Prepared in cooperation with the Bureau of Land Management, 

Nevada Department of Wildlife, and U.S. Fish and Wildlife Service

A Hierarchical Integrated Population Model for 

Greater Sage-Grouse (Centrocercus urophasianus) in the 

Bi-State Distinct Population Segment, California and Nevada

U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2014-1165
Cover: Photograph of two male greater sage-grouse performing a courtship display on a lek in Nevada.

Photograph courtesy of Tatiana Gettleman.
A Hierarchical Integrated Population Model for Greater 

Sage-Grouse (Centrocercus urophasianus) in the Bi-State 

Distinct Population Segment, California and Nevada

By Peter S. Coates, Brian J. Halstead, Erik J. Blomberg, Brianne Brussee, Kristy B. Howe, Lief Wiechman, 

Joel Tebbenkamp, Kerry P. Reese, Scott C. Gardner, and Michael L. Casazza

Prepared in cooperation with the Bureau of Land Management, Nevada Department of Wildlife, and 

U.S. Fish and Wildlife Service

Open-File Report 2014–1165 

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2014

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Coates, P.S., Halstead, B.J., Blomberg, E J., Brussee, B., Howe, K.B., Wiechman, L., Tebbenkamp, J., Reese, K.P.,

Gardner, S.C., and Casazza, M.L., 2014, A hierarchical integrated population model for greater sage-grouse

(Centrocercus urophasianus) in the Bi-State Distinct Population Segment, California and Nevada: U.S. Geological 

Survey Open-File Report 2014-1165, 34 p., http://dx.doi.org/10.3133/ofr20141165..

ISSN 3221-1258 (online)

Any use of trade, product, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government. 

Although this report is in the public domain, permission must be secured from the individual 

copyright owners to reproduce any copyrighted material contained within this report.
iii

Contents

Background ................................................................................................................................................................... 1

Study Objective ............................................................................................................................................................. 2

Study Area..................................................................................................................................................................... 2

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

Lek Surveys ............................................................................................................................................................... 4

Sage-Grouse Telemetry Monitoring ........................................................................................................................... 4

Data Compilation ....................................................................................................................................................... 5

Integrated Population Model ...................................................................................................................................... 6

Lek Count Model .................................................................................................................................................... 7

Yearling and Adult Survival Model.......................................................................................................................... 8

Fecundity Model..................................................................................................................................................... 9

Joint Likelihood......................................................................................................................................................12

Results and Interpretation.............................................................................................................................................14

Pine Nut Subpopulation ............................................................................................................................................14

Desert Creek Subpopulation.....................................................................................................................................14

Fales Subpopulation .................................................................................................................................................14

Bodie Hills Subpopulation .........................................................................................................................................15

Parker Meadows Subpopulation ...............................................................................................................................15

Long Valley Subpopulation .......................................................................................................................................15

Bi-State DPS Summary and Synthesis .....................................................................................................................19

Acknowledgments ........................................................................................................................................................25

References Cited..........................................................................................................................................................25

Appendix A. Summary of Derived Posterior Distributions for Greater Sage-Grouse (Centrocercus urophasianus) 

Population Vital Rates by Subpopulation within the Bi-State Distinct Population Segment Study Area, 2003–12........27

Appendix B. Summary of Derived Posterior Distributions for Greater Sage-Grouse (Centrocercus 

urophasianus)Population Vital Rates by Year, 2003–12...............................................................................................30

Figures

Figure 1. Schematic map showing location of the greater sage-grouse (Centrocercus urophasianus) 

Bi-State Distinct Population Segment (DPS) study area, California and Nevada .......................................................... 3

Figure 2. Diagram showing demographic components of the integrated population model for greater 

sage-grouse in the Bi-State Distinct Population Segment study area, California and Nevada ...................................... 6

Figure 3. Diagram showing integrated population model [modified from Kéry and Shaub (2012)] for greater

sage-grouse in the Bi-State Distinct Population Segment study area, California and Nevada .................................... 13

Figure 4. Graphs showing estimated number of male sage-grouse per lek (solid line) and lek observations 

(dashed line), Bi-State Distinct Population Segment study area, California and Nevada, 2003–12............................. 16

Figure 5. Graphs showing annual lek attendance counts (solid line) and estimates (dashed line) across all 

Bi-State Distinct Population Segment study area sites, California and Nevada, 2003–12........................................... 17

Figure 6. Graphs showing population growth rate (λ) for each monitored site (A–F), Distinct Population 

Segment study area, California and Nevada, 2003–12 ............................................................................................... 18

Figure 7. Graph showing annual population growth rate (λ) across all Bi-State Distinct Population 

Segment study area sites, California and Nevada, 2003–12 ....................................................................................... 20
iv

Figure 8. Graphs showing ln(odds ratio) of population increase to decrease for each monitored site (A–F),

Bi-State Distinct Population Segment study area, California and Nevada, 2003–12 ................................................... 21

Figure 9. Graph showing ln(odds ratio) of increase to decrease across all Bi-State Distinct Population Segment 

study area subpopulations, California and Nevada, 2003–12...................................................................................... 22

Tables

Table 1. Summary of lek survey data averaged across years for greater sage-grouse (Centrocercus urophasianus) 

in the Bi-State Distinct Population Segment study area, California and Nevada, 2003–12 ........................................... 7

Table 2. Summary of posterior distributions of derived population vital rate parameters for greater sage-grouse 

(Centrocercus urophasianus) in the Bi-State Distinct Population Segment study area, California and Nevada, 

2003–12...................................................................................................................................................................... 23

Conversion Factors and Datum

Conversion Factors

SI to Inch/Pound

Multiply By To obtain

Length

meter (m) 3.281 foot (ft) 

Area

square kilometer (km2) 247.1 acre

square kilometer (km2) 0.3861 square mile (mi2)

Datum

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

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

Acronyms and Abbreviations

CDFW California Department of Fish and Wildlife

CI confidence interval 

CRI credible interval

DPS Distinct Population Segment

GPS Global Positioning System 

IPM integrated population modeling

PMU population management unit 

PTT Platform Transmitter Terminal

NDOW Nevada Department of Wildlife

USGS U.S. Geological Survey 

VHF Very High Frequency
1

A Hierarchical Integrated Population Model for Greater 

Sage-Grouse (Centrocercus urophasianus) in the Bi-State 

Distinct Population Segment, California and Nevada

By Peter S. Coates1, Brian J. Halstead1, Erik J. Blomberg2, Brianne Brussee1, Kristy B. Howe1, Lief Wiechman3, 

Joel Tebbenkamp4, Kerry P. Reese4, and Michael L. Casazza1 

Background

Greater sage-grouse (Centrocercus urophasianus, hereafter referred to as “sage-grouse”) are 

endemic to sagebrush (Artemisia spp.) ecosystems throughout Western North America. Populations of 

sage-grouse have declined in distribution and abundance across the range of the species (Schroeder and 

others, 2004; Knick and Connelly, 2011), largely as a result of human disruption of sagebrush 

communities (Knick and Connelly, 2011). The Bi-State Distinct Population Segment (DPS) represents 

sage-grouse populations that are geographically isolated and genetically distinct (Benedict and others, 

2003; Oyler-McCance and others, 2005) and that are present at the extreme southwestern distribution of 

the sage-grouse range (Schroeder and others, 2004), straddling the border of California and Nevada. 

Subpopulations of sage-grouse in the DPS may be at increased risk of extirpation because of a 

substantial loss of sagebrush habitat and lack of connectivity (Oyler-McCance and others, 2005). 

Sage-grouse in the Bi-State DPS represent small, localized breeding populations distributed across 

18,325 km2

. 

The U.S. Fish and Wildlife Service currently (2014) is evaluating the Bi-State DPS as threatened 

or endangered under the Endangered Species Act of 1973, independent of other sage-grouse 

populations. This DPS was designated as a higher priority for listing than sage-grouse in other parts of 

the species’ range (U.S. Department of the Interior, 2010). Range-wide population analyses for sagegrouse have included portions of the Bi-State DPS (Sage and Columbian Sharp-tailed Grouse Technical 

Committee 2008; Garton and others, 2011). Although these analyses are informative, the underlying 

data only represent a portion of the DPS and are comprised of lek count observations only. A thorough 

examination of population dynamics and persistence that includes multiple subpopulations and 

represents the majority of the DPS is largely lacking. Furthermore, fundamental information on 

population growth rate (i.e., finite rate of change, λ) and specific demographic parameters that explain 

sources of variation in λ within different subpopulations would be valuable for making conservation and 

management decisions for this DPS.

