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Ruffed grouse selection of drumming sites in the Black Hills National Forest.

INTRODUCTION

Ruffed grouse (Bonasa umbeUus) are the management indicator species for the condition of quaking aspen (Populus tremuloides) in the Black Hills National Forest of western South Dakota and northeastern Wyoming (BHNF; U.S. Forest Service, 1997) because of their dependence on multiple age-classes of aspen (Populus spp.) for food and cover (Bump et al., 1947; Gullion and Svoboda, 1972; Kubisiak, 1985, 1989). Given their status and popularity as a game bird, there has been interest by the U.S. Forest Service and South Dakota Department of Game, Fish and Parks to assess the status of ruffed grouse in the Black Hills and develop greater knowledge of the vegetative features that influence ruffed grouse occurrence. Recent ruffed grouse drumming surveys showed that the probability of ruffed grouse occupying a sample site (550-m buffer surrounding the survey point) was positively associated with the amount of aspen-dominated vegetation within the site (Hansen, 2009). Results from that study describe ruffed grouse selection of dominant vegetation types at a landscape scale (95 ha), but do not consider micro-site vegetation attributes that might also influence selection.

During the spring, male ruffed grouse "drum" on elevated structures, such as fallen logs, stumps and rocks to attract females and maintain their territory (Bump et al., 1947). Thus, characteristics of the drumming structure (e.g., height, diameter, length) and the adjacent vegetation (e.g., stem density, basal area, visibility, overstory canopy cover) might be important in the selection of drumming sites. Studies investigating the selection of ruffed grouse drumming sites throughout the United States and Canada have found that selection is positively correlated with the amount of understory cover (Stoll et al., 1979; Palmer, 1963; Thompson et al., 1987; Stauffer and Peterson, 1985; Buhler and Anderson, 2001). However, not all studies agree that drumming structure characteristics affect ruffed grouse site selection of drumming sites. No research has been conducted in the BHNF to determine the characteristics associated with ruffed grouse selection of drumming sites and whether factors affecting selection of drumming sites are similar to previously recorded relationships.

Understanding selection of drumming sites is an important complement to landscape-scale investigations of occupancy (Hansen, 2009) because forest management at multiple scales might be necessary to improve the quality of ruffed grouse habitat (e.g., Fearer and Stauffer, 2003) in the BHNF. Our objective was to determine the characteristics associated with ruffed grouse selection of drumming sites in the BHNF and ascertain the relative importance of drumming structure and adjacent vegetation on selection of drumming sites.

METHODS

STUDY AREA

The BHNF is located in the western portion of South Dakota and includes the Bear Lodge Mountains of northeastern Wyoming (Fig. 1). Elevation ranges from 1066 m-2207 m. Annual rainfall in the BHNF exceeds 50.8 cm per year and varies with elevation (Ball et al., 1996). The BHNF encompasses 500,000 ha and consists mostly of ponderosa pine (Pinus ponderosa, 84%), quaking aspen/paper birch (Betula papyrifera, 4%) and white spruce (Picea glauca, 2%). Other vegetation types comprise <10% of the BHNF and include bur oak (Quercus macrocarpa), hop-hornbeam (Ostrya virginiana) and green ash (Fraxinus pennsylvanica) (Hoffman and Alexander, 1987; Froiland, 1990). Common shrubs include western snowberry (Symphoricarpos occidentalis), white coralberry (S. albus), kinnikinnick (Arctostaphylos uva-ursi) and common juniper (Juniperus comunis) (Hoffman and Alexander, 1987; Severson and Thilenius, 1976).

FIELD METHODS

During spring 2007 and 2008, we completed ruffed grouse drumming surveys on the northern two-thirds of the BHNF (Hansen, 2009). When we heard a grouse drumming during a survey, we completed the 5 min survey (to maintain the monitoring protocol) then immediately located the drumming ruffed grouse. Ruffed grouse are typically faithful to one "primary" structure and, occasionally, use 1-5 "alternate" structures within 100 m of the primary structure (Bump et al., 1947; Gullion, 1967; Archibald, 1974; Kubisiak, 1989; Lovallo et al., 2000). To determine whether a structure was primary or alternate, we counted the number of droppings on the structure. We assumed a structure with [greater than or equal to] 20 droppings was the primary structure because it had been visited for an extended period of time by a ruffed grouse (Gullion, 1967). We only considered primary structures in our analyses.

