictable environment, with potentially substantial rewards. As 

another contrast, dry nonforest areas (habitat type 2) typically 

supported low densities of feeding activity that were of low to 

moderate value, whereas the whitebark pine type (habitat type 

10201) supported high densities of high-value feeding activity 

during hyperphagia.

In most habitat types, much of the mean productivity per 

feedsite (as distinct from total productivity) was associated 

with consumption of ungulates (figs. 7–9). This was especially 

the case for wet nonforest (habitat types 5 and 8), mesic and 

dry forest openings (habitat types 10600 and 10100), 

Douglas-fir types (habitat types 10301 and 10801), low elevation spruce (habitat type 10601), and low elevation lodgepole 

pine (habitat type 10501). Dry, lithic, and mesic nonforest 

types (habitat types 2, 4, and 6) derived much of their value 

from root foods, while whitebark pine and subalpine fir types 

(habitat types 10201, 10101, and 10701) derived much or most 

of their value from whitebark pine seeds. The same is true 

for forests dominated by grouse whortleberry (habitat type 

10401), depending on whether bison were or were not present 

in substantial numbers. In areas with substantial numbers of 

bison, peak productivity was shifted from spring or late hyperphagia to estrus or early hyperphagia. This shift reflected grizzly bear use of bison that died either from injuries sustained 

during the rut (early hyperphagia) or trauma associated with 

calving (spring and estrus) (Green and others, 1997; Mattson, 

1997b).

Final coefficients in Appendix 11 are presented by habitat 

type, season, year type, and region, and by location in or out 

of forest/nonforest edge. Coefficients in Appendix 12 are averaged over year types. In regions where a type was so sparse 

that a coefficient could not be estimated, values were assigned 

Table 12. Estimated dry weights of grizzly bear foods not sampled during this study. Values were obtained from the referenced literature.

Food Dry weight Assumptions References

 (grams)

Cutthroat trout 47.3 75% body water, 42% consumption Mattson and Reinhart, 1994

Adult pocket gopher 22.0 Hansen and Bear, 1964

 Hansen and Reid, 1973

Pocket gopher litter 3.5 0.7 g per neonate, 5 neonates per litter Hansen and Bear, 1964

 Anderson and MacMahon, 1981

 Chase and others, 1982

Adult vole 5.8 78% body water Pitts and Bullard, 1968

 Campbell and Dobson, 1992

Vole litter 1.1 0.2 g per neonate, 5.5 neonates per litter Pinter, 1979

Earthworm 0.062 85% body water Lawrence and Millar, 1945

 Grant, 1955

 Lee, 1985

Ants per log 1.7 75% body water, body mass and colony sizes of Brian, 1978

 representative species Peakin and Josen, 1978

Ants per hill 4.7 As per above and 25% utilization, based on mean 

percent excavation per nest = 41 ± 21 (n = 143)

Ants per rock 0.1 As per above

Hornet nest 1.4 10 mg per hornet and 25% utilization Akre and others, 1980

 Redford and Dorea, 1984

Army cutworm moth 0.09 7% body water O’Brien and Lindzey, 1994

 White, 1996

Fleshy fruit (per bite)

 Globe huckleberry 0.60 1.5 berries per bite Welch and others, 1997

 Buffaloberry 0.32 As above

 Strawberry 0.30 As above and assuming 0.2 g per fruit

Grouse whortleberry 0.15 As above and comparable in size to Ross and LaRoi, 1990

 Vaccinium vitis-idaea

Whitebark pine 7.2 80 seeds per cone, 0.09 g per seed Mattson and Reinhart, 1994

seeds (per cone)
Discussion 25

Table 13. Mean (SD) values (in kilograms) obtained from a claw-o-meter used to excavate grizzly bear feeding sites in a way that 

simulated the observed bear signs, Yellowstone ecosystem, 1987-92. 

[Values represent averages for sites based on 10 samples per site; sample size (n) denotes number of sites. Excavations averaged 2.2 ± 1.9 dm3 (n = 48) in size]

Feeding activity Year-round Estrus Early hyperphagia Late hyperphagia

(SD) n (SD) n (SD) n (SD) n

Excavating squirrel 11.7 (9.0) 14

middens (pine seeds) 

Excavating mushrooms 9.1 (13.9) 3 

Excavating logs (ants) 13.3 (11.9) 15 

Excavating debris hills (ants) 4.7 (3.6) 3 

Excavating rodent nests and caches 6.6 (10.5) 14 

Excavating yampa rootsa 9.9 (9.9) 6 19.9 (15.4) 21 27.4 (21.4) 3

Excavating biscuitroot rootsa 9.7 (20.6) 14 15.9 (17.4) 17 16.1 (21.4) 10

a

Means differed (α = 0.10) by season.

to it from the next most similar type. This circumstance 

occurred in most regions for habitat types 4 and 7, 10301 and 

10801, and 10101 and 10201. Only in the east were values 

estimated separately for types 10101 and 10301. The west and 

east were the only regions where coefficients were estimated 

for ungulate winter ranges during spring; the west was the 

only region with coefficients estimated for bison winter range. 

Bear Management Units were distinguished as being with 

and without bison, year-long, only in the south and west. This 

distinction was not made for the north because there is little 

evidence that grizzly bears in this region made substantial use 

of the relatively numerous resident bison (Green and others, 

1997; Mattson, 1997b). Even so, the use of bison that did 

occur in this region is reflected in the associated coefficients.

Coefficients for ZOIs associated with army cutworm 

moth aggregation sites and cutthroat trout spawning streams 

are presented in table 14 along with supporting information 

for their calculation. These ZOI coefficients are roughly two 

times the maximum value of any coefficient associated with a 

specific habitat type. Cutworm moths and trout provide a high 

concentration of net digested energy, similar to that of ungulates. The food sources and feeding activity associated with 

these ZOIs are also highly concentrated. Although of relatively 

limited extent, these ZOIs predictably constitute “ecocenters” 

of habitat productivity (Craighead and others, 1995).

Discussion

Applying the Coefficients

For maximum comparability among analysis areas, coefficients should be weighted by the proportional area of the 

spatial strata to which they apply. A weighted summation across 

types yields a unit area average productivity for the analysis 

area. Such a value is useful for most spatial and temporal comparisons because (1) the effects of differences in the spatial 

extent of different analysis areas are eliminated and (2) the 

calculated value is of a magnitude better suited to human cognition than those values obtained by absolute area-weighted 

summations. Total productivity can be easily obtained by 

multiplying average productivity by total area.

The spatial resolution of grizzly bear habitat productivity should correspond to the temporal resolution and associated time-specific uncertainty of the coefficients. Coefficients 

are specific only to season and are therefore generalized at 

that scale with respect to time units such as weeks, days, or 

hours. In other words, the coefficients represent a probabilistic statement within the span of a season regarding anything 

that might happen during a time period of shorter duration. 

Seasonal range sizes constitute the obvious spatial resolution 

corresponding to seasonal coefficients. Given that seasonal 

grizzly bear ranges in the Yellowstone ecosystem are about 50 

times larger than the resolution of habitat mapping for the Yellowstone grizzly bear CEM (about 100 km2

 compared to 2 ha), 

some method needs to be employed to generalize productivityattributed CEM maps to a scale that matches seasonal grizzly 

bear movements, especially for purposes of display.

This type of generalization is most logically achieved 

by focal-area analysis. Such an approach entails calculating average productivity for a seasonal-range-sized area, or 

“window,” and applying that average value to the focal cell 

(centroid). This is repeated for each cell of the map base. The 

resulting generalized “surface” of productivity is considerably 

smoothed relative to any representation of raw values used in 

the calculation. Intuitively, such a smoothed output is a more 

plausible representation of seasonally averaged productivity. 

This kind of smoothing is especially important for purposes of 

display.
26 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Figure 7. Fractions of mean seasonal feedsite value attributable to broad classes of grizzly bear foods in the Yellowstone ecosystem for five nonforest habitat types. Names and codes are given for each habitat type; E. hyper. = early hyperphagia, and L. hyper. = 

late hyperphagia.
 27

Figure 8. Fractions of mean seasonal feedsite value attributable to broad classes of grizzly bear foods in the Yellowstone ecosystem for six forest habitat types. Names and codes are given for each habitat type; E. hyper. = early hyperphagia, and L. hyper. = 

late hyperphagia.

Discussion
28 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Figure 9. Fractions of mean seasonal feedsite value attributable to broad classes of grizzly bear foods in the Yellowstone ecosystem for three habitat types distinguished by whether they occur in areas with or without substantial use of bison by grizzly bears. 

Names and codes are given for each habitat type; E. hyper. = early hyperphagia, and L. hyper. = late hyperphagia.
 29

For some purposes, productivity may best be displayed 

by categories. Five-part categories were determined based on 

quintiles for untransformed or natural-log transformed distributions, as appropriate, of raw values and values generated by 

focal area analysis. These categories are described in table 15.

Region-specific coefficients are designed to apply to all 

BMUs within the region, regardless of whether those units 

were used in derivations. A good match to BMUs #12, #13, 

and #18 on the western edge of the ecosystem has yet to be 

determined. If coefficients are applied outside of the current 

Yellowstone recovery area, a set should be selected from the 

region, by season, within the recovery area that most closely 

matches the conditions of the extralimital analysis area. Finding such a match from within the recovery area will be most 

problematic for areas that produce substantial amounts of 

fruits. Consumption of fruits is not well-represented by the 

coefficients because the Yellowstone ecosystem is notable for 

its lack of berries and the related consumption of them by grizzly bears (Mattson and others, 1991a).

Interpreting the Coefficients

As discussed in the “Methods” section, these coefficients 

are a partial accounting of the net digested energy obtained 

by Yellowstone grizzly bears from different habitat types, 

accounting for the effects of season, type of year, region, winter range, and proximity to forest/nonforest edge. Coefficient 

values are relative insofar as the estimate of expended energy 

is expressed as an index and total production of net energy is 

not tallied for lack of a comprehensive census of bear activity. 

Coefficient values also directly reflect the exhibited behavior 

of grizzly bears at any given time and place, specifically in 

terms of the quality and quantity of food that was ingested. 

Coefficients reflect the availability of foods within any given 

temporal or spatial strata only to the extent that these attributes 

are reflected in grizzly bear foraging activity. In essence, the 

approach taken here has the decided advantage of directly 

capturing information regarding the choices that bears make in 

their acceptance or rejection of foods and foraging patches.

These coefficients account primarily for energetic costs 

at the level of the bite. They do not account for the costs of 

search and travel within or among feeding sites. Even so, costs 

of search and travel were accounted for to the extent that these 

nonfeeding activities did not contribute to calculated habitat 

type values. This indirect accounting of nonfeeding costs 

implicitly assumes that these costs did not differ among types. 

There has been no test of this assumption, but there is evidence 

that travel through forest stands or harvest units with substantial amounts of undergrowth and coarse woody debris is more 

costly for bears than travel in open conditions (Smith, 1978; 

Mattson, 1997a). Even so, it is unclear how much energy such 

Discussion

Table 14. Parameters for calculating and applying coefficients (coefjklmn) associated with army cutworm moth and cutthroat 

trout feeding areas in the Yellowstone grizzly bear cumulative effects model.

Parameter Feeding area type

Army cutworm moth aggregation sites Cutthroat trout spawning streams

Season of application Early hyperphagia Estrus

Zones-of-influence (kilometer radius) Mapped polygon + 500 m buffer 2.0

(A) Relative density of bear activity 12.1 9.7

(B) Proportion of time feeding 0.67 0.30

(C) Relative density of feeding activitya 8.1 2.9

(D) Net digested energy per gram (kilocalories) 4.62 4.50

(E) Grams ingested per feedsite 367 1234

(F) Net kcal digested per feedsiteb 1361d 5268 

 1594e

Coefficientc 11024d 15277 

 12911e

Sources Pritchard and Robbins, 1990 Pritchard and Robbins, 1990

 Mattson and others, 1991b French and French, 1990

 French and others, 1994 Mattson and Reinhart, 1994

 O’Brien and Lindzey, 1994

 White, 1996

 Kevan and Kendall, 1997

a

A × B b

D × E c

C × F d

For WBP = Y years.

e

For WBP = N years.
30 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

differences in travel-related cost might entail, with the possibility that these costs are a relatively small fraction of a grizzly 

bear’s energetic budget (see Hainsworth and Wolf, 1979; Pyke, 

1984; Fancy and White, 1985; Grünbaum, 1998). Such is 

likely to be the case if, as all evidence suggests, grizzly bears 

possess a sophisticated memory and related cognitive map of 

travel routes and foraging opportunities (Schleyer and others, 

1984; Haroldson and Mattson, 1985; Harting, 1985). Under 

such circumstances, travel to potential foraging sites would 

be relatively efficient. Within a site, an increasing body of 

evidence suggests that bite size (and quality) more than food 

density, per se, largely governs rate of intake and associated 

energetics (Gross and others, 1993a, 1993b; Mattson, 1997c; 

Welch and others, 1997). By implication, within-site costs of 

search may be negligible compared to the costs of handling 

food. Thus, it is likely that energetic considerations at the level 

of the bite are, indeed, the most critical.

Coefficient values have unit area and unit time specificity 

and can therefore be summed over time and space. They also 

can be explicitly compared among seasons and types of years, 

assuming that there are equal numbers of bears in a given 

BMU during different seasons and years. Coefficients can be 

compared among regions, but only assuming that density of 

bear activity is equal. As mentioned before, this assumption is 

dubious but subject to remedy if and when reliable estimates 

of bear density are obtained for ecosystem regions where the 

bear population is locally at or near carrying capacity. With 

this information, region-specific coefficients can be weighted 

by region-specific bear densities and can therefore allow for 

comparison of values among regions without assuming that 

densities of bear activity are equal.

