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

Abstract

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.

Site‐selection bias and apparent population declines in long‐term studies

“…; Weiser et al. ). Of course, there are perfectly sensible reasons why researchers may choose to begin work where their study organisms are abundant, and many inferences are not affected by such decisions—but estimates of population trends are.…”

“…First, long-term studies should always report site selection criteria (for an analogous argument, see Coppolillo et al [2004]). Second, where possible, researchers should consider random sampling of available habitat as a means of choosing study populations or formally consider the spatial variability of population trends (Vos et al 2000;Yoccoz et al 2001;Weiser et al 2019). Of course, there are perfectly sensible reasons why researchers may choose to begin work where their study organisms are abundant, and many inferences are not affected by such decisions-but estimates of population trends are.…”

Quantifying the statistical power of monitoring programs for marine protected areas

“…The panel of study areas or sites that are grouped for analysis needs careful consideration, with higher power likely to be achieved when grouped sites have similar responses (Weiser et al 2018). Our simulations assumed the same trend across the three study areas, an assumption that is unlikely to hold true, as areas probably experienced different fishing pressure before MPAs were established and likely experience different levels of recruitment.…”

“…For example, Hamilton et al (2010) showed that grouping areas biogeographically for MPAs around the Channel Islands, California, improved statistical power to detect trends. Alternatively, different trends can also be included in hierarchical models for multiple sites (e.g., Urquhart 2012, Perkins et al 2017), although power to detect overall trends may be low when trends among sites differ substantially (Weiser et al 2018). Further work exploring the influence of including a larger number of study areas with differing levels of response is warranted.…”

Site-selection bias can drive apparent population declines in long-term studies

“…First, long-term studies should always report site selection criteria (for an analogous argument, see Coppolillo et al (2004)). Second, where possible, researchers should consider random sampling of suitable habitat as a means of choosing study populations, or formally consider the spatial variability of population trends (Vos et al 2000;Yoccoz et al 2001, Weiser et al 2018. Of course, there are perfectly sensible reasons why researchers may choose to begin work where their study organisms are abundant, and many inferences are not affected by such decisions -but estimates of population trends are.…”