 PDO index (PDO y ) on the expected count (µ i,y ), σ L and σ Y are the standard deviations (SDs) of the random effects of lek and year. In our parameterization of the negative binomial the parameter φ controls the overdispersion scaled by the square of µ, i.e., Key model parameters are also described in Table 1.
To identify the most important spatial scale (distance from each lek when calculating the areal disturbance) and temporal lags, a total of 64 models were fitted to the lek count data representing all combinations of the four lek distances (0.8, 1.6, 3.2 and 6.4 km) and independent lags of one to four years in the areal disturbance (Walker et al., 2007;Doherty et al., 2010;Harju et al., 2010;Gregory and Beck, 2014) and PDO index. The relative importance of each spatial scale and temporal lag as a predictor of individual lek counts was assessed by calculating it's Akaike's weight (w i ) across all 64 models (Burnham and Anderson, 2002).
Once the model with the most important spatial scale and temporal lags was identified, the relative importance of β A and β P was quantified by calculating their Akaike's weights across the selected full model and the three reduced variants representing all combinations of the two parameters (Burnham and Anderson, 2002) and by calculating their effect sizes with 95% confidence/credible limits (CLs Bradford et al., 2005;Claridge-Chang and Assam, 2016). The effect sizes, which represent the expected percent change in the lek count with an increase in the predictor of one SD, were calculated for the final full model and by averaging across all four models (Burnham and Anderson, 2002;Turek, 2015).

Population Models
The calculated annual population densities (mean males per lek) in each working group were analysed using Gompertz State-Space Population Models (Dennis et al., 2006;Garton et al., 2011;Knape and de Valpine, 2012) with the standardized areal disturbance and PDO index as fixed effects and year and group as random effects. Gompertz State-Space Population Models (GSSPMs) were used because they incorporate density-dependence (Dennis et al., 2006;Knape and de Valpine, 2012) and process error (Dennis et al., 2006;Auger-Méthé et al., 2016); have well-known statistical properties (Dennis et al., 2006;Knape, 2008); and because Gompertz models have performed well in explaining rates of change for sage-grouse in general and for Wyoming sage-grouse in particular (Garton et al., 2011).
The population model is described by the following equations where M g,y is the density at the gth group in the yth year, µ g,y and µ g,0 are the expected densities at the gth group in the yth and initial year, respectively, β D is the typical density-dependence and α Gg is the group-level random effect on the density-dependence, σ ε and α η g,y are observer and process error (Dennis et al., 2006) and the other terms are approximately equivalent to those in the lek count model. The equivalence is only approximate as the terms in the population model act on the change in density (as opposed to density). The carrying capacity, which represents the long-term expected density around which a population fluctuates (Dennis et al., 2006), is given by

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The primary question this study attempts to answer is whether the sage-grouse population-level responses to oil and gas are consistent with the local studies. Consequently, the average areal disturbance in each working group was calculated at the spatial scale that was most important in the local analyses. However, as the timing of effects could differ between the local count models and the population dynamic models, the Akaike's weight for each lag of one to four years in the areal disturbance and one to four years in the PDO index was calculated across the 16 models representing all lag combinations. Once the full model with the most important temporal lags had been identified, the relative importance of β A and β P was once again quantified from their effect sizes with 95% CLs and their Akaike's weights across the full model and the three reduced variants.

Predicted Population Impacts
To examine whether the population-level responses are consistent with the lek-level results, the expected effect of OAG on the long-term mean densities in each working group was calculated for the local and population models. In the case of the local model, the predicted population impacts represent the percent difference in the sum of the expected counts for the observed levels of OAG versus no OAGacross all leks in the working group after accounting for annual and climatic effects. In the case of the population model, the predicted population impacts represent the percent difference in the expected carrying capacity with the observed levels of OAG versus no OAGaccounting for annual and climatic effects. Finally, to test whether the results are consistent, the odds ratio that the predicted Wyoming-wide impact from the population model is less than the summation of the Wyoming-wide local impacts was calculated for the most recent year.

Statistical Methods
For reasons of computational efficiency, the intial 64 local and 16 population-level models were fit using the frequentist method of Maximum Likelihood (ML, Millar, 2011). The Akaike's weights were calculated from the marginal Akaike's Information Criterion values corrected for small sample size (mAICc, Burnham and Anderson, 2002;Vaida and Blanchard, 2005;Greven and Kneib, 2010). Model adequacy was assessed by plotting and analysis of the standardized residuals from the final full ML model (Burnham and Anderson, 2002) with the most important spatial scale and lags. As both the local and population models used log-link functions, the effect sizes (percent change in the response for an increase in one SD) were calculated from exp(β ) − 1 where β is the fixed effect of interest or its upper or lower CL. The ML effect sizes were calculated from the full model and averaged across the full model and three reduced variants (Lukacs et al., 2010).
To allow the predicted population impacts to be estimated with CLs, the final full models were also fitted using Bayesian methods (Gelman et al., 2014). The prior for all paramaters was an uninformative (Gelman et al., 2014) normal distribution with a mean of 0 and a SD of 5. A total of 2,000 MCMC samples were drawn from the second halves of four chains. Convergence was confirmed by ensuring that Rhat was less than 1.05 (Gelman et al., 2014) for all the estimated parameters.

Software
The data preparation, analysis and plotting were performed using R version 3.4.2 (R Core Team, 2017) and the R packages TMB (Kristensen et al., 2016) and rstan (Stan Development Team, 2016). The clean and tidy analysis data and R scripts are archived at https://doi.org/10.5281/zenodo.837866. The raw sage-grouse data, which provide the lek locational information, are available from the Wyoming Department of Fish and Game. The raw data are not required to replicate the analyses.

Local Models
The Akaike weights for the spatial scales indicate that 3.2 km is unanimously supported (w i = 1.00) as the most important lek distance for predicting individual lek counts from the areal disturbance due to well pads (Table S1). The Akaike weights for the lags in the areal disturbance also provided unanimous support for a single candidate with the lag of one year receiving a weight of 1.00 (Table S2). The situation with the PDO index lags was less clear-cut (Table 2), although a lag of two years received the majority of the support (w i = 0.73). Consequently, the local model with a lek distance of 3.2 km and lags of one and two years years in the areal disturbance due to well pads and the PDO index, respectively, was selected as the final model. The standardized residuals, with the exception of a small number of high outliers, were approximately normally distributed and displayed homogeneity of variance. Most leks had an expected count of male sage-grouse in the absence of OAG of approximately 10 birds (Fig. S1).
The Akaike weights for β A (w i = 1) and β P (w i = 0.98) across the final full model and the three reduced models indicate that both are very strongly supported as predictors of individual lek counts. The effect size estimates (Fig. 5) indicate that β A and β P have large negative (Fig. 6) and positive (Fig. 7) impacts of similar magnitudes on the lek counts and that the estimates are insensitive to the statistical framework (ML of Bayesian) or model-averaging (Tables S3-S5). Despite the inclusion of the PDO index as an important predictor there was still substantial remaining annual variation in the lek counts (Fig. S2) which was modelled by the random effect of year.

Population Models
Based on the results of the local models, the level OAG development in each working group was calculated in terms of the average areal disturbance due to well pads within 3.2 km of each lek (Fig. 8). The Akaike weights for the lag in the areal disturbance (Table 3) were largely indifferent (w i between 0.23 and