Expanded power analysis of the Channel Islands National Park Kelp Forest Monitoring Program

Broms, Kristin; Lincome-Hatfield, Travis

doi:10.36967/2294207

A 2020 protocol review of the Mediterranean Coast Network kelp forest monitoring program (Rassweiler et al. 2020) included power analyses tied to sample sizes. This report augments that protocol review by recalculating some of those power analyses to account for nonnormality of the data. It specifically augments: ● Precision in estimates of mean abundance ● Power to detect year-to-year change at a given site ● Power to detect trends in abundance The overarching goal of this expanded power analysis is to answer whether an appropriate number of samples are being collected for each method and if any sampling efforts can be reduced without losing significant power to detect trends. These questions are restated in each section because they are addressed differently in each analysis method. For example, using the random point contact (RPC) method involves collecting data at 40 points at 15 replicates per site, so changes to both the number of points and the number of replicates per site could be considered. The following conclusions were reached: ● The data include many zero counts, exhibit mean-variance relationships, and often fail to pass normality tests. ● The data exhibit a huge variation in precisions among species, sites, and years. Standard errors were relatively high compared to mean counts, leading to low precision for most species-site-year combinations. ● Power to detect year-to-year changes was low for many species-site-year combinations, but there was large variability across the species, sites, and year combinations and the assumption of normality was likely to be rejected for species-site-year combinations with low counts. When only examining the combinations where the assumption of normality failed to be rejected, the numbers of replicates would have to double for the 1-m quadrat, band transects, and RPC method in order to meet the desired requirements (80% power to detect a 40% change in abundance), but fewer 5-m quadrat replicates could be taken. ● The power analysis to detect trends in abundance in which we combined all sites and years into one model for each species showed power varied widely by species. The estimated power to detect a 10% annual change for 20 years was 49% for the purple sea urchin (Strongylocentrotus purpuratus), 79% for the red sea urchin (Strongylocentrotus franciscanus), 98% for the California spiny lobster (Panulirus interruptus), and 100% for the warty sea cucumber (Parastichopus parvimensis). For these analyses, all sites were included in one model and although the models allowed for variation in slope among sites and variation among years, the power was based on an overall, parkwide trend. ● The power analysis to detect trends in abundance by island (Appendix B) showed considerable variation in power among islands for purple and red sea urchins but was very high for the California spiny lobster and the warty sea cucumber. Estimated power to detect a 10% annual change for 20 years was highest for the purple sea urchin on Anacapa Island although still well below the desired 80% power at all islands included in the analysis. Estimated power to detect a 10% annual change for 20 years for the red sea urchin was approximately 80% or higher for Anacapa, Santa Barbara and Santa Rosa islands, and only about 55% at Santa Cruz Island. Estimated power to detect a 10% annual change was very high after only 10 years for both the California spiny lobster and the warty sea cucumber on the four islands included in the analysis. ● The time and cost savings, as well as the feasibility and safety of any reduction in sampling must be considered for the many species monitored by each protocol before any changes are made to the long-term program. The analysis contained herein may be used to support changes in the sampling design, but because of the wide range of conclusions for each species, site, and year combination, it is not possible to use these results without consideration of the cost and large nu

Expanded power analysis of the Channel Islands National Park Kelp Forest Monitoring Program

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