Spatial heterogeneity in statistical power to detect changes in lake area in Alaskan National Wildlife Refuges

Over the past 50 years, the number and size of high-latitude lakes have decreased throughout many regions; however, individual lake trends have been variable in direction and magnitude. This spatial heterogeneity in lake change makes statistical detection of temporal trends challenging, particularly in small analysis areas where weak trends are difficult to separate from inter- and intra-annual variability. Factors affecting trend detection include inherent variability, trend magnitude, and sample size. In this paper, we investigated how the statistical power to detect average linear trends in lake size of 0.5, 1.0 and 2.0 %/year was affected by the size of the analysis area and the number of years of monitoring in National Wildlife Refuges in Alaska. We estimated power for large (930–4,560 sq km) study areas within refuges and for 2.6, 12.9, and 25.9 sq km cells nested within study areas over temporal extents of 4–50 years. We found that: (1) trends in study areas could be detected within 5–15 years, (2) trends smaller than 2.0 %/year would take >50 years to detect in cells within study areas, and (3) there was substantial spatial variation in the time required to detect change among cells. Power was particularly low in the smallest cells which typically had the fewest lakes. Because small but ecologically meaningful trends may take decades to detect, early establishment of long-term monitoring will enhance power to detect change. Our results have broad applicability and our method is useful for any study involving change detection among variable spatial and temporal extents.