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ISRAEL JOURNAL OF ECOLOGY & EVOLUTION, Vol. 54, 2008, pp. 389–419

DOI: 10.1560/IJEE.54.3–4.389

*Author to whom correspondence should be addressed. E-mail: cameron.aldridge@usgs.gov

†Current address: NREL, Colorado State University and U.S. Geological Survey, 2150 Centre Avenue, Build-

ing C, Fort Collins, CO 80526-8118 USA.

Received 19 November 2007, accepted 17 July 2008.

ACCOUNTING FOR FITNESS: COMBINING SURVIVAL AND SELECTION WHEN

ASSESSING WILDLIFE–HABITAT RELATIONSHIPS

Cameron L. aLdridge*,† and mark S. BoyCe

Department of Biological Sciences, University of Alberta, Edmonton,

Alberta T6G 2E9, Canada

ABSTRACT

Assessing the viability of a population requires understanding of the resources

used by animals to determine how those resources affect long-term popula-

tion persistence. To understand the true importance of resources, one must

consider both selection (where a species occurs) and tness (reproduction

and survival) associated with the use of those resources. Failure to do so may

result in incorrect assessments of habitat quality and inappropriate manage-

ment activities. We illustrate the importance of considering both occurrence

and tness metrics when assessing habitat requirements for the endangered

greater sage-grouse in Alberta, Canada. This population is experiencing low

recruitment, so we assess resource use during the brood-rearing period to

identify management priorities. First, we develop logistic regression occur-

rence models tted with habitat covariates. Second, we use proportional haz-

ard survival analysis to assess chick survival (tness component) associated

with habitat and climatic covariates. Sage-grouse show strong selection for

sagebrush cover at both patch (smaller) and area (larger) spatial scales, and

weak selection for forbs at the patch scale only. Drought conditions based on

an index combining growing degree days and spring precipitation strongly

reduced chick survival. While hens selected for taller grass and more sage-

brush cover, only taller grass cover also enhanced chick survival. We show

that sage-grouse may not recognize all ecological cues that enhance chick sur-

vival. Management activities targeted at providing habitats that sage-grouse

are likely to use in addition to those that enhance survival are most likely to

ensure the long-term viability of this population. Our techniques account for

both occurrence and tness in habitat quality assessments and, in general, the

approach should be applicable to other species or ecosystems.

Keywords: tness, greater sage-grouse, habitat, occurrence, persistence, sage-

brush, selection, survival

390 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

INTRODUCTION

Species–habitat relationships have become a priority in conservation biology (Boyce

and McDonald, 1999; Morrison, 2001; Brotons et al., 2004). Simply predicting the oc-

currence of animals across habitats is useful, but becomes much more valuable and in-

formative if occurrence (or abundance) is related to tness (Tyre et al., 2001; Breininger

and Carter, 2003; Bock and Jones, 2004; Aldridge and Boyce, 2007). Understanding

spatial variation in tness is critical to the conservation of many species of concern

(Donovan and Thompson, 2001), allowing for population viability assessment (Boyce

et al., 1994; Boyce and McDonald, 1999) and identifying appropriate management

objectives. High-quality habitats should be dened as those where animals are likely to

occur and achieve high levels of tness (reproduction and survival; Van Horne, 1983;

Morrison, 2001; Aldridge and Boyce, 2007). However, density dependence resulting in

individuals sorting themselves according to the ideal free distribution could in turn result

in higher density in selected habitats without apparent tness variation (Fretwell and Lu-

cas, 1969). Regardless, conservation of wildlife populations must make this crucial link

between resources and tness (Franklin et al., 2000; Morrison, 2001; Bock and Jones,

2004; Larson et al., 2004; Nielsen et al., 2005).

We illustrate the importance of considering both occurrence and tness metrics when

assessing habitat requirements for the endangered greater sage-grouse (Centrocercus

urophasianus; hereafter sage-grouse) in Alberta, Canada. Sage-grouse inhabit shrub-

steppe ecosystems that once covered a large portion (1.2 million km2; Schroeder et al.,

2004) of the northwestern United States and small southern portions of three western

provinces of Canada. During the last century, these ecosystems have been transformed

by agricultural activities (Connelly et al., 2004), invasion by non-native plant species

(Knick et al., 2003; Connelly et al., 2004), energy-extraction activities and develop-

ments (Braun et al., 2002; Lyon and Anderson, 2003), intense grazing pressures (Beck

and Mitchell, 2000; Hayes and Holl, 2003; Crawford et al., 2004), and climate change

(Neilson et al., 2005), resulting in direct loss of nearly half of those habitats and the

degradation and fragmentation of that which remains. All sage-grouse populations have

declined by approximately 2% per year since 1965 (Connelly et al., 2004), and low

reproductive success (Connelly and Braun, 1997; Braun, 1998; Crawford et al., 2004)

resulting from poor nesting success (Crawford and Lutz, 1985; Aldridge and Brigham,

2001; Connelly et al., 2004) and chick survival (Aldridge and Brigham, 2001; Burkepile

et al., 2002) has been identied as a potential driver of these declines. The Alberta sage-

grouse population inhabits the northern fringe of the species’ range and has declined by

66–92% since 1965 (Aldridge and Brigham, 2003).

Chick survival is one of the demographic parameters most limiting for prairie grouse

(Johnson and Braun, 1999; Aldridge and Brigham, 2002, 2003; Connelly et al., 2004;

Hagen et al., 2004) and has been identied as a priority in most conservation and recov-

ery strategies for sage-grouse throughout their range (Harris et al., 2000; Connelly et al.,

2004; Crawford et al., 2004). Thus, when identifying habitat requirements for chicks,

assessing habitat selection (occurrence) alone may result in insufcient assessments of

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 391

habitat quality (Van Horne, 1983; Morrison, 2001), potentially leading to inappropriate

management (but see Bock and Jones, 2004). The exception might occur if density de-

pendence forces sage-grouse to use sub-optimal habitats. However, sound management

strategies should assess how resources affect tness parameters such as chick survival

as well as habitat selection if sage-grouse are to persist (Aldridge, 2005; Aldridge and

Boyce, 2007).

Herein, we focus on habitats selected for brood-rearing at two spatial scales, while

simultaneously assessing how these habitats inuence chick survival for sage-grouse in

Alberta, Canada. We rst use logistic regression occurrence models to identify habitat

characteristics selected by females with broods. We then link habitat covariates to sur-

vival using a shared frailty Cox proportional hazards model to assess chick survival rela-

tive to habitat and climatic covariates. We hypothesize that sage-grouse select sagebrush

and herbaceous habitat components, as has been previously demonstrated (see Hagen

et al., 2007, for a review). Similarly, we predict that vegetation components such as

increased herbaceous cover (food) and structural cover afforded by shrubs will enhance

chick survival, whereas conditions associated with drier climate periods resulting in

reduced cover and abundance of mesic habitats containing forbs and insects (Crawford

et al., 2004) will adversely affect chick survival. However, habitat selection and survival

may not necessarily be related, particularly if sage-grouse fail to recognize ecological

factors linked to habitat quality. We then use these models to suggest minimum habi-

tat-quality thresholds that could be used by managers to maintain viable sage-grouse

populations.

