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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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Average, by combination of parameters, of all posterior mean estimates of the treatment effect estimator ‘Alpha3’ (see Eq 2) in the multi-scale occupancy model.Results are shown on the logit scale. Panels show the results for different combinations by simulated detection probability and post-treatment occupancy. Horizontal dashed lines show the true coefficient value.
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pone.0142903.g002: Average, by combination of parameters, of all posterior mean estimates of the treatment effect estimator ‘Alpha3’ (see Eq 2) in the multi-scale occupancy model.Results are shown on the logit scale. Panels show the results for different combinations by simulated detection probability and post-treatment occupancy. Horizontal dashed lines show the true coefficient value.

Mentions: The hierarchical single-scale model showed consistent results for the average posterior mean of the treatment effect estimator for all sample sizes when detection probability was 0.5, but some evidence of bias when detection probability was 0.15 (Fig 1). Bias was generally small (<10%) for all detection probabilities when the number of harvest units was at least 40. Estimator bias for the multi-scale model was strongly dependent on both the number of simulated harvest units as well as the number of plots per harvest unit, particularly at lower detection probabilities (Fig 2). Although bias was generally low when detection probability was 0.5, substantial bias existed with low detection probabilities, particularly in cases with less than 50 harvest units (Fig 2). However, these trends suggest that with sufficient sample size at both the primary and secondary sampling units, approximately unbiased estimates can be obtained for the treatment effect estimator under either model in a BACI design, at least for the prior distributions and range of parameter values considered in this study.


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)

Average, by combination of parameters, of all posterior mean estimates of the treatment effect estimator ‘Alpha3’ (see Eq 2) in the multi-scale occupancy model.Results are shown on the logit scale. Panels show the results for different combinations by simulated detection probability and post-treatment occupancy. Horizontal dashed lines show the true coefficient value.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0142903.g002: Average, by combination of parameters, of all posterior mean estimates of the treatment effect estimator ‘Alpha3’ (see Eq 2) in the multi-scale occupancy model.Results are shown on the logit scale. Panels show the results for different combinations by simulated detection probability and post-treatment occupancy. Horizontal dashed lines show the true coefficient value.
Mentions: The hierarchical single-scale model showed consistent results for the average posterior mean of the treatment effect estimator for all sample sizes when detection probability was 0.5, but some evidence of bias when detection probability was 0.15 (Fig 1). Bias was generally small (<10%) for all detection probabilities when the number of harvest units was at least 40. Estimator bias for the multi-scale model was strongly dependent on both the number of simulated harvest units as well as the number of plots per harvest unit, particularly at lower detection probabilities (Fig 2). Although bias was generally low when detection probability was 0.5, substantial bias existed with low detection probabilities, particularly in cases with less than 50 harvest units (Fig 2). However, these trends suggest that with sufficient sample size at both the primary and secondary sampling units, approximately unbiased estimates can be obtained for the treatment effect estimator under either model in a BACI design, at least for the prior distributions and range of parameter values considered in this study.

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