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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 ‘Beta3’ (see Eq 1) in the hierarchical single-scale occupancy model under a relaxed set of priors.Note we ran only a subset of cases in Table 1 for this analysis. 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. Prior sensitivity can be assessed by comparing with Fig 1.
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pone.0142903.g007: Average, by combination of parameters, of all posterior mean estimates of the treatment effect estimator ‘Beta3’ (see Eq 1) in the hierarchical single-scale occupancy model under a relaxed set of priors.Note we ran only a subset of cases in Table 1 for this analysis. 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. Prior sensitivity can be assessed by comparing with Fig 1.

Mentions: All of the above results are based on a single set of prior distributions, chosen beforehand to reflect subject matter knowledge regarding plethodontid salamander behavior. Although we think that this choice of priors is appropriate for our current application, these priors are potentially informative and have the potential to affect estimator properties such as bias and precision. At the suggestion of a reviewer, we repeated our simulation study with relaxed priors—N(μ = 0, σ2 = 10) for covariate parameters—for a reduced set of the conditions in Table 1. Results for this simulation study are summarized in S5 and S6 Tables. The hierarchical single-scale model with relaxed priors showed a negative bias in the treatment estimator expected value across most conditions (Fig 7). The magnitude of bias was affected by both sample size and detection probability, showing relatively small bias with moderate detection probabilities and larger sample sizes, and substantial bias with low detection probabilities. Results for the multi-scale model with relaxed priors showed a mix of positive and negative bias depending on the simulation conditions (Fig 8). Under both the single-scale and multi-scale models, estimator precision and coverage probabilities using the relaxed priors were substantially the same as with our original choice of priors (S5 and S6 Tables).


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 ‘Beta3’ (see Eq 1) in the hierarchical single-scale occupancy model under a relaxed set of priors.Note we ran only a subset of cases in Table 1 for this analysis. 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. Prior sensitivity can be assessed by comparing with Fig 1.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0142903.g007: Average, by combination of parameters, of all posterior mean estimates of the treatment effect estimator ‘Beta3’ (see Eq 1) in the hierarchical single-scale occupancy model under a relaxed set of priors.Note we ran only a subset of cases in Table 1 for this analysis. 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. Prior sensitivity can be assessed by comparing with Fig 1.
Mentions: All of the above results are based on a single set of prior distributions, chosen beforehand to reflect subject matter knowledge regarding plethodontid salamander behavior. Although we think that this choice of priors is appropriate for our current application, these priors are potentially informative and have the potential to affect estimator properties such as bias and precision. At the suggestion of a reviewer, we repeated our simulation study with relaxed priors—N(μ = 0, σ2 = 10) for covariate parameters—for a reduced set of the conditions in Table 1. Results for this simulation study are summarized in S5 and S6 Tables. The hierarchical single-scale model with relaxed priors showed a negative bias in the treatment estimator expected value across most conditions (Fig 7). The magnitude of bias was affected by both sample size and detection probability, showing relatively small bias with moderate detection probabilities and larger sample sizes, and substantial bias with low detection probabilities. Results for the multi-scale model with relaxed priors showed a mix of positive and negative bias depending on the simulation conditions (Fig 8). Under both the single-scale and multi-scale models, estimator precision and coverage probabilities using the relaxed priors were substantially the same as with our original choice of priors (S5 and S6 Tables).

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