STUDY AREA

The study area is located in the dry, mixed-grass prairie of southeastern Alberta, Canada

(49º24¢N, 110º42¢W, ca. 900 m elevation). Daily summer (July–August) temperatures

average 19.1 °C and annual precipitation is ca. 358 mm (AAFC–AAC 2004 unpublished

weather data). The area is characterized by many coulee draws and creeks with gentle

slopes. The dominant shrub species is silver sagebrush (Artemisia cana) and the domi-

nant forb species include pasture sage (A. frigida), several species of clover (Trifolium

spp. and Melilotus spp.), vetch (Astragalus spp.), and common dandelion (Taraxacum

ofcinale). Needle-and-thread grass (Stipa comata), june grass (Koeleria macrantha),

blue grama (Bouteloua gracilis), and western wheatgrass (Pascopyrum smithii) are the

dominant grass species (Coupland, 1961; Aldridge and Brigham, 2003).

Whereas agricultural expansion in the 1970s apparently isolated Alberta sage-grouse

from more southern populations (Schroeder et al., 2004), there has been little conver-

sion to cropland within the study region and grazing is the dominant land-use practice

(Adams et al., 2004). The landscape, however, is heavily fragmented by infrastructure

associated with oil and gas development, including roads and power lines (Braun et al.,

2002; Aldridge and Boyce, 2007). An increased frequency of extended drought condi-

tions (Aldridge and Brigham, 2002) and the introduction of West Nile virus (Naugle et

al., 2004) also adversely affect this sage-grouse population.

392 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

MATERIALS AND METHODS

FIELD TECHNIQUES

Chick captures and relocations

Chicks of radiocollared females were captured by hand as soon as possible after hatch

by ushing the hen from her brood (May–July, 2001–2003). Chicks averaged 2.5 days

of age (range 0–8 days) at capture. From each brood we randomly selected two chicks

and attached radio transmitters to them with two sutures (similar to the technique de-

scribed by Burkepile et al. (2002; but see Aldridge, 2005). Transmitters weighed 1.6 g

and had a battery life of 10–12 weeks (BD-2G transmitters; Holohil Systems Ltd., Carp,

ON Canada). Chicks were returned to the point of capture and remotely monitored via

telemetry until the hen returned (usually within minutes).

Using standard telemetry techniques, radiomarked chicks were relocated every two

days following Aldridge and Boyce (2007). When both telemetry and ush methods

failed to detect the presence of chicks, we continued to monitor the hen every two days

to conrm brood status. Chicks were monitored through 8 weeks of age, the age at which

chicks can survive independent of the hen (Schroeder, 1997; Schroeder et al., 1999).

Habitat measurements

We assessed vegetation characteristics at one brood use location per week for each

brood tracked—typically two days after the brood was located at the site. Behaviors

were not assessed at use locations, preventing us from separating different types of

use (i.e., foraging, roosting, dispersing). We estimated the percent cover and height of

vegetation classes according to methods outlined in Aldridge and Brigham (2002; see

Table 1 for a complete list of variables). A 1-m2 quadrat was placed at the identied use

site. To identify the scale at which habitat characteristics might be selected, we took

measurements at 8 additional quadrats placed 7.5 and 15 m (two in each of the 4 cardi-

nal directions) away from the use site. The areas enclosed within the 7.5-m “patch” (the

center quadrat and the 4 quadrats 7.5 m from the center quadrat) and the 15-m “area”

(all 9 quadrats) scales were 177 and 707 m2, respectively. To obtain a potentially more

accurate estimate of percent sagebrush canopy cover (hereafter cover) we measured the

line intercept (1-cm increments) of live green sagebrush along 4–15-m line transects ra-

diating from the use site in each cardinal direction (Caneld, 1941). Measurements were

recorded separately for the rst 0–7.5 m (patch scale) and the entire 0–15 m (area scale)

transect. We recorded the same measurements at a (dependent) random location within

100–500 m of each use site, using a random azimuth and distance from the use site. From

1998–2000, Aldridge and Brigham (2002) made these same habitat assessments at a

(independent) sample of brood locations, which we use to evaluate our occurrence mod-

els. Additional variables measured only in our study from 2001–2003 included residual

grass and percent litter cover in quadrats, and we used Robel pole (Robel et al., 1970)

measurements of vertical obstruction cover at 2.5-m intervals along all 4 line-intercept

transects (Table 1).

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 393

Table 1

Explanatory habitat variables, means, and standard errors (in parentheses) of values used to assess brood occurrence and chick survival for 139

brood sites and 139 paired random locations at “patch” (177 m2) and “area” (707 m2) scales in southeastern Alberta, 2001–2003. ForbOth was

not used in survival models. When grass was absent, grass height values were considered zero. Initially, models for brood occurrence were t

with parameters above the dashed line, evaluated using an independent dataset collected from 1998–2000, and then additional parameters mea-

sured only from 2001–2003 (below dashed line) were added to the top model. No independent data were available for evaluating the nal chick

survival model

Variable 177-m2 patch scale 707-m2 area scale

code Description Brood site Random site Brood Site Random site

SBint Sagebrush cover (%) estimated using line intercept 6.12 1.76 5.12 1.94

(0.52) (0.22) (0.42) (0.22)

SB Sagebrush cover (%) estimated with 1-m2 quadrats 8.85 2.79 7.05 2.95

(0.67) (0.34) (0.49) (0.30)

Bush Cover (%) of all shrubs (including sagebrush) 11.65 4.82 10.02 5.06

estimated with 1-m2 quadrats (0.77) (0.56) (0.65) (0.53)

Gr Grass cover (%) estimated with 1-m2 quadrats 21.20 20.27 21.69 20.65

(1.15) (1.30) (1.14) (0.28)

GrHgt Mean maximum grass height (cm) 35.82 30.50 35.38 30.66

within each 1-m2 quadrat (1.20) (1.20) (13.40) (1.15)

Forb Forb cover (%) estimated with 1-m2 quadrats 8.88 8.07 8.69 8.01

(0.77) (0.72) (0.70) (0.72)

ForbOth Unpalatable (other) forb cover (%) 0.60 0.94 0.62 0.94

estimated with 1-m2 quadrats (0.10) (0.12) (0.08) (0.11)

Robel Visual obstruction reading (height in cm) 10.30 4.95 9.16 5.20

measured at 2 m from pole (0.58) (0.48) (0.46) (0.47)

Resid Residual grass cover (%) estimated using 3.61 3.62 3.63 3.65

1-m2 quadrats (0.38) (0.38) (0.37) (0.37)

Litter Estimate of the cover (%) of litter 21.20 16.86 21.22 17.27

(dead organic matter) using 1-m2 quadrats (1.02) (0.92) (0.99) (0.87)

394 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

Chick survival

Date of death for a radiomarked chick was estimated as the date we failed to detect

the chick with the hen and no brooding behaviors were observed (see Aldridge and

Boyce, 2007). Chicks were recorded as having died on the date they were no longer

located with the hen.

DATA ANALYSES

We used a design IV approach (Erickson et al., 2001) to evaluate 4th-order (Johnson,

1980) sage-grouse brood habitat selection and chick survival. Our dependent locations

represented a random sample of unused control sites and were compared to used sites

(brood locations) for occurrence modeling using a case-control logistic regression. Sage-

grouse were not observed at any unused control sites and, given the low population density,

the proportion of control sites actually “used” by sage-grouse was low over the course of

our study (i.e., low contamination rate; Keating and Cherry, 2004). Thus, we generated a

resource selection function (RSF) contrasting used and control locations, which is propor-

tional to the probability of use (Manly et al., 2002; Keating and Cherry, 2004).

Survival analyses were based solely on used locations, comparing sage-grouse chicks

that survived (0) to those that died (1) over a particular interval. We assessed brood oc-

currence and chick survival at both measured scales (7.5-m patch and 15-m area) sur-

rounding the identied use and paired random locations. All analyses were conducted in

STATA 8.2 (STATA 2004).