1

U.S. Geological Survey, Western Ecological Research Center, 800 Business Park Drive, Suite D, Dixon, California 95620. 2

Department of Wildlife, Fisheries, and Conservation Biology, University of Maine. 3

U.S. Fish & Wildlife Service, Mountain-Prairie Region. 4

Department of Fish and Wildlife Sciences, University of Idaho.
2

During 2003–12, agencies and universities collaborated to conduct extensive monitoring of sagegrouse populations within the Bi-State DPS. Data regarding lek attendance, movement, and survival of 

sage-grouse across multiple life stages were documented. Specifically, sage-grouse from nearly all 

subpopulations were marked and tracked across multiple seasons using radio-telemetry techniques. A 

hierarchical integrated population modeling (IPM) approach was used to derive demographic 

parameters for the Bi-State DPS using the large amount of data collected over a 10-year period. This 

modeling approach allows integration of multiple data sources to inform population growth rates and 

population vital rates for the Bi-State DPS overall, as well as for individual subpopulations. These 

models are more informative than other models because they integrate inputs of demographic data (for 

example, survival and fecundity rates) and survey data (for example, lek observations). The findings 

here will help characterize population growth rates within the Bi-State DPS. 

Study Objective

This report describes the IPM, which is the first step of a multi-step population analysis. The

overall study objective was to develop a stage-based, stochastic population model that included age 

structure for the Bi-State DPS. A major component of this objective was to compile and quantify 

multiple sources of survey and demographic data collected over a 10-year period. Recent developments 

in Bayesian statistical analysis provide the most useful framework to integrate multiple data sources and 

refine parameter estimation (Kéry and Shaub, 2012). Therefore, we integrated our data into a Bayesian 

modeling framework with the purpose of deriving numerous population parameters to better understand 

population dynamics in the Bi-State DPS. In the first step of the analysis, we derived these parameters 

specifically to: (1) estimate population growth rates (λ) for the Bi-State; (2) estimate population vital 

rates for each life history stage; (3) identify differences in rates between age classes; (4) identify

differences in rates between subpopulations; and (5) identify temporal patterns in population vital rates 

and λ. A second step of this analysis will be carried out to estimate the relative importance of specific 

vital rates (for example, adult survival, nest success, chick survival) to sage-grouse persistence using 

sensitivity, elasticity, and retrospective correlation analyses. In a final step, environmental covariates 

will be fit to the estimated rates. This report provides methods and results for the first step of the 

analysis only. The report findings will be useful as decision support for conservation and management 

of the Bi-State DPS, as well as for specific subpopulations. 

Study Area

The study area encompasses 18,325 km2 of land in Mono, Alpine, and Inyo Counties, California, 

and Carson City, Douglas, Esmeralda, Lyon, and Mineral Counties, Nevada. The Bi-State DPS 

consisted of six PMUs—Pine Nut Mountains, Desert Creek-Fales, Mount Grant, Bodie Hills, South 

Mono, and White Mountains. The PMU boundaries were delineated by state wildlife management 

agencies using land-tenure and ecologically-based rationale. For this study, we monitored sage-grouse 

within 6 subpopulations (Pine Nut, Desert Creek, Fales, Bodie Hills, Parker Meadows, and Long 

Valley) across 4 of those PMUs (fig. 1). No subpopulations were monitored within the Mount Grant and 

White Mountain PMU. Based on existing knowledge of sage-grouse movement within the Bi-State 

DPS, we assumed that movement between these subpopulations was negligible or nonexistent. The 

number of subpopulations and their spatial distribution provided a reliable representation of 
3

demography for the Bi-State DPS. Elevation ranged from 1,386 to 4,344 m. Wyoming big sagebrush 

(Artemisia tridentata ssp. wyomingensis) and black sagebrush (Artemisia nova) dominated landscapes at 

low elevations below about 2,100 m, whereas mountain big sagebrush (Artemisia tridentata ssp. 

vaseyana) and low sagebrush (Artemisia arbuscula) dominated high elevations. Other common shrubs 

in sagebrush communities included rabbitbrush (Chrysothamnus spp.), Mormon tea (Ephedra viridis),

snowberry (Symphoricarpos spp.), western serviceberry (Amelanchier alnifolia), and antelope 

bitterbrush (Purshia tridentata). Although sagebrush communities within the Bi-State DPS were typical 

of those present elsewhere in the Great Basin, this region had relatively greater amounts of singleleaf 

pinyon (Pinus monophylla; hereafter referred to as “pinyon”) and Utah juniper (Juniperus osteosperma; 

hereafter referred to as “juniper”). Jeffery pine (Pinus jeffreyi) and other conifer species were present at 

some sites, but were less abundant than pinyon and juniper. Common grasses included needle and 

thread (Hesperostipa comata), Indian ricegrass (Achnatherum hymenoides), and bottlebrush squirreltail 

(Elymus elymoidess); and common forbs included phlox (Phlox spp.), lupine (Lupinus spp.), buckwheat 

(Eriogonum spp.), mule-ears (Wyethia spp.), and hawksbeard (Crepis spp.). 

Figure 1. Schematic map showing location of the greater sage-grouse (Centrocercus urophasianus) Bi-State 

Distinct Population Segment (DPS) study area, California and Nevada. Data from six distinct subpopulations were 

used to develop integrated population models for the Bi-State DPS. Subpopulations were labeled as PN, Pine Nut; 

DC, Desert Creek; FS, Fales; BH, Bodie Hills; PM, Parker Meadows; and LV, Long Valley. Dark lines in larger, 

more detailed schematic map represent boundaries of Population Management Units.
4

Methods

Lek Surveys

Lek survey protocol generally followed published methodologies (Connelly and others, 2003) 

and were performed collaboratively by a team of interagency personnel from CDFW, NDOW, Bureau 

of Land Management, U.S. Forest Service, University of Nevada Reno, University of Idaho, Los 

Angeles Department of Water and Power, and the USGS. The Bi-State DPS surveys employ a 

“saturation count” method for deriving the maximum count for a single day. Saturation counts required 

that all known active leks be counted simultaneously by experienced observers. Male sage-grouse were

counted at each lek at least three times in the spring (March–May) to estimate maximum count. The 

three counts were typically spaced equally in time and overlapped with peak lek attendance by males. 

Lek counts were conducted between 30 minutes before sunrise and 90 minutes after sunrise. Binoculars, 

a spotting scope, or both were used to count sage-grouse from a suitable viewing location that afforded a 

view of the entire lek. A total of three counts per survey were conducted at 10-minute intervals, and the 

highest count was selected for each survey. The lek count for the peak lek attendance day was obtained 

for each season.

Sage-Grouse Telemetry Monitoring

Over the 10-year period, field technicians conducted intensive on-the-ground monitoring of 

sage-grouse movement, survivorship, and reproduction following release of radio-marked birds. Field 

data-collection protocols were consistent across the 10-year period. In some situations of differing datacollection procedures, we employed statistical techniques that provided adjustment to the derived 

demographic parameter estimation (e.g., adjustment for unequal periods to estimate chick survival; see 

Chick Survival section). 

Sage-grouse were captured in close proximity to leks in the spring (March–April) and at various 

concentration areas in the autumn (October–December) during 2002–12 using spotlighting techniques at 

night (Giesen and others, 1982; Wakkinen and others, 1992). Sage-grouse captured in 2002 were 

marked for monitoring in 2003 and subsequent years. Captured sage-grouse were outfitted with 

necklace-style VHF radio-transmitters (Kolada and others, 2009). During 2012, a subsample of sagegrouse were outfitted with Global Positioning Systems (GPS), Platform Transmitter Terminals (PTTs;

North Star Science and Technology, LLC, King George, Virginia), and VHF transmitters (combined 

weight was <3 percent of body mass). The purpose of the GPS transmitter was to collect locations 

remotely and to transmit (using PTT) to a central database by satellites. The VHF-marked sage-grouse 

were relocated using hand-held radio receivers and antennae at least twice per week during spring and 

summer, and at least once per month during winter. Each grouse was circled at a radius of 30–50 m 

using the loudest signal method to help minimize location error. We approximated the distance and 

recorded the azimuth from the observer’s location (recorded using GPS) to estimate the location 

coordinates (Universal Transverse Mercator) of the grouse. 
5

Radio-marked sage-grouse were divided into two age categories for monitoring: (1) sage-grouse 

that entered their first breeding year but were less than 2 years old were classified as yearlings; and (2) 

sage-grouse that entered their second breeding year were classified as adults. Deaths within both age 

categories were documented. Transmitters were equipped with mortality signals and immediately 

retrieved following sage-grouse fatality. Date of fatality was recorded and corresponded to band 

identifications. Aerial telemetry was conducted periodically, especially during times when sage-grouse 

were thought to be missing. Ground locations generally were determined following flights. Data 

recorded in the field consisted of date of transmitter placement, last date observed alive, date of 

observed fatality, and date censored from analysis. 

