Correction to: Trend estimation for complex survey designs of water chemistry indicators from Sierra Nevada Lakes.

The original version of this article contained a misaligned equation. The following equation replaces the online printed on the 5th page of the article.

Trend estimation for complex survey designs of water chemistry indicators from Sierra Nevada Lakes.

Surveys for long-term monitoring programs managing natural resources often incorporate sampling design complexity. However, design weights are often ignored in trend models of data from complex sampling designs. Generalized random tessellation stratified samples of a simulated population of lakes are selected with various levels of survey design complexity, and three trend approaches are compared. We compare an unweighted trend model, linear regression models of the trend in design-based estimates of annual status, and a probability-weighted iterative generalized least squares (PWIGLS) approach with a linearization variance. The bias and confidence interval coverage of the trend estimate and the size and power of the trend test are used to evaluate weighted and unweighted approaches. We find that the unweighted approach often outperforms the other trend approaches by providing high power for trend detection and nominal confidence interval coverage of the true trend regression parameter. We also find that variance composition and revisit design structure affect the performance of the PWIGLS estimator. When a subpopulation exhibiting an extreme trend is sampled disproportionately to its occurrence in the population, the unweighted approach may produce biased estimates of trend with poor confidence interval coverage. We recommend considering variance composition and potential subpopulation trends when selecting sampling designs and trend analysis approaches.

Long-term monitoring of western aspen--lessons learned.

Aspen woodland is an important ecosystem in the western United States. Aspen is currently declining in western mountains; stressors include conifer expansion due to fire suppression, drought, disease, heavy wildlife and livestock use, and human development. Forecasting of tree species distributions under future climate scenarios predicts severe losses of western aspen within the next 50 years. As a result, aspen has been selected as one of 14 vital signs for long-term monitoring by the National Park Service Upper Columbia Basin Network. This article describes the development of a monitoring protocol for aspen including inventory mapping, selection of sampling locations, statistical considerations, a method for accounting for spatial dependence, field sampling strategies, and data management. We emphasize the importance of collecting pilot data for use in statistical power analysis and semi-variogram analysis prior to protocol implementation. Given the spatial and temporal variability within aspen stem size classes, we recommend implementing permanent plots that are distributed spatially within and among stands. Because of our careful statistical design, we were able to detect change between sampling periods with desired confidence and power. Engaging a protocol development and implementation team with necessary and complementary knowledge and skills is critical for success. Besides the project leader, we engaged field sampling personnel, GIS specialists, statisticians, and a data management specialist. We underline the importance of frequent communication with park personnel and network coordinators.