[FIGURE 1 OMITTED]

For each unique drumming site, we characterized the drumming structure and vegetation within 12.5 m of the structure. Ruffed grouse select drumming sites that increase their probability of attracting mates (Johnsgard, 1989; McBurney, 1989). Thus, to characterize the drumming structure, we recorded type, length, diameter, height, number of branches >15 cm in length and percent bark on the structure, if appropriate (McBurney, 1989; Buhler and Anderson, 2001; Zimmerman and Gutierrez, 2008). We also recorded the azimuth and percent topographic slope the drumming grouse faced, which was determined either visually or by the accumulation of droppings on the structure (Table 1). Finally, we measured distance of the drumming stage (location on the drumming structure where the grouse drummed) to the nearest end of the drumming structure and used that measurement to determine the location of the plot center on random structures.

Ruffed grouse often select drumming sites that have a dense understory for protection from avian predators and little ground cover to detect mammalian predators (Boag and Sumanik, 1969; Stoll et al., 1979; Hale et al., 1982; Buhler and Anderson, 2001). Thus, to characterize surrounding vegetation, we recorded visibility (%), stem density (no./ha), overstory canopy cover (%) and tree basal area ([m.sup.2]/ha). We estimated visibility using a modified cover board partitioned into 6, 1.2 m wide x 0.3 m tall vertical sections, each containing 144 black dots spaced 5 cm apart (Nudds, 1977; Hale et al., 1982). We placed the cover board directly in front of the drumming stage, facing each cardinal direction and counted the number of visible dots in each section from a distance of 5 m and the same height as the section we were counting. We used this count to estimate visibility at multiple heights surrounding the drumming stage.

We counted stems of forbs and woody vegetation with a diameter <2.54 cm in 1- [m.sup.2] plots at 2-m intervals along 12-m transects radiating from the drumming structure in each cardinal direction. We tabulated woody vegetation and forbs in two categories: "short stems" (15 cm to 1 m tall) and "tall stems" ([greater than or equal to] 1 m tall). These were summed for all plots to estimate stem density of both size classes.

We used a moose-horn densiometer to tabulate overstory canopy cover at 1-m intervals along 12-m transects radiating out from the drumming structure in each cardinal direction. From these data we calculated percent overstory canopy cover. We also estimated percent canopy cover immediately above the drumming structure using a spherical densiometer positioned at approximately ruffed grouse height (30 cm) directly above the drumming stage.

Finally, we measured all trees >2.54 cm DBH [diameter at breast height (1.37 m)] within , a 12.5 m, fixed-radius plot centered over the drumming structure. For trees [greater than or equal to] 10 cm DBH, we recorded species, DBH and condition (alive or dead). For trees <10 cm DBH (hereafter referred to as saplings), we recorded species and condition. We calculated total basal area and basal area of aspen, spruce and pine for trees [greater than or equal to] 10 cm DBH and calculated total density of saplings and density of aspen, spruce and pine saplings.

After completing measurements at the drumming site, we collected the same measurements at three random locations within a radius of 50 to 300 m of the drumming structure. We assumed a radius of 300 m represented an approximate territory size of male ruffed grouse (Kubisiak, 1989) and because alternate drumming structures are typically located <50 m from the primary structure (Lovallo et al., 2000), we constrained our random locations to be >50 m from the primary structure. Random locations were selected without replacement using ArcGIS 9.2 (Environmental Systems Research Institute, Redlands, California, USA) or a random number generator to determine the random direction and distance from the drumming site. Upon arriving at a random location, we located the nearest elevated structure >10 cm diameter and searched the structure for ruffed grouse droppings to ensure a ruffed grouse was not using the structure. If there was evidence of previous use by ruffed grouse, we selected a different random site. Also, if the structure was <10 cm diameter or the site occurred in a meadow or field, we selected a different random site because these conditions were unsuitable for drumming.

MODEL DEVELOPMENT

Preliminary examination of our data suggested that many of the covariate associations with selection of drumming sites might be non-linear. As a result, we determined the most supported structural form of each covariate from four possible forms: linear, quadratic, pseudothreshold (i.e., asymptotic) and exponential (Franklin et al., 2000). We used Akaike's Information Criterion (AIC) to compare relative support for structural forms of each covariate separately, and retained the structural form with the lowest AIC value (Burnham and Anderson, 2002). Using the structural form for each covariate that was most supported, we fit models to evaluate literature-based hypotheses on the relationship of drumming structure and adjacent vegetation characteristics with ruffed grouse selection of drumming sites in the BHNF.

