Impacts of temporal revisit designs on the power to detect trend with a linear mixed model: An application to long-term monitoring of Sierra Nevada lakes

Long-term ecological monitoring programs often use linear mixed models to estimate trend in an ecological indicator sampled across large landscapes. A linear mixed model is versatile for estimating a linear trend in time as well as components of spatial and temporal variation in the case of unbalanced data structures, which are common in complex monitoring designs where limited sampling effort must be optimized over time and space. A power analysis was used to inform a lake chemistry monitoring design, including selecting the most appropriate temporal revisit design. Pilot data from surveys of lakes across large wilderness national parks (Sequoia, Kings Canyon, and Yosemite national parks) were used to obtain variance components for a Monte Carlo power simulation. Using a linear mixed model for a range of temporal revisit designs, sample sizes, and trend magnitudes, we evaluated the power to detect trend, the trend test size, and the relative bias of trend coefficient estimates for four continuous and normally distributed indicators. Contrary to prior research based on large-sample approximations that identified a single panel of sites visited annually as the revisit design generating the highest power, we found that the power to detect a 12-year trend based on the Wald t-test from a linear mixed model may be optimized by obtaining unbalanced data sets with limited to no annual replication. We emphasize the importance of examining variance composition, sample size, and the power and size of the trend test with Monte Carlo simulation when allocating sampling effort over time and space.