Model development

A priori candidate brood occurrence models were developed using habitat data

collected from 2001–2003. These models were consistent with data collected from

1998–2000 (Aldridge and Brigham, 2002). Additional parameters (Robel, obstruction

cover; Resid, residual grass cover; and Litter, dead fallen matter) were then added in an

attempt to improve model t (Table 1).

Candidate chick survival models included all habitat variables as well as climate

covariates (Onefour Agriculture and Agri-food Canada Research Station, AAFC–AAC

2004 unpublished weather data). Small sample size limited the number of parameters we

were able to model for survival. Consequently, before testing a set of combined models

based on top models within the three groups, we chose to evaluate relative support for

candidate models within three general hypotheses describing chick survival: (1) climate,

(2) herbaceous cover and structure, and (3) sagebrush and shrub cover. We calculated

several climate variables used for survival models. Growing degree days (GDD) were

estimated as the number of degrees above 5º C for each mean daily temperature (Ball

et al., 2004), summed over the growing season (beginning 1 March and ending with the

tracking date of that year). We also developed a dryness index, which was the GDD for

that year divided by the cumulative spring precipitation since the 1 March beginning

of the growing season. We assessed all models for outliers and non-linearities (Hosmer

and Lemeshow, 1999, 2000), tested for colinearity between parameters (|r| > 0.7), and

assessed multicollinearity using variance ination factors (Menard, 1995).

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 395

Matched case-control occurrence analyses

We estimated an RSF for paired observations using a case-control logistic regression

and present coefcients for occurrence models as unstandardized linear estimates and

standard errors. This 1-to-1 matched case-control design (Hosmer and Lemeshow 2000:

223; Manly et al., 2002:150) constrains availability temporally and spatially within

similar range ecosite communities, controlling for factors that might otherwise lead to

incorrect null models or biases in habitat selection (Compton et al., 2002). We used the

Huber–White sandwich variance estimator to account for the lack of independence of

repeated habitat samples for the same brood (Pendergast et al., 1996).

Proportional hazards survival analyses

On average, chicks were relocated every 2.3 ± 0.09 days, allowing us to estimate dai-

ly survival rates using a Kaplan–Meier (KM) product limit estimator (Kaplan and Meier,

1958) with a staggered-entry design (Pollock et al., 1989; Winterstein et al., 2001). To

assess the effect of various habitat and climate covariates on chick survival, we used the

Cox proportional hazards regression model (Cox, 1972), which accommodates left and

right censoring (Andersen and Gill, 1982; Cleves et al., 2004). We used a shared frailty

model, which incorporates a latent random effect (Burnham and White, 2002) for each

brood (cluster) accounting for non-independence of chicks within broods (Cleves et al.,

2004; Wintrebert et al., 2005). We present coefcients for all survival models as hazard

ratios (exp[βi]) and standard errors.

We compared the basic KM chick survival function to the baseline cumulative survival

function without tting any covariates, but we did t a latent random effect for chicks

within broods. This method accounts for the lack of independence among siblings and

determines whether a shared frailty model is necessary. We developed Cox proportional

hazards models for each a priori candidate model using habitat (time varying) and cli-

matic (some time varying and some xed) covariates. Because we did not measure habitat

characteristics at every relocation, we carried forward habitat covariates across intervals,

assuming exposure was constant until the subsequent weekly habitat measurement loca-

tion. Independent climate variables were used for each interval (see results section).

Deaths with known “failure” times were partitioned using the Breslow estimation of

the continuous-time likelihood calculation (Cleves et al., 2004). We assessed the propor-

tional hazards assumption (Winterstein et al., 2001) for each candidate model (effects of

the covariates on survival do not change over time, except for ways in which the model

is already parameterized, Cleves et al., 2004). Models violating this assumption were

removed. We report survival estimates as means ± standard errors.

Model selection, assessment, and evaluation

We used an information-theoretic approach to model selection using Akaike’s Infor-

mation Criteria (AIC) with a correction for small sample size (AICc). We used the differ-

ences in AICc scores (Δi) to identify the best approximating occurrence or survival model

within the candidate set and AICc weights (wi) to assess the probability that a given model

was the best within the set of candidate models (Burnham and Anderson, 2002).

396 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

We used the Wald χ2 statistic (Hosmer and Lemeshow, 2000) to asses the t of each sur-

vival or occurrence model and estimated the variance explained by calculating the reduc-

tion in log-likelihood for the given model from the null model (deviance explained). For

survival models, we compared the “relative” deviance estimates between survival models

within the same set of candidate models, as outlined by Hosmer and Lemeshow (1999).

We used estimates of the receiver operating characteristic (ROC) area under the

curve (Fielding and Bell, 1997) to assess the predictive accuracy of top AICc-selected

occurrence models (Swets, 1988; Manel et al., 2001). The percent of correctly classied

(PCC) observations at the optimal cut-off was used to estimate the predictive capacity

of the top occurrence models (Nielsen et al., 2004). Predicted probabilities above the

optimal probability cut-off point (point that maximized both the sensitivity and specic-

ity curves; Swets, 1988; Nielsen et al., 2004; Liu et al., 2005) were classied as pres-

ence and those below the cutoff point were classied as absence. Prior to adding the

Robel, Resid, and Litter variables, we evaluated the top models developed with training

data (2001–2003) using an independent sample of 113 brood locations collected from

1998–2000 for 17 different broods (see Aldridge and Brigham, 2002).

To assess the t of the top combined AICc-selected chick survival models, we pre-

dicted cumulative hazard using the top model at each scale and tested for differences in

daily relative hazard for chicks that died (1) compared to those that survived (0) using

a t-test with unequal variances. Finally, we developed predictive survival curves for top

combination models to assess risk of chick mortality across the 90th percentile of the

range of availability for that parameter, while holding all other parameters at their mean

values. This allowed us to generate dose-response curves and suggest threshold levels

for the risk of chick mortality in relation to each parameter of interest based on the as-

ymptote of the curve. We could not generate similar curves for occurrence models due

to the conditional nature of the case-control analyses.

RESULTS

We tracked 24 broods from 2001–2003 and assessed vegetation characteristics at 139

brood sites: 42 sites from 8 broods in 2001, 15 sites from 3 broods in 2002, and 82 sites

from 13 broods in 2003. Habitat characteristics were measured at an average of 5.8 ±

0.86 sites for each brood. We captured a total of 130 chicks from 23 of the 24 tracked

broods, and radiomarked 41 chicks from 22 different broods. We obtained an average

of 11.0 (range 1–43) relocations per chick. One chick death was research related, two

chicks died from exposure (i.e., drowned in a spring rain storm), and two chicks moved

onto lands for which we could not obtain permission to access. Data on all individuals

were right censored on their last location date.

CANDIDATE MODELS

Sagebrush cover estimated by either the quadrat method (SB) or Caneld line inter-

cept method (SBint) was positively correlated at both spatial scales (r ≥ 0.87). Thus, only

one measure of sagebrush cover could be included in a given model. Grass height was

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 397

the only measure of vegetation height that was not correlated with its respective measure

of cover. All other correlated height variables were less predictive than cover estimates,

based on deviance explained in univariate models, and were not included in a priori

candidate models. Variable means at use and random locations are shown in Table 1.

Occurrence candidate models

Hypothesizing that selection for shrub cover might not be linear, we t both linear

and quadratic relationships for each shrub variable. The six different shrub component

variables were combined with six different combinations of herbaceous variables, result-

ing in 36 different a priori candidate models for sage-grouse brood occurrence (Table 2).