Female sage-grouse were located every 3 days during the nesting season (March–June) to 

estimate the nest initiation date. When a nest was located, subsequent nest checks were conducted every 

2–3 days until nest fate was determined. Nest fate was categorized as either successful (≥1 egg hatched) 

or unsuccessful (depredated or abandoned). Data recorded in the field consisted of: (1) date each nest 

was found; (2) date each nest was last checked alive; (3) date of nest fate determined; and (4) fate of 

each nest. Clutch sizes were measured opportunistically throughout the incubation period (for example, 

during incidental flushing or incubation recesses). Clutch sizes also were measured following hatch or 

depredation by counting egg shells, egg shell membranes, or both. Field technicians noted unreliable 

clutch size counts and such counts were omitted from analyses. Eggs that failed to hatch and exceeded 

30 days of incubation were inspected for fertility and recorded. 

Following hatch of nests, broods were monitored intensively. Initial brood sizes were estimated 

by counting hatched egg shells. Brood-rearing sage-grouse were relocated every 2–3 days with periodic 

checks of chicks. A final brood count was conducted after a fixed period of time, which differed across 

years (2003–05, 50 days; 2007–09, 35 days; 2010–11, 28 days; 2012, 50 days). During final brood 

counts, female sage-grouse were flushed and intensive searches were conducted to count chicks. If no 

chicks were detected, a second brood check was conducted within 48 hours to confirm brood failure.

Data Compilation

We obtained and compiled all lek data from databases and data forms that were known to us. We 

assured that protocols for counting males at lek sites were similar across all years of study and 

subpopulations. Leks with a recorded integer value of zero or greater for male attendance were included 

in the analysis. Leks with a blank value were not included (i.e., not surveyed, hence attendance was 

unknown). Survey data were derived from >1,500 independent lek survey observations. From these 

observations, we derived a total of 429 lek counts that reflected annual maximum male attendance for

each lek. We then averaged the maximum lek counts across the subpopulation by year and used these 

values as data inputs to state-space models. The purpose of averaging was because most subpopulations 

consisted of more than one lek and we sought to prevent biased low estimates for years of missing data 

for any given lek. 

A total of 358 sage-grouse were marked with VHF transmitters during this 10-year period. 

Protocols used in monitoring individually marked sage-grouse were similar across all years. We 

determined a set of decision rules that excluded data from the analysis during a quality assessment 

process. Because we conducted a female-based demographic analysis, we first excluded marked male 

sage-grouse from the data set, as well as female sage-grouse that were not relocated following marking. 

We then excluded data under specific criteria, which were: (1) relocation dates that were needed to 

derive demographic parameters were missing; (2) information regarding the status of nest, brood, or 

sage-grouse were not recorded (e.g., sage-grouse fatality or alive); 3) unique identification of sagegrouse could not be determined; and (4) study site of sage-grouse could not be determined. Following 
6

this quality control and assessment, we determined that telemetry and survey data were of adequate 

quality to conduct a female- and stage-based population modeling analysis over a 10-year period (2003–

2012). The sizes of specific sample sets used to derive parameters for population vital rates are reported 

in the description of each analysis below.

Integrated Population Model

The framework for the IPM followed published procedures that were described in Kéry and 

Shaub (2012). The modeling procedures were modified to include comprehensive datasets of life history 

stages and age classification of sage-grouse populations, as shown in figure 2. Specifically, we modeled 

male breeding population size (N) as a result of observed male lek counts, as well as annual survival (S) 

and fecundity (F) of adult and yearling female sage-grouse. Submodels of population vital rates also 

consisted of stochastic processes, where posterior distributions of population vital rate parameters were 

derived. From the derived N we calculated the finite rate of population change (λ; Caswell, 2001; 

Gotelli and Ellison, 2004), which took the form: 

λij = Nij+1

Nij

(1)

where i represents site, j represents year, and j+1 represents a subsequent year. The instantaneous per 

capita rate of change (r) then was calculated by natural log (ln) transformation (Gotelli and Ellison, 

2006), and is expressed as: 

rij = ln Nij+1

Nij

(2)

The purpose of calculating r was to appropriately average change in populations across years and sites

to make inferences at broader temporal and spatial scales. We performed back calculation to express 

rate of change as λ at broader scales. 

Figure 2. Diagram showing demographic components of the integrated population model for greater sage-grouse 

in the Bi-State Distinct Population Segment study area, California and Nevada. F, fecundity estimate; S, survival 

estimate.
7

Lek Count Model

For each year, the number of leks, maximum number of males per lek, number of active leks, 

and percentage of active leks were compiled by subpopulation combination (table 1). Averaged 

maximum counts were compiled per year for each subpopulation and entered into a state-space model

(Kéry and Shaub, 2012), which is a hierarchical model that decomposed the observed time series of lek 

counts into process variation and observation error. This model is appropriate for Markovian processes 

of time-series data where observations are imperfect. Observations (yobs) were linked with breeding 

male population size N at site i and year j using the equation: 

yobs, ij = Nij + εij (3)

εij ~Normal(0, σy

2)

where ε represents the magnitude of a normally distributed error with mean zero and variance σy

2. We 

assumed that the probability of over counting males was similar to the probability of undercounting 

males and independent of the number of observed males. For sage-grouse counts, this normal 

distribution most appropriately represents error in observations because sage-grouse can be 

undercounted and over counted during observations. Undercounting can take place when grouse are 

difficult to observe and over counting is possible when grouse move around during the counting 

process. Initial breeding population size for each site was drawn from a discrete uniform(0, 1,000) 

distribution. Average number of males per lek at each site was used as a count index for the state-space 

model. 

Table 1. Summary of lek survey data averaged across years for greater sage-grouse (Centrocercus urophasianus) 

in the Bi-State Distinct Population Segment study area, California and Nevada, 2003–12.

[Number pairs in parentheses are lower and upper limits of 95-percent confidence interval] 

Subpopulation

Average number

of leks

Average number of 

males per lek

Average number

of active leks

Percentage of

active leks

Pine Nut 2.9 (1.3, 4.5) 12.0 (8.0, 15.9) 2.2 (1.1, 3.3) 88.1 (71.8, 104.3)

Desert Creek 6.2 (4.8, 7.6) 18.0 (13.7, 22.3) 5.1 (4.0, 6.2) 85.1 (74.4, 95.8)

Fales 3.5 (2.9, 4.1) 9.2 (7.7, 10.7) 2.5 (2.1, 2.9) 74.3 (62.1, 86.5)

Bodie Hills 11.2 (10.4, 12.0) 21.2 (15.4, 27.0) 9.1 (8.3, 9.9) 81.7 (74.8, 88.7)

Parker Meadows 3.0 (3.0, 3.0) 4.7 (2.9, 6.4) 1.6 (1.3, 1.9) 53.3 (42.6, 64.0)

Long Valley 8.8 (8.0, 9.6) 35.6 (30.4, 40.7) 7.3 (6.6, 8) 83.3 (77.4, 89.3)
8

Yearling and Adult Survival Model

Using telemetry data, we located individual monitored sage-grouse (n=248) and modeled 

survival as a continuous process observed at discrete monthly intervals. Encounter histories for survival 

of yearlings and adults were developed for each sage-grouse. Thus, each month individual sage-grouse 

were scored as alive or dead. We right censored individuals from the data, meaning we did not always 

observe the date of death and only had knowledge that individuals survived beyond a certain point. We 

considered censoring to be a random process, in that sage-grouse were censored under multiple 

circumstances, including: (1) the study period ended before death was determined; (2) the transmitter 

failed; or (3) sage-grouse was lost to follow-up monitoring. Thus, all individuals either died or were 

eventually right censored. We also allowed for graduation of yearling sage-grouse to adults within 

years. Inference was based on a constant hazards model, meaning the probability of mortality did not 

change across months. The unit hazard (UH) was modeled where each encounter interval represented a 

Bernoulli process per month. Modeling procedures for survival followed those described in Halstead 

and others (2013). The model was expressed as: 

UHhkij = exp (αi + β ∗ xhik + γj) (4)

αi~ Normal(θ, σα

2)

γj~ Normal�0, σγ

2�

where UH was a function of random effect for site αj, a random effect for year γi, both of which were 

assumed to arise from Normal distributions with mean θ and zero, respectively, and variances σα

2 and 

σγ

2, respectively, and expected change in the ln(hazard ratio) of magnitude β, where the indicator of age 

was equal to one for adults. The hazard ratio represented the ratio of hazard rates (in this case, monthly 

risk of morality) between the two age classes. Subscripts h, k, i, and j reference grouse, month, site, and 

year. Following the modeling process, we derived the annual survival parameter (San) as:

San,ij = e−CHij

CHij = ∑ UHki

T=12

j=1 (5)

where CH represented the cumulative hazard (T=12 months represented annual survival). We also 

attempted to fit a first-order autoregressive hazard model; adding this complexity caused very slow 

mixing with no convergence to a stationary distribution. 
9

Fecundity Model

Methods of collecting reproductive data across all sites and years were relatively consistent. 