Yellowstone CEM Coefficients in Context

A number of models have been developed for appraising 

the suitability, capability, or productivity of bear habitat. These 

models fall into three basic categories: (1) those based on the 

abundance of bear foods, often weighted by some ranking of 

their relative quality (e.g., energy content and digestibility) or 

acceptance by bears (e.g., Craighead and others, 1982; Hadden and others, 1986; Mace, 1986; Mace and Bissell, 1986; 

Hamilton and Bunnell, 1987; Kansas and Raine, 1990; Noyce 

and Coy, 1990; Powell and Seaman, 1990; Costello and Sage, 

1994); (2) those based directly on exhibited univariate selection of vegetation types or other natural features (e.g., Schoen 

and others, 1994); and (3) those based on multivariate or 

multivariable analyses of habitat selection, including humanrelated effects such as those of roads (e.g., Clark and others 

1993; Mace and others, 1997). Several models of the first type 

have been tested by comparing food-based values with levels 

of selection exhibited by radio-marked bears (e.g., Hamilton 

and Bunnell, 1987; Kansas and Raine, 1990; Costello and 

Sage, 1994). Such comparisons implicitly test the assumption 

that digested energy, or some related quality, is the sole determinant of habitat use by bears (Hamilton and Bunnell, 1987). 

Models of the second and third types assume that the probability or level of bear activity within a given spatial stratum is the 

Table 15. Five-part categories for displaying raw and smoothed productivity values for Yellowstone grizzly bear habitat. 

[“Scale” refers to whether transformed or untransformed values were used to define categories. “ln” refers to natural-log transformed. “Range” refers to the total 

range of values. “Min-max” refers to the range of values for each category]

Spring Estrus Early hyperphagia Late hyperphagia

Scale Range Min-max Scale Range Min-max Scale Range Min-max Scale Range Min-max

Raw values

 ln 5-500 0-13 ln 5-750 0-14 ln 5-1000 0-14 ln 5-3000 0-18

 14-32 15-37 15-42 19-65

 33-80 38-100 43-120 66-233

 81-200 101-275 121-350 234-835

 200+ 275+ 350+ 835+

Smoothed values

 ln 5-500 0-13 Untrans. 5-750 0-14 Untrans. 5-1000 0-14 ln 5-3000 0-18

 14-32 15-37 15-42 19-65

 33-80 38-100 43-120 66-233

 81-200 101-275 121-350 234-835

 200+ 275+ 350+ 835+
 31

primary factor of interest to managers. The energetics of bear 

activity are not a consideration.

We developed Yellowstone grizzly bear CEM coefficients so as to include as much information as possible, not 

just about when bears used a site but also about what they 

were doing there. We emphasized letting the bears inform the 

model as much as possible regarding what foods they chose 

to eat, when and where they ate, the quality of those foods, 

and the per bite expense of feeding. This level of empiricism 

was possible because, to our knowledge, nowhere else has the 

full suite of information required for such calculations been 

collected for a bear population. The approach described here 

is unique compared to previous models of bear habitat because 

we incorporate information on bear distributions expressed as 

relative densities, in contrast to indices of selection or relative probabilities of location. We introduce some degree of 

control for the effects of proximity to townsites and roads on 

the behavior of bears as well as the behavior of researchers 

sampling the bears. We also incorporate information on the 

amount and quality of food consumed by bears, in contrast to 

information on the amount and quality of food that was available. This last distinction is important because, as mentioned 

above, bears exercise a significant level of choice in their use 

of foods and habitats that may or may not reflect what is considered to be available or preferable by a researcher (Hamilton 

and Bunnell, 1987; Kansas and Raine, 1990; Costello and 

Sage, 1994).

Additional Issues and Areas of Future Research

Much of the information germane to these calculations 

comes from grizzly bear signs encountered at or on route to 

and from radio-telemetry locations. We likely oversampled 

feeding activity at lower elevations and nearer roads because 

greater time was spent there by field crews. We likely 

undersampled grazing during feedsite examinations because 

grazing is difficult to detect (Mattson, 1997a). Both of these 

potential biases were either not relevant to the analysis or were 

mitigated in calculations. We used feedsites to specify the proportion of activity within habitat types. We did not use them to 

determine overall density of activity. This latter estimate was 

based on radio-telemetry locations, which were modeled so as 

to control for the effects of proximity to roads and other major 

human facilities. Because habitat types are distributed primarily by elevation (Pfister and others, 1977; Mueggler and Stewart, 1980; Steele and others, 1983), as are roads and human 

facilities in the Yellowstone ecosystem (Mattson and others, 

1987, 1992), the calculation of proportional feeding activity 

within types was predictably little affected by oversampling 

feedsites nearer roads. As discussed above (see “Results: 

Coefficients of Habitat Productivity,” p. 21), we used feces to 

correct for the bias towards undersampling grazing activities. 

If anything, grazed foods were probably overrepresented by 

feces (see following paragraph). Conversion factors based on 

fecal content (cfctrij) not only converted the different units by 

which feeding activity was measured to the common currency 

of grams but also, to some extent, corrected for different probabilities of detection among different feeding activities.

The content of feces is an important part of the calculations upon which the Yellowstone grizzly bear CEM coefficients are founded. Much of the critical information needed 

to convert fecal contents to an estimate of ingested biomass 

is available (Hewitt and Robbins, 1996). We know little, 

however, about biases affecting the detection and collection 

of feces, especially how these biases relate to feces of different compositions. Preliminary analysis of Yellowstone data 

suggests that feces comprising the remains of pure meat are 

substantially underrepresented because they are ephemeral, 

difficult to detect, and often aggregated. By contrast, feces 

containing ants or grazed foods are probably overrepresented 

because such feces are large, durable, and often deposited 

along travel routes. Consequently, the current coefficients 

probably underrepresent grizzly bear use of meat (i.e., ungulates) and overrepresent the use of ants and grazed foods. Even 

so, because energy from ants and graminoids currently makes 

only a minimal contribution to coefficient values, any changes 

that may arise from further investigation of this issue would 

probably have little effect on overall results.

Other important information that we used to calculate the 

coefficients remains weak or speculative. In particular, bite 

sizes associated with the consumption of meat need better documentation. Of importance to calculating net digested energy 

from cutthroat trout, the proportion of time spent feeding and 

the rate of consumption during that time are highly uncertain 

because of small sample sizes. Additional information on 

these parameters would be important to future revisions of 

coefficients. Information also needs to be collected on the 

energy expended during grazing and during the use of ungulates, ideally in terms that are comparable to existing estimates 

of resistance to excavation. In general, a method for directly 

and unambiguously estimating energy expenditure specific to 

the use of different foods is needed. More data on all parameters used in calculations would be beneficial and would allow 

for greater temporal and spatial specificity.

The issue of error propagation through multiple operations on multiple estimates is of consequence to a reductionistic approach such as this one. There are several ways that 

the magnitude and nature of this error can be appraised. One 

expedient means is to determine whether the coefficients and 

the derivative analyses are broadly consistent with the results 

of other research. For example, the large fraction of energy 

obtained from roots in the lithic high-elevation and mesic 

nonforest types (fig. 7) is consistent with the concentration 

of feeding on roots in these habitats (Haroldson and Mattson, 

1985; Mattson, 1997c). The large fraction of energy obtained 

from ungulates in the majority of types is similarly consistent 

with the large fraction of energy estimated to be contributed 

by this food to the diet of Yellowstone’s grizzly bears (figs. 

7–9; Mattson and others, 1991a; Mattson, 1997b; Jacoby and 

others, 1999), as is the case with the large amounts of energy 

obtained from whitebark pine seeds in the whitebark pine 

Discussion
32 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

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type (fig. 8; Mattson and others, 1991a, 1994; Mattson and 

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tests of this nature could involve comparing calculations of 

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and reproductive classes could be tested for consistency with 

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2000). These patterns also could be tested for consistency 

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Sensitivity analysis is an obvious next step for appraising 

the relative importance of different variables used to calculate 

the coefficients and the consequent importance of error and 

uncertainty in each. Sensitivity analysis can be approached 

several ways, none of which are mutually exclusive. Values 

for each variable can be set at the mean of relevant strata, and 

an aggregate change in coefficients can be calculated, such 

as change in seasonal habitat productivity for representative 

BMUs. The range of values for each variable can be symmetrically extended around the mean by some fixed percent and 

change in coefficients similarly calculated. Finally, variables 

identified as being highly uncertain or potentially highly 

influential (e.g., proportion of time spent fishing and catch rate 

for cutthroat trout and factors for converting units of activity 

to grams ingested [cfctrij]) could be set at the extremes of a 

biologically plausible range of values.

Additional information on compensatory changes in grizzly bear foraging behavior is desirable if CEM coefficients are 

to be used to project or otherwise anticipate habitat change. 

Grizzly bears exhibit a high degree of dietary flexibility in 

the Yellowstone ecosystem (Mattson and others, 1991a), 

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cutworm moths increased substantially during the 1970s and 

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others, 1991b). Grizzly bears also use more ungulates during 

the summer and fall of years when whitebark pine seeds are 

scarce (Mattson, 1997b). Whereas diminishment in any currently important food will likely result in diminished use by 

grizzly bears, it is unclear to what extent bears can compensate 

by reverting to extant alternate foods. It is also unclear what 

foods might increase in abundance. These factors are germane 

to representing future conditions that might arise from the loss 

of cutthroat trout, army cutworm moths, or whitebark pine. 

The mere reduction or increase of landscape features in future 

projections coupled with static CEM coefficients can only be 

a crude representation of potential consequences arising from 

the effects of disease, climate change, or introduced predators. 

Because of these limitations, future projections should 

consider a range of possible compensatory responses operationalized either by changes in the extent of map units or 

changes in the coefficients themselves.

Acknowledgments

Many people contributed to the collection of data used in 

this analysis. Dan Reinhart, Gerry Green, Roger Swalley, Jeff 

Henry, and Erin Shannahan contributed substantially to studies 

of grizzly bear habitat use and activities. Mark Haroldson, 

Bart Schleyer, and Jamie Jonkel were especially important 

in trapping and marking bears. Dave Stradley made major 

contributions as pilot and observer during radio-relocation 

flights. Funding and other support for this analysis was provided by the U.S. Forest Service, Shoshone National Forest, 

the USGS Forest and Rangeland Ecosystem Science Center, 

and the USGS Southwest Biological Science Center. Charles 

Schwartz, Mark Haroldson, Steve Cherry, and Steve Cain of 

the Interagency Grizzly Bear Study Team and Barrie Gilbert 

of Utah State University provided reviews that were much 

appreciated. Ron Kirby and Ruth Jacobs of the USGS Forest 

and Rangeland Ecosystem Science Center provided support 

for completion and publication of this work.
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Appendix 1 37

Common name Scientific name

Animals

 Ants, bees, wasps Hymenoptera (order)

 Army cutworm moth(s) Euxoa auxiliaris

 Bison Bos bison

 Black bear(s) Ursus americanus

 Cutthroat trout Oncorhynchus clarki1

 Earthworm(s) Oligochaeta (class)

 Grizzly bear(s) Ursus arctos

 Ground squirrel(s) Spermophilus columbianus

 Moose Alces alces

 Mule deer Odocoileus hemionus

 Pocket gopher(s) Thomomys talpoides

 Red squirrel(s) Tamiasciurus hudsonicus

 Rodent(s) Rodentia (order)

 Vole(s) Microtus spp.

 Wapiti Cervus elaphus

 Wasp(s) Vespidae (family)

Plants

 Alfalfa Medicago sativa2

 Alpine avens Geum rossii

 Alpine timothy Phleum alpinum

 Antelope bitterbrush Purshia tridentata

 Arrowleaf groundsel Senecio triangularis

 Ballhead sandwort Arenaria congesta

 Baltic rush Juncus balticus

 Beaked sedge Carex rostrata

 Big sagebrush Artemisia tridentata

 Biscuitroot(s) Lomatium cous2

 Bluebunch wheatgrass Agropyron spicatum2

(Pseudoroegneria spicata4)

 Bluegrass Poa spp.

 Bluejoint reedgrass Calamagrostis canadensis

 Broadleaf arnica Arnica latifolia

 Buffaloberry Sheperdia canadensis2

 Clover Trifolium spp.

 Common snowberry Symphoricarpos albus

 Common juniper Juniperus communis

 Cow parsnip Heracleum lanatum2

(Heracleum maximum3)

 Dandelion Taraxacum spp.

 Douglas-fir Pseudotsuga menziesii

 Elephanthead lousewort Pedicularis groenlandica

 Elk thistle Cirsium scariosum2

 Elk sedge Carex geyerii

 Engelmann spruce Picea engelmannii

 Fireweed Epilobium angustifolium2

(Chamerion angustifolium3)

 Geyer willow Salix geyeriana

 Globe huckleberry Vaccinium globulare2

(Vaccinium membranaceum3)

 Graminoids Poaceae and Cyperaceae (families)

Appendix 1. Common and Scientific Names of Species in this Report

[Scientific names are from the International Taxonomic Information System [ITIS, available at http://itis.usda.gov/index.html] unless those named were found to 

be in error or unless otherwise noted]

Common name Scientific name

Plants, continued

 Grouse whortleberry Vaccinium scoparium

 Heartleaf arnica Arnica cordifolia

 Horsetail Equisetum arvense

 Idaho fescue Festuca idahoensis

 Inflated sedge Carex vesicaria

 Lingonberry Vaccinium vitis-idaea

 Little larkspur Delphinium bicolor

 Lodgepole pine Pinus contorta

 Mountain snowberry Symphoricarpos oreophilus

 Mushroom(s) Hymenomycetes (class)

 Nineleaf biscuitroot Lomatium triternatum

 Olney’s bulrush Scirpus olneyi2

(Schoenoplectus americanus3)

 Oregon grape Berberis repens2 (Mahonia repens3)

 Ovalhead sedge Carex microptera

 Parry’s clover Trifolium parryi

 Pinegrass Calamagrostis rubescens

 Pinyon pine Pinus edulis

 Pondweed Potamogeton spp.