We present results only for occurrence models that represent the 90% condence set

(∑wi > 0.90). Additional parameters measured in 2001–2003 (visual obstruction cover

[Robel], residual grass cover [Resid], and litter ground cover [Litter]) were added to the

top model at each scale, resulting in six additional model combinations (Table 2c).

Survival candidate models

We examined seven different univariate climate models (Table 3), consisting of

various GDD and precipitation measures. The GDD model by itself violated the propor-

tional hazards assumption and was dropped from further analyses. The same six shrub

variables used for the brood occurrence analyses were used for chick survival models.

We used 13 different 1- and 2-parameter herbaceous component models (Table 4), which

we assessed both as stand-alone models and in combination with the shrub variables.

Model 12 violated the proportional hazards assumption and was dropped from our set

of candidate models.

Conditional xed-effects occurrence analyses

Tabular details for occurrence model results are shown in the Appendix. The top

brood occurrence models at both scales had weak support (wi < 0.90; Table A1), but

coefcient (βi) estimates were stable across all candidate models. When the additional

parameters were added to the top models at both spatial scales, they only marginally

increased predictive capacity and original models still had the most support (wi = 0.364

and 0.234, area and patch scales, respectively). We restricted our inferences about brood

site selection to the most parsimonious models, Model 10 and Model 28 (patch and area

scale, respectively).

Patch-scale brood occurrence

All ten highest ranked candidate models (∑wi > 0.90) contained sagebrush cover

estimated with the quadrat sampling method (SB), and the two best models included

the quadratic term. All models were highly predictive, explaining about 50% of the

variation (deviance explained) in brood occurrence (Table A1). Model #10 was the top

AICc-selected brood occurrence model and had good t (Wald χ2

4 = 43.96, p < 0.0001)

but weak support (wi = 0.16) within our set of candidate models. This model, however,

had great accuracy when predicted on both the training and testing data sets (ROCtrain =

398 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

Table 2

(a) Shrub and herbaceous component models used to generate a priori candidate brood occurrence

models based on 139 brood sites and 139 paired random locations in southeastern Alberta from

2001–2003 at the patch (177 m2) and area (707 m2) scales. (b) Each of the six shrub and herba-

ceous component models were combined into 36 different initial candidate models. (c) The model

structure of the top AICc-selected model when the additional parameters were added

(a)

Shrub component variables Herbaceous component variables

A = SB g = Gr

B = SB + SB2 h = Gr + GrHgt

C = Bush i = Gr + Forb

D = Bush + Bush2 j = Gr + GrHgt + Forb

E = SBint k = Forb + GrHgt

F = SBint + SBint2 l = Gr + GrHgt + Forb + ForbOth

(b)

# Sagebrush # Bush models # Sagebrush

quadrat models intercept models

1 A + g 13 C + g 25 E + g

2 B + g 14 D + g 26 F + g

3 A + h 15 C + h 27 E + h

4 B + h 16 D + h 28 F + h

5 A + i 17 C + i 29 E + i

6 B + i 18 D + i 30 F + i

7 A + j 19 C + j 31 E + j

8 B + j 20 D + j 32 F + j

9 A + k 21 C + k 33 E + k

10 B + k 22 D + k 34 F + k

11 A + l 23 C + l 35 E + l

12 B + l 24 D + l 36 F + l

(c)

Model # Additional parameter models

Top model (Top AICc-selected model for a given scale)

1 (Top model ) + Robel

2 (Top model ) + Resid

3 (Top model ) + Litter

4 (Top model ) + Robel + Resid

5 (Top model ) + Robel + Litter

6 (Top model ) + Resid + Litter

7 (Top model ) + Robel + Resid + Litter

0.992, ROCtest = 0.841) and excellent (84.1%) and good prediction (77.0%), respectively

(Table A2).

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 399

Inferences based on this top model indicate strong positive but decreasing selection

for sagebrush cover (concave function; Table A3). Hens selected strongly for taller grass

at brood sites, and weakly for greater percent forb cover (Table A3).

Area-scale brood occurrence

Of the 12 models at the area scale within the 90% condence set (Table A1), 8 con-

tained the SBint variable as either a linear or quadratic term, and all contained the GrHgt

variable. All models explained >41.0% of the variation in brood habitat selection, with

the top model (Model 28) explaining 44.1%. Similar to that of the patch-scale model, this

model had weak support (wi = 0.18) as the top candidate model, but it had good t (Wald

χ2

4 = 56.42, p < 0.0001) and good model accuracy for both training and testing datasets

(ROCtrain = 0.900, ROCtest = 0.802, Table A2). Model 28 also had good prediction (79%)

for the training dataset and reasonable prediction on the independent testing dataset (71%,

Table A2). Inference based on Model 28 at the area scale again indicated strong positive

but decreasing selection for sagebrush cover (concave function; Table A3). Broods were

found in areas with taller grass but avoided areas with greater grass cover.

PROPORTIONAL HAZARDS SURVIVAL ANALYSES

Using a basic Kaplan Meier (KM) curve, chick survival to 8 weeks (56 days) was

estimated at 0.296 ± 0.081 (Fig. 1). There were no between-year differences in survival

Table 3

Explanatory climate variables and models used to assess chick survival for 41 radiomarked chicks

from 22 different broods in southeastern Alberta, 2001–2003. Variables were generated for each

year that chicks were followed. Due to small sample sizes, a priori climate models consisted of

single parameters only

Model # Variable code Description

1a GDDb Cumulative growing degree days (above 5 ºC)

from 1 March to the chick location date

2 Sp_PPT_Cumm Cumulative growing season (since 1 March)

precipitation

3 Dry_Index An overall dryness index, calculated as the GDD

(above) divided by Sp_PPT_Cumm (above)

4 Sp_PPT_Prior Total spring (April through June) precipitation for the

prior spring

5 Sp-Su_PPT_Prior Total spring and summer precipitation (April though

August) of the prior year

6 Tot_PPT_Prior Total precipitation for the prior full calendar year

7 GDD_Prior Total growing degree days (above 5 ºC) from March

through August for the prior year

aThe GDD model was dropped due to violations of the proportional hazards assumption.

bAll weather data were provided by Onefour Agriculture and Agri-food Canada Research Station,

located in the study area (Onefour, Alberta, Canada).

400 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

(log rank χ2

2 = 2.86, p = 0.24) nor between rst (n = 33) and second (n = 8; log rank χ2

1 =

2.32, p = 0.13) nesting attempts, allowing us to pool data for further survival analyses.

The baseline hazard chick survival model using the shared frailty produced lower

survival estimates to 56 days (0.123) than the KM estimate, and was outside the 95%

CI for the KM model (range 0.151 to 0.497, Fig. 1). The estimate of the frailty variance,

theta (θ = 0.96), was large and signicant at α = 0.10 (likelihood ratio χ2

1 = 1.87, p =

0.086). Therefore we t a shared frailty model for all candidate models.

Climate chick survival models

Of the six climate models tested, Model 3 (dryness index only) was the top AICc-se-

lected model. This model had only moderate support (wi = 0.34), but it had reasonable

t (Wald χ2

1 = 3.48, p = 0.06). By itself, the dryness index explained more than twice

as much variation in chick survival as any other individual climate variable (10.97%).

Climate Model 3 (Dry_Index) was selected for use in our combined models.