We first hypothesized drumming structure characteristics were correlated with drumming site selection; therefore, we developed eight additive models that included a combination of structure characteristics (Table 1). Second, we hypothesized adjacent vegetation might be related to drumming site selection so we created seven additive models including adjacent vegetation covariates (Table 1). Finally, we predicted both structure and vegetation covariates could be correlated with selection; thus, we developed two models which included both drumming structure and adjacent vegetation covariates. Because ruffed grouse selection of drumming sites might not be influenced by structure or vegetation characteristics, we included one null model which contained no covariates. A detailed description of each model, hypothesized parameter effects and a rationale for each model is available in Hansen (2009).

ANALYTICAL METHODS

We assumed available resources were unique for each individual ruffed grouse, requiring the pairing of used and available (random) sites. Thus, we used discrete-choice models (Cooper and Millspaugh, 1999) to evaluate hypotheses associated with selection of primary drumming sites by ruffed grouse. Classic discrete-choice models take the form of the conditional multinomial logit model (McFadden, 1974), which estimates the probability (p) of an individual selecting the jth unit on the ith choice using:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

We used PROC MDC to fit models and calculate covariate estimates (SAS Institute, 2006).

We ranked our candidate models using an information-theoretic approach (Burnham and Anderson, 2002) and based our model rankings on [DELTA][AIC.sub.c] and Akaike weights (Burnham and Anderson, 2002) for each model. We calculated odds ratios and 95% confidence intervals for covariate estimates to assess the strength of each covariate's relationship with selection of drumming sites. Finally, we determined goodness-of-fit of our models by calculating the likelihood ratio index ([rho]) for each model using:

[rho] = 1 - LL([??])/LL([??]) (2)

where LL([??]) is the log-likelihood of the parameterized model and LL([??]) is the log-likelihood of the null model (Train, 2003). The likelihood ratio index ranges from 0 to 1, with higher values signifying a better performing model compared to the null model (Train, 2003). Thus, we assumed a well-fit model should have a likelihood ratio index value close to 1.

MODEL VALIDATION

To evaluate the predictive ability of our most supported discrete-choice model for selection of drumming sites, we used a modified k-fold cross-validation design (Boyce et al., 2002). We randomly extracted 80% of our paired used and available drumming site data and calculated a new discrete-choice model from these data, while incorporating the covariates from the most-supported discrete-choice model. We then evaluated how the discrete-choice model predicted the remaining 20% of the data by comparing the relative probabilities of paired used and available drumming sites (Boyce et al., 2002). We repeated this process five times and calculated the proportion of paired used and available drumming sites in which the selected choice (i.e., the used drumming site) had the highest probability of being selected, compared to the available drumming sites in the surrounding area. We expected a good predictive model to demonstrate a large proportion of used sites with high relative probabilities of selection. We assumed a proportion [less than or equal to] 25% meant the model had no ability to distinguish between used and available sites.

RESULTS

We located 56 ruffed grouse drumming sites; 41 in spring 2007 and 15 during spring 2008. Drumming structures consisted of 53 fallen logs (94.6%), 1 stump (1.8%), 1 dirt mound (1.8%) and 1 rock cliff (1.8%). Seven of these structures (4 fallen logs, 1 stump, 1 dirt mound and 1 rock cliff) were considered alternate structures because they had less than 20 droppings. Thus, our analyses were based on 49 independent drumming sites and 147 random sites.

The most supported model contained 96% of the Akaike weight (Table 2); thus, we considered only this model for interpretation. In this model, visibility between 0.9 m and 1.8 m was related in an exponential form, tall stem density was related in an asymptotic form and aspen sapling density was related in a linear form with drumming site selection. No drumming structure covariates were included. Covariate estimates and odds ratios suggested that visibility between 0.9 m and 1.8 m and the density of tall stems were the most important to drumming site selection, while aspen sapling density was less important (Table 3). Decreasing the visibility between 0.9 m and 1.8 m around the drumming structure from 40% to 0% increased the relative probability a site would be selected for drumming by ruffed grouse 9-fold (Fig. 2). The density of tall stems had a positive relationship with selection of drumming sites. Increasing the density of tall stems from 8000 stems/hectare to 24,000 stems/hectare increased the relative probability of selection 20-fold (Fig. 3).