 Quaking aspen Populus tremuloides

 Red baneberry Actaea rubra

 Richardson’s stipa Stipa richardsonii2

(Acnatherum richardsonii5)

 Ross’s sedge Carex rossii

 Shrubby cinquefoil Potentilla fruticosa2

(Dasiphora floribunda3)

 Silver sagebrush Artemisia cana

 Silvery lupine Lupinus argenteus

 Slender wheatgrass Agropyron caninum2

(Elymus trachycaulus4)

 Spring beauty Claytonia lanceolata

 Sticky geranium Geranium viscosissimum

 Strawberry Fragaria spp.

 Subalpine fir Abies lasiocarpa2 (Abies bifolia6)

 Sweet bedstraw Galium triflorum

 Sweet-cicely Osmorhiza spp.

 Tea-leaved willow Salix phylicifolia2 (Salix planifolia3)

 Thick-leaved wild strawberry Fragaria virginiana

 Tufted hairgrass Deschampsia caespitosa

 Water sedge Carex aquatilis

 Western meadowrue Thalictrum occidentale

 Western coneflower Rudbeckia occidentalis

 White spirea Spiraea betulifolia

 Whitebark pine Pinus albicaulis

 Wolf willow Salix wolfii

 Yampa Perideridia gairdneri

1

Behnke, 1992.

2

Hitchcock and Cronquist, 1973.

3

ITIS.

4

Barkworth and Dewey, 1985.

5

Weber and Whittmann, 1996.

6

Flora of North America Committee, 1993.
38 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Appendix 1 References 

Barkworth, M.E., and Dewey, D.R., 1985, Genomically based 

genera in the perennial Triticeae of North America: identification and membership: American Journal of Botany, v. 72, 

p. 767-776.

Behnke, R.J., 1992, Native trout of western North America: 

Bethesda, Md., American Fisheries Society, 275 p.

Flora of North America Committee, ed., 1993, Flora of North 

America north of Mexico, volume 2: Pteridophytes and 

Gymnosperms: New York, N.Y., Oxford University Press, 

496 p.

Hitchcock, C.L., and Cronquist, A., 1973, Flora of the Pacific 

Northwest: Seattle, Wash., University of Washington Press, 

730 p.

Weber, W.A., and Whittmann, R.C., 1996, Colorado flora: 

eastern slope, second edition: Niwot, Colo., University 

Press of Colorado, 524 p.
Appendix 2 39

Appendix 2. Coefficients of Habitat Effectiveness for Yellowstone’s Grizzly Bear 

Habitat

others, 1996; Pease and Mattson, 1999), together with normal 

avoidance of human facilities by the relatively more numerous 

wary individuals. By contrast, because grizzly bears exhibit 

such a high degree of behavioral plasticity (Herrero, 1985, 

1989; Gilbert, 1989), it is highly unlikely that such underuse is 

a consequence of some fundamental inability of grizzly bears 

to tolerate humans (Mattson and others, 1996).

Because grizzly bears apparently avoid humans and 

human facilities with their avoidance contingent on behavioral 

characteristics of the bear population (which is, in turn, contingent on relative rates of human-caused mortality), the application of research to management is complicated. Avoidance of 

human facilities is typically expressed as relative underuse of 

habitat that varies with distance. Because bears have rarely 

been differentiated by their tolerance of humans, research 

results strongly reflect historical patterns of human-caused 

mortality. Judging the effects of human facilities on grizzly 

bears from this kind of research presupposes that (1) the same 

relative mix of habituated and wary bears is desired for the 

future and (2) wary and adult bears will continue to be killed 

by humans at the same rates as before. However, it may be that 

managers want to judge the impacts by humans, assuming that 

humans are much more tolerant of habituated animals. If it 

were assumed that humans were highly tolerant, simple representations of habitat productivity could be sufficient for judging the impacts of management. More likely, decisionmakers 

will want to judge the impacts of humans on wary bears since 

these animals have behavioral and demographic characteristics that are more desirable than those of habituated bears. In 

either case, research results that pool behavioral types deprive 

decisionmakers of relevant information.

The effects of humans or human facilities on use of 

habitats and foods by grizzly bears have been investigated in 

three primary ways. Most commonly, such effects have been 

inferred from spatial patterns of telemetry locations of radiomarked bears. Less often, effects have been inferred from 

direct observation of bears or the observation of durable signs. 

Each approach has its strengths and weaknesses. Telemetry 

locations have the advantage of potentially being classified 

according to the type of bear, whether on the basis of behavior, 

gender, age, or reproductive status. At the same time, telemetry locations are potentially subject to several biases. As evident in this study, there is a tendency to oversample bears that 

live near roads, especially in large study areas with few roads 

and prohibitions on low-level helicopter activity in wilderness 

areas. Trapping may modify the behavior of bears and interject 

additional bias in subsequent observations of captured animals 

(Gilbert, 1989). There is also a strong bias towards locating 

animals during daylight hours, with the possibility that nighttime use of areas near humans goes undetected (Olson and 

others, 1998). Radio-telemetry locations also do not reveal 

Section 2.1: Background

Grizzly bears exhibit a wide range of tolerances for 

humans and human facilities. While some bears use only areas 

remote from humans, others use heavily human-influenced 

niches, often with humans immediately nearby (Herrero, 1985; 

Aumiller and Matt, 1994; Mattson and others, 1996). Bears 

that exhibit extremes of these behaviors are called either wary 

or habituated. Although a gradient of individual behaviors 

exists, anecdotes and case histories from the Yellowstone 

ecosystem suggest that the transition from wariness to habituation can be rapid. Pease and Mattson (1999) show a theoretical exponential increase in levels of habituation to humans 

among animals that have survived initial contacts. For these 

reasons, we treated grizzly bears in this analysis as one of two 

behavioral types (wary or habituated), although we realized 

that transitional individuals would exhibit intermediate traits 

(Mattson and others, 1992; Pease and Mattson, 1999).

The relative extent to which grizzly bears use areas near 

human facilities is likely to be a relative function of the number of habituated animals in a population and the proximity 

of overall population density to habitat carrying capacity (K). 

Habituated bears tend to disproportionally use habitats near 

humans, especially in populations at or near K (Mattson, 1990; 

Mattson and others, 1992; Mattson and others, 1996). By contrast, wary bears disproportionally use habitats far away from 

humans. Thus, if habituated and wary bears are present in 

numbers proportional to the relative extent of areas influenced 

and uninfluenced by humans, no relative underuse of habitat 

near human facilities may be evident. By contrast, if a population is composed solely of wary bears, there may be virtually 

no use of human-influenced habitats. Habitat effectiveness, 

insofar as it varies with humans and their facilities, is largely 

an artifact of the relative numbers of habituated bears in any 

given population.

Relative numbers of habituated and wary bears in a population are predictably an artifact of the relative rates at which 

they die and are recruited (Pease and Mattson, 1999). Given 

that humans are almost always the cause of death for adult 

grizzly bears (Mattson and others, 1996), and given that reproductive rate varies little between habituated and wary females 

in places like the Yellowstone ecosystem (Pease and Mattson, 

1999), relative numbers of habituated and wary bears are 

determined largely by differences in the rate at which they are 

killed by humans. In most places, habituated bears are likely 

killed at a greater rate (see Meagher and Fowler, 1989). In the 

Yellowstone ecosystem, this differential is twofold (Pease and 

Mattson, 1999). Thus, population-level underuse of habitat 

in the Yellowstone ecosystem near human facilities (Mattson 

and others, 1987) is likely a consequence of humans killing 

habituated bears at a greater rate than wary bears (Mattson and 
40 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

anything about the associated activity of the bear, that is, a 

bear could be near humans but engaging in much less efficient 

foraging behavior compared to when it is in the back country 

(Mattson and others, 1987). Direct observation provides much 

valuable information about the details of human-grizzly bear 

interactions and the potential to differentiate behaviors of 

individual bears (e.g., Warner, 1987; Fagan and Fagan, 1994; 

Olson and Gilbert, 1994; Olson and others, 1997, 1998). On 

the other hand, direct observation is typically restricted to 

daylight hours and areas with good visibility. The geographic 

scope of research is also typically limited. Observation of 

durable signs has several advantages. It can focus on use of 

specific high-quality foods, provided that use of these foods 

is easily detected. Activity not related to the consumption of 

important foods is also implicitly censored. Such an approach 

is additionally not subject to biases interjected by the daily 

activity patterns of researchers. Among the disadvantages of 

observing durable signs, activity by different bear species is 

not readily differentiated and signs cannot be easily classified 

according to different types of bears. In short, the strengths 

and weaknesses of these different research tools require that 

scientists and managers be discriminating in their applications 

and judicious with their interpretations.

Section 2.2: Approach

For purposes of the Yellowstone grizzly bear cumulative 

effects model (CEM), we defined “effective habitat productivity” as that part of the net digested energy potentially derived 

from an area available to bears according to their response to 

humans or human facilities. We calculated effective habitat 

productivity as the product of “habitat productivity” (described 

previously) times “coefficients of habitat effectiveness” (hejp), 

applied contingent on a location being within a “zone-ofinfluence” (zoijp); hejp and zoijp were specific to a given season 

(j) and type of human activity or facility (p). Coefficients 

of habitat effectiveness were, in theory, proportional to the 

fraction of potential net digested energy that was extracted by 

bears within a zone-of-influence (ZOI).

We categorized human activities and facilities according to a generalized scheme described by Weaver and others 

(1986). Activities were first classed as motorized or nonmotorized. Features were then classed as linear, point, or dispersed. 

Levels of activity were categorized as low or high and as 

diurnal or 24-hour. Habitat adjacent to human-related features 

was further classified as “no-cover” or “high-cover.” Major 

facilities, such as recreational developments or towns (for 

definition see “Density of Feeding Activity” under “Analysis 

Methods,” p. 5 of the main body of the report), were placed in 

a category of their own.

We used research regarding the influences of humans and 

human facilities on grizzly bear behavior to define coefficients 

of habitat effectiveness (HE) and ZOIs for each of the generalized human features. This application of research results 

required that we translate conventionally identified features 

and activities such as roads, trails, campgrounds, and recreational developments into the more functional types used in 

the Yellowstone grizzly bear CEM. Where there were substantial differences in research results, we used a qualitative rule 

set for selecting which results to use. We gave first priority to 

results from the Yellowstone ecosystem. Among those studies, we gave priority to results obtained from the observation 

of durable signs. As indicated above, this type of data was 

less affected by some significant biases that otherwise compromised radio-telemetry data. Observation of durable signs 

was also more directly relevant to estimating the amount of 

energy obtained by bears, as signified by use of high-quality 

foods such as ungulates (Green and others, 1997), whitebark 

pine seeds (Mattson and Reinhart, 1997), and cutthroat trout 

spawning streams (Reinhart and Mattson, 1990). Finally, we 

gave priority to results that represented the probable responses 

of wary animals.

The behavior of wary bears is potentially of great interest 

to grizzly bear managers in the Yellowstone ecosystem. These 

bears have the highest survival rates (Mattson and others, 

1992; Pease and Mattson, 1999) and are less of a threat to 

humans, primarily because they are less often in contact with 

humans (Herrero, 1985, 1989; Herrero and Fleck, 1990). 

Where possible, we selected coefficients from the available 

research results that represented the behavior of wary bears. 

In almost all cases, our judgement as to whether the results 

pertained to wary bears or not required that we interpret the 

study design and study area conditions. In areas with a history 

of grizzly bear hunting and at least moderate levels of humancaused mortality, or in areas with a recent episode of substantial grizzly bear mortality that was selective against known 

food-conditioned or human-habituated animals, we assumed 

that the majority of bears were wary.

In several instances, we were not able to interpret 

research results in terms that directly related to HE or ZOIs. 

In other cases, we could not find research results germane 

to a specific human feature. Under these circumstances, we 

used subjective judgement to assign HE and ZOI values, 

based primarily on effects ascribed to the next most similar 

human activity or facility. When the Yellowstone grizzly bear 

CEM was first developed in 1984, many coefficients were the 

result of subjective judgement by those involved (Weaver and 

others, 1986; Dixon, 1997). Subsequently, values have been 

revised twice, in 1994 and in this publication, to reflect recent 

research. As a result, most HE coefficients and ZOIs currently 

have some empirical basis.

Even the most recent research does not provide much 

detailed information on differences in grizzly bear responses 

to humans when in the open (no-cover) compared to when 

in cover (high-cover). Even so, there are strong indications 

that responses are more extreme when encounters occur in 

the open (Schleyer and others, 1984; Haroldson and Mattson, 

1985; McLellan and Shackleton, 1989). In the absence of 

results concerning cover/noncover responses by grizzly bears 

to specific human features, we quantified the judgement of 

those who had estimated HE in 1984 for more systematic 
Appendix 2 41

applications to subsequently revised coefficients. This quantification took the form of predicting absolute differences in 

HE between the mean and cover and noncover values for each 

category of human activity or facilities; the mean was typically 

the value with greatest empirical support. This relationship 

took the form of a polynomial and approached 0 at high (→ 1) 

and low (→ 0) values of HE (fig. 2-1).