Shrub chick survival models

Tabular details for survival model results are shown in the Appendix. At the patch

scale, the top AICc-selected chick proportional hazards shrub model contained the SB

variable, suggesting a linear relationship with chick survival (Table A4). This model (#1)

had only moderate support (wi = 0.44), but the Akaike weight was more than double the

second best model (SBint). The model had signicant t (Wald χ2

1 = 6.13, p = 0.01),

Table 4

Candidate models used to identify the shrub and herbaceous models that best predicted sage-

grouse chick survival for 41 radiomarked chicks from 22 different broods in southeastern Alberta,

2001–2003. We did not have an independent testing dataset for candidate models containing “ad-

ditional” parameters (Resid, Robel, and Litter)

Shrub Shrub component Herbaceous Herbaceous component

Model # variables model # variables

1 SB 1 Forb

2 SB + SB2 2 Forb + Gr

3 Bush 3 Forb + Robel

4 Bush + Bush2 4 Forb + Resid

5 SBint 5 Robel

6 SBint + SBint2 6 Robel + GrHgt

7 Robel + Resid

8 Gr + GrHgt

9 Resid + GrHgt

10 Litter

11 Litter + Forb

12a Litter + Robel

13 Litter + GrHgt

aHerbaceous model #12 was dropped due to violations of the proportional hazards assumption.

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 401

explained 14.22% of the variation, and was used for combined model building at the

patch scale.

At the area scale, the top AICc-selected chick proportional hazards model contained

the quadratic for sagebrush estimated with the line intercept method (SBint + SBint2;

Table A4). This model had moderate support (wi = 0.34) and the Akaike weight was

about twice that of the next best model. This model had good t (Wald χ2

1 = 6.09, p <

0.05) and explained the most variation within the candidate set at this scale (22.56%

deviance explained, Table A4). We used shrub Model 6 (SBint + SBint2) for combined

candidate models at the area scale.

Herbaceous chick survival models

At both the patch and area scales, Model 8 (Gr + GrHgt) was the top AICc-selected

herbaceous survival model (Table A5). At the patch scale this model had weak support

Fig. 1. Kaplan Meier (KM) cumulative chick survival curves for 41 radiomarked sage-grouse

chicks from 22 different broods in southeastern Alberta, 2001–2003. The basic KM curve (solid

line) does not take into account the correlation of marked chicks within the same brood, whereas

the frailty model (dashed line) represents the baseline Cox proportional hazard survival (i.e., no

covariates) and accounts for lack of independence of siblings within the same brood. We could not

generate 95% condence intervals for the frailty model due to the conditional nature of the Cox

model on covariates within the model.

402 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

(wi = 0.30) and moderate t (Wald χ2

1 = 4.76, p = 0.09), but explained the greatest devi-

ance (18.53%) of all herbaceous models. Similarily, at the area scale, Model 8 had a poor

t (Wald χ2

1 = 3.70, p = 0.16) and weak support (wi = 0.20), but explained the greatest

deviance (14.35%; Table A5). We retained Model 8 as the herbaceous model for com-

bined survival models at both scales.

Combination chick survival models

Using the top shrub and herbaceous models for each spatial scale, and the top climate

model, we developed seven candidate models for each scale. The candidate model set

consisted of the top models from each group and all possible combinations of these mod-

els (Table A6). The patch scale combination model SB + Dry_Index failed to converge

and was removed.

Model 5, which contained a climate and herbaceous component, was the top AICc-

selected model at the patch scale (Table A7). This model had good t (Wald χ2

1 = 12.12,

p = 0.007), moderate support (wi = 0.65), and explained 42.68% of the variation in sur-

vival. Risk of chick mortality increased as the drought index increased, was strongly re-

duced with increased grass cover, but increased with grass height (Table A8). Threshold

response curves suggested a signicant reduction in risk to sage-grouse chicks if grass

cover was greater than about 20–25% (Fig. 2a). Although risk increased with increas-

ing grass height, this risk is realized only when grass height is greater than ca. 40 cm

(Fig. 2b). The model also demonstrates that the moderate-to-high dryness index values

dramatically increase the risk of chick death (Fig. 2c).

At the area scale, Model 6 was the top AICc-selected survival model (Table A7).

This model had good t (Wald χ2

1 = 16.74, p = 0.005), strong support as the top can-

didate model (wi = 0.91), and explained considerably more variation in chick survival

(58.27%) than any other model. Risk of death again increased with the dryness index,

and was positive but decreasing with sagebrush cover (Table A8), suggesting higher

chick survival in less dense sagebrush habitats. Risk of chick death was slightly re-

duced with increased grass cover but increased with grass height (Table A8). Threshold

response curves indicate that the relative risk of chick death increased with greater

sagebrush cover, and tailed off in denser sagebrush habitats (Fig. 3a). Risk was higher

above about 3% sagebrush cover (line-intercept) but was reduced if cover was greater

than ~9%. Similar to the patch-level threshold curves (Fig. 3a), risk was reduced

with increased grass cover at the area scale, but the threshold was lower (>5% cover,

Fig. 3b). Risk also increased with increasing grass height at the area scale, but only

when grass was taller than about 30–35 cm (Fig. 3c). Again, the area-level-threshold

model also illustrates that hot and dry growing seasons (high dryness index values)

reduce chick survival (Fig. 3d).

Both the patch- and area-scale models validated well on the within-sample training

dataset. The mean daily hazard was signicantly greater for chicks that died within the

56-day monitoring period compared to those that survived or were censored (patch

scale: t37.2 = 4.17, p < 0.001; area scale: t31.9 = 3.73, p < 0.001). Based on model covari-

ates, chicks that died were exposed to more hazardous or risky conditions.

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 403

Fig. 2. Threshold response curves for the top AICc-selected model (combined Model #5) at the

patch scale (177 m2) for relative risk (hazard) for sage-grouse chicks in southeastern Alberta, from

2001–2003. Responses are shown across the 90th percentile of availability for each parameter in

the model while holding the other parameters in the model at their mean values.

404 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

DISCUSSION

Our results highlight the importance of accounting for tness components when as-

sessing wildlife–habitat relationships (Van Horne, 1983; Morrison, 2001; Aldridge and

Boyce, 2007). Sage-grouse may not always select for habitat characteristics (e.g., high

selection for dense sagebrush cover and tall grasses) that enhance tness measured by

chick survival (e.g., increased chick mortality in dense sagebrush and in sites with tall

[>35 cm] grasses). Thus, management efforts should strive to maintain and enhance

habitats that are likely to increase survival, in addition to those selected by the birds. For

this population, dening brood habitat requirements as those that enhance juvenile sur-

vival, and ultimately recruitment, are necessary to appropriately identify management

needs for the species (Aldridge and Brigham, 2001; Crawford et al., 2004).

Overall, we were able to explain 44–50% of sage-grouse brood habitat selection and

chick survival using only climatic and habitat covariates. Dose-response curves from

survival models allowed us to generate threshold levels for habitat variables such as

sagebrush cover, grass cover, and grass height, which will allow for enhanced chick

survival. These thresholds provide initial targets for managing sage-grouse brood-rear-

ing habitat in Alberta.

Fig. 3. Threshold response curves for the top AICc-selected model (combined Model #6) at the

area scale (707 m2) for relative risk (hazard) for sage-grouse chicks in southeastern Alberta, from

2001–2003. Responses are shown across the 90th percentile of availability for each parameter in

the model while holding the other parameters in the model at their mean values.

