Update Overview

In this update, I provide two more stratification and allocation schemes that are based on finding the best stratification and allocation considering only either latitude and longitude (No Depth, ND) or latitude and depth (No Longitude, NL) covariates. As with the optimum stratification based on latitude, longitude, and depth covariates, “best” is defined as the minimum sample size that satisfies the specified CV of the mean trap catch for each species. This is accomplished by repeatedly applying the Bethel Algorithm to different stratification options and using a genetic optimization algorithm to approach a near-optimal solution. I specified the CV as 0.10 for each species and I chose to allow the optimization to operate on the covariates in continuous space rather than group each covariate into factor levels prior to determining the optimal stratification.

The results shown here use 4 stratification schemes: 1) optimal stratification considering latitude, longitude, and depth covariates, 2) optimal stratification considering latitude and longitude covariates, 3) optimal stratification considering latitude and depth covariates, and stratification based on multivariate regression tree analysis (using either equal or Bethel sample allocations to each stratum; Figure 1).

Figure 1 Maps of stratification schemes where latitude and longitude boundaries and individual sampling sites are color coded by strata.
Figure 1 Maps of stratification schemes where latitude and longitude boundaries and individual sampling sites are color coded by strata.

Sampling Process

Gray triggerfish, black sea bass, red porgy, gag grouper, red snapper, scamp grouper, vermilion snapper, and red grouper were annually sampled in each of 12 years. I summarized runs across a grid of sample sizes (n= 1500,1000, and 500) and total declines (25%, 50%, and 75%). Unlike previous simulations, I chose to eliminate variation about the depletion patterns (e.g., Figures 2-3). This was done so that differences among estimated index CVs were not influenced by stochasticity in the depletion trends

Figure 2 Grey triggerfish true abundance trend with a 25% reduction (red line) and 1000 replicate index trends from sampling (n=1500) using chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Top Left), stratified sampling with Bethel allocation (Bottom Left), stratified sampling with equal allocation (Top Middle), optimal stratification and allocation using latitude, longitude, and depth covariates (Bottom Middle),optimal stratification and allocation using latitude and longitude covariates (Top Right), and optimal stratification and allocation using latitude and depth covariates (Bottom Right).
Figure 2 Grey triggerfish true abundance trend with a 25% reduction (red line) and 1000 replicate index trends from sampling (n=1500) using chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Top Left), stratified sampling with Bethel allocation (Bottom Left), stratified sampling with equal allocation (Top Middle), optimal stratification and allocation using latitude, longitude, and depth covariates (Bottom Middle),optimal stratification and allocation using latitude and longitude covariates (Top Right), and optimal stratification and allocation using latitude and depth covariates (Bottom Right).
Figure 3 Gag grouper true abundance trend with a 25% reduction (red line) and 1000 replicate index trends from sampling (n=1500) using chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Top Left), stratified sampling with Bethel allocation (Bottom Left), stratified sampling with equal allocation (Top Middle), optimal stratification and allocation using latitude, longitude, and depth covariates (Bottom Middle),optimal stratification and allocation using latitude and longitude covariates (Top Right), and optimal stratification and allocation using latitude and depth covariates (Bottom Right).
Figure 3 Gag grouper true abundance trend with a 25% reduction (red line) and 1000 replicate index trends from sampling (n=1500) using chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Top Left), stratified sampling with Bethel allocation (Bottom Left), stratified sampling with equal allocation (Top Middle), optimal stratification and allocation using latitude, longitude, and depth covariates (Bottom Middle),optimal stratification and allocation using latitude and longitude covariates (Top Right), and optimal stratification and allocation using latitude and depth covariates (Bottom Right).

Evaluation Process

I computed average annual coefficients of variation for each abundance index by species, observation method (trap and video), stratification and sample allocation scheme, sample size (1500, 1000, and 500), and depletion magnitude (25%, 50%, and 75%).


Figure 4. Chevron trap average annual abundance index coefficient of variation (CV) by species, sample size, reduction magnitude, and sampling scheme (SRS=simple random sample, Strat=multiple regression tree stratification (MRT) with equal sample allocation among strata, Bstrat= MRT with Bethel algorithm sample allocation among strata, Ostrat=optimum stratification and allocation with latitude, longitude, and depth covariates, Ostrat_ND=optimum stratification and allocation with latitude and longitude covariates, and Ostrat_NL=optimum stratification and allocation with latitude and depth covariates.
Figure 4. Chevron trap average annual abundance index coefficient of variation (CV) by species, sample size, reduction magnitude, and sampling scheme (SRS=simple random sample, Strat=multiple regression tree stratification (MRT) with equal sample allocation among strata, Bstrat= MRT with Bethel algorithm sample allocation among strata, Ostrat=optimum stratification and allocation with latitude, longitude, and depth covariates, Ostrat_ND=optimum stratification and allocation with latitude and longitude covariates, and Ostrat_NL=optimum stratification and allocation with latitude and depth covariates.


Figure 5. Video average annual abundance index coefficient of variation (CV) by species, sample size, reduction magnitude, and sampling scheme (SRS=simple random sample, Strat=multiple regression tree stratification (MRT) with equal sample allocation among strata, Bstrat= MRT with Bethel algorithm sample allocation among strata, Ostrat=optimum stratification and allocation with latitude, longitude, and depth covariates, Ostrat_ND=optimum stratification and allocation with latitude and longitude covariates, and Ostrat_NL=optimum stratification and allocation with latitude and depth covariates.
Figure 5. Video average annual abundance index coefficient of variation (CV) by species, sample size, reduction magnitude, and sampling scheme (SRS=simple random sample, Strat=multiple regression tree stratification (MRT) with equal sample allocation among strata, Bstrat= MRT with Bethel algorithm sample allocation among strata, Ostrat=optimum stratification and allocation with latitude, longitude, and depth covariates, Ostrat_ND=optimum stratification and allocation with latitude and longitude covariates, and Ostrat_NL=optimum stratification and allocation with latitude and depth covariates.

Conclusions and Possible Next Steps

Considering these results, the three optimum allocation stratification and allocation schemes (Ostrat, Ostrat_ND, and Ostrat_NL) generally perform best across all species, sample size, and depletion magnitude.

I am unaware of other stratification methods to try except methods that would attempt to model spatial correlation specifically. However, given these results my intuition is that not much more variation will be explained and that the the high correlation between depth and longitude will complicate the analysis.

At this point I feel like I am near the end of this analysis and I would like input from the group to finalize the range of sample sizes, depletion levels, and species to consider in a final set of runs prior to reporting. I would also like input as to how you interpret the significance of these results related to guidance to modify SERFS sampling design.