Section 2.3: Coefficients of Habitat 

Effectiveness

Coefficients of habitat effectiveness (HE) and zones-ofinfluence (ZOIs) for human features in the Yellowstone grizzly 

bear CEM were quite variable (table 2-1). At one extreme, HE 

was reduced to about 10% within 5 km of major human facilities such as towns and sizable recreational developments. This 

level of reduction was based on three studies of durable sign 

and was interpreted primarily to reflect the behavior of wary 

bears (Reinhart and Mattson, 1990; Green and others, 1997; 

Mattson and Reinhart, 1997). At the other extreme, low levels 

of dispersed nonmotorized human activity were assumed to 

have virtually no average effect (98% HE) on the feeding 

behavior and habitat use of bears, accounting for the fact that 

infrequent and unpredictable back-country encounters with 

humans resulted in only short-term responses by bears (Jope 

and Shelby, 1984; Jope, 1985; Schleyer and others, 1984; 

Haroldson and Mattson, 1985; Wilker and Barnes, 1998). This 

latter effect, as well as all others related to dispersed human 

activity, was based on professional judgement shaped by the 

results of many studies of interactions between humans and 

bears in the back country, including interactions off-trail (e.g., 

Chester, 1980; Schleyer and others, 1984; Haroldson and 

Mattson, 1985; McLellan and Shackleton, 1989; Gunther, 

1990; Albert and Bowyer, 1991; Revenko, 1994). Compared 

to the responses of bears to major human facilities, at one 

extreme, and dispersed back-country human activity, at the 

other extreme, all other human features had intermediate 

effects on bear behavior that were as much dependent on 

the extent of the ZOI as on the value of HE. For example, 

Figure 2-1. Relationship between the difference in value between cover and noncover for coefficients 

of habitat effectiveness (HE; range of habitat effectiveness) and the mean of these two values. Data are 

from original values assigned in 1984 and 1994 on the basis of professional judgement.
42 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 2-1. Coefficients of habitat effectiveness and the associated extent of the zone-of-influence for human features in the Yellowstone grizzly bear cumulative effects model. Coefficient of habitat effectiveness Category Mean (Noncover References Zone-of-influence References /cover) Aircraft 0.61 (0.42/0.79) Harding and Nagy, 1980; McLellan and mapped polygons Shackleton, 1988; Wilker and Barnes, 1998 Major development 0.08 (0.08/0.08) Green and others, 1997; Mattson and Reinhart, 5000 m Green and others, 1997; Mattson and Reinhart, 1997; Reinhart and Mattson, 1990 1997; Mattson and others, 1987, 1992 Linear motorized/high use 0.33 (0.21/0.45) Green and others, 1997; Mattson and Reinhart, 500 m Gilbert, 1989; Mattson and Reinhart, 1997; 1997 Mattson and others, 1987 Linear motorized/low use 0.20 (0.19/0.21) Archibald and others, 1987; Kasworm and 300 m Archibald and others, 1987; Aune, 1994; Manley, 1990; McLellan and Shackleton, 1988 Kasworm and Manley, 1990 Linear motorized/incidental 0.40a (0.27/0.53) 300 m Motorized point diurnal/high use 0.28b (0.18/0.38) 1000 m Motorized point diurnal/low use 0.57 (0.47/0.67) Gunther, 1990 1000 m Harding and Nagy, 1980 Motorized point/24-hr 0.28b (0.18/0.38) 1000 m Motorized dipsersed/high use 0.31 (0.13/0.48) mapped polygons Motorized dispersed/low use 0.75 (0.66/0.84) mapped polygons Nonmotorized linear/high use 0.25c (0.18/0.32) 300 m Nonmotorized linear/low use 0.51 (0.39/0.62) Kasworm and Manley, 1990 300 m Kasworm and Manley, 1990 Nonmotorized point/diurnal 0.57 (0.47/0.67) Gunther, 1990 500 m Gunther, 1990 Nonmotorized point/24-hr 0.28b (0.18/0.38) 500 m Nonmotorized dispersed/high use 0.95 (0.92/0.98) mapped polygons Nonmotorized dipsersed/low use 0.98 (0.97/0.99) mapped polygons

aThis value is twice that of the “linear motorized/low use.”

bThis value is one-half that of “motorized point diurnal/low use.”cThis value is one-half that of “nonmotorized linear/low use.”
Appendix 2 43

although HE for little-used roads was less than that of heavily used roads, the corresponding ZOI was only two-thirds as 

extensive. Thus, the overall effect of a major road was less 

per unit area but more widespread. Similarly, the effects of 

motorized point activities were distinguished from those of 

nonmotorized point activities by a ZOI that encompassed a 

geometrically larger area. In general, varying both HE and the 

ZOI allowed for greater sensitivity to the behavior of bears as 

reflected in diverse research results.

Section 2.4: Discussion

As discussed earlier, at the scale of population-level 

movements grizzly bears underuse habitats near humans 

largely to the extent that human-caused mortality has been 

selective against habituated animals. In other words, 

population-level patterns predictably are determined by the 

relative numbers of habituated and wary animals, who typically select, respectively, for and against areas near humans. 

Population-level patterns are thus an amalgam of effects attributable to selective human-caused mortality and the distinct 

behavioral characteristics of surviving individual bears.

It is important for management and research purposes to 

differentiate the effects of bear mortality and bear behavior 

as much as possible. Human-caused mortality is determined 

as much by human behavior as by bear behavior. Conversely, 

use of areas near humans by surviving bears is determined, at 

least proximally, by behavior of the bears alone. Bear behaviors and human-caused mortality entail different management 

issues and different related management decisions. Managing habituated bears and their death rate is intimately tied 

to managing humans. Moreover, managing human-caused 

mortality is almost wholly contingent on human values and 

world views that engender either tolerance or intolerance for 

grizzly bears that can live near us. Managing wary bears is 

a different class of problem. The preservation of wary bears 

largely depends on providing them with areas remote from 

humans where they can meet their energy needs without losing 

their fear of humans. The main concern is preventing habituation to humans and a doubled death rate. Thus, insofar as 

management of native habitat is concerned, it is the behavioral 

responses of wary bears that are germane. By contrast, the 

management of habituated bears largely entails the modification of human behavior and the management of bear attractants at human facilities.

The coefficients of habitat effectiveness presented here 

are, at best, a crude representation of the behavior of wary 

grizzly bears. However, the coefficients have merits. They constitute an effort to present information in a way that is maximally relevant to management deliberations both by emphasizing the behavior of wary bears and by being attentive to the 

many types of human activities that are present in grizzly bear 

habitat. By contrast, analyses of radio-telemetry data from 

the Yellowstone ecosystem to detect patterns of habitat use 

have, with one exception (Mattson and others, 1992), admixed 

habituated and wary animals and have not very well accounted 

for spatial sampling biases introduced either through trapping 

or radio-telemetry location efforts. Also, the available samples 

are not large enough in size to estimate the many parameters 

needed to control for spatial and temporal biases as well as the 

parameters that characterize responses of radio-marked bears 

to different types of human activities. Future analyses could 

exclusively focus on wary bears, but such parsing would only 

exacerbate problems with sample sizes.

Managers who rely on decision-support systems such as 

the Yellowstone grizzly bear CEM are thus confronted with 

the commonplace tension between a need for relevance and 

the limits of empiricism. Wholesale speculation is obviously 

undesirable because it entails substantial risk of leading to 

unintentionally harmful decisions. Hide-bound empiricism is 

also undesirable because, by default, all of the effects unable 

to be estimated, either because of deficient sample sizes or 

research designs, are typically assumed to be zero. Quite often, 

in the absence of statistical empiricism, management decisions are made based on undisclosed premises about the state 

of a system, without benefitting from well-developed qualitative scientific understanding. The overly empirical approach 

clearly also entails substantial risk. From the perspective of 

risk to the managed resource, some middle ground is optimal. 

In this analysis, we strove to find the middle ground between 

empiricism and informed speculation in developing coefficients of habitat effectiveness for the Yellowstone grizzly bear 

CEM.

Appendix 2 References

Albert, D.M., and Bowyer, R.T., 1991, Factors related to 

grizzly bear-human interactions in Denali National Park: 

Wildlife Society Bulletin, v. 19, p. 339-349.

Archibald, W.R., Ellis, R., and Hamilton, A.N., 1987, 

Responses of grizzly bears to logging truck traffic in the 

Kimsquit River Valley, British Columbia: International 

Conference on Bear Research and Management, v. 7, p. 

251-257.

Aumiller, L.D., and Matt, C.A., 1994, Management of McNeil 

River State Game Sanctuary for viewing brown bears: International Conference on Bear Research and Management, v. 

9, p. 51-61.

Aune, K.E., 1994, Comparative ecology of black and grizzly 

bears on the Rocky Mountain Front, Montana: International 

Conference on Bear Research and Management, v. 9, p. 

365-374.

Chester, J.M., 1980, Factors influencing human-grizzly bear 

interactions in a backcountry setting: International Conference on Bear Research and Management, v. 4, p. 351-357.
44 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Dixon, B.G., 1997, Cumulative effects modeling for grizzly 

bears in the Greater Yellowstone Ecosystem: Bozeman, 

Mont., Montana State University, M.S. thesis, 192 p.

Fagan, J.M., and Fagan, R., 1994, Interactions between 

wildlife viewers and habituated brown bears, 1987-1992: 

Natural Areas Journal, v. 14, p. 159-164.

Gilbert, B.K., 1989, Behavioural plasticity and bear-human 

conflicts, in Bromley, M., ed., Bear-people conflicts 

— proceedings of a symposium on management strategies: 

Yellowknife, Northwest Territories, Canada, Northwest Territories Department of Renewable Resources, p. 1-8.

Green, G.I., Mattson, D.J., and Peek, J.M., 1997, Spring feeding on ungulate carcasses by grizzly bears in Yellowstone 

National Park: Journal of Wildlife Management, v. 61, p. 

1040-1055.

Gunther, K.A., 1990, Visitor impact on grizzly bear activity 

in Pelican Valley, Yellowstone National Park: International 

Conference on Bear Research and Management, v. 8, p. 

73-78.

Harding, L., and Nagy, J.A., 1980, Responses of grizzly bears 

to hydrocarbon exploration on Richards Island, Northwest 

Territories, Canada: International Conference on Bear 

Research and Management, v. 3, p. 277-280.

Haroldson, M., and Mattson, D.J., 1985, Response of grizzly 

bears to backcountry human use in Yellowstone National 

Park: Bozeman, Mont., National Park Service, Interagency 

Grizzly Bear Study Team Report, 38 p.

Herrero, S., 1985, Bear attacks: their causes and avoidance: 

Piscataway, N.J., Nick Lyons Books/Winchester Press, 287 

p.

Herrero, S., 1989, The role of learning in some fatal grizzly 

bear attacks on people, in Bromley, M., ed., Bear-people 

conflicts — proceedings of a symposium on management 

strategies: Yellowknife, Northwest Territories, Canada, 

Northwest Territories Department of Renewable Resources, 

p. 9-14.

Herrero, S., and Fleck, S., 1990, Injury to people inflicted by 

black, grizzly or polar bears: recent trends and new insights: 

International Conference on Bear Research and Management, v. 8, p. 25-32.

Jope, K.L., 1985, Implications of grizzly bear habituation to 

hikers: Wildlife Society Bulletin, v. 13, p. 32-37.

Jope, K.L., and Shelby, B., 1984, Hiker behavior and the 

outcome of interactions with grizzly bears: Leisure Science, 

v. 6, p. 257-270.

Kasworm, W.F., and Manley, T.L., 1990, Road and trail 

influences on grizzly bears and black bears in northwest 

Montana: International Conference on Bear Research and 

Management, v. 8, p. 79-84.

Mattson, D.J., 1990, Human impacts on bear habitat use: International Conference on Bear Research and Management, v. 

8, p. 33-56.

Mattson, D.J., Blanchard, B.M., and Knight, R.R., 1992, Yellowstone grizzly bear mortality, human habituation, and 

whitebark pine seed crops: Journal of Wildlife Management, v. 56, p. 432-442.

Mattson, D.J., Herrero, S., Wright, R.G., and Pease, C.M., 

1996, Designing and managing protected areas for grizzly 

bears: how much is enough?, in Wright, R.G., ed., National 

Parks and protected areas: their role in environmental protection: Cambridge, Mass., Blackwell Science, p. 133-164.

Mattson, D.J., Knight, R.R., and Blanchard, B.M., 1987, The 

effects of developments and primary roads on grizzly bear 

habitat use in Yellowstone National Park, Wyoming: International Conference on Bear Research and Management, v. 

7, p. 259-273.

Mattson, D.J., and Reinhart, D.P., 1997, Excavation of red 

squirrel middens by Yellowstone grizzly bears: Journal of 

Applied Ecology, v. 34, p. 926-940.

McLellan, B.N., and Shackleton, D.M., 1988, Grizzly bears 

and resource-extraction industries: effects of roads on 

behaviour, habitat use and demography: Journal of Applied 

Ecology, v. 25, p. 451-460.

McLellan, B.N., and Shackleton, D.M., 1989, Immediate reactions of grizzly bears to human activities: Wildlife Society 

Bulletin, v. 17, p. 269-274.

Meagher, M., and Fowler, S., 1989, The consequences of 

protecting problem grizzly bears, in Bromley, M., ed., 

Bear-people conflicts — proceedings of a symposium on 

management strategies: Yellowknife, Northwest Territories, 

Canada, Northwest Territories Department of Renewable 

Resources, p. 141-144.

Olson, T.L., and Gilbert, B.K., 1994, Variable impacts of 

people on brown bear use of an Alaskan river: International 

Conference on Bear Research and Management, v. 9, p. 

97-106.

Olson, T.L., Gilbert, B.K., and Squibb, R.C., 1997, The effects 

of increasing human activity on brown bear use of an Alaskan river: Biological Conservation, v. 82, p. 95-99.

Olson, T.L., Squibb, R.C., and Gilbert, B.K., 1998, Brown 

bear diurnal activity and human use: a comparison of two 

salmon streams: Ursus, v. 10, p. 547-555.