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 405

Similar to previous studies, we conclude that the lack of forb-rich habitats that exist

in this study likely contributed to the observed selection of sagebrush throughout the

brood-rearing period (Aldridge and Brigham, 2002). Although we detected selection

for forbs at the patch scale, a similar pattern was not evident at the area scale. Some of

the herbaceous survival models that contained forbs had reasonable deviance explained

(Table A5), yet none of the patch- or area-scale chick survival models containing forbs

were selected as the most predictive model. However, as suggested (but not assessed)

in other studies (Peterson, 1970; Schoenberg, 1982; Drut et al., 1994a; Sveum et al.,

1998; Aldridge and Brigham, 2002), the risk of chick death in our study was reduced

with greater forb cover, but the effect was weak (95% CI overlapped 1). The uniformly

low availability of forbs in southeastern Alberta may limit our ability to detect differ-

ences in selection and survival relative to forb availability. If forbs are important for

survival but abundance is low everywhere, survival rates may be uniformly low relative

to forb cover, limiting variation in survival and our ability to detect trends. More than 50

marked individuals (41 in our study) might also be required to generate robust survival

estimates (Winterstein et al., 2001).

The scale of habitat measurement appeared to play a minor role in chick survival and

habitat selection. Chick mortalities were predicted by grass cover and height at both the

patch and area scales. Taller grass at both spatial scales appeared to have negative con-

sequences for chick survival, but threshold models illustrate that habitats are not risky

until grass is taller than 35–40 cm (Figs. 2b,3c). Hens appear to recognize this, selecting

only moderately for tall grass at both scales. Conversely, patches containing grass cover

beyond 20–25% (Fig. 2a) greatly reduced the risk of chick mortality.

However, hens appear not to recognize tness ties to greater grass cover, showing

strong avoidance of dense grass cover. While dense grass cover may reduce the risk of

chick mortality, hens may be forced to make a trade-off between these less risky grass-

dominated habitats and foraging on forbs and insects in mesic habitats that are open and

thus, more risky (less grass and structural cover). The low availability of mesic forb-rich

habitats in Alberta may force hens to spend more time meeting dietary requirements, which

may put their chicks, and possibly themselves, at greater risk of predation—an ecological

trap (Delibes et al., 2001; Breininger and Carter, 2003). In Alberta, management strategies

that enhance cover of grass and increase the abundance of mesic habitats to elevate forb

abundance would enhance habitat quality and population viability for sage-grouse. Further

research is required to understand these relationships, possibly in larger populations with

more variability in forb abundance and where larger sample sizes could be obtained.

Our results suggest that precipitation and climate (dryness index) play a pivotal role

in sage-grouse chick survival. Spring precipitation has long been suggested to correlate

with sage-grouse productivity (June, 1963; Gill, 1966; Schroeder et al., 1999), but

until now quantitative studies addressing its effects have not been conducted. Warm

years with high amounts of precipitation in the growing season likely result in greater

structural growth and protective cover. This may enhance nesting success (June, 1963;

Aldridge and Brigham, 2002) and can elevate chick survival. Precipitation prevents forb

desiccation and enhances insect abundance, both of which are important food resources

406 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

for sage-grouse chicks (Klebenow and Gray, 1968; Dunn and Braun, 1986; Johnson and

Boyce, 1990; Drut et al., 1994b).

Although we cannot manage climate to benet sage-grouse populations, it is important

to recognize that weather patterns are highly variable and will affect chick survival. To

ensure that populations remain viable when subjected to stochastic events, such as extreme

weather or disease outbreaks, it would be important for managers to ensure the availability

of high-quality brood-rearing habitats that encourage sage-grouse use and maximize sur-

vival (and reproduction) when using those habitats. Ensuring these habitats are in proximity

to high-quality nesting habitats within a landscape context (Aldridge and Boyce, 2007) will

increase the probability that hens will use these habitats and successfully edge chicks.

An obvious and interesting difference in factors affecting chick survival was evident

between models at patch and area scales. While sagebrush cover was an important

component of the area-scale model, no sagebrush or shrub variables entered into the top

model at the patch scale. This lack of relationship with sagebrush cover and survival at the

patch scale was surprising, given that brood occurrence models indicated that brood hens

select strongly for moderate ranges of sagebrush cover. Previous research has shown that

sage-grouse select for sagebrush cover early in the brood-rearing cycle, prior to moving

away from sagebrush uplands (Patterson, 1952; Dunn and Braun, 1986) and into forb-rich

mesic habitats containing 14–40% forb cover (Peterson, 1970; Schoenberg, 1982; Drut et

al., 1994a). However, avoidance of dense sagebrush during brood-rearing has also been

detected in Washington (Sveum et al., 1998). While hens move their chicks into sage-

brush habitats, it appears to compromise chick survival and might be maladaptive, again

resulting in an ecological trap (Delibes et al., 2001; Donovan and Thompson, 2001; Bock

and Jones, 2004). This is signicant, given that reproduction and juvenile survival drive

population dynamics for sage-grouse (Johnson and Braun, 1999).

We strongly suggest that future studies assessing wildlife–habitat relationships con-

sider both processes that determine habitat quality for a given species: occurrence and

tness (Van Horne, 1983; Morrison, 2001; Aldridge and Boyce, 2007). Selection by

individuals for certain resources may not result in tness enhancements. Thus, man-

agement objectives developed based on occurrence information alone may result in

misguided conservation efforts, as we have demonstrated for sage-grouse in Alberta.

Whereas tness data often are more difcult and costly to gather, we encourage fur-

ther research into occurrence–tness relationships, across local and landscape scales

(Aldridge and Boyce, 2007). The techniques we used here for linking occurrence and

survival, although limited in wildlife and conservation elds, offer a proven and prom-

ising approach for accurately assessing habitat quality and developing habitat-based

population viability assessments for a variety of species (Boyce et al., 1994; Boyce and

McDonald, 1999; Aldridge and Boyce, 2007).

ACKNOWLEDGMENTS

We thank all the landowners who allowed us to conduct our research on their lands.

This research was supported by the Alberta Conservation Association; Alberta Sustain-

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 407

able Resource Development; Alberta Sport Recreation Parks and Wildlife Foundation;

Cactus Communications (Medicine Hat, Alberta); Challenge Grants in Biodiversity;

Endangered Species Recovery Fund (World Wildlife Fund Canada and the Canadian

Wildlife Service); Esso Imperial Oil, Manyberries, Alberta; Murray Chevrolet, Medi-

cine Hat, Alberta; the North American Waterfowl Management Plan; and the University

of Alberta. C.L. Aldridge was personally supported by the Andrew Stewart Memorial

Graduate Prize, Bill Shostak Wildlife Award, Dorothy J. Killam Memorial Graduate

Prize, Edmonton Bird Club Scholarship, Izaak Walton Killam Memorial Scholarship,

John and Patricia Schlosser Environment Scholarship, Macnaughton Conservation

Scholarship, and Natural Science and Engineering Research Council Scholarship. C.

Nielsen and H. Beyer provided valuable GIS assistance. C. Johnson, J. Frair, S. Nielsen,

and M.M. Club assisted with statistical issues. T. Bush, J. Carpenter, L. Darling, C.

Dockrill, Q. Fletcher, J. Ng, M. Olsen, J. Saher, J. Sanders, D. Sharun, M. Swystun, and

M. Watters assisted with eld data collection. D. Eslinger and J. Nicholson assisted with

logistics. E. Bork, D. Coltman, M. Gillingham, S. Hannon, J. Saher, D. Neubaum, G.

Chong, W. Wetzel, C. Melcher, D. Howerter, and one anonymous reviewer improved

previous drafts of this manuscript.