The k-fold validation procedures using the most supported discrete choice model resulted in the observed choice (i.e., the used drumming site) in the test data being ranked as the most probable choice out of the available drumming sites 94% of the time. Thus, our discrete-choice model predicted activity center selection well.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

DISCUSSION

Ruffed grouse drumming sites were associated with the height of vegetative cover surrounding the drumming structure, suggesting that predator avoidance might potentially be a factor determining selection of sites. During drumming, ruffed grouse are especially susceptible to predation, causing them to select drumming sites with substantial understory vegetative cover >1 m in height to avoid avian predators and less ground-level cover to detect approaching ground predators and potential mates (Johnsgard, 1989; McBurney, 1989; Furtman, 1999). Ruffed grouse in the BHNF selected drumming sites characterized by low visibility between 0.9 m and 1.8 m and tall stem density, which might make it more difficult for avian predators to detect and approach the drumming ruffed grouse. Similar findings were reported in Georgia and northern Michigan, where drumming sites were characterized by shrub thickets that reduced visibility between 0.5 and 4 m (Hale et al., 1982) and high densities of stems >2.4 m tall (Palmer, 1963). However, these studies also found that ruffed grouse avoided drumming sites with high visibility below 0.5 m and high densities of stems <60 cm tall. We did not find a negative relationship with visibility below 0.9 m and short stem density as we hypothesized; however, the absence of these covariates in the most supported model suggests that height of vegetation is important to drumming site selection. These results are consistent with the predation hypothesis and imply that ruffed grouse selection of drumming sites in the BHNF is driven by the height and density of vegetation surrounding the structure. While no research has examined survival and predation rates of drumming ruffed grouse in the BHNF, we hypothesize that avoidance of predation strongly influences ruffed grouse selection of drumming sites.

Ruffed grouse selection of drumming sites in the BHNF was not related to characteristics of the drumming structure. It has been suggested that male ruffed grouse select drumming structures to increase the distance at which a potential mate can detect their drum (Johnsgard, 1989; McBurney, 1989). However, models that included characteristics associated with the drumming structure had essentially no support in our analysis. In Alberta (Canada) and Ohio (U.S.), the only requirement for a drumming structure was a level drumming stage on a slightly elevated structure (Boag and Sumanik, 1969; Stoll et al., 1979). Similarly, Zimmerman and Gutierrez (2008) reported that logs were the only drumming structure characteristic important to selection of a drumming site in Minnesota. We did not evaluate the association of drumming structure type with selection of drumming sites. However, every primary drumming structure we evaluated was a log, suggesting that ruffed grouse in the BHNF also prefer to drum on logs. While it is plausible that the absence of logs could limit the occurrence of ruffed grouse, we assume logs are abundant on the forest floor of the BHNF. As a result, type and characteristics of potential drumming structures are probably not the determining factor of ruffed grouse distribution or selection of drumming sites.

Species composition of forest vegetation was not related to selection of sites in our study. In Alberta Canada, drumming sites had high densities of white spruce and aspen vegetation (Boag and Sumanik, 1969). Also, Zimmerman and Gutierrez (9008) and Felix-Locher and Campa (2010) reported higher densities of aspen vegetation surrounding drumming sites in Minnesota and Michigan, respectively. Aspen sapling density was included in our most supported model, but there was not sufficient evidence to conclude that aspen sapling density was a driving factor in selection of drumming sites within breeding territories. Further, models including aspen or spruce basal area had no support in our analysis. Ruffed grouse drumming sites occurred in quaking aspen, white spruce, paper birch, bur oak and ponderosa pine vegetation types. The diversity of vegetation types might have diluted any relationship between species composition and selection of drumming sites. Alternatively, species composition might not be important to ruffed grouse resource selection at a small scale. Stoll et al. (1979) and Hale et al. (1982) observed that the physical structure of vegetation was more important to ruffed grouse drumming site selection than species composition in Ohio and Georgia, respectively. Our results corroborate this hypothesis and suggest that species composition might not be as important at local (drumming site) scale as it is at determining landscape-scale (95 ha) distribution (Hansen, 2009). These findings and Hansen (2009) suggest ruffed grouse select early successional structure for drumming sites within aspen-dominated vegetation communities.