Pease, C.M., and Mattson, D.J., 1999, Demography of the Yellowstone grizzly bears: Ecology, v. 80, p. 957-975.

Reinhart, D.P., and Mattson, D.J., 1990, Bear use of cutthroat 

trout spawning streams in Yellowstone National Park: International Conference on Bear Research and Management, v. 

8, p. 343-350.
Appendix 2 45

Revenko, I.A., 1994, Brown bear (Ursus arctos piscator) reaction to humans on Kamchatka: International Conference on 

Bear Research and Management, v. 9, p. 107-108.

Schleyer, B., Jonkel, J., Rhoades, K., and Dunbar, D., 1984, 

The effects of nonmotorized recreation on grizzly bear 

behavior and habitat use: Bozeman, Mont., National Park 

Service, Interagency Grizzly Bear Study Team Report, 83 p.

Warner, S.H., 1987, Visitor impact on brown bears, Admiralty 

Island, Alaska: International Conference on Bear Research 

and Management, v. 7, p. 377-382.

Weaver, J., Escano, R., Mattson, D., and Puchlerz, T., 1986, 

Cumulative effects process for the Yellowstone ecosystem, 

in Contreras, G., and Evans, K., compilers, Proceedings 

— grizzly bear habitat symposium: U.S. Forest Service 

General Technical Report INT-207, p. 234-246.

Wilker, G.A., and Barnes, V.G., Jr., 1998, Responses by brown 

bears to human activities at O’Malley River, Kodiak Island, 

Alaska: Ursus, v. 10, p. 557-561.
46 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Appendix 3. Habitat Types and Corresponding Codes Used in the Yellowstone 

Grizzly Bear Cumulative Effects Model

Habitat New codes Previously mapped codes

Nonforest types

 Clover patches 00001 Not mapped1

 Dry meadows and grasslands 00002 00013, 00024, 00035, 000074

 High-water-table flux wetlands 00003 Not mapped1

 Lithic ridges 00004 00015, 00034, 00051

 Marshes and fens 00005 00021, 00031, 00071

 Mesic meadows and grasslands 00006 00012, 00023, 00033, 00042, 00057, 00058, 00073

 Talus and scree 00007 0053

 Wet meadows 00008 00011, 00014, 00022, 00032, 00041, 00072, 00081, 00082

 Miscellaneous other existing nonforest 00009 00052, 00054, 00055, 00056, 00059, 00060, 88808, 99909; these will be 

 codes assigned coefficients of 0. Code 66606 (agricultural lands) will be retained and 

assigned a coefficient pending further discussion.

Forest types

 Dry forest openings created by timber 10100 All “0” cover types (__10, __20, __30, __40, __50, __60, __70, __80) of types 

 harvest or fire designated by the new codes as: 10101, 10201, 10301, 10401, or 10501, 

respectively.

 High elevation subalpine fir climax sites 10101 All cover types except “0” cover (__10, __20, __30, __40, __50, __60, __70, __80)

and except whitebark pine-dominated cover types (__51, __52, __53, __54, __63)

of the following habitat types (old codes): 461, 462, 475, 493, 497, 670, 671, 690,

701, 707, 710, 711, 745, 770, 780, 781, 782, 783, 784, 810, 811, 830, 840, or 842. 

 High elevation whitebark pine-dominated 10201 All cover types except “0” cover types (__10, __20, __30, __40, __50, __60, 

 sites __70, __80) of the following habitat types (old codes): 734, 812, 820, 821, 825, 

850, 870, 875, 880, 881, 885, 887, 891, 895, or 897; plus all whitebark pine cover 

types (__51, __52, __53, __54, __63), excluding __50, associated with any other 

habitat type.

 High elevation or dry Douglas-fir-dominated 10301 All cover types except “0” cover types (__10, __20, __30, __40, __50, 

 sites __60, __70, __80) and whitebark pine-dominated cover types (__51, __52, __53, 

__54, __63) of the following habitat types (old codes): 040, 050, 051, 060, 070, 

080, 092, 093, 095, 210, 212, 220, 221, 311, 321, 330, 360, 370, 371, 372, 373, 

380, 385, 395, 396, 397, 398, 399, 495, 702, 703, or 704.

 Sites dominated by grouse whortleberry 10401 All cover types except “0” cover types (__10, __20, __30, __40, __50, __60, 

__70, __80) and whitebark pine-dominated cover types (__51, __52, __53, __54, 

__63) of the following habitat types (old codes): 460, 485, 640, 663, 692, 721, 

730, 731, 732, 733, 735, 831, 920, or 940.

 Low elevation lodgepole pine-dominated 10501 All cover types except “0” cover types (__10, __20, __30, __40, __50, __60, 

 sites __70, __80) and whitebark pine-dominated cover types (__51, __52, __53, __54, 

__63) of the following habitat types (old codes): 790, 791, 792, 795, 896, 901, 

902, 903, 910, 935, 945, 950, 955, 956, 965, or 970.

 Low elevation spruce-dominated sites 10601 All cover types except “0” cover types (__10, __20, __30, __40, __50, __60, 

__70, __80) and whitebark pine-dominated cover types (__51, __52, __53, __54, 

__63) of the following habitat types (old codes): 410, 421, 440, 470, 480, 490, 

660, 661 or 911.

 Mesic subalpine fir climax sites 10701 All cover types except “0” cover types (__10, __20, __30, __40, __50, __60, 

__70, __80) and whitebark pine-dominated cover types (__51, __52, __53, __54, 

__63) of the following habitat types (old codes): 415, 601, 609, 610, 620, 621, 

623, 630, 635, 636, 650, 651, 653, 654, 740, 750, 751, 752, 760, 761, 762.

 Mesic forest openings created by timber 10600 All “0” cover types (__10, __20, __30, __40, __50, __60, __70, __80) 

 harvest or fire of types designated by the new codes as: 10601, 10701, or 10801, 

respectively.

 Mesic Douglas-fir-dominated sites 10801 All cover types except “0” cover types (__10, __20, __30, __40, __50, __60, 

__70, __80) and whitebark pine-dominated cover types (__51, __52, __53, __54, 

__63) of the following habitat types (old codes): 260, 261, 262, 280, 281, 290, 

291, 292, 293, 310, 312, 313, 320, 322, 323, 325, 340, 341, 343, 375, 390, 391, 

430, 432, 603, 607, 645, 647, 691, 705, 720, 722, 723, 724, or 990.

1

These habitat components are identified and mapped based on site-specific knowledge.
Appendix 4 47

Appendix 4. Relative Net Energy (kilocalories) Digested per Gram of Food 

Ingested by Yellowstone Grizzly Bears

Food Season Digested (eeij) (neteij) 

or Activity kilocalories Expended Net energy

 per gram energy per gram per gram 

 (index) (index)

Ungulates Wapiti calves estrus 4.23 0.34 3.99

 Adult wapiti spring 4.10 0.21 3.99

 Adult wapiti estrus 4.10 0.42 3.78

 Adult wapiti early hyperphagia 5.17 0.34 4.93

 Adult wapiti late hyperphagia 6.08 0.34 5.84

 Bison spring 4.29 0.28 4.11

 Bison estrus 4.29 0.28 4.11

 Bison early hyperphagia 4.85 0.25 4.70

 Bison late hyperphagia 5.49 0.25 5.34

 Moose spring 4.29 0.28 4.11

 Moose estrus 4.29 0.28 4.11

 Moose early hyperphagia 4.85 0.34 4.61

 Moose late hyperphagia 5.49 0.34 5.25

Hymenoptera

 In logs year-round 3.25 3.25 0.10

 In hills year-round 3.25 0.31 3.04

 Under logs year-round 3.25 1.76 1.59

 Under rocks year-round 3.25 2.35 1.00

 Under dung year-round 3.25 1.50 1.85

 Hornets year-round 2.74 2.67 0.17

Excavated animals and caches

 Pocket gophers spring 1.98 0.24 1.84

 Pocket gophers estrus 2.08 0.23 1.95

 Pocket gophers early hyperphagia 2.66 0.86 1.90

 Pocket gophers late hyperphagia 2.55 0.94 1.71

 Voles spring 3.27 0.87 2.50

 Voles estrus 3.27 0.47 2.90

 Voles early hyperphagia 3.27 2.30 1.07

 Voles late hyperphagia 1.88 0.12 1.86

 Worms year-round 3.19 1.14 2.15

 Whitebark pine early hyperphagia 2.73 0.37 2.46

 Whitebark pine late hyperphagia 2.73 0.28 2.55

 Mushrooms year-round 1.67 0.02 1.75

 Huckleberry year-round 2.74 0.03 2.81

 Whortleberry year-round 2.70 0.11 2.69

 Buffaloberry year-round 2.75 0.05 2.80

 Strawberry year-round 2.71 0.06 2.75

Roots

 Yampa spring 2.85 0.50 2.45

 Yampa estrus 2.82 0.19 2.73

 Yampa early hyperphagia 2.82 0.43 2.49

 Yampa late hyperphagia 2.82 0.55 2.37

 Biscuitroot spring 2.44 0.18 2.36

 Biscuitroot estrus 2.41 0.18 2.33

 Biscuitroot early hyperphagia 2.36 0.30 2.16

 Biscuitroot late hyperphagia 2.36 0.30 2.16

 Sweet-cicely year-round 2.47 0.33 2.24

 Pondweed year-round 2.13 0.31 1.92
48 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Grazed foods

 Graminoids spring 1.29 0.12 1.27

 Graminoids estrus 1.21 0.08 1.23

 Graminoids early hyperphagia 0.68 0.06 0.72

 Graminoids late hyperphagia 0.68 0.06 0.72

 Clover spring 2.01 0.08 2.03

 Clover estrus 1.53 0.08 1.55

 Clover early hyperphagia 1.47 0.04 1.53

 Clover late hyperphagia 1.47 0.04 1.53

 Dandelion year-round 1.64 0.05 1.69

 Thistle year-round 0.67 0.03 0.74

 Fireweed spring 1.69 0.06 1.73

 Fireweed estrus 1.69 0.06 1.73

 Fireweed early hyperphagia 2.18 0.06 2.22

 Fireweed late hyperphagia 2.18 0.06 2.22

 Horsetail year-round 1.06 0.03 1.13

 Spring beauty year-round 1.77 0.17 1.70

Appendix 4. —Continued.

Food Season Digested (eeij) (neteij) 

or Activity kilocalories Expended Net energy

 per gram energy per gram per gram 

 (index) (index)
Appendix 5 49

Appendix 5. Conversion Factors (cfctrij) from Units of Activity Measured at 

Grizzly Bear Feeding Sites to Relative Grams of Food Obtained by Bears

[Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]

 Food or Activity Season

 Spring Estrus Early hyperphagia Late hyperphagia

Ungulates

 Ungulate meat (g/kg) 6.51 17.44 14.17 4.68

Hymenoptera

 Ants_logs (g/dm3) 0.11 0.17 0.24 0.93

 Ants_hills (g/dm3) 1.57 1.59 0.40 0.40

 Ants_under logs (g/dm3) 0.05 0.08 0.12 0.46

 Ants_under rocks (g/rock) 0.05 0.08 0.12 0.46

 Ants_under dung (g/feces) 0.08 0.12

 Hornets (g/dm3) 0.75 0.75 0.75

Excavated animals and caches

 Pocket gophers (g/dm3) 0.01 0.02 0.49 1.28

 Worms (g/dm3) 0.01 0.02

 Voles (g/dm3) 0.01 0.02 0.49 1.28

Fruits, sporophytes, and seeds

 Whitebark pine (g/m2) 26.18 13.09 5.04 25.16

 Mushrooms (g/dig) 1.77 2.32 1.77

 Huckleberry (g/feces) 2.00 38.80 30.50

 Whortleberry (g/feces) 2.00 38.80 30.50

 Buffaloberry (g/feces) 17.56

 Strawberry (g/feces) 48.00

 Other berries (g/feces) 20.80 20.80

Roots

 Yampa (g/dig) 0.52 0.52 0.18 4.00

 Biscuitroot (g/dig) 0.03 0.03 0.07 0.07

 Sweet-cicely (g/dig) 1.60 1.60

 Pondweed (g/dm3) 0.01 0.01 0.01 0.01

Grazed foods

 Graminoids (g/feces) 9.44 20.19 52.24 24.99

 Clover (g/feces) 1.79 10.32 18.41 18.41

 Dandelion (g/feces) 22.90 22.90 18.48 18.48

 Thistle (g/stem) 10.06 10.06

 Fireweed (g/feces) 15.70 42.86 76.02 76.02

 Horsetail (g/feces) 4.32 4.32 12.77

 Spring beauty (g/feces) 3.48 4.11
50 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Appendix 6. Mean Level of Feeding Activity by Grizzly Bears for Different Foods (fslvijk), in Food-specific Units [“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type] H.T. Spring Estrus Early hyperphagia Late hyperphagia Code Misc. Wapiti Wapiti Bison Moose Wapiti Wapiti Bison Moose Misc. Wapiti Wapiti Bison Moose Misc. Wapiti Wapiti Bison Moose Ung. calf adult calf adult Ung. calf adult Ung. calf adult Ungulates = “ung.” (kilograms dry weight)2 12 23 90 2 31 124 34 37 1344 28 396 22 91 3 36 94 68 146 1418 29 69 100 39 3 39 92 3 48 163 89 14610100 14 23 149 1 2 1410101 3510201 20 310301 1 38 4310401 130 3 118 65 66 158 114 30 170 11410501 29 39 80 3 34 115 76 65 8510600 9 3 35 6010601 32 52 3 10 72 9010701 23 20 254 51 3 33 159 41 29 4 54 36 15410801 3 38 20 3Mean 2 26 29 111 44 4 36 117 47 3 7 53 150 102 3 2 50 116 134
Appendix 6 5

