Data and code from: Modeling observational uncertainty improves estimation of breeding-season parameters that inform lek-based monitoring for Centrocercus urophasianus (Greater Sage-Grouse)
Data files
Sep 07, 2026 version files 4.50 MB
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Figure3.R
13.80 KB
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Figure4.R
25.74 KB
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Figure5.R
21.76 KB
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Figure6.R
13.23 KB
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Figure7.R
18.59 KB
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MSMR.inp
325.71 KB
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MSMRSU.inp
325.88 KB
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ParameterEstimatesFig3.xlsx
359.75 KB
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ParameterEstimatesFig5.xlsx
110.49 KB
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ParameterEstimatesFig6.xlsx
359.75 KB
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ParameterEstimatesFig7.xlsx
2.04 MB
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PrecipParameterEstimates.xlsx
359.22 KB
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README.md
11.43 KB
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WindSpeedParameterEstimates.xlsx
513.46 KB
Abstract
Counts of males on leks are widely used as abundance indices to monitor populations of lek-breeding species, but they can be influenced by variation in male attendance, inter-lek movement, and mortality. When there is imperfect observability of males on leks, estimates of lek attendance and inter-lek movement are likely to be biased low. We compared traditional multi-state mark–recapture (MSMR) and MSMR models with state uncertainty (MSMR-SU) to determine how accounting for uncertainty in GPS-derived lek attendance improves inference of rates underlying lek-based abundance indices for male Centrocercus urophasianus (Greater Sage-Grouse). We found that modeling observational uncertainty with MSMR-SU models consistently reduced bias in lek attendance and inter-lek movement estimates for adult and yearling males compared to MSMR models. Estimates of daily maximum male lek attendance (adults: 0.79; yearlings: 0.68) and inter-lek movement rates (adults: 0.10; yearlings: 0.07) from MSMR-SU models were higher than daily maximum lek attendance (adults: 0.74; yearlings: 0.55) and inter-lek movement rates (adults: 0.01; yearlings: 0.04) from MSMR models. Consistent with previous studies, adults exhibited higher lek attendance and mortality rates than yearlings. However, unlike earlier studies, inter-lek movement rates were similar between age classes, with adults tending to move earlier in the lekking season than yearlings. Wind speed and precipitation had a weak negative effect on lek attendance. Greater distance to the nearest known lek strongly reduced inter-lek movement. Accounting for lekking-season mortality shifted the estimated date of maximum lek attendance earlier in the season by 8–9 days for adults and 1–3 days for yearlings. Accounting for state uncertainty due to error in state assignment should reduce bias in demographic estimates for use in wildlife conservation and management decisions.
Dataset DOI: 10.5061/dryad.rxwdbrvq6
Description of the data and file structure
Incomplete telemetry data and morning movements of male sage-grouse (Centrocercus urophasianus) on and off leks introduce uncertainty in the process of observing males on leks. If males are incorrectly classified as off lek, estimates of lek attendance and inter-lek movement may be biased low. We used multi-state mark-recapture models with state uncertainty (MSMR-SU) to model the observation process and estimate daily lek attendance, inter-lek movement, and mortality for GPS-marked male greater sage-grouse during four lekking seasons in northwestern Colorado and southwestern Wyoming. We then compared our results against those from traditional MSMR models. Additionally, we estimated mortality-adjusted lek attendance to quantify the cumulative effect of lekking-season mortality on maximum lek attendance
This repository contains R scripts for generating Program MARK input files, input files for Program MARK, and R scripts for generating figures.
Files and variables
Program MARK input
Program MARK input files created from raw telemetry data, lek locations, and weather data. Raw GPS telemetry data is available by request from Brett Walker, Colorado Parks and Wildlife (Brett.Walker@state.co.us). Lek location data is available from Kathy Griffin, Colorado Parks and Wildlife (Kathy.Griffin@state.co.us).
File: MSMRSU.inp
Description: Input file for Program MARK (multistate mark-recapture with state uncertainty model) generated by RawData_MARKinp.R.
File: MSMR.inp
Description: Input file for Program MARK (traditional multistate mark-recapture model) generated by RawData_MARKinp.R.
Graphs
File: ParameterEstimatesFig3.xlsx
Description: Real estimates of transition parameters from Program MARK used to generate figure 3. Sheet names indicate model (MSMRSU or MSMR), age (Adult or yearling), and year (2011-2014). No yearlings were captured in 2014.
Variables
- TimeInterval: day of lekking season where 1 = 10 March
- Parameter: transition parameter (Ψ)
- AB: (ΨAB) daily probability of inter-lek movement from same lek (state A) to new lek (state B)
- AO: (ΨAO) daily probability of transitioning from same lek (state A) to off-lek (state O)
- AD: (ΨAD) daily mortality or transition from same lek (state A) to dead (state D)
- BA: (ΨBA) daily probability of remaining at new lek, given that the individual switched in the previous time step
- BO: (ΨBO) daily probability of transitioning from new lek (state B) to off-lek (state O)
- BD: (ΨBD) daily mortality or transition from new lek (state B) to dead (state D)
- OA: (ΨOA) daily probability of transitioning from off-lek (state O) to the same lek (state A)
- OB: (ΨOB) daily probability of transitioning from off-lek (state O) to new lek (state B)
- OD: (ΨOD) daily mortality or transition from off-lek (state O) to dead (state D)
- Estimate: daily real estimate
- SE: standard error
- LCI: lower 95% confidence interval
- UCI: upper 95% confidence interval
File: PrecipParameterEstimates.xlsx
Description: Real estimates of transition parameters from Program MARK used to create figure 4. Sheet names indicate model (MSMRSU or MSMR) and precipitation level (0-3 cm).
Variables
- TimeInterval: day of lekking season where 1 = 10 March
- Parameter: transition parameter (Ψ)
- AB: (ΨAB) daily probability of inter-lek movement from same lek (state A) to new lek (state B)
- AO: (ΨAO) daily probability of transitioning from same lek (state A) to off-lek (state O)
- AD: (ΨAD) daily mortality or transition from same lek (state A) to dead (state D)
- BA: (ΨBA) daily probability of remaining at new lek, given that the individual switched in the previous time step
- BO: (ΨBO) daily probability of transitioning from new lek (state B) to off-lek (state O)
- BD: (ΨBD) daily mortality or transition from new lek (state B) to dead (state D)
- OA: (ΨOA) daily probability of transitioning from off-lek (state O) to the same lek (state A)
- OB: (ΨOB) daily probability of transitioning from off-lek (state O) to new lek (state B)
- OD: (ΨOD) daily mortality or transition from off-lek (state O) to dead (state D)
- Estimate: daily real estimate
- SE: standard error
- LCI: lower 95% confidence interval
- UCI: upper 95% confidence interval
File: WindSpeedParameterEstimates.xlsx
Description: Real estimates of transition parameters from Program MARK used to create figure 4. Sheet names indicate model (MSMRSU or MSMR) and wind speed level (5-50 kph).
Variables
- TimeInterval: day of lekking season where 1 = 10 March
- Parameter: transition parameter (Ψ)
- AB: (ΨAB) daily probability of inter-lek movement from same lek (state A) to new lek (state B)
- AO: (ΨAO) daily probability of transitioning from same lek (state A) to off-lek (state O)
- AD: (ΨAD) daily mortality or transition from same lek (state A) to dead (state D)
- BA: (ΨBA) daily probability of remaining at new lek, given that the individual switched in the previous time step
- BO: (ΨBO) daily probability of transitioning from new lek (state B) to off-lek (state O)
- BD: (ΨBD) daily mortality or transition from new lek (state B) to dead (state D)
- OA: (ΨOA) daily probability of transitioning from off-lek (state O) to the same lek (state A)
- OB: (ΨOB) daily probability of transitioning from off-lek (state O) to new lek (state B)
- OD: (ΨOD) daily mortality or transition from off-lek (state O) to dead (state D)
- Estimate: daily real estimate
- SE: standard error
- LCI: lower 95% confidence interval
- UCI: upper 95% confidence interval
File: ParameterEstimatesFig5.xlsx
Description: Real estimates of transition parameters from Program MARK used to create figure 5. Sheet names indicate model (MSMRSU or MSMR) and age (adult or yearling).
Variables
- TimeInterval: day of lekking season where 1 = 10 March
- Parameter: transition parameter (Ψ)
- AB: (ΨAB) daily probability of inter-lek movement from same lek (state A) to new lek (state B)
- AO: (ΨAO) daily probability of transitioning from same lek (state A) to off-lek (state O)
- AD: (ΨAD) daily mortality or transition from same lek (state A) to dead (state D)
- BA: (ΨBA) daily probability of remaining at new lek, given that the individual switched in the previous time step
- BO: (ΨBO) daily probability of transitioning from new lek (state B) to off-lek (state O)
- BD: (ΨBD) daily mortality or transition from new lek (state B) to dead (state D)
- OA: (ΨOA) daily probability of transitioning from off-lek (state O) to the same lek (state A)
- OB: (ΨOB) daily probability of transitioning from off-lek (state O) to new lek (state B)
- OD: (ΨOD) daily mortality or transition from off-lek (state O) to dead (state D)
- Estimate: daily real estimate
- SE: standard error
- LCI: lower 95% confidence interval
- UCI: upper 95% confidence interval
File: ParameterEstimatesFig6.xlsx
Description: Real estimates of transition parameters from Program MARK used to create figure 6. Sheet names indicate model (MSMRSU or MSMR), age (Adult or yearling), and year (2011-2014). No yearlings were captured in 2014.
Variables
- TimeInterval: day of lekking season where 1 = 10 March
- Parameter: transition parameter (Ψ)
- AB: (ΨAB) daily probability of inter-lek movement from same lek (state A) to new lek (state B)
- AO: (ΨAO) daily probability of transitioning from same lek (state A) to off-lek (state O)
- AD: (ΨAD) daily mortality or transition from same lek (state A) to dead (state D)
- BA: (ΨBA) daily probability of remaining at new lek, given that the individual switched in the previous time step
- BO: (ΨBO) daily probability of transitioning from new lek (state B) to off-lek (state O)
- BD: (ΨBD) daily mortality or transition from new lek (state B) to dead (state D)
- OA: (ΨOA) daily probability of transitioning from off-lek (state O) to the same lek (state A)
- OB: (ΨOB) daily probability of transitioning from off-lek (state O) to new lek (state B)
- OD: (ΨOD) daily mortality or transition from off-lek (state O) to dead (state D)
- Estimate: daily real estimate
- SE: standard error
- LCI: lower 95% confidence interval
- UCI: upper 95% confidence interval
File: ParameterEstimatesFig7.xlsx
Description: Real estimates of transition parameters from Program MARK used to create figure 7. Sheet names indicate model (MSMRSU or MSMR), distance from second nearest lek (0-15 km), and year (2011-2014).
Variables
- TimeInterval: day of lekking season where 1 = 10 March
- Parameter: transition parameter (Ψ)
- AB: (ΨAB) daily probability of inter-lek movement from same lek (state A) to new lek (state B)
- AO: (ΨAO) daily probability of transitioning from same lek (state A) to off-lek (state O)
- AD: (ΨAD) daily mortality or transition from same lek (state A) to dead (state D)
- BA: (ΨBA) daily probability of remaining at new lek, given that the individual switched in the previous time step
- BO: (ΨBO) daily probability of transitioning from new lek (state B) to off-lek (state O)
- BD: (ΨBD) daily mortality or transition from new lek (state B) to dead (state D)
- OA: (ΨOA) daily probability of transitioning from off-lek (state O) to the same lek (state A)
- OB: (ΨOB) daily probability of transitioning from off-lek (state O) to new lek (state B)
- OD: (ΨOD) daily mortality or transition from off-lek (state O) to dead (state D)
- Estimate: daily real estimate
- SE: standard error
- LCI: lower 95% confidence interval
- UCI: upper 95% confidence interval
Code/software
Software
Program MARK download: https://sites.warnercnr.colostate.edu/gwhite/program-mark/
R download: https://www.r-project.org/
Code: Figure3.R
Description: R script for projection matrix and generating figure 3 using parameter estimates from Program MARK.
Code: Figure4.R
Description: R script for projection matrix and generating figure 4 using parameter estimates from Program MARK.
Code: Figure5.R
Description: R script for projection matrix and generating figure 5 using parameter estimates from Program MARK.
Code: Figure6.R
Description: R script for projection matrix and generating figure 6 using parameter estimates from Program MARK.
Code: Figure7.R
Description: R script for projection matrix generating figure 7 using parameter estimates from Program MARK.
Access information
Weather data was downloaded from Climatology Lab (https://www.climatologylab.org/gridmet.html)
