Consequences of ignoring spatial variation in population trend when conducting a power analysis

Long-term, large-scale monitoring programs are becoming increasingly common to document status and trends of wild populations. A successful program for monitoring population trend hinges on the ability to detect the trend of interest. Power analyses are useful for quantifying the sample size needed for trend detection, given expected variation in the population. Four components of variation (within-year variation at a given site, interannual variation within a site, variation among sites in the interannual variation, and variation among sites in mean abundance or density) are commonly considered in power analyses for population trend, but a fifth is rarely considered: variation among sites in the local trend. Spatial variation in trend is expected to reduce statistical power, but the magnitude of this reduction has not been fully explored. We used computer simulations to evaluate the consequences of ignoring spatial variation in trend under a variety of sampling designs and wide ranges of other components of variation. The effect of spatial variation in trend on power was minor when other input parameters took extreme values that made the trend either very difficult or very easy to detect. However, at moderate values of the other parameters, spatial variation in trend had a strong effect, reducing statistical power by up to 60%. In some cases, ignoring spatial variation in trend resulted in an 80% probability of a type I error (falsely detecting a trend in a stable population). Spatial variation in trend is therefore an important consideration when designing a long-term monitoring program for many species, especially those affected by local conditions at sites that are repeatedly surveyed. If variation in trend is ignored, as in many previous power analyses, the recommended sampling design will likely be insufficient to detect the trend of interest and lead to potentially false conclusions of a stable population.