1

Mean level of feeding activity by grizzly bears for different foods (fslvijk), in food-specific units.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

Grass Clover Dandelion Grass Clover Dandelion Thistle Grass Clover Dandelion Thistle Grass Clover Dandelion

Grazed foods (grasses and sedges [grass], clover, and dandelion [number of feces]; thistle [number of stems])

2 2.9 5.1 2.0 2.1 1.8 2.2 14.0 1.8 7.0 12.0 1.74 1.5 1.0 1.0 1.0 2.0 4.4 13.06 1.7 2.5 3.0 2.5 2.0 1.6 13.0 3.6 1.0 3.2 9.0 1.58 5.8 10.2 6.0 4.4 4.3 1.7 16.0 6.5 10.0 1.5 6.0 2.6 9.0 2.010100 2.3 2.0 2.0 16.0 1.0 1.0 4.0 2.0 3.010101 1.7 2.0 2.010201 2.0 3.3 2.010301 1.0 1.010401 1.0 3.0 1.010501 1.0 2.0 5.010600 1.7 2.0 1.0 1.9 1.5 2.8 2.0 3.5 8.9 1.3 1.0 1.010601 2.0 3.0 7.2 1.0 1.010701 2.2 1.0 2.1 1.5 1.4 2.0 1.2 1.5 1.8 7.0 1.2 15.0 1.010801 2.7 2.2 2.0 2.0 2.0 5.0 2.0Mean 2.3 5.0 2.5 2.1 3.6 1.8 8.0 3.6 4.8 1.8 7.7 2.1 5.8 2.0
52 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Other invertebrates Ants under rocks 239 90 101 46 (decimeter3

)

Ants under logs (n) 68 55 60 16Ants under dung (n) 21Hornets 28 48 28 (decimeter3

)

Mean level of feeding activity by grizzly bears for different foods (fslvijk), in food-specific units.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

Logs Hills Logs Hills Logs Hills Logs Hills

Ants in logs and hills (decimeter3 excavated)

2 181 5 32 37 805 28 59 284 1 606 123 14 49 18 92 76 17 68 78 36 86 7 14 8 555 5410100 22 3 48 1 13110101 129 68 19 3410201 114 111 62 6310301 5 238 17 208 8110401 89 85 89 5610501 49 1 50 1 110 19 4310600 21 55 111 5410601 51 108 363 3410701 36 111 8 108 139 8310801 178 217 96 47 111 6 73Mean 90 49 84 17 168 37 101 29Food Source Spring Estrus Early hyperphagia Late hyperphagia
Appendix 6 53

Mean level of feeding activity by grizzly bears for different foods (fslvijk), in food-specific units.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]

Food Source Spring Estrus Early hyperphagia Late hyperphagia

Excavated root caches and animal foods: Other (decimeter3 excavated)

Worms 2153 15247Voles 38 99 99 121

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

Excavated root caches and animal foods: Pocket gophers (decimeter3 excavated)

2 213 1704 65 34 180 386 412 475 110 1168 440 198 15210100 361010110201 121030110401 2810501 110910600 370 601060110701 2 10 46810801 13 70Mean 216 412 85 164
54 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Mean level of feeding activity by grizzly bears for different foods (fslvijk), in food-specific units.— Continued. [“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type] Food Source Spring Estrus Early hyperphagia Late hyperphagia Fruits (number of feces) Huckleberry 1.4 1.0 Whortleberry 3.0 1.2 1.0 Buffaloberry 3.7 3.7 Strawberry 1.7 Other berries 4.7 1.5 H.T. Code Spring Estrus Early hyperphagia Late hyperphagia Seeds Mushrooms Seeds Mushrooms Seeds Mushrooms Seeds Mushrooms Whitebark pine seeds from middens and mushrooms (seeds = meter2 excavated; mushrooms = number of digs)24681010010101 43 28 24 2110201 7 31 53 2 77 3410301 2010401 28 22 6 25 1810501 8 6 9 55 25 26106001060110701 27 27 96 37 510801 24 10 14Mean 7 27 6 26 34 34 21
 55

Mean level of feeding activity by grizzly bears for different foods (fslvijk), in food-specific units.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]Food Source Spring Estrus Early hyperphagia Late hyperphagia

Other roots

Sweet-cicely (n) 26 65Pondweed (decimeter3) 15096 34056Food Source Spring Estrus Early hyperphagia Late hyperphagia

Other grazed foods (number of feces)

Fireweed 1.0 1.3 2.2 3.0Horsetail 2.6 2.6 2.6Spring beauty 2.0 2.4H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

Yampa Biscuitroot Yampa Biscuitroot Yampa Biscuitroot Yampa Biscuitroot

Yampa and biscuitroot (number of digs)

2 12 82 11 457 339 161 40 804 516 115 304 36 514 12 3156 9 455 116 28 366 78 718 50 262 7510100 2 170 144 413 971010110201 48 4 1 3110301 10010401 2 810501 3 1 310600 27 1410601 6110701 19 1410801 5Mean 7 184 62 166 207 136 42 142

Appendix 6
56 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Appendix 7. Mean Index of Net Energy per Feeding Site (fsneijk) for Consumption of Different Foods by Grizzly Bears [“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type] Spring Estrus Early hyperphagia Late hyperphagia H.T. Misc. Wapiti Wapiti Bison Moose Wapiti Wapiti Bison Moose Misc. Wapiti Wapiti Bison Moose Misc. Wapiti Wapiti Bison Moose Code ung. calf adult calf adult ung. calf adult ung. calf adult Ungulates = “ung.”2 301 596 2414 139 2040 8917 2408 2606 89514 728 25846 567 2447 230 2386 6764 4750 9703 35308 752 1784 2685 1050 202 2564 6567 153 3367 10856 2424 365310100 995 1586 9897 23 49 39410101 92910201 520 19510301 21 988 282110401 3470 176 8458 4688 4639 10496 7473 829 4248 281110501 754 1012 2155 202 2241 8272 5309 1789 212610600 234 195 2307 420510601 857 1392 174 560 5030 587910701 65 598 519 6787 1355 188 2182 11404 2910 2019 108 1482 911 378810801 998 524 200Mean 29 681 747 2974 1182 270 2391 8397 3335 200 357 3723 9981 6676 66 49 1384 2894 3300
Appendix 7 5

7

H.T. Spring Estrus Early hyperphagia Late hyperphagiaCode Grass Clover Dandelion Grass Clover Dandelion Thistle Grass Clover Dandelion Thistle Grass Clover Dandelion

Grazed foods (grasses and sedges [grass], clover, dandelion, and thistle)

2 35 19 77 52 28 85 101 66 197 87 304 18 25 16 39 75 124 936 20 9 116 62 32 64 95 135 28 102 66 278 69 37 232 110 69 67 119 245 282 94 41 47 254 6310100 27 77 50 256 39 7 151 56 9410101 41 32 3610201 24 125 3610301 25 3910401 75 1810501 50 18810600 21 7 39 47 24 107 15 132 251 40 7 2810601 50 116 273 28 31 42310701 27 39 53 24 55 15 45 42 56 48 23 56 3110801 32 56 32 77 75 90 163Mean 30 18 97 53 51 69 59 137 136 65 57 38 163 62Mean index of net energy per feeding site (fsneijk) for consumption of different foods by grizzly bears.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]
58 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

H.T. Spring Estrus Early hyperphagia Late hyperphagia Code Logs Hills Logs Hills Logs Hills Logs Hills Ants in logs and hills2 1.9 24.8 0.5 177.8 19.5 33.5 5.4 34.74 0.0 5.56 1.3 64.8 0.8 89.5 2.2 93.0 1.6 7.88 0.8 172.6 1.4 35.8 0.3 10.0 51.5 65.310100 0.4 12.1 1.2 1.0 12.110101 2.2 1.6 22.6 3.110201 1.2 1.9 1.5 5.910301 0.1 4.0 80.3 5.0 7.510401 1.0 1.4 2.2 5.210501 0.5 5.7 0.8 4.8 2.7 23.4 4.010600 100.6 0.9 2.7 5.010601 0.5 1.8 8.8 41.410701 0.4 1.9 38.7 2.6 169.0 7.710801 1.9 1035.3 1.6 227.5 2.7 6.8 6.7Mean 1.0 234.0 1.4 83.3 4.1 44.5 9.3 35.9

Food source Spring Estrus Early hyperphagia Late hyperphagia

Other invertebrates

Ants under rocks 20.3 12.0 19.4 33.6Ants under logs 3.6 4.7 7.2 7.4Ants under dung 3.3 0.3Hornets 3.5 6.2 3.6

Mean index of net energy per feeding site (fsneijk) for consumption of different foods by grizzly bears.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]
Appendix 7 5

9

Mean index of net energy per feeding site (fsneijk) for consumption of different foods by grizzly bears.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]

Food Source Spring Estrus Early hyperphagia Late hyperphagia

 Excavated root caches and animal foods: Other

Worms 54.6 646.9Voles 1.1 5.7 51.7 287.9

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

Excavated root caches and animal foods: Pocket gophers

2 4.6 65.4 60.6 6.34 6.9 34.96 8.9 18.2 102.3 252.28 9.6 7.6 141.410100 1.41010110201 0.51030110401 1.110501 42.610600 14.2 55.91060110701 0.1 0.4 33.310801 0.2 151.8Mean 4.7 15.8 79.0 110.9
60 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

 H.T. Spring Estrus Early hyperphagia Late hyperphagia Code Seeds Mushrooms Seeds Mushrooms Seeds Mushrooms Seeds Mushrooms Whitebark pine seeds from middens and mushrooms24681010010101 1468 351 1545 6510201 454 1068 655 8 2759 10410301 24210401 986 270 24 1610 5710501 283 19 113 222 1626 80106001060110701 947 332 390 2355 1510801 298 41 917Mean 454 950 19 323 137 1802 64

Food Source Spring Estrus Early hyperphagia Late hyperphagia

Fruits

Huckleberry 153 86Whortleberry 16 127 82Buffaloberry 180 180Strawberry 226Other berries 268 86

Mean index of net energy per feeding site (fsneijk) for consumption of different foods by grizzly bears.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]
Appendix 7 61

H.T. Spring Estrus Early hyperphagia Late hyperphagiaCode Yampa Biscuitroot Yampa Biscuitroot Yampa Biscuitroot Yampa Biscuitroot

Yampa and biscuitroot

2 15.8 5.7 15.2 31.6 148.4 25.2 380.8 12.54 36.2 162.2 21.0 15.5 80.5 113.8 49.36 11.4 31.9 162.7 1.9 160.2 12.2 744.68 70.0 114.8 711.410100 0.1 239.1 10.0 180.5 15.21010110201 3.4 0.3 0.2 4.910301 15.710401 0.1 11.310501 3.8 1.4 0.510600 38.0 3.710601 4.210701 4.7 132.810801 6.3Mean 9.3 12.9 87.5 11.5 89.7 21.4 416.7 22.2

Food Source Spring Estrus Early hyperphagia Late hyperphagia

Other roots

Sweet-cicely 92 233Pondweed 339 552 765Food source Spring Estrus Early hyperphagia Late hyperphagia

Other grazed foods

Fireweed 27 104 368 506Horsetail 8 8 23Spring beauty 34 40Mean index of net energy per feeding site (fsneijk) for consumption of different foods by grizzly bears.—Continued.[“H.T. Code” refers to habitat type code. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]
62 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Appendix 8. Proportion of Grizzly Bear Radio-relocations with Feeding Activity 

(p = pactjkl)

[Sample sizes (n) are given. Years are distinguished by whether carrion was abundant or not (Ung = Y or N) and by whether whitebark pine seeds were abundant or not (Wbp = Y or N). “H.T. Code” refers to habitat type code]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

 p n p n p n p n p n p n p n

2 0.30 23 0.22 16 0.51 65 0.64 11 0.43 10 0.45 11 0.44 9

4 0.86 7 0.86 7 0.91 43 0.86 14 1.00 12 0.60 10 0.60 10

6 0.88 25 0.86 21 0.82 65 0.92 27 0.90 21 0.77 13 0.83 12

7 0.86 7 0.86 7 0.91 43 0.86 14 1.00 12 0.60 10 0.60 10

5 and 8 0.64 11 0.64 11 0.66 32 0.81 16 0.67 24 0.85 13 0.85 13

10100 0.59 22 0.56 18 0.29 63 0.21 14 0.25 24 0.25 8 0.36 11

10101 0.18 11 0.18 11 0.10 31 0.48 25 0.64 11 0.57 14 0.50 18

10201 0.27 11 0.27 11 0.35 74 0.54 57 0.48 23 0.73 113 0.67 15

10301 0.11 9 0.11 9 0.21 19 0.33 6 0.33 6 0.17 6 0.17 6

10401 0.22 9 0.11 18 0.23 116 0.33 27 0.41 22 0.41 34 0.58 19

10501 0.33 21 0.42 24 0.20 41 0.50 24 0.32 19 0.48 23 0.50 18

10600 0.72 18 0.69 13 0.42 71 0.42 33 0.67 24 0.40 5 0.40 5

10601 0.14 7 0.14 7 0.22 37 0.60 10 0.64 11 0.58 12 0.58 12

10701 0.36 14 0.21 19 0.35 125 0.44 64 0.52 33 0.53 30 0.59 37

10801 0.38 16 0.42 12 0.34 50 0.57 14 0.80 15 0.67 9 0.83 12
Appendix 9 63

Appendix 9. Relative Density of Grizzly Bear Feeding Activity by Region, Habitat 

Type, Season, and Year Type

[Years are distinguished by whether carrion was abundant or not (Ung = Y or N) and by whether whitebark pine seeds were abundant or not (Wbp = Y or N). 