Given we tested a large set of models and did not validate our model using independent data, there is potential for spurious results. However, when placed in a biological context, our results were consistent with literature and the biology of ruffed grouse. Thus, management to improve overall ruffed grouse habitat in the BHNF should focus on increasing the extent of aspen vegetation and density of cover > 1 m in height within aspen communities.

Acknowledgments.--We thank L. Benkobi, K. Burns, P. Christensen, A. Crosby, R. Crowhurst, S. Deisch, R. Everett, T. Juntti, C. Lehman, C. Mehls, A. Nolan, J. Shulz, C. Stanton and M. Tarby for their assistance with fieldwork and T. Bonnot for his assistance with fitting discrete-choice models in SAS. H. He and F. Thompson provided valuable input that greatly improved the quality of the study. We also thank W. Conway, R. Gitzen, F. Thompson, III and two anonymous reviewers for their helpful comments on the manuscript. This research was supported by the U.S. Forest Service, Rock Mountain Research Station, Rapid City, SD (05-JV-11221609-239), U.S. Forest Service, Black Hills National Forest, South Dakota Department of Game, Fish and Parks [Grant No.: W-75-R-49, AM4 (under grant amendment #171)] and the University of Missouri.

SUBMITTED 27 APRIL 2010

ACCEPTED 11 OCTOBER 2010

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CHRISTOPHER P. HANSEN (1)

Department of Fisheries and Wildlife Sciences, 302 Natural Resources, University of Missouri, Columbia 65211

MARK A. RUMBLE

U.S. Forest Service, Rocky Mountain Research Station, 8221 South Highway 16, Rapid City, South Dakota 57701

AND

JOSHUA J. MILLSPAUGH

Department of Fisheries and Wildlife Sciences, 302 Natural Resources, University of Missouri, Columbia 65211

(1) Corresponding author: Telephone: (573) 808-5578; FAX: (573) 884-5070; e-mail: hansench@ missouri.edu
TABLE 1.--Description of the covariates to be used in discrete-
choice models which assess the  relationship of drumming structure
and adjacent vegetative characteristics with selection of ruffed
grouse drumming sites in the Black Hills National Forest during
spring 2007 and 2008

Covariate                             Description

Structure
  Height          Height (cm) of drumming structure at the drumming
                    stage
  Diameter        Diameter (cm) of drumming structure at the drumming
                    stage
  Slope           Topographic slope (%) that the drumming grouse faced
  BarkO           0-20% drumming structure covered by bark
  Barkl           21-60% drumming structure covered by bark
  Bark2           61-100% drumming structure covered by bark
  Length          Length (cm) of drumming structure
  Branch          Number of branches >15 cm on the drumming structure
  Stage_canopy    Overstory canopy cover (%) directly above drumming
                    stage

Vegetation
  QA_basal        Basal area ([m.sup.2]/ha) of quaking aspen [greater
                    than or equal to] 10 cm DBH (a)
  WS_basal        Basal area ([m.sup.2]/ha) of white spruce [greater
                    than or equal to] 10 cm DBH (a)
  PP_basal        Basal area ([m.sup.2]/ha) of ponderosa pine [greater
                    than or equal to] 10 cm DBH (a)
  Basal_total     Basal area ([m.sup.2]/ha) of all vegetation [greater
                    than or equal to] 10 cm DBH (a)
  Coverl          Visibility (%) from 0-0.9 m in height
  Covert          Visibility (%) from 0.91-1.8 m in height
  Cover_total     Visibility (%) from 0-1.8 m in height
  QA_sapling      Density (no./ha) of quaking aspen saplings (aspen
                    vegetation [greater than or equal to] 1.37 m  tall
                    and 10 cm > DBH (a) [greater than or equal to]
                    2.54 cm)
  WS_sapling      Density (no./ha) of white spruce saplings (spruce
                    vegetation [greater than or equal to] 1.37 m tall
                    and 10 cm > DBH (a) [greater than or equal to]
                    2.54 cm)
  PP_sapling      Density (no./ha) of ponderosa pine saplings (pine
                    vegetation [greater than or equal to] 1.37 m tall
                    and 10 cm > DBH (a) [greater than or equal to]
                    2.54 cm)
  Sapling_total   Density (no./ha) of all saplings (vegetation
                    [greater than or equal to] 1.37 m tall and 10 cm >
                    DBH (a) [greater than or equal to] 2.54 cm)
  Steml           Density (no./ha) of woody and herbaceous stems
                    (excluding grasses) 15 cm < stem height < 1 m
  Stem2           Density (no./ha) of woody and herbaceous stems
                    (excluding grasses) [greater than or equal to]
                    1 m tall
  Plot_canopy     Canopy cover (%) throughout the drumming site

