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Evaluating Multi-Level Models to Test Occupancy State Responses of Plethodontid Salamanders.

Kroll AJ, Garcia TS, Jones JE, Dugger K, Murden B, Johnson J, Peterman S, Peerman S, Brintz B, Rochelle M - PLoS ONE (2015)

Bottom Line: Empirical data indicated Oregon slender salamander occupancy was associated strongly with the amount of coarse woody debris (posterior mean = 0.74; SD = 0.24); Ensatina occupancy was not associated with amount of coarse woody debris (posterior mean = -0.01; SD = 0.29).Our simulation results indicate that either model is suitable for use in an experimental study of Plethodontid salamanders provided that sample sizes are sufficiently large.As a result, we recommend careful consideration of study questions and objectives prior to sampling data and fitting models.

View Article: PubMed Central - PubMed

Affiliation: Weyerhaeuser, Federal Way, Washington, United States of America.

ABSTRACT
Plethodontid salamanders are diverse and widely distributed taxa and play critical roles in ecosystem processes. Due to salamander use of structurally complex habitats, and because only a portion of a population is available for sampling, evaluation of sampling designs and estimators is critical to provide strong inference about Plethodontid ecology and responses to conservation and management activities. We conducted a simulation study to evaluate the effectiveness of multi-scale and hierarchical single-scale occupancy models in the context of a Before-After Control-Impact (BACI) experimental design with multiple levels of sampling. Also, we fit the hierarchical single-scale model to empirical data collected for Oregon slender and Ensatina salamanders across two years on 66 forest stands in the Cascade Range, Oregon, USA. All models were fit within a Bayesian framework. Estimator precision in both models improved with increasing numbers of primary and secondary sampling units, underscoring the potential gains accrued when adding secondary sampling units. Both models showed evidence of estimator bias at low detection probabilities and low sample sizes; this problem was particularly acute for the multi-scale model. Our results suggested that sufficient sample sizes at both the primary and secondary sampling levels could ameliorate this issue. Empirical data indicated Oregon slender salamander occupancy was associated strongly with the amount of coarse woody debris (posterior mean = 0.74; SD = 0.24); Ensatina occupancy was not associated with amount of coarse woody debris (posterior mean = -0.01; SD = 0.29). Our simulation results indicate that either model is suitable for use in an experimental study of Plethodontid salamanders provided that sample sizes are sufficiently large. However, hierarchical single-scale and multi-scale models describe different processes and estimate different parameters. As a result, we recommend careful consideration of study questions and objectives prior to sampling data and fitting models.

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Comparison of the standard deviation of posterior mean estimates of ‘Alpha3’ vs. the average posterior standard deviation of ‘Alpha3’ in the multi-scale model.Results are shown only for combinations with seven plots. Results for five and nine plots are not shown, but have trends similar to those shown here. Panels show the results for different combinations of detection probability and post-treatment occupancy.
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pone.0142903.g006: Comparison of the standard deviation of posterior mean estimates of ‘Alpha3’ vs. the average posterior standard deviation of ‘Alpha3’ in the multi-scale model.Results are shown only for combinations with seven plots. Results for five and nine plots are not shown, but have trends similar to those shown here. Panels show the results for different combinations of detection probability and post-treatment occupancy.

Mentions: Coverage probabilities for the single-scale model treatment effect estimator (Table 2, S3 Table) were close to nominal, but somewhat conservative with an average value of 0.97. Coverage probabilities for the multi-scale model treatment effect estimator were highly conservative, with 100% of all intervals containing the true value. This result indicates that the posterior standard deviation of the treatment effect parameter is not a good surrogate for the standard deviation of the estimator sampling distribution. The hierarchical single-scale model (Fig 5, S3 Table) showed generally good calibration between sampling variability and posterior estimates of variability when detection probability was 0.5 for all sample sizes considered in this study. As detection probability decreased, posterior variability tended to be greater than the sampling variability of the treatment estimator. Results from the multi-scale model show, across all conditions included in this study, that the average posterior variability is substantially greater than the sampling variability of the treatment estimator (Fig 6). The trends for the multi-scale model (S4 Table) suggest that posterior credible intervals for the treatment effect estimate will tend to be highly conservative, exceeding nominal coverage rates and limiting the efficiency of estimating the sign and magnitude of putative treatment effects.