Fecundity was decomposed into several submodels—specifically, nest propensity (np), nest survival 

(ns), clutch size (c), egg hatchability (h), chick survival (cs), juvenile survival (js). To derive fecundity 

parameters, a female-based, age classified population projection model was used. The life history stage 

parameters were estimated for (1) first nests, and (2) second nests. No third nest attempts were recorded. 

Thus, the equation for fecundity (F) took the form: 

Fija = �np1a × c1ija × ns1ija × ha × csija × jsa� +

�(1 − ns1ija) × np2ija × c2ija × ns2ija × ha × csija × jsa� (6) 

where F was estimated for each site i, year j, and age class a combination. F was divided by 2 because 

this model is female-based and an even sex ratio as reported in Atamian and Sedinger (2010) was 

assumed. We derived posterior distributions of parameters for each of the components of F using 

separate models.

We accounted for the hierarchical structure of the data (spatial and temporal) by fitting random 

intercept effect structures for site and year (Zuur and others, 2009). We also incorporated female age as 

a fixed effect. These effects were fit as additive and nested structures (i.e., random site was nested 

within year; Zuur and others, 2009). Final λ values were similar under both scenarios. However, the 

derived demographic parameters (i.e., S and F as a function of np, c, and ns) often differed for 

individual population vital rates. The additive random effect structure is more robust in cases where data 

are sparse (missing site and year combinations). This structure allows other site and year data to help 

inform those combinations of missing data and provides more stable estimates with narrower credible 

intervals. Findings in this analysis are a result of the additive random effect structure because this 

structure demonstrated better model stability and was more appropriate for the sampling within the BiState DPS. 

Nest propensity parameters for first nests (np1) were not derived directly from data collected in 

the Bi-State DPS during this study period. The reliability of these data is questionable largely because of 

a relatively high probability of missing the first nest attempt while tracking sage-grouse. However, an 

extensive study conducted by Taylor and others (2012) provided information across numerous sagegrouse studies range-wide and reported 0.96 (95-percent confidence interval [CI]=0.94–0.97) and 0.89 

(95-percent CI=0.87–0.91) for adults and yearlings. These values were considered reliable because of 

the large number of studies used in the analysis. However, we provided priors that were slightly wider 

than these published confidence intervals as a more conservative approach. We set informative priors 

for adults=Beta(97, 5) and yearlings=Beta(90, 12). In the absence of additional information, we 

assumed this proportion to be constant among sites and years. 
10

Parameters were derived for the propensity to nest a second time (np2) directly from data 

collected in the Bi-State DPS. Data to estimate second nest propensity were more reliable than those for 

the first nests because females were monitored intensively (relocated every 1–3 days) following first 

nest failures (nfailed nests=44). Field technicians were able to determine whether or not a female attempted 

a second nest by approaching sage-grouse and confirming nesting when sage-grouse were located at the 

same coordinate as the previous location. Second-nest propensity data were modeled as arising from a 

Binomial distribution as follows: 

ynp2,ij ~ Binomial(pnp2,ij, nnp2,ij) 

logit�pnp2,ij� = ai + β ∗ xij + γj (7) 

αi~ Normal(θ, σα

2)

γj~ Normal�0, σγ

2�

where the number of unsuccessful nests at each site in each year were denoted by nnp2,ij. In this model, 

ynp2,ij represents the number of renests and logit(pnp2,ij) is a linear function of random site effects αi, 

random year effects γj, both of which were assumed to arise from Normal distributions with mean θ and 

zero, respectively, and variances σα

2 and σγ2, respectively, and a change in the expected count of 

magnitude β, where the indicator of age was equal to one for adults. 

Data for clutch size of first nests (c1; nclutches=190) were modeled as arising from the Poisson 

distribution as follows: 

yc1,cij~ Poisson�μc1,cij�

log�μc1,cij� = ai + β ∗ xcij + γj (8)

αi~ Normal(θ, σα

2)

γj~ Normal�0, σγ

2�

Thus, the log expected count of clutch size μc1 at clutch c, site i, and year j is a linear function of random 

site effects αi, random year effects γj, both of which were assumed to arise from Normal distributions 

with mean θ and zero, respectively, and variances σα

2 and σγ2, respectively, and a change in the expected 

count of magnitude β if the indicator of age is equal to 1. Parameter estimates for clutch sizes of second 

nests (c2) were derived in a separate modeling process that followed the same procedures. 
11

Survival parameters of first (ns1) and second nests (ns2) were derived separately. Nest survival 

(nnests=251) was modeled as proportional hazards as expressed in equation 4. However, for nest survival 

estimation, encounter histories were developed for each nest and modeled as a continuous process at 

discrete daily intervals. In this case, T=38 was used to estimate survival during 10 days of laying and 28 

days of incubation. Female age was used as a fixed effect in this model, which also included random 

effects for site and year. 

Data on egg hatchability (h; nhatchability=111) in the Bi-State DPS were derived for most nests that 

were successful. Hatchability was modeled as arising from a Binomial distribution (logit-link function) 

following equation 7, where the indexing differs as: 

yh,eij ~ Binomial(ph,eij, nh,eij)

logit�ph,eij� = ai + β ∗ xeij + γj (9)

αi~ Normal(θ, σα

2)

γj~ Normal�0, σγ

2�

where the initial number of eggs laid in a clutch e represented the number of trials (nh,eij) at site i and 

year j, and the number of hatched eggs represented successes (yh,eij). The logit(ph,eij) is a linear function 

of random site effects αi, random year effects γj, both of which were assumed to arise from Normal 

distributions with mean θ and zero, respectively, and variances σα

2 and σγ2, respectively, and a change in 

the expected count of magnitude β, where the indicator of age was equal to one for adults.. 

As described previously, chicks were not directly marked and followed using radio-telemetry to 

reduce researcher disturbance. Thus, chick survival (cs) probabilities were derived from the two brood 

counts (nbroods=120) with time interval lengths that varied across the 10-year study period. However, the 

number of days elapsed from nest hatch to brood count varied by study year (2003–05, 50 days; 2007–

09, 35 days; 2010–11, 28 days; 2012, 50 days). Therefore, we employed an adjustment in estimating 

survival probabilities depending on the year of study. We modeled chick survival based on brood count 

data as arising from a Binomial distribution where the initial brood size was scored as the number of 

trials and chicks that survived to days d were scored as successes and took the form: 

ycs,bij ~ Binomial(pcs,bijd, ncs,bij)

where d on the binomial probability p is d=d(j) and represents one of three survival periods depending 

on the year j of data collection (d=28, 35, or 50). For a 35-day interval, the probability of survival is 

modeled by this logistic relationship:
12

logit�pcs,bij,35� = ai + β ∗ xbij + γj (10) 

αi~ Normal(θ, σα

2)

γj~ Normal�0, σγ

2�

In this model, ycs,bi,j represents the number of chicks that survived for each brood b at site i year j. The 

logit(pcs,bij,35) is a linear function of random site effects αj, random year effects γi, and a change in the 

expected count of magnitude β, where the indicator of age was equal to one for adults. We assumed a 

constant hazard function, and consistent with this assumption the probabilities of survival for the other 

intervals are related as follows:

pcs,bijd = �

�pcs,bij,35�

28/35, t = 28

pcs,bij,35, t = 35

�pcs,bij,35�

50/35, t = 50

Juvenile sage-grouse (post-fledging, >35 days and <1 year old) were not radio-marked and 

tracked in the Bi-State DPS. However, we derived a posterior distribution of juvenile survival rates (js) 

during this period by using an informative prior of 0.75 (95-percent CI =0.67–0.82) reported in Taylor 

and others (2012) in the form of Beta(100, 34). 