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412 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

APPENDIX

Table A1

Rankings by Akaike’s information criterion corrected for small sample size (AICc) for brood

occurrence models, difference in AICc value between the ith and top-ranked model (Δi), and

Akaike weights (wi) for all models within a cumulative summed AICc weight (∑wi) of 0.90 for 139

brood locations at the patch (177 m2) and area (707 m2) scale for greater sage-grouse in Alberta,

2001–2003. All model Wald χ2 tests were signicant at p < 0.0001. Percent deviance explained

(Dev. exp.) indicates the reduction in the log-likelihood from the null model

Model Model Model % Dev.

# structure AICc Δi wi ∑ wi Wald χ2 exp.

Patch 10 SB + SB2 + Forb + 104.803 0.000 0.163 0.163 43.96 49.92

GrHgt

4 SB + SB2 + Gr + 104.925 0.121 0.153 0.316 43.97 49.86

GrHgt

3 SB + Gr + GrHgt 105.270 0.467 0.129 0.446 39.40 48.58

9 SB + Forb + GrHgt 105.400 0.597 0.121 0.567 39.41 48.51

8 SB + SB2 + Gr + 105.501 0.698 0.115 0.682 49.15 50.67

GrHgt + Forb

7 SB + Gr + GrHgt + 106.007 1.204 0.089 0.771 44.33 49.29

Forb

12 SB + SB2 + Gr + 107.574 2.770 0.041 0.812 59.42 50.73

GrHgt + Forb + ForbOth

6 SB + SB2 + Gr + Forb 107.739 2.936 0.038 0.849 43.98 48.39

11 SB + Gr + GrHgt + 108.043 3.240 0.032 0.882 55.28 49.35

Forb + ForbOth

5 SB + Gr + Forb 108.846 4.043 0.022 0.903 35.23 46.72

Area 28 SBint + SBint2 + 116.021 0.000 0.182 0.182 56.42 44.10

Gr + GrHgt

27 SBint + Gr + GrHgt 116.876 0.855 0.119 0.301 53.00 42.55

36 SBint + SBint2 + Gr + 117.212 1.192 0.100 0.401 81.46 45.73

GrHgt + Forb + ForbOth

32 SBint + SBint2 + Gr + 117.394 1.374 0.092 0.493 62.47 44.50

GrHgt + Forb

35 SBint + Gr + GrHgt + 117.395 1.374 0.092 0.584 73.14 44.50

Forb + ForbOth

31 SBint + Gr + GrHgt + 118.150 2.129 0.063 0.647 56.97 42.99

Forb

4 SB + SB2 + Gr + GrHgt 118.435 2.414 0.054 0.701 46.33 42.84

34 SBint + SBint2 + Forb + 118.504 2.484 0.053 0.754 40.43 42.81

GrHgt

10 SB + SB2 + Forb + 118.838 2.817 0.044 0.798 44.66 42.64

GrHgt

33 SBint + Forb + GrHgt 119.044 3.023 0.040 0.839 32.95 41.43

3 SB + Gr + GrHgt 119.220 3.199 0.037 0.875 47.98 41.34

9 SB + Forb + GrHgt 119.233 3.212 0.037 0.912 39318 41.33

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 413

Table A2

Comparison of top AICc-selected brood occurrence models, metrics for overall model signicance, model t, and classication accuracy for both

training (139 brood sites from 2001–2003) and testing data (113 brood sites from 1998–2000) across different scales for greater sage-grouse in

Alberta. All model Wald χ2 tests were signicant at p < 0.0001. Percent deviance explained (Dev. exp.) indicates the reduction in the log-likeli-

hood from the null model. The area under the receiver operating characteristic curves (ROC [SE]) and the percent correctly classied (PCC)

observations based on the training dataset’s optimal cutoff point were used to assess model classication accuracy

Scale Model Model % Dev. Optimal Training data Testing data

# AICc-selected model AICc Wald χ2 exp. cutoff ROC PCC ROC PCC

177-m2- 10 SB + SB2 + Forb + GrHgt 104.803 43.96 49.92 0.5012 0.992 84.17 84.09 76.99

patch scale (0.015) (0.027)

707-m2-

area scale 28 SBint + SBint2 + Gr + GrHgt 116.021 56.42 44.10 0.5014 0.900 79.14 0.8024 70.80

(0.017) (0.029)

414 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

Table A3

Estimated coefcients (βi), standard errors (shown in parentheses), and 95% condence intervals

for top AICc-selected candidate brood occurrence models for greater sage-grouse in southeastern

Alberta. Models were developed on 139 brood sites and 139 paired random locations collected

from 2001–2003

Condence Condence

intervals intervals

Patch scale Lower Upper Area scale Lower Upper

Variable Model #10 Model #28

SB 0.460 0.296 0.623

(0.083)

SB2 –0.007 –0.009 –0.004

(0.001)

SBint 0.757 0.425 1.090

(0.170)

SBint2 –0.024 –0.039 –0.009

(0.008)

Gr –0.040 –0.062 –0.017

(0.011)

GrHgt 0.058 0.010 0.107 0.115 0.060 0.170

(0.025) (0.028)

Forb 0.038 –0.004 0.080

(0.021)

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 415

Table A4

AICc-selected shrub variable proportional hazards chick survival models and Akaike weights (wi) for all models at the 177-m2-patch and 707-m2-

area scales for 41 chicks in southeastern Alberta, 2001–2003. The Wald χ2 indicates the t of the model to the data, and K indicates the number

of model parameters estimated, which includes the covariates and the estimate of the random effect (theta). Theta is the estimate of the shared

frailty variance and the p-value for the likelihood ratio tests (LR) for the signicance of the correlation. Percent deviance explained (Dev. exp.)

indicates the reduction in the log-likelihood from the null model

Model # Shrub model Theta LR Log- Model Model Dev.

structure estimate p-value likelihood K AICc Δi AICc wi Wald χ2 χ2 p-value exp. (%)

177-m2-patch scale

1 SB <0.001 0.437 72.022 2 148.616 0.000 0.441 6.13 0.013 14.22

5 SBint 0.052 0.483 72.854 2 150.279 1.663 0.192 3.96 0.047 8.07

2 SB + SB2 <0.001 0.500 71.974 3 151.149 2.532 0.124 5.91 0.052 14.56

3 Bush 0.777 0.158 73.363 2 151.298 2.682 0.115 1.08 0.30 4.08

4 Bush + Bush2 0.805 0.169 72.522 3 152.244 3.628 0.072 2.60 0.272 10.57

6 SBint + SBint2 <0.001 0.466 72.777 3 152.755 4.138 0.056 4.25 0.120 8.65

707-m2-area scale

6 SBint + SBint2 0.348 0.342 70.795 3 148.790 0.000 0.346 6.09 0.048 22.56

4 Bush + Bush2 0.805 0.154 71.455 3 149.924 1.134 0.196 4.34 0.114 9.42

1 SB 0.059 0.475 72.676 2 150.111 1.321 0.179 4.30 0.038 18.18

2 SB + SB2 0.109 0.455 72.034 3 151.046 2.257 0.112 4.65 0.098 5.08

5 SBint 0.326 0.351 73.237 2 151.267 2.478 0.100 2.02 0.155 14.14

3 Bush 0.871 0.125 73.759 2 152.089 3.300 0.066 0.22 0.636 0.86

416 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

Table A5

AICc-selected herbaceous variable proportional hazards chick survival models and Akaike weights (wi) for all models at the patch (177 m2) and

area (707 m2) scale for 41 chicks in southeastern Alberta, 2001–2003. The Wald χ2 indicates the t of the model to the data, and K indicates the

number of model parameters estimated, which includes the covariates and the estimate of the random effect (theta). Theta is the estimate of the

shared frailty variance and the p-value for the likelihood ratio tests (LR) for the signicance of the correlation. Percent deviance explained (Dev.

exp.) indicates the reduction in the log-likelihood from the null model

Model Model Theta LR Model Model Dev.

