Update Overview

Following my last update, I repeated the multivariate regression tree analysis based on chevron trap catches using the species composition recommended during our last meeting (Figure 1). Note that this analysis resulted in fewer statra prior to the stopping rule and while this stratification did not incorporate longitude, the depth and latitude breaks are identical.


Here are the boundaries and numbers of sample stations within each stratum:

Strata                      Boundary                                                          Number of Sample Stations

1                  d<29.5 & lat>=30.22                                                                         1171

2                  d<29.5 & lat<30.22                                                                            296

3                  d>=29.5 & lat<29.7                                                                            291

4                  d>=29.5 & lat>=29.7 & d>=38.5                                                        1525

5                  d>=29.5 & lat>=29.7 & d<38.5                                                           797



Figure 1. Multivariate Regression Tree.
Figure 1. Multivariate Regression Tree.