Joint Likelihood

In a final step of the IPM, we followed procedures described in Kéry and Shaub (2012) and 

formulated a joint likelihood which represents the component likelihoods of population count data 

(state-space model described in equation 3), yearling and adult survival data (proportional hazards 

model described in equation 4), and fecundity data (submodel components described in equation 6). The 

subcomponents of the IPM used in deriving posterior distributions for the breeding population indices 

(N) are shown in figure 3. We then calculated population growth rate across spatial and temporal scales 

using equations 1 and 2. For each subpopulation, we calculated the probability that the subpopulation 

was increasing, stable, and decreasing based on the posterior distributions of derived parameters. We 

then calculated the odds of increase from the probability values, where the odds of increase represented 

the probability of increase divided by the sum of the probability of decrease and stability. Likewise, we 

calculated the odds of decrease. We then created a ratio of the two odds (increase:decrease) and applied 

natural logarithmic transformation to that ratio. The purpose of this procedure was to quantify evidence 

for population trends (when ratio equals 0, then the odds of increase are the same as decrease). Plots 

were created for N, λ, and ln(odds ratio). Posterior distributions of parameters were summarized as 

median and 95 percent credible intervals (CRI) were expressed as 0.025 quantile–0.975 quantile. Lek 

count observation data were summarized by mean and 95 percent confidence intervals (CI) as 1.96 

multiplied by the standard error.
13

We used JAGS 3.3.0 (R version 3.0.0), using the package rjags to obtain posterior samples of 

parameters. We used Markov chain Monte Carlo methods and ran five independent chains of 100,000, 

following a burn-in of 100,000. Chains were thinned by a factor of 500 because of storage limitations 

given the large number of parameters. We found no evidence for lack of convergence, observed by 

examining history plots. 

Figure 3. Diagram showing integrated population model [modified from Kéry and Shaub (2012)] for greater sagegrouse in the Bi-State Distinct Population Segment study area, California and Nevada. Ovals represent derived 

parameters and dashed squares represent submodels. Ovals overlapping more than one square represents 

parameters informed by multiple data sources; arrows indicate flow of information; np1, propensity of first nest; ynp2, 

second nesting propensity; yc1, clutch size from first nest; yc2, clutch size from second nest; Sns1, survival of first nest;

Sns2, survival of second nest; yh, hatchability; Ycs, chick survival; js, juvenile survival; F, fecundity; San, annual survival; 

σ2, error of lek observations; N, breeding number of sage-grouse; i, site; j, year; a, age class.
14

Results and Interpretation

This document consists of key findings for each subpopulation as well as inferences at the

regional scale (Bi-State DPS). These findings represent information regarding population vital rate 

estimation, observed lek counts, N, λ, and odds ratios for each subpopulation and the Bi-State DPS.

Derived parameters were averaged across years and listed by site (appendix A) and averaged across 

sites and listed by years (appendix B). In the following subsections, general estimates of survival (S) and 

fecundity (F) for adults (a) and yearlings (y) for each subpopulation were reported, as well as 

subpopulation vital rate estimates that appear to differ from inferences at the regional scale. 

Pine Nut Subpopulation

The average number of observed males on leks was 12.0 (95-percent CI=8.0–15.9; table 1), which 

was slightly less than N at 12.1 (95-percent CRI=7.2–17.6; fig. 4). The pattern of N across years is 

similar to that of N averaged across the entire Bi-State DPS (fig. 5). Within the Pine Nut subpopulation, 

growth rate (λ) was 1.04 (95-percent CRI =0.92–1.51; fig. 6) and per capita growth (r) was 0.04 (95-

percent CRI=-0.08–0.41). The fecundity rate for adults (Fa=0.47, 95-percent CRI=0.19–1.00) and

yearlings (Fy=0.36, 95-percent CRI=0.13–0.93) in the Pine Nut subpopulation was similar to the rates 

for other subpopulations. Survival for adults (Sa) was 0.70 (95 CRI=0.54–0.84), and survival for

yearlings (Sy) was 0.70 (95-percent CRI=0.53–0.85). 

Desert Creek Subpopulation

The average number of observed males on leks was 18.0 (95-percent CRI=13.7–22.3; table 1), 

which was slightly lower than the N at 18.1 (95-percent CRI=12.8–24.3; fig. 4). Within the Desert 

Creek subpopulation, λ was 1.03 (95-percent CRI=0.92–1.41; fig. 6) and r was 0.03 (95-percent CRI=-

0.09–0.34). Fa in the Desert Creek subpopulation was highest (0.53, 95-percent CRI=0.25–1.16), 

whereas Fy was similar (0.40, 95-percent CRI=0.15–1.13) to Fy of other subpopulations. Survival for 

adults (Sa=0.68; 95-percent CRI=0.51–0.81) and yearlings (Sy=0.68; 95-percent CRI=0.51–0.82) was 

similar to survival for other subpopulations. 

Fales Subpopulation

The average number of observed males on leks was 9.2 (95-percent CRI=7.7–10.7; table 1), 

higher than N at 8.7 (95-percent CRI=0.7–14.6; fig. 4). Within the Fales subpopulation, λ was 0.98 (95-

percent CRI=0.84–1.55; fig. 6). Per capita growth (r=-0.02, 95-percent CRI=-0.18–0.44) was the second 

lowest among all subpopulations. The fecundity rate for Fales (Fa=0.50, 95-percent CRI=0.20–1.72; 

Fy=0.49, 95-percent CRI=0.16–4.65) was similar to the rates for other subpopulations. Survival 

(Sa=0.58, 95-percent CRI=0.03–0.76; Sy=0.57, 95-percent CRI=0.04–0.76) was lower for Fales than for 

other subpopulations. However, chick survival rates for both adults (c1a=0.45, 95-percent CRI=0.27–

0.69) and yearlings (c1y=0.38, 95-percent CRI=0.20–0.63) were higher for Fales than for other 

subpopulations. 
15

Bodie Hills Subpopulation

The average number of observed males on leks was 21.2 (95-percent CRI=15.4–27.0; table 1). N

was the second highest of the six subpopulations (21.4; 95-percent CRI=15.5–27.8; fig. 4). Bodie Hills 

had the highest λ (1.08, 95-percent CRI=0.97–1.42) and r (0.08, 95-percent CRI=-0.03–0.35) among all 

subpopulations (fig. 6). The fecundity rate for Bodie Hills (Fa=0.49, 95-percent CRI=0.25–0.90; 

Fy=0.42, 95-percent CRI=0.17–1.17) was similar to the rates for other subpopulations. Survival of the 

first nest generally was highest for Bodie Hills (ns1a=0.46, 95-percent CRI=0.27–0.65; ns1y=0.48, 95-

percent CRI=0.27–0.68). However, chick survival (cs1a=0.38, 95-percent CRI=0.23–0.57; cs1y=0.31, 

95-percent CRI=0.17–0.51) was lowest when compared to chick survival in other subpopulations. 

Parker Meadows Subpopulation

The average number of observed males on leks was 4.7 (95-percent CRI=2.9–6.4; table 1) and N

was 4.5 (95-percent CRI=1.6–8.7; fig. 4). Parker Meadows had the lowest overall λ (0.85, 95-percent

CRI=0.74–1.29; fig. 6) and r (-0.16, 95 CRI=-0.31–0.25) compared to other subpopulations (fig. 6). The 

fecundity rate for Parker Meadows (Fa=0.15, 95-percent CRI=0.06–0.39; Fy=0.17, 95-percent 

CRI=0.05–0.49) was the lowest rate of all subpopulations. Survival (Sa=0.67, 95-percent CRI=0.47–

0.80; Sy=0.66, 95-percent CRI=0.47–0.81) was similar to survival for other subpopulations. Egg 

hatchability for adults (ha=0.34, 95-percent CRI=0.15–0.61) and yearlings (hy=0.51, 95-percent 

CRI=0.24–0.78) was substantially lower than ha and hy of other subpopulations. 

Long Valley Subpopulation

The average number of observed males on leks was 35.6 (95-percent CRI=30.4–40.7; table 1)

and N was 35.6 (95-percent CRI=28.7–42.8; fig. 4). Within the Long Valley subpopulation, λ was 1.02 

(95-percent CRI=0.94–1.28; fig. 6) and r was 0.02 (95-percent CRI=-0.06–0.25). The fecundity rate for 

Long Valley (Fa=0.46, 95-percent CRI=0.22–0.92; Fy=0.36, 95-percent CRI=0.13–0.99) was similar to 

the other subpopulations. Survival (Sa=0.68, 95-percent CRI=0.54–0.80; Sy=0.68, 95-percent CRI=0.52–

0.81) also was similar to survival for other subpopulations. Nest survival for first nests (ns1a=0.37, 95-

percent CRI=0.18–0.56; ns1y=0.39, 95-percent CRI=0.16–0.60) was the lowest of all subpopulations. 
16

Figure 4. Graphs showing estimated number of male sage-grouse per lek (solid line) and lek observations (dashed 

line), Bi-State Distinct Population Segment study area, California and Nevada, 2003–12. Gray shading represents 

the 95-percent credible interval. 
17

Figure 5. Graphs showing annual lek attendance counts (solid line) and estimates (dashed line) across all 

Bi-State Distinct Population Segment study area sites, California and Nevada, 2003–12. Gray shading represents 

the 95-percent credible interval. 
18

Figure 6. Graphs showing population growth rate (λ) for each monitored site (A–F), Distinct Population Segment

study area, California and Nevada, 2003–12. Gray shading represents the 95-percent credible interval. The dashed 

horizontal line represents a stable population.
19

Bi-State DPS Summary and Synthesis

The preponderance of evidence suggests that sage-grouse populations are stable (λ was 1.00; 95-

percent CRI=0.88–1.41) within Bi-State DPS in its entirety over the period of 2003–2012 (fig. 7; 

population vital rate parameters are reported in table 2). Based on the posterior distribution of λ across 

the Bi-State DPS, the following probabilities were calculated for the period 2003–2012: (1) increased 

population, 42.5 percent; (2) stable population, 15.8 percent; and (3) decreased population, 41.6 percent. 