Habitat types are also differentiated by whether they occur near to or far from a forest edge (Edge = Y [near] or N [far]). “H.T. Code” refers to habitat type code. 

“Wntrr” denotes ungulate winter range, “B” denotes bison winter range, “E” denotes elk winter range, and “N” denotes areas that are not ungulate winter range. 

Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]

Table 9-1. North.

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Edge = Y Edge = N Wbp = Y Wbp = N Wbp = Y Wbp = N

 Edge = Y Edge = N Edge = Y Edge = N

2 0.12 0.09 0.16 0.13 0.15 0.11 0.27 0.17 0.06 0.42

4 0.51 0.45 0.42 0.34 0.37 0.26 0.38 0.24 0.84 0.40

6 1.14 1.36 1.69 1.35 1.15 0.82 1.67 1.07 0.88 0.98

7 0.51 0.45 0.42 0.34 0.37 0.26 0.38 0.24 0.84 0.40

5 and 8 0.00 0.52 1.01 0.80 0.67 0.48 0.70 0.45 0.63 0.64

10100 0.12 0.09 0.31 0.25 0.15 0.11 0.06 0.04 0.13 0.21

10101 0.15 0.61 0.34 0.27 1.27 0.91 0.78 0.50 1.99 1.03

10201 0.15 0.61 0.34 0.27 1.27 0.91 0.78 0.50 1.99 1.03

10301 1.51 0.77 0.50 0.40 0.41 0.29 1.07 0.68 0.49 0.97

10401 0.12 0.05 0.09 0.07 0.36 0.26 0.54 0.34 0.31 0.47

10501 0.22 1.30 0.56 0.45 0.62 0.45 1.53 0.98 1.01 0.69

10600 1.42 2.30 1.07 0.85 1.75 1.25 3.10 1.98 1.06 0.49

10601 0.22 0.15 0.56 0.45 0.62 0.45 1.53 0.98 1.01 0.69

10701 0.27 0.23 0.63 0.50 0.68 0.49 1.20 0.76 0.86 0.87

10801 1.51 0.77 0.50 0.40 0.41 0.29 1.07 0.68 0.49 0.97

Table 9-2. East.

H.T. Spring Estrus Early hyperphagia Late hyperphagia

Code Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

 Wntrr = E Wntrr = N Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N

2 0.13 0.04 0.11 0.06 0.23 0.27 0.13 0.25 0.18 0.17 0.12

4 1.15 0.35 1.17 0.60 0.60 0.90 0.88 0.51 0.36 0.30 0.20

6 2.91 0.89 2.42 1.25 0.60 0.80 0.56 0.76 0.54 0.87 0.56

7 1.85 0.57 1.19 0.60 0.60 0.90 0.88 0.51 0.36 0.30 0.20

5 and 8 1.97 0.61 0.63 0.33 0.94 0.36 0.73 0.76 0.54 4.96 3.42

10100 1.30 0.40 1.24 0.64 0.66 0.26 0.67 0.32 0.22 0.39 0.23

10101 0.37 0.11 0.35 0.18 0.14 0.45 0.54 0.88 0.62 1.30 0.90

10201 0.16 0.05 0.65 0.34 0.23 0.55 0.49 1.38 0.98 1.26 0.95

10301 0.07 0.02 0.06 0.03 0.11 0.19 0.12 0.08 0.06 0.02 0.15

10401 0.54 0.16 0.32 0.16 0.15 0.60 0.53 1.28 0.90 1.35 0.76

10501 0.32 0.10 0.29 0.15 0.29 1.11 1.01 1.30 0.92 1.42 0.98

10600 6.15 1.89 0.67 0.34 1.67 2.61 1.79 1.11 0.79 1.73 1.19

10601 0.32 0.10 0.29 0.15 0.29 1.11 1.01 1.30 0.92 1.42 0.98

10701 1.04 0.32 0.87 0.45 0.43 0.36 0.53 0.70 0.50 0.78 0.43

10801 1.04 0.32 0.87 0.45 0.43 0.36 0.53 0.70 0.50 0.78 0.43
64 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 9-3. South.

H.T. Spring Estrus Early hyperphagia Late hyperphagia

Code Ung = Y Ung = N Edge = Y Edge = N Wbp = Y Wbp = N Wbp = Y Wbp = N

 Edge = Y Edge = N Edge = Y Edge = N

2 0.74 0.48 0.33 0.42 0.32 0.26 0.25 0.20 0.31 0.29

4 0.67 0.44 0.46 0.49 0.37 0.33 0.72 0.24 0.38 0.44

6 0.19 0.12 0.61 0.75 0.60 1.06 0.42 0.89 1.41 0.53

7 0.67 0.44 0.46 0.49 0.37 0.33 0.72 0.24 0.38 0.44

5 and 8 0.74 0.51 0.94 0.85 0.64 1.01 0.86 0.45 0.71 1.38

10100 0.74 0.49 0.33 0.42 0.32 0.26 0.25 0.20 0.31 0.29

10101 0.09 0.06 0.17 0.32 0.24 0.72 0.61 1.32 2.10 0.78

10201 0.09 0.06 0.17 0.32 0.24 0.72 0.61 1.32 2.10 0.78

10301 1.48 0.98 0.60 0.30 0.22 0.65 1.15 0.68 1.08 1.13

10401 0.37 0.25 0.12 0.35 0.27 0.38 0.35 0.44 0.71 0.48

10501 1.82 1.20 0.69 0.37 0.28 0.37 0.54 0.23 0.37 1.64

10600 0.94 0.62 0.67 0.63 0.48 0.59 0.96 0.27 0.43 0.22

10601 0.15 0.10 0.13 0.22 0.17 0.67 0.17 0.63 0.99 0.39

10701 0.86 0.57 0.45 0.70 0.53 0.68 0.95 0.48 0.77 0.68

10801 1.48 0.98 0.60 0.30 0.22 0.65 2.70 0.68 1.08 1.13
Appendix 9 6

5

Table 9-4. West.H.T. Spring Estrus Early hyperphagia Late hyperphagiaCode Ung = Y Ung = N Edge = Edge = Wbp = Y Wbp = N Wbp = Y Wbp = N

Wntrr = B Wntrr = E Wntrr = N Edge = Edge = Y N Edge = Edge = Edge = Edge = Edge = Edge = Edge = Edge = 

Edge = Edge = Edge = Edge = Edge = Edge = Y N Y N Y N Y N Y N

Y N Y N Y N

2 0.31 0.14 0.09 0.04 0.09 0.04 0.12 0.10 0.20 0.10 0.40 0.18 0.44 0.28 0.21 0.13 0.23 0.134 Missing values6 2.17 0.97 0.63 0.28 0.65 0.29 1.21 0.71 1.65 0.84 0.83 0.38 2.72 1.21 0.88 0.55 1.50 0.827 Missing values5 and 8 7.52 3.35 2.17 0.97 2.24 1.00 2.41 1.38 1.88 0.95 2.88 1.30 2.73 2.57 1.61 1.00 2.35 1.2810100 0.82 0.36 0.24 0.10 0.24 0.11 0.31 0.19 0.50 0.25 0.49 0.22 0.33 0.10 0.07 0.04 0.34 0.1910101 0.79 0.35 0.23 0.10 0.24 0.10 0.27 0.15 0.22 0.11 0.25 0.11 0.03 0.02 2.32 1.45 0.26 0.1410201 0.79 0.35 0.23 0.10 0.24 0.10 0.27 0.15 0.22 0.11 0.25 0.11 0.03 0.02 2.32 1.45 0.26 0.1410301 4.95 2.21 1.43 0.64 1.48 0.66 1.23 0.63 0.82 0.41 2.27 1.03 0.34 1.02 0.42 0.26 1.16 0.6310401 0.54 0.24 0.16 0.07 0.16 0.07 0.12 0.14 0.27 0.14 0.70 0.32 3.28 0.12 0.56 0.35 0.75 0.4110501 0.96 0.43 0.28 0.12 0.29 0.13 0.33 0.15 0.23 0.12 0.82 0.37 0.71 0.49 1.20 0.75 1.36 0.7410600 3.94 1.76 1.14 0.51 1.18 0.52 1.50 0.90 0.88 0.44 1.09 0.49 2.21 0.61 0.40 0.25 0.34 0.1910601 0.48 0.22 0.14 0.06 0.14 0.06 0.19 0.11 0.17 0.09 0.29 0.13 0.42 0.17 1.63 1.01 1.26 0.6910701 1.22 0.54 0.35 0.16 0.36 0.15 0.40 0.38 1.07 0.54 0.94 0.42 1.69 0.63 1.39 0.86 1.19 0.6510801 4.95 2.21 1.43 0.64 1.48 0.66 1.23 0.63 0.82 0.41 2.27 1.03 3.28 1.02 0.42 0.26 1.16 0.63
66 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Appendix 10. Mean Energetic Value of a Feedsite (avefsjklm; index)

[Years are distinguished by whether carrion was abundant or not (Ung = Y or N) and by whether whitebark pine seeds were abundant or not (Wbp = Y or N). 

“H.T. Code” refers to habitat type code. “Wntrr” denotes ungulate winter range, “B” denotes bison winter range, “E” denotes elk winter range, and “N” denotes 

areas that are not ungulate winter range. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be 

consolidated with another type]

Table 10-1. North.

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

2 441 101 176 223 154 120 370

4 344 48 51 91 70 60 90

6 14 116 158 249 215 503 612

7 344 48 51 91 70 60 90

5 and 8 614 1168 427 318 258 1042 1296

10100 259 101 303 223 452 102 85

10101 0 185 765 500 299 2570 1440

10201 0 185 765 500 299 2570 1440

10301 404 325 110 34 9 206 92

10401 77 185 276 99 29 1219 164

10501 713 11 258 678 635 790 788

10600 93 103 388 289 233 48 48

10601 713 11 258 678 635 790 788

10701 1322 1199 250 145 100 1397 202

10801 404 164 56 34 9 206 92

Table 10-2. East.

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

2 313 76 176 163 159 120 370

4 189 53 51 91 70 60 86

6 4 115 158 218 215 503 609

7 29 53 51 91 70 60 86

5 and 8 773 494 429 314 258 747 913

10100 258 44 303 299 452 102 85

10101 324 5 384 331 224 862 3

10201 0 185 765 500 299 2568 1440

10301 238 408 720 85 5 926 8

10401 76 158 276 99 29 1220 164

10501 713 11 258 678 574 790 788

10600 93 103 164 289 674 48 48

10601 713 11 258 678 674 790 788

10701 404 324 110 20 9 23 93

10801 404 324 110 20 9 23 93
Appendix 10 67

Table 10-3. South, without bison.

[BMUs #14, #15, and #17]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

2 258 34 255 290 158 121 71

4 181 138 52 9 70 59 16

6 15 110 158 98 121 515 33

7 181 138 51 9 70 59 16

5 and 8 710 1164 426 69 17 1151 699

10100 258 34 255 290 158 121 71

10101 0 185 768 484 289 2568 1410

10201 0 185 768 484 289 2568 1410

10301 404 324 110 17 2 206 13

10401 77 158 276 79 20 1220 131

10501 190 616 32 58 12 219 2

10600 92 92 164 168 138 31 23

10601 712 11 257 590 570 811 730

10701 1322 1199 248 107 62 1410 76

10801 308 324 110 17 2 206 13

Table 10-4. South, with bison.

[BMU #8]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

2 924 432 709 532 611 82 226

4 182 34 25 91 70 59 86

6 329 104 568 356 316 931 1036

7 182 34 25 91 70 59 86

5 and 8 303 880 665 1310 1248 458 631

10100 924 432 709 532 611 82 226

10101 0 81 771 500 299 2568 1440

10201 0 81 771 500 299 2568 1440

10301 263 185 152 34 9 206 92

10401 654 51 1261 99 28 1286 230

10501 753 663 544 1323 1303 346 206

10600 23 8 129 2200 2116 9 22

10601 0 696 18 125 119 1048 999

10701 182 34 107 186 168 1476 250

10801 263 185 152 34 9 206 92
68 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 10-5. West, with bison.

[BMUs #10 and #11]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

Wntrr = B Wntrr = E Wntrr = N 

2 726 439 439 662 1176 884 871 116 370

4 Missing values

6 322 16 16 105 583 355 352 924 1029

7 Missing values

5 and 8 441 819 819 898 664 1311 1248 327 603

10100 23 272 272 44 287 80 234 23 6

10101 0 0 0 82 771 500 299 2568 1440

10201 0 0 0 82 771 500 299 2568 1440

10301 263 403 403 185 120 35 9 214 92

10401 654 102 102 51 1249 99 29 1286 231

10501 753 189 189 662 544 1323 1305 346 206

10600 27 96 96 70 129 2200 2144 10 26

10601 1 713 713 706 15 125 140 1029 1025

10701 4184 1358 1358 7 1070 186 138 1468 267

10801 263 403 403 185 120 35 9 214 92

Table 10-6. West, without bison. 

[BMUs #12, #13, and #18]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

2 439 75 176 163 216 116 370

4 Missing values

6 16 112 173 218 215 507 612

7 Missing values

5 and 8 819 496 426 319 258 1020 1296

10100 272 44 303 298 452 102 85

10101 0 185 765 500 299 2568 1440

10201 0 185 765 500 299 2568 1440

10301 403 210 110 35 9 214 92

10401 102 158 276 99 29 1219 164

10501 189 297 32 85 66 219 79

10600 96 82 164 289 233 31 48

10601 713 11 254 641 692 718 788

10701 1358 127 249 145 97 1388 190

10801 403 209 110 35 9 214 92
Appendix 11 69

Appendix 11. Coefficients of Productivity (coefjklmn) for the Yellowstone Grizzly 

Bear Cumulative Effects Model

[Years are distinguished by whether carrion was abundant or not (Ung = Y or N) and by whether whitebark pine seeds were abundant or not (Wbp = Y or N). 