(a) Signifies the diameter at breast height (1.37 m)

TABLE 2.--Ranking of drumming site models after considering non-
linear relationships of structure and vegetation covariates with
ruffed grouse selection of drumming sites during spring 2007 and 2008
in the Black Hills National Forest. The most supported structural
form for each covariate [linear (L_), quadratic (Q_), asymptotic
(A_), exponential (E_)] was determined individually using single
covariate models and AIC. [AIC.sub.c] represents Akaike's information
criterion adjusted for small sample size and [DELTA][AIC.sub.c] is
the difference in [AIC.sub.c] value from the top model

                                            -2 * log-       No. of
Model (a)                                  likelihood     covariates

E_Cover2 + A_Stem2 + L_QA_sapling             25.84            3
Q_Height + Q_QA_basal + A_WS_basal +
  E_Cover2 + A_Stem2 + L_QA_sapling +
  A_Plot_canopy + E_Stage_canopy              14.78           10
E_Coverl + E_Cover2 + A_Steml +
  A_Stem2 + L_QA_sapling +
  A_WS_sapling + E_PP_sapling                 23.87            7
Q_QA_basal + A_WS_basal + E_Coverl +
  E_Cover2 + A_Steml + A_Stem2 +
  L_Sapling_total + A_Plot_canopy +
  E_Stage_canopy                              18.33           10
Q_QA_basal + A_WS_basal + A_Plot_canopy
  + E_Stage_canopy + E_Cover2 + A_Stem2
  + L_QA_sapling + A_WS_sapling +
  JE_PP_sapling                               19.31           10
L_Slope + Q_Diameter + BarkO + Barkl +
  Bark2 + Q_QA_basal + A_WS_basal +
  E_Covert + A_Stem2 + L_Sapling_total
  + A_Plot_canopy + E_Stage_canopy            10.15           14
Q_Diameter + A_Length + BarkO + Barkl
  + Bark2                                     37.37            6
Q_Height + L_Slope + Q_Diameter +
  BarkO + Barkl + Bark2 + A_Branch
  + A_Length                                  26.76           10
Q_Height + L_Slope + Q_Diameter +
  BarkO + Barkl + Bark2                       33.71            8
Q_Height                                      49.11            2
Q_Diameter                                    48.94            3
Q_Diameter + BarkO + Barkl + Bark2            49.92            5
Q_QA_basal + A_Plot_canopy +
  E_Stage_canopy                              72.79            4
Q_QA_basal + A_WS_basal +
  A_Plot_canopy + E_Stage_canopy              72.31            5
Q_QA_basal + A_WS_basal + L_PP_basal
  + A_Plot_canopy + E_Stage_canopy            72.26            6
A_Branch                                     123.45            1
Constant                                     135.28            0

                                                            [DELTA]
Model (a)                                  [AIC.sub.c]    [AIC.sub.c]