The odds of increase to decrease is 1.03, meaning that the odds that the trend in the population is 

increasing was 3 percent greater than odds of it decreasing (fig. 9). However, substantial variation was 

detected in λ across years and sites as reported above. For example, data suggest that the odds that the 

Parker Meadows subpopulation is decreasing was 17.4 times greater than the odds that this 

subpopulation is increasing. Based on these findings, this subpopulation appears to be the only one with 

compelling evidence within the Bi-State that is currently at risk of extinction. The derived parameters 

for hatchability at Parker Meadows (median; hy, 0.51; ha, 0.34; appendix B) were approximately half of 

those values that were derived across the Bi-State overall (0.5 quantile; hy, 0.89; ha, 0.83; table 2). Field 

observations concluded that decreased hatchability was a result of low egg fertility rates. Recent 

evidence indicate that the Parker Meadows subpopulation contains substantially lower mitochondrial 

and nuclear genetic variation than other subpopulations within the Bi-State DPS (Oyler-McCance and 

others, in press), which may be concerning because this subpopulation is isolated and small. Parker 

Meadows may benefit from a translocation program aimed at augmenting greater sage-grouse (OylerMcCance and others, in press). Nevertheless, these data indicate that the Bi-State DPS in its entirety is 

stable, despite the strong evidence of a declining trend in the Parker Meadows subpopulation. In other 

words, the Parker Meadows subpopulation, which consisted of two leks with less than 5 males on 

average (table 1), had relatively low influence on the overall population trend averaged across the entire 

DPS (fig. 7). 
20

Figure 7. Graph showing annual population growth rate (λ) across all Bi-State Distinct Population Segment study 

area sites, California and Nevada, 2003–12. Gray shading represents the 95-percent credible interval. The dashed 

horizontal line represents a stable population.
21

Figure 8. Graphs showing ln(odds ratio) of population increase to decrease for each monitored site (A–F), Bi-State 

Distinct Population Segment study area, California and Nevada, 2003–12. The ratio consisted of the odds of the 

population increasing to that of decreasing.The dashed horizontal line represents a stable population. The solid line 

is overall average for the 10-year period (red=decrease, green=increase). The missing value in Bodie Hills (D) was 

based on a probability of decrease of zero. 
22

Figure 9. Graph showing ln(odds ratio) of increase to decrease across all Bi-State Distinct Population Segment

study area subpopulations, California and Nevada, 2003–12. The ratio consisted of the odds of the population 

increasing to that of decreasing. The dashed horizontal line represents a stable population. The solid green line is 

overall average for the 10-year period. 
23

Table 2. Summary of posterior distributions of derived population vital rate parameters for greater sage-grouse

(Centrocercus urophasianus) in the Bi-State Distinct Population Segment study area, California and Nevada, 

2003–12.

Quantileb

Population vital ratea Age class 0.5 0.025 0.975

Nest propensity (np1) Adult 0.96 0.91 0.99

Yearling 0.89 0.82 0.94

Nest propensity (np2) Adult 0.30 0.07 0.73

Yearling 0.18 0.01 0.77

Nest survival (ns1) Adult 0.42 0.21 0.64

Yearling 0.45 0.21 0.67

Clutch size (cs1) Adult 6.82 5.58 8.19

Yearling 6.50 5.17 8.00

Nest survival (ns2) Adult 0.45 0.04 0.90

Yearling 0.63 0.05 0.97

Clutch size (cs2) Adult 5.98 1.71 54.58

Yearling 7.37 1.68 78.92

Hatchability Adult 0.83 0.65 0.92

Yearling 0.89 0.74 0.96

Chick survival Adult 0.41 0.24 0.63

Yearling 0.34 0.18 0.57

Fecundity Adult 0.43 0.19 1.01

Yearling 0.37 0.13 1.56

Survival Adult 0.66 0.43 0.80

Yearling 0.66 0.43 0.81

Juvenile 0.78 0.71 0.85

a

Propensity of first nest and juvenile survival were derived from input from informative priors based on Taylor and others, 

2012. 

b

Median is 0.5 quantile and 95 percent credible interval is 0.025 quantile–0.975 quantile.

Although short-term declining trends have been identified in many sage-grouse populations 

range-wide and outside of the Bi-State DPS (Connelly and others, 2004; Sage and Columbian Sharptailed Grouse Technical Committee, 2008; Garton and others, 2011), the findings here indicate that the 

Bi-State DPS overall is not experiencing similar declines. These results corroborate other population 

analyses conducted for sage-grouse specifically within the Bi-State subpopulations (Sage and 

Columbian Sharp-tailed Grouse Technical Committee, 2008; Garton and others, 2011). For example, 

estimation of N and λ reported here show a similar pattern to that estimated by Garton and others (2011) 

across the years of 2003–2007, when both analyses overlapped. Both analyses independently 

demonstrated consistency in N (no change) during years 2003–2006, then a decline in N between 2006 

and 2007. The population reconstruction approach employed by Garton and others (2011) differed from 

those described here, in that the sole source of data for the previous study was lek counts. Furthermore, 

a mixed effects modeling approach using lek counts (Sage and Columbian Sharp-tailed Grouse 

Technical Committee, 2008) reached similar conclusions as the findings reported here and those of 
24

Garton and others (2011). Our modeling approach expands on previous analyses in multiple ways. First, 

we extend the period of investigation to include data from more recent years (2008–2012). When taking 

additional data into consideration, the period with the lowest population growth rate (λ=0.84, 95-percent 

CRI=0.72–1.21) over the 10-years of investigation was 2007–08, whereas the highest growth rates 

followed those years (2009–2010, λ=1.28, 95-percent CRI=1.15–1.90) and all years since 2008 have 

experienced λ greater than 1. Second, the analytical approach used here integrates demographic data 

beyond raw lek counts (e.g., nesting and survival) to further inform N and λ. This approach creates a 

more thorough understanding of population dynamics because λ is a deterministic result of demographic 

rates and those data provide more information to estimate λ. Lastly, we provide data over a broader 

spatial scale which more appropriately represents population trend for the Bi-State DPS. Previous 

analyses (Sage and Columbian Sharp-tailed Grouse Technical Committee, 2008; Garton and others, 

2011) relied on lek data from only two study areas, which were named Mono Lake and South Mono 

Lake, and correspond to Bodie Hills and Long Valley subpopulations, respectively. This study provided 

information on an additional 4 subpopulations that extend to borders of the DPS and data modeled here 

represent nearly all subpopulations within the DPS. 

Several studies have indicated that sage-grouse populations have experienced long-term (i.e., 

decadal) declines in population sizes range-wide (Connelly and others, 2004; Sage and Columbian 

Sharp-tailed Grouse Technical Committee 2008; Garton and others, 2011). This study did not 

investigate population trends that exceed 10 years. The rationale for not including data prior to the 10-

year period was two-fold. First, the lek data across the Bi-State DPS did not meet high enough quality 

standards to allow for reliable inferences for this specific analysis prior to this 10-year period. For 

example, many lek locations were unknown, or believed non-existent, within the majority of 

subpopulations and thus not counted. The population reconstruction approach employed by Garton and 

others (2011) evaluated trends across periods that date back to 1965 within two areas (i.e., Mono Lake 

and South Mono Lake). The study concluded that no consistent long-term trend was detected at either 

area over 40 years (Garton and others, 2011). However, the confidence intervals in the first few decades 

were relatively wide. Second, demographic data was not available for any subpopulation during years 

prior to 2003, which are fundamental modeling components of this study. Nevertheless, the objective of 

this study was not to compare to historic levels but instead to reliably estimate if current population size 

is decreasing, stable, or increasing. A 10-year period was sufficient to reliably estimate trends, while 

accounting for the cyclic nature of sage-grouse populations. For example, sage-grouse generally exhibit 

a degree of short-term oscillation in population that has a regular period of 6–9 years (Fedy and others, 