Habitat types are also differentiated by whether they occur near or far from a forest edge (Edge = Y [near] or N [far]). “H.T. Code” refers to habitat type code. 

“Wntrr” denotes ungulate winter range, “E” denotes elk winter range, and “N” denotes areas that are not ungulate winter range. Values are missing in the table if 

corresponding habitat types were not present in a region or were so sparse as to be consolidated with another type]

Table 11-1. North.

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Edge = Y Edge = N Wbp = Y Wbp = N Wbp = Y Wbp = N

 Edge = Y Edge = N Edge = Y Edge = N

2 52 9 28 23 34 25 42 27 8 154

4 177 22 22 17 33 24 26 17 51 36

6 16 157 266 212 249 179 359 229 441 599

7 177 22 22 17 33 24 26 17 51 36

5 and 8 0 598 430 343 213 152 180 115 657 825

10100 178 9 94 75 34 25 26 17 14 18

10101 0 113 261 208 636 455 234 149 5112 1485

10201 0 113 261 208 636 455 234 149 5112 1485

10301 610 249 55 44 14 10 9 6 102 90

10401 9 7 26 21 36 26 15 10 374 77

10501 160 2 146 116 424 303 972 621 800 547

10600 133 237 415 331 504 361 723 462 51 24

10601 160 2 146 116 424 303 972 621 800 547

10701 358 275 157 125 99 71 119 76 1202 175

10801 610 249 55 44 14 10 9 6 102 90

Table 11-2. East.

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Wbp = Y Wbp = N Wbp = Y Wbp = N

 Wntrr = E Wntrr = N Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N

2 41 13 8 4 40 44 20 30 22 63 45

4 217 67 63 32 29 82 61 31 22 25 17

6 10 3 280 144 94 176 119 383 271 533 339

7 53 16 63 32 29 82 61 31 22 25 17

5 and 8 1526 469 313 162 403 114 189 567 401 452 3121

10100 336 103 55 28 200 78 304 32 23 33 20

10101 120 37 2 1 55 150 120 762 539 4 3

10201 0 0 120 62 180 273 148 3542 2506 1822 1367

10301 16 5 25 13 83 16 1 74 52 0 1

10401 41 13 51 26 42 59 15 1207 1103 222 125

10501 184 36 3 2 75 753 680 1024 725 1122 774

10600 351 177 69 36 274 752 418 54 38 83 57

10601 184 36 3 2 75 753 680 1024 725 1122 774

10701 421 129 284 146 47 7 5 16 11 73 40

10801 421 129 284 146 47 7 5 16 11 73 40
70 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 11-3. South, without bison. 

[BMUs #14, #15, and #17]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Edge = Y Edge = N Wbp = Y Wbp = N Wbp = Y Wbp = N

 Edge = Y Edge = N Edge = Y Edge = N

2 192 126 11 106 80 74 40 24 38 22

4 122 80 63 25 19 3 50 14 23 6

6 3 2 67 118 90 105 51 458 726 47

7 122 80 63 25 19 3 50 14 23 6

5 and 8 550 362 1099 363 275 70 14 514 815 495

10100 192 126 11 106 80 74 40 24 38 22

10101 0 0 32 245 186 350 177 3401 5398 2964

10201 0 0 32 245 186 350 177 3401 5398 2964

10301 601 395 196 32 25 11 3 140 222 14

10401 29 19 19 97 73 30 7 543 861 93

10501 346 228 418 12 9 22 6 51 81 1

10600 87 57 62 103 78 99 133 8 13 10

10601 106 70 1 57 43 395 94 508 806 726

10701 1143 752 537 175 133 72 59 683 1082 58

10801 601 395 196 32 25 11 3 140 222 14

Table 11-4. South, with bison.

[BMU #8]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Ung = Y Ung = N Edge = Y Edge = N Wbp = Y Wbp = N Wbp = Y Wbp = N

 Edge = Y Edge = N Edge = Y Edge = N

2 687 452 145 294 223 136 156 16 25 65

4 123 81 16 12 9 30 50 14 23 38

6 61 41 64 426 323 378 133 828 1314 553

7 123 81 16 12 9 30 50 14 23 38

5 and 8 235 154 831 565 429 1321 1073 205 324 874

10100 687 452 145 294 223 136 156 16 25 65

10101 0 0 14 247 187 362 183 3401 5398 1123

10201 0 0 14 247 187 362 183 3401 5398 1123

10301 391 228 112 45 34 22 10 140 222 104

10401 245 162 6 441 335 37 10 572 908 110

10501 1370 902 458 199 151 491 700 80 127 338

10600 22 14 6 81 62 1305 2038 3 4 5

10601 0 0 88 4 3 84 20 656 1041 388

10701 157 103 15 752 570 126 159 714 1133 170

10801 391 228 112 45 34 22 10 140 222 104
Appendix 11 7

1

Table 11-5. West, with bison.[BMUs #10 and #11]H.T. Spring Estrus Early hyperphagia Late hyperphagiaCode Ung = Y Ung = N Edge = Edge = Wbp = Y Wbp = N Wbp = Y Wbp = N

Wntrr = B Wntrr = E Wntrr = N Edge = Edge = Y N Edge = Edge = Edge = Edge = Edge = Edge = Edge = Edge = 

Edge = Edge = Edge = Edge = Edge = Edge = Y N Y N Y N Y N Y N

Y N Y N Y N

2 222 99 39 17 40 18 80 63 236 120 357 162 383 247 24 15 87 474 Missing values6 698 311 10 5 10 5 126 74 962 488 296 134 958 427 817 509 1544 8417 Missing values5 and 8 3316 1478 1779 793 1837 819 2164 1241 1248 634 3773 1705 3408 3212 525 327 1415 77010100 19 8 64 29 66 30 14 8 144 73 39 18 78 24 2 1 2 110101 0 0 0 0 0 0 22 13 166 85 125 57 10 5 5966 3714 380 20710201 0 0 0 0 0 0 22 13 166 85 125 57 10 5 5966 3714 380 20710301 1302 580 576 257 595 265 227 117 98 50 80 36 29 9 90 56 107 5810401 353 157 16 7 16 7 6 7 339 172 69 31 10 3 724 451 174 9510501 726 324 53 23 54 24 217 100 125 64 1087 492 932 642 416 259 280 15210600 107 48 110 49 113 51 106 63 114 58 2395 1083 4743 1312 4 2 0 010601 0 0 99 44 103 46 132 76 3 1 37 17 58 24 1677 1044 1296 70510701 224 100 477 212 492 205 3 3 1145 581 175 79 234 87 2038 1269 317 17210801 1302 580 576 257 595 265 227 117 98 50 80 36 29 9 90 56 107 58
72 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 11-6. West, without bison. [BMUs #12, #13, and #18] H.T. Spring Estrus Early hyperphagia Late hyperphagia Code Ung = Y Ung = N Edge = Y Edge = N Wbp = Y Wbp = N Wbp = Y Wbp = N Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N2 40 18 9 7 35 18 66 30 95 61 24 15 87 474 Missing values6 10 5 135 79 285 145 182 82 584 260 449 279 919 5007 Missing values5 and 8 1837 819 1195 686 801 407 919 415 704 663 1639 1021 3044 165710100 66 30 14 8 152 77 145 66 151 47 7 4 29 1610101 0 0 50 29 165 84 125 57 10 5 5966 3714 380 20710201 0 0 50 29 165 84 125 57 10 5 5966 3714 380 20710301 595 265 50 132 89 45 80 36 29 9 90 56 107 5810401 16 7 19 22 75 38 69 31 10 3 687 428 124 6810501 54 24 19 45 7 4 70 31 48 33 263 164 108 5810600 113 51 97 74 144 73 314 142 515 142 13 8 0 010601 103 46 123 1 44 23 189 85 289 119 1171 729 996 54210701 492 205 2 49 266 135 137 62 165 61 1928 1200 225 12310801 595 265 50 132 89 45 80 36 29 9 90 56 107 58 
Appendix 12 73

Appendix 12. Coefficients of Productivity (coefjklmn) for the Yellowstone Grizzly 

Bear Cumulative Effects Model, Averaged Over Year Types Within Seasons

[“H.T. Code” refers to habitat type code. “Wntrr” denotes ungulate winter range, “B” denotes bison winter range, “E” denotes elk winter range, and “N” denotes 

areas that are not ungulate winter range. Values are missing in the table if corresponding habitat types were not present in a region or were so sparse as to be 

consolidated with another type]

Table 12-1. North.

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Edge = Y Edge = N Edge = Y Edge = N

2 31 28 23 38 26 81

4 99 22 17 30 20 43

6 87 266 212 304 204 520

7 99 22 17 30 20 43

5 and 8 299 430 343 197 134 741

10100 93 94 75 30 21 16

10101 56 261 208 435 302 3298

10201 56 261 208 435 302 3298

10301 429 55 44 12 8 96

10401 8 26 21 25 18 225

10501 81 146 116 698 462 674

10600 185 415 331 614 412 37

10601 81 146 116 698 462 674

10701 316 157 125 109 74 688

10801 429 55 44 12 8 96

Table 12-2. East.

H.T. Spring Estrus Early hyperphagia Late hyperphagia

Code Wntrr = E Wntrr = N Edge = Y Edge = N

 Edge = Y Edge = N Edge = Y Edge = N 

2 25 23 11 8 40 32 47 33

4 140 125 65 50 29 72 28 20

6 145 77 141 74 94 147 458 305

7 58 43 40 24 29 72 28 20

5 and 8 920 844 391 315 403 151 2547 1761

10100 196 182 79 66 200 191 33 21

10101 61 60 19 19 55 135 383 271

10201 60 31 60 31 180 211 2682 1936

10301 20 14 15 9 83 8 37 27

10401 46 34 32 19 42 37 714 614

10501 94 93 20 19 75 717 1073 749

10600 210 193 123 106 274 585 68 48

10601 94 93 20 19 75 717 1073 749

10701 352 284 207 138 47 6 44 26

10801 352 284 207 138 47 6 44 26
74 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat 

Table 12-3. South, without bison.

[BMUs #14, #15, and #17]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N

2 101 69 106 80 57 23 30

4 93 72 25 19 27 10 14

6 35 34 118 90 78 252 387

7 93 72 25 19 27 10 14

5 and 8 824 730 363 275 42 505 655

10100 101 69 106 80 57 23 30

10101 16 16 245 186 264 3183 4181

10201 16 16 245 186 264 3183 4181

10301 399 296 32 25 7 77 118

10401 24 19 97 73 18 318 477

10501 382 323 12 9 14 26 41

10600 74 59 103 78 116 9 12

10601 54 35 57 43 244 617 766

10701 840 644 175 133 66 370 570

10801 399 296 32 25 7 77 118

Table 12-4. South, with bison.

[BMU #8]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N

2 416 298 294 223 146 41 45

4 69 48 12 9 40 26 30

6 63 52 426 323 255 690 934

7 69 48 12 9 40 26 30

5 and 8 533 493 565 429 1197 539 599

10100 416 298 294 223 146 41 45

10101 7 7 247 187 273 2262 3261

10201 7 7 247 187 273 2262 3261

10301 251 170 45 34 16 122 163

10401 126 84 441 335 24 341 509

10501 914 680 199 151 595 209 233

10600 14 10 81 62 1672 4 4

10601 44 44 4 3 52 522 715

10701 86 59 752 570 143 442 651

10801 251 170 45 34 16 122 163
Appendix 12 7

5

Table 12-5. West, with bison.[BMUs #10 and #11]H.T. Spring Estrus Early hyperphagia Late hyperphagia

Code Wntrr = B Wntrr = E Wntrr = N Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N

Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N

2 151 81 60 40 60 40 236 120 370 204 55 314 Missing values6 412 193 68 39 68 39 962 488 627 280 1180 6757 Missing values5 and 8 2740 1360 1971 1017 2000 1030 1248 634 3590 2458 970 54910100 16 8 39 18 40 19 144 73 59 21 2 110101 11 6 11 6 11 6 166 85 68 31 3173 196010201 11 6 11 6 11 6 166 85 68 31 3173 196010301 764 349 402 187 411 191 98 50 54 23 98 5710401 180 82 11 7 11 7 339 172 39 17 449 27310501 471 212 135 62 136 62 125 64 1010 567 348 20610600 107 56 108 56 110 57 114 58 3569 1197 2 110601 66 38 116 60 117 61 3 1 48 20 1487 87510701 113 51 240 108 248 104 1145 581 204 83 1178 72110801 764 349 402 187 411 191 98 50 54 23 98 57
76 Coefficients of Productivity for Yellowstone’s Grizzly Bear Habitat

Table 12-6. West, without bison.

[BMUs #12, #13, and #18]

H.T. Code Spring Estrus Early hyperphagia Late hyperphagia

 Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N Edge = Y Edge = N

2 25 13 35 18 80 46 55 31

4 Missing values

6 73 42 285 145 383 171 684 390

7 Missing values

5 and 8 1516 752 801 407 811 539 2341 1339

10100 40 19 152 77 148 56 18 10

10101 25 14 165 84 68 31 3173 1960

10201 25 14 165 84 68 31 3173 1960

10301 323 199 89 45 54 23 98 57

10401 18 14 75 38 39 17 405 248

10501 37 34 7 4 59 32 185 111

10600 105 62 144 73 414 142 6 4

10601 113 23 44 23 239 102 1083 635

10701 247 127 266 135 151 61 1077 661

10801 323 199 89 45 54 23 98 57

 

Published in the Central Region, Lafayette, Louisiana.

USGS Publishing Staff: Charron, T., Davis, R., Farris, G., Lauritzen, S., 

Vairin, B.

Johnson Controls, Inc. Staff: Trahan, N., Wiggins, L.