E_Cover2 + A_Stem2 + L_QA_sapling             32.37           0.00
Q_Height + Q_QA_basal + A_WS_basal +
  E_Cover2 + A_Stem2 + L_QA_sapling +
  A_Plot_canopy + E_Stage_canopy              40.57           8.20
E_Coverl + E_Cover2 + A_Steml +
  A_Stem2 + L_QA_sapling +
  A_WS_sapling + E_PP_sapling                 40.60           8.23
Q_QA_basal + A_WS_basal + E_Coverl +
  E_Cover2 + A_Steml + A_Stem2 +
  L_Sapling_total + A_Plot_canopy +
  E_Stage_canopy                              44.12          11.75
Q_QA_basal + A_WS_basal + A_Plot_canopy
  + E_Stage_canopy + E_Cover2 + A_Stem2
  + L_QA_sapling + A_WS_sapling +
  JE_PP_sapling                               45.10          12.73
L_Slope + Q_Diameter + BarkO + Barkl +
  Bark2 + Q_QA_basal + A_WS_basal +
  E_Covert + A_Stem2 + L_Sapling_total
  + A_Plot_canopy + E_Stage_canopy            50.50          18.13
Q_Diameter + A_Length + BarkO + Barkl
  + Bark2                                     51.37          19.00
Q_Height + L_Slope + Q_Diameter +
  BarkO + Barkl + Bark2 + A_Branch
  + A_Length                                  52.55          20.18
Q_Height + L_Slope + Q_Diameter +
  BarkO + Barkl + Bark2                       53.31          20.94
Q_Height                                      53.37          21.00
Q_Diameter                                    55.47          23.10
Q_Diameter + BarkO + Barkl + Bark2            61.32          28.94
Q_QA_basal + A_Plot_canopy +
  E_Stage_canopy                              81.70          49.33
Q_QA_basal + A_WS_basal +
  A_Plot_canopy + E_Stage_canopy              83.71          51.33
Q_QA_basal + A_WS_basal + L_PP_basal
  + A_Plot_canopy + E_Stage_canopy            86.26          53.89
A_Branch                                     125.54          93.17
Constant                                     135.28          98.74

                                             Akaike       Likelihood
Model (a)                                    weight       ratio index

E_Cover2 + A_Stem2 + L_QA_sapling             0.96           0.81
Q_Height + Q_QA_basal + A_WS_basal +
  E_Cover2 + A_Stem2 + L_QA_sapling +
  A_Plot_canopy + E_Stage_canopy              0.02           0.89
E_Coverl + E_Cover2 + A_Steml +
  A_Stem2 + L_QA_sapling +
  A_WS_sapling + E_PP_sapling                 0.02           0.82
Q_QA_basal + A_WS_basal + E_Coverl +
  E_Cover2 + A_Steml + A_Stem2 +
  L_Sapling_total + A_Plot_canopy +
  E_Stage_canopy                              0.00           0.86
Q_QA_basal + A_WS_basal + A_Plot_canopy
  + E_Stage_canopy + E_Cover2 + A_Stem2
  + L_QA_sapling + A_WS_sapling +
  JE_PP_sapling                               0.00           0.86
L_Slope + Q_Diameter + BarkO + Barkl +
  Bark2 + Q_QA_basal + A_WS_basal +
  E_Covert + A_Stem2 + L_Sapling_total
  + A_Plot_canopy + E_Stage_canopy            0.00           0.92
Q_Diameter + A_Length + BarkO + Barkl
  + Bark2                                     0.00           0.72
Q_Height + L_Slope + Q_Diameter +
  BarkO + Barkl + Bark2 + A_Branch
  + A_Length                                  0.00           0.80
Q_Height + L_Slope + Q_Diameter +
  BarkO + Barkl + Bark2                       0.00           0.75
Q_Height                                      0.00           0.64
Q_Diameter                                    0.00           0.64
Q_Diameter + BarkO + Barkl + Bark2            0.00           0.63
Q_QA_basal + A_Plot_canopy +
  E_Stage_canopy                              0.00           0.46
Q_QA_basal + A_WS_basal +
  A_Plot_canopy + E_Stage_canopy              0.00           0.47
Q_QA_basal + A_WS_basal + L_PP_basal
  + A_Plot_canopy + E_Stage_canopy            0.00           0.47
A_Branch                                      0.00           0.09
Constant                                      0.00           0.00

(a) See Table 1 for definition of covariate symbols

TABLE 3.--Covariate estimates, standard errors (SE), odds ratios and
95% odds ratio confidence intervals for the most supported discrete-
choice model after considering non-linear relationships [linear (L_),
quadratic (Q_), asymptotic (A_), exponential (E_)] with ruffed grouse
selection of drumming sites in the Black Hills National Forest during
2007 and 2008

                                      Odds     Lower     Upper 95%
Covariate (a)    Estimate     SE     ratio     95% CI       CI

E_Cover2          -4.65      1.41      0.01    0.001          0.15
A_Stem2            5.41      2.06    224.15    3.94      12,751.80
L_QA_sapling       1.38      0.76      3.99    0.90          17.80

(a) See Table 1 for a definition of covariate symbols
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Article Details
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Author:Hansen, Christopher P.; Rumble, Mark A.; Millspaugh, Joshua J.
Publication:The American Midland Naturalist
Article Type:Report
Geographic Code:1USA
Date:Apr 1, 2011
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