2013). Thus, 10-years will fully encompass the cyclicity, whereas estimates from a shorter term period 

might be misleading in only capturing a portion of the cycle. However, although the 10-year period we 

evaluated represented climatic variation that might influence population dynamics, a period of severe 

and prolonged drought did not occur in this time. Thus, the effects of drought on sage-grouse population 

trends are uncertain for the Bi-State and studies that investigate these effects would be beneficial 

This report provides results for the first of three steps of a comprehensive population dynamics 

analysis for the Bi-State DPS. As mentioned above, in a second step, a retrospective analysis that 

evaluates the relative importance of specific population vital rates to λ will be conducted to further 

understand those life-stages that regulate changes in population size. As a prospective analysis, 

sensitivities and elasticities for each population vital rate will also be calculated. A final step will entail 

linking environmental factors (e.g., climatic variables) to the derived population demographic 

parameters and λs. Individually and collectively, these analyses should be useful in the decision-making 

process for land stewards, managers, and policy-makers within the Bi-State DPS.
25

Acknowledgments

We are indebted to the many biologists and technicians who spent countless hours capturing and 

tracking radio-marked sage-grouse and conducting lek counts that made this modeling effort possible, 

especially M. Farinha and E. Kolada. We thank the Bi-State Technical Advisory Committee and the BiState Executive Oversight Committee for recognizing the need for this research and providing support. 

In particular, we thank T. Koch, S. Abele, and R. Kearney from the U. S. Fish and Wildlife Service; S. 

Espinosa, T. Wasley, and J. Tull from the Nevada Department of Wildlife; S. Nelson, S. Lisius, P. 

Ziegler, and A Lueders from the Bureau of Land Management; T. Taylor from California Department of 

Fish and Wildlife; J. Sedinger from University of Nevada Reno; and D. Delehanty from Idaho State 

University. We also thank D. Blankenship, D. Racine, J. Fatooh, A. Halford R. Haldeman, L. Fields, 

and D. House. Excellent reviews by J. Yee, T. Edwards, C. Hagen, T. Kimball, and K. Miles greatly 

improved this manuscript. This work was a collaborative effort between California Department of Fish 

and Wildlife, Nevada Department of Wildlife, University of Idaho, University of Nevada Reno, U. S. 

Fish and Wildlife Service, Bureau of Land Management, U. S. Department of Agriculture Forest 

Service, Los Angeles Department of Water and Power, and Quail Unlimited. 

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27

Appendix A. Summary of Derived Posterior Distributions for Greater SageGrouse (Centrocercus urophasianus) Population Vital Rates by Subpopulation

within the Bi-State Distinct Population Segment Study Area, 2003–12. 

Quantileb

Subpopulationa Vital rate Age 0.5 0.025 0.975

– Nesting propensity (np1) Adult 0.96 0.91 0.99

– Nesting propensity (np1) Yearling 0.89 0.82 0.94

– Survival Juvenile 0.78 0.71 0.85

Pine Nut Nesting propensity (np2) Adult 0.23 0.00 0.70

Yearling 0.04 0.00 0.55

Nest survival (ns1) Adult 0.44 0.21 0.67

Yearling 0.46 0.22 0.68

Clutch size (cs1) Adult 6.70 5.18 8.07

Yearling 6.37 4.87 7.89

Nest survival (ns2) Adult 0.45 0.00 0.95

Yearling 0.63 0.00 0.98

Clutch size (cs2) Adult 6.07 0.62 57.62

Yearling 7.52 0.63 87.17

Hatchability Adult 0.90 0.65 0.98

Yearling 0.95 0.77 0.99

Chick survival Adult 0.42 0.24 0.70

Yearling 0.35 0.17 0.64

Fecundity Adult 0.47 0.19 1.00

Yearling 0.36 0.13 0.93

Survival Adult 0.70 0.54 0.84

Yearling 0.70 0.53 0.85

Desert Creek Nesting propensity (np2) Adult 0.35 0.06 0.83

Yearling 0.09 0.00 0.80

Nest survival (ns1) Adult 0.46 0.24 0.69

Yearling 0.48 0.24 0.72

Clutch size (cs1) Adult 6.93 5.72 8.44

Yearling 6.60 5.29 8.18

Nest survival (ns2) Adult 0.50 0.05 0.93

Yearling 0.67 0.08 0.98

Clutch size (cs2) Adult 6.24 0.66 48.34

Yearling 7.83 0.75 70.80

Hatchability Adult 0.91 0.75 0.97

Yearling 0.96 0.84 0.99

Chick survival Adult 0.41 0.25 0.61

Yearling 0.34 0.18 0.56

Fecundity Adult 0.53 0.25 1.16

Yearling 0.40 0.15 1.13

Survival Adult 0.68 0.51 0.81

Yearling 0.68 0.51 0.82
28

Quantileb

Subpopulationa Vital rate Age 0.5 0.025 0.975

Fales Nesting propensity (np2) Adult 0.24 0.00 0.72

Yearling 0.35 0.02 0.96

Nest survival (ns1) Adult 0.41 0.17 0.65

Yearling 0.43 0.16 0.66

Clutch size (cs1) Adult 6.81 5.54 8.34

Yearling 6.49 5.18 8.07

Nest survival (ns2) Adult 0.38 0.00 0.89

Yearling 0.55 0.00 0.96

Clutch size (cs2) Adult 6.36 1.02 155.31

Yearling 7.97 1.11 199.36

Hatchability Adult 0.93 0.72 0.99

Yearling 0.97 0.83 0.99

Chick survival Adult 0.45 0.27 0.69

Yearling 0.38 0.20 0.63

Fecundity Adult 0.50 0.20 1.72

Yearling 0.49 0.16 4.65

Survival Adult 0.58 0.03 0.76

Yearling 0.57 0.04 0.76

Bodie Hills Nesting propensity (np2) Adult 0.33 0.12 0.70

Yearling 0.31 0.04 0.83

Nest survival (ns1) Adult 0.46 0.27 0.65

Yearling 0.48 0.27 0.68

Clutch size (cs1) Adult 6.76 5.66 8.00

Yearling 6.44 5.20 7.83

Nest survival (ns2) Adult 0.50 0.08 0.89

Yearling 0.67 0.11 0.96

Clutch size (cs2) Adult 6.17 3.04 23.87

Yearling 7.49 2.72 42.80

Hatchability Adult 0.93 0.80 0.98

Yearling 0.97 0.87 0.99

Chick survival Adult 0.38 0.23 0.57

Yearling 0.31 0.17 0.51

Fecundity Adult 0.49 0.25 0.90

Yearling 0.42 0.17 1.17

Survival Adult 0.65 0.50 0.78

Yearling 0.65 0.49 0.79

Parker Meadows Nesting propensity (np2) Adult 0.24 0.07 0.63

Yearling 0.07 0.00 0.73

Nest survival (ns1) Adult 0.41 0.20 0.63

Yearling 0.43 0.19 0.65

Clutch size (cs1) Adult 6.72 5.49 8.07

Yearling 6.41 5.07 7.86

Nest Survival (ns2) Adult 0.41 0.01 0.87

Yearling 0.60 0.02 0.96
29

Quantileb

Subpopulationa Vital rate Age 0.5 0.025 0.975

Clutch Size (cs2) Adult 5.34 2.17 20.89

Yearling 6.39 2.13 37.33

Hatchability Adult 0.34 0.15 0.61

Yearling 0.51 0.24 0.78

Chick Survival Adult 0.40 0.23 0.61

Yearling 0.33 0.17 0.55

Fecundity Adult 0.15 0.06 0.39

Yearling 0.17 0.05 0.49

Survival Adult 0.67 0.47 0.80

Yearling 0.66 0.47 0.81

Long Valley Nesting propensity (np2) Adult 0.45 0.18 0.80

Yearling 0.21 0.02 0.73

Nest Survival (ns1) Adult 0.37 0.18 0.56

Yearling 0.39 0.16 0.60

Clutch Size (cs1) Adult 7.00 5.90 8.25

Yearling 6.67 5.39 8.16

Nest Survival (ns2) Adult 0.45 0.08 0.86

Yearling 0.64 0.08 0.96

Clutch Size (cs2) Adult 5.71 2.74 21.42

Yearling 7.02 2.75 36.04

Hatchability Adult 0.94 0.82 0.98

Yearling 0.97 0.88 0.99

Chick Survival Adult 0.40 0.24 0.58

Yearling 0.33 0.18 0.54

Fecundity Adult 0.46 0.22 0.92

Yearling 0.36 0.13 0.99

Survival Adult 0.68 0.54 0.80

Yearling 0.68 0.52 0.81

a

A constant rate across the Bi-State Distinct Population Segment study area was assumed for those population vital rates 

without a subpopulation listed. Propensity of first nest and juvenile survival were derived from input from informative priors 

based on Taylor and others, 2012.

b

Median is 0.5 quantile and 95 percent credible interval is 0.025 quantile–0.975 quantile.
30

Appendix B. Summary of Derived Posterior Distributions for Greater SageGrouse (Centrocercus urophasianus)Population Vital Rates by Year, 2003–12.