# structure estimate p-value K AICc Δi AICc wi Wald χ2 χ2 p-value exp. (%)

Patch 8 Gr + GrHgt 0.215 0.352 3 150.007 0.000 0.300 4.76 0.093 18.53

2 Forb + Gr <0.001 0.500 3 151.412 1.405 0.149 4.83 0.089 13.62

1 Forb 0.798 0.110 2 151.696 1.689 0.129 0.60 0.439 2.47

5 Robel 0.923 0.091 2 152.234 2.227 0.098 0.06 0.801 0.26

10 Litter 0.939 0.099 2 152.290 2.283 0.096 0.01 0.930 0.03

4 Forb + Resid 0.403 0.351 3 153.998 3.991 0.041 1.35 0.509 3.79

11 Litter + Forb 0.800 0.115 3 154.324 4.318 0.035 0.60 0.742 2.48

3 Forb + Robel 0.798 0.110 3 154.325 4.318 0.035 0.60 0.741 2.47

6 Robel + GrHgt 0.909 0.100 3 154.494 4.487 0.032 0.43 0.808 1.78

9 Resid + GrHgt 0.789 0.170 3 154.590 4.583 0.030 0.37 0.832 1.39

7 Robel + Resid 0.723 0.190 3 154.706 4.700 0.029 0.29 0.867 0.91

13 Litter + GrHgt 0.976 0.096 3 154.759 4.752 0.028 0.17 0.920 0.69

Area 8 Gr + GrHgt 0.296 0.307 3 151.208 0.000 0.202 3.70 0.157 14.35

1 Forb 0.779 0.117 2 151.920 0.713 0.142 0.40 0.529 1.56

5 Robel 0.878 0.099 2 151.995 0.787 0.136 0.30 0.583 1.25

2 Forb + Gr 0.034 0.483 3 152.119 0.911 0.128 4.02 0.134 11.04

10 Litter 0.995 0.083 2 152.248 1.040 0.120 0.05 0.822 0.21

4 Forb + Resid 0.201 0.444 3 154.248 3.040 0.044 1.61 0.448 2.79

6 Robel + GrHgt 0.843 0.115 3 154.289 3.081 0.043 0.62 0.734 2.62

3 Forb + Robel 0.779 0.118 3 154.439 3.231 0.040 0.50 0.777 2.01

11 Litter + Forb 0.805 0.114 3 154.490 3.282 0.039 0.45 0.800 1.80

7 Robel + Resid 0.745 0.204 3 154.584 3.376 0.037 0.39 0.822 1.41

13 Litter + GrHgt 1.016 0.083 3 154.814 3.606 0.033 0.11 0.944 0.47

9 Resid + GrHgt 0.802 0.188 3 154.817 3.610 0.033 0.14 0.933 0.45

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 417

Table A6

Overall combined candidate proportional hazards chick survival models for 41 radiomarked

chicks from 22 different broods at the patch (177 m2) and area (707 m2) scales in southeastern

Alberta, 2001–2003. The top climate (Climate), shrub (Shrub), and herbaceous (Herb) models

were used at each scale for combination models. The top within each group was also considered

as candidate models within this set. The patch-scale model with the combination of sagebrush and

the dryness index (SB + Dry _Index) would not converge on a Maximum Likelihood estimate and

was therefore not estimated

Model Patch scale Model Area scale

# combination models # combination models

1st Shrub 1- SB 1st Shrub 1- SBint + SBint2

1st Herb 2- Gr + GrHgt 1st Herb 2- Gr + GrHgt

1st Climate 3- Dry_Index 1st Climate 3- Dry_Index

4- SB + Gr + GrHgt 4- SBint + SBint2 + Gr +

GrHgt

5- Gr + GrHgt + Dry_Index 5- Gr + GrHgt

Dry_Index

6- SB + Dry_Index + Gr + 6- SBint + SBint2 +

GrHgt Dry_Index + Gr +

GrHgt

418 C.L. ALDRIDGE AND M.S. BOYCE Isr. J. Ecol. Evol.

Table A7

AICc-selected combined proportional hazards chick survival models and Akaike weights (wi) for all models at the patch (177 m2) and area

(707 m2) scales for 41 chicks in southeastern Alberta, 2001–2003. The Wald χ2 indicates the t of the model to the data, and K indicates the

number of model parameters estimated, which includes the covariates and the estimate of the random effect (theta). Theta is the estimate of the

shared frailty variance and the p-value for the likelihood ratio tests (LR) for the signicance of the correlation is presented. Percent deviance

explained (Dev. exp.) indicates the reduction in the log-likelihood from the null model

Model # Combined Theta LR Log- Model Model Dev.

model structure estimate p-value Likelihood K AICc Δi AICc wi Wald χ2 χ2 p-value exp. (%)

177-m2-patch scale

5 Dry_Index + Gr + <0.001 0.500 67.184 4 144.474 0.000 0.650 12.12 0.007 42.68

GrHgt

6 SB + Dry_Index + <0.001 0.500 67.053 5 147.440 2.966 0.148 13.11 0.011 43.30

Gr + GrHgt

1 SB <0.001 0.437 72.022 2 148.616 4.142 0.082 6.13 0.013 14.22

3 Dry_Index <0.314 0.283 72.468 2 149.508 5.034 0.052 3.48 0.062 10.97

2 Gr + GrHgt 0.215 0.352 71.403 3 150.007 5.533 0.041 4.76 0.093 18.53

4 SB + Gr + GrHgt 0.001 0.500 70.362 4 150.829 6.355 0.027 8.18 0.042 25.31

707-m2-area scale

6 SBint + SBint2 + 0.314 0.283 63.377 5 140.087 0.000 0.905 16.74 0.005 58.27

Dry_Index + Gr +

GrHgt

1 SBint + SBint2 0.348 0.342 70.795 2 146.161 6.074 0.043 6.09 0.048 22.56

5 Dry_Index + Gr + 0.034 0.483 68.299 4 146.704 6.617 0.033 10.55 0.014 37.10

GrHgt

3 Dry_Index 0.779 0.117 72.468 2 149.508 9.421 0.008 3.48 0.062 10.97

4 SB + Gr + GrHgt 0.878 0.099 69.893 4 149.892 9.805 0.007 7.49 0.112 28.17

2 Gr + GrHgt 0.296 0.307 72.003 3 151.208 11.121 0.003 3.70 0.157 14.35

VOL. 54, 2008 ASSESSING OCCURRENCE AND FITNESS 419

Table A8

Estimated hazard ratios (exponentiated coefcients—exp[βi]), standard errors (shown in parenthe-

ses), and condence intervals for top AICc-selected candidate proportional hazards chick survival

combined models for 41 chicks from 22 different broods in southeastern Alberta, 2001–2003. The

top combined model at both scales had the Dry_Index, the Gr + GrHgt herbaceous component

model, and a sagebrush component

Condence Condence

Patch scale intervals Area scale intervals

Variable model # 5 Lower Upper model # 6 Lower Upper

Dry_Index 1.441 1.123 1.850 1.707 1.256 2.321

(0.183) (0.268)

SBint 2.068 1.230 3.479

(0.549)

SBint2 0.941 0.898 0.985

(0.022)

Gr 0.932 0.882 0.985 0.953 0.894 1.017

(0.026) (0.031)

GrHgt 1.056 1.015 1.098 1.076 1.025 1.130

(0.021) (0.027)