Evaluating Multi-Level Models to Test Occupancy State Responses of Plethodontid Salamanders.

Kroll AJ, Garcia TS, Jones JE, Dugger K, Murden B, Johnson J, Peterman S, Peerman S, Brintz B, Rochelle M - PLoS ONE (2015)

Comparison of the standard deviation of posterior mean estimates of ‘Alpha3’ vs. the average posterior standard deviation of ‘Alpha3’ in the multi-scale model.Results are shown only for combinations with seven plots. Results for five and nine plots are not shown, but have trends similar to those shown here. Panels show the results for different combinations of detection probability and post-treatment occupancy.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4664280&req=5

pone.0142903.g006: Comparison of the standard deviation of posterior mean estimates of ‘Alpha3’ vs. the average posterior standard deviation of ‘Alpha3’ in the multi-scale model.Results are shown only for combinations with seven plots. Results for five and nine plots are not shown, but have trends similar to those shown here. Panels show the results for different combinations of detection probability and post-treatment occupancy.
Mentions: Coverage probabilities for the single-scale model treatment effect estimator (Table 2, S3 Table) were close to nominal, but somewhat conservative with an average value of 0.97. Coverage probabilities for the multi-scale model treatment effect estimator were highly conservative, with 100% of all intervals containing the true value. This result indicates that the posterior standard deviation of the treatment effect parameter is not a good surrogate for the standard deviation of the estimator sampling distribution. The hierarchical single-scale model (Fig 5, S3 Table) showed generally good calibration between sampling variability and posterior estimates of variability when detection probability was 0.5 for all sample sizes considered in this study. As detection probability decreased, posterior variability tended to be greater than the sampling variability of the treatment estimator. Results from the multi-scale model show, across all conditions included in this study, that the average posterior variability is substantially greater than the sampling variability of the treatment estimator (Fig 6). The trends for the multi-scale model (S4 Table) suggest that posterior credible intervals for the treatment effect estimate will tend to be highly conservative, exceeding nominal coverage rates and limiting the efficiency of estimating the sign and magnitude of putative treatment effects.

Bottom Line: Empirical data indicated Oregon slender salamander occupancy was associated strongly with the amount of coarse woody debris (posterior mean = 0.74; SD = 0.24); Ensatina occupancy was not associated with amount of coarse woody debris (posterior mean = -0.01; SD = 0.29).Our simulation results indicate that either model is suitable for use in an experimental study of Plethodontid salamanders provided that sample sizes are sufficiently large.As a result, we recommend careful consideration of study questions and objectives prior to sampling data and fitting models.

View Article: PubMed Central - PubMed

Affiliation: Weyerhaeuser, Federal Way, Washington, United States of America.

ABSTRACT
Plethodontid salamanders are diverse and widely distributed taxa and play critical roles in ecosystem processes. Due to salamander use of structurally complex habitats, and because only a portion of a population is available for sampling, evaluation of sampling designs and estimators is critical to provide strong inference about Plethodontid ecology and responses to conservation and management activities. We conducted a simulation study to evaluate the effectiveness of multi-scale and hierarchical single-scale occupancy models in the context of a Before-After Control-Impact (BACI) experimental design with multiple levels of sampling. Also, we fit the hierarchical single-scale model to empirical data collected for Oregon slender and Ensatina salamanders across two years on 66 forest stands in the Cascade Range, Oregon, USA. All models were fit within a Bayesian framework. Estimator precision in both models improved with increasing numbers of primary and secondary sampling units, underscoring the potential gains accrued when adding secondary sampling units. Both models showed evidence of estimator bias at low detection probabilities and low sample sizes; this problem was particularly acute for the multi-scale model. Our results suggested that sufficient sample sizes at both the primary and secondary sampling levels could ameliorate this issue. Empirical data indicated Oregon slender salamander occupancy was associated strongly with the amount of coarse woody debris (posterior mean = 0.74; SD = 0.24); Ensatina occupancy was not associated with amount of coarse woody debris (posterior mean = -0.01; SD = 0.29). Our simulation results indicate that either model is suitable for use in an experimental study of Plethodontid salamanders provided that sample sizes are sufficiently large. However, hierarchical single-scale and multi-scale models describe different processes and estimate different parameters. As a result, we recommend careful consideration of study questions and objectives prior to sampling data and fitting models.

Show MeSH