Quantileb

Vital ratea Age Year 50 2.5 97.5

Nesting propensity (np1) Adult – 0.96 0.91 0.99

Nesting propensity (np1) Yearling – 0.89 0.82 0.94

Nesting propensity (np2) Adult 2003 0.26 0.04 0.70

2004 0.24 0.05 0.62

2005 0.21 0.03 0.62

2006 0.25 0.00 0.93

2007 0.12 0.00 0.62

2008 0.29 0.07 0.66

2009 0.25 0.04 0.67

2010 0.66 0.25 0.91

2011 0.65 0.24 0.92

2012 0.14 0.00 0.66

Nesting propensity (np2) Yearling 2003 0.17 0.01 0.73

2004 0.15 0.01 0.72

2005 0.30 0.04 0.86

2006 0.16 0.00 0.94

2007 0.09 0.00 0.64

2008 0.28 0.04 0.88

2009 0.07 0.00 0.53

2010 0.12 0.00 0.69

2011 0.31 0.03 0.94

2012 0.11 0.00 0.76

Nest survival (ns1) Adult 2003 0.39 0.16 0.59

2004 0.41 0.22 0.61

2005 0.42 0.23 0.62

2006 0.41 0.14 0.67

2007 0.45 0.24 0.69

2008 0.41 0.21 0.61

2009 0.48 0.29 0.71

2010 0.44 0.25 0.65

2011 0.41 0.19 0.62

2012 0.42 0.21 0.66

Nest survival (ns1) Yearling 2003 0.41 0.15 0.63

2004 0.43 0.22 0.64

2005 0.44 0.21 0.65

2006 0.44 0.13 0.69

2007 0.47 0.24 0.71

2008 0.43 0.19 0.63

2009 0.50 0.29 0.72

2010 0.47 0.24 0.68

2011 0.43 0.18 0.65

2012 0.44 0.21 0.68
31

Quantileb

Vital ratea Age Year 50 2.5 97.5

Clutch size (cs1) Adult 2003 7.11 6.03 8.50

2004 6.44 5.44 7.41

2005 6.26 5.05 7.32

2006 6.76 5.11 8.72

2007 6.76 5.32 8.31

2008 7.19 6.04 8.59

2009 7.01 5.91 8.31

2010 7.08 5.99 8.38

2011 6.91 5.73 8.32

2012 6.68 5.20 8.08

Clutch size (cs1) Yearling 2003 6.80 5.56 8.22

2004 6.13 4.95 7.43

2005 5.97 4.62 7.35

2006 6.44 4.76 8.42

2007 6.43 5.10 7.88

2008 6.86 5.58 8.39

2009 6.67 5.54 7.97

2010 6.74 5.54 8.25

2011 6.58 5.25 8.19

2012 6.36 4.78 7.89

Nest survival (ns2) Adult 2003 0.09 0.00 0.73

2004 0.37 0.02 0.84

2005 0.50 0.05 0.90

2006 0.43 0.00 0.97

2007 0.47 0.00 0.96

2008 0.70 0.15 0.96

2009 0.52 0.05 0.93

2010 0.41 0.05 0.83

2011 0.51 0.07 0.89

2012 0.46 0.00 0.97

Nest survival (ns2) Yearling 2003 0.26 0.00 0.89

2004 0.57 0.04 0.95

2005 0.69 0.09 0.97

2006 0.61 0.00 0.99

2007 0.65 0.00 0.99

2008 0.83 0.16 0.99

2009 0.71 0.06 0.98

2010 0.61 0.04 0.96

2011 0.70 0.09 0.97

2012 0.64 0.00 0.99
32

Quantileb

Vital ratea Age Year 50 2.5 97.5

Clutch size (cs2) Adult 2003 6.33 1.74 110.00

2004 6.09 1.40 55.21

2005 6.22 1.59 60.69

2006 5.89 0.93 51.40

2007 6.05 1.18 59.38

2008 5.98 2.39 40.39

2009 6.03 2.24 39.38

2010 6.10 2.56 38.88

2011 5.10 1.93 33.57

2012 6.02 1.14 56.85

Clutch size (cs2) Yearling 2003 7.83 1.74 163.05

2004 7.46 1.55 74.84

2005 7.79 1.61 86.55

2006 7.04 1.17 68.25

2007 7.48 1.40 89.66

2008 7.34 2.01 59.44

2009 7.49 1.98 57.50

2010 7.61 2.13 59.12

2011 6.34 1.98 46.12

2012 7.34 1.24 84.64

Hatchability Adult 2003 0.85 0.72 0.94

2004 0.77 0.62 0.86

2005 0.79 0.65 0.87

2006 0.82 0.39 0.97

2007 0.88 0.70 0.98

2008 0.87 0.76 0.95

2009 0.92 0.84 0.96

2010 0.74 0.58 0.84

2011 0.79 0.63 0.88

2012 0.82 0.60 0.93

Hatchability Yearling 2003 0.91 0.80 0.97

2004 0.84 0.70 0.92

2005 0.86 0.73 0.93

2006 0.88 0.51 0.98

2007 0.93 0.80 0.99

2008 0.92 0.83 0.97

2009 0.95 0.90 0.98

2010 0.83 0.67 0.91

2011 0.86 0.73 0.93

2012 0.88 0.70 0.97
33

Quantileb

Vital ratea Age Year 50 2.5 97.5

Chick survival Adult 2003 0.53 0.39 0.69

2004 0.46 0.35 0.60

2005 0.39 0.29 0.52

2006 0.36 0.10 0.67

2007 0.32 0.16 0.52

2008 0.32 0.21 0.47

2009 0.58 0.34 0.91

2010 0.41 0.29 0.57

2011 0.33 0.19 0.51

2012 0.41 0.12 0.80

Chick survival Yearling 2003 0.45 0.30 0.62

2004 0.39 0.27 0.54

2005 0.31 0.19 0.49

2006 0.29 0.07 0.59

2007 0.25 0.13 0.44

2008 0.25 0.14 0.43

2009 0.50 0.26 0.87

2010 0.34 0.20 0.52

2011 0.27 0.13 0.45

2012 0.34 0.08 0.75

Fecundity Adult 2003 0.52 0.24 1.32

2004 0.41 0.21 0.84

2005 0.36 0.19 0.81

2006 0.33 0.06 0.87

2007 0.34 0.14 0.76

2008 0.38 0.19 0.87

2009 0.76 0.39 1.49

2010 0.48 0.26 1.13

2011 0.37 0.17 0.95

2012 0.37 0.10 1.10

Fecundity Yearling 2003 0.46 0.17 2.61

2004 0.36 0.16 1.27

2005 0.35 0.14 2.08

2006 0.28 0.05 1.24

2007 0.28 0.10 1.20

2008 0.33 0.13 1.59

2009 0.62 0.27 1.77

2010 0.35 0.15 1.12

2011 0.30 0.10 1.10

2012 0.33 0.07 1.64
34

Quantileb

Vital ratea Age Year 50 2.5 97.5

Survival Adult 2003 0.60 0.36 0.75

2004 0.66 0.46 0.78

2005 0.67 0.45 0.79

2006 0.65 0.39 0.83

2007 0.58 0.35 0.74

2008 0.60 0.39 0.74

2009 0.72 0.51 0.85

2010 0.72 0.50 0.85

2011 0.75 0.53 0.88

2012 0.65 0.39 0.80 

Survival Yearling 2003 0.60 0.36 0.75

2004 0.65 0.44 0.79

2005 0.66 0.44 0.80

2006 0.65 0.39 0.83

2007 0.58 0.36 0.74

2008 0.60 0.36 0.75

2009 0.72 0.51 0.85

2010 0.72 0.50 0.85

2011 0.75 0.52 0.88

2012 0.65 0.38 0.81

Survival Juvenile – 0.78 0.71 0.85

a

Propensity of first nest and juvenile survival were derived from input from informative priors based on Taylor and others, 

2012.

b

Median is 0.5 quantile and 95 percent credible interval is 0.025 quantile–0.975 quantile.
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For more information concerning the research in this report, contact the

 Director, Western Ecological Research Center

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Coates and others—A Hierarchical Integrated Population Model for Greater Sage-Grouse in the Bi-State Distinct Population Segment—Open-File Report 2014–1165

ISSN 2331-1258 (online)

http://dx.doi.org/10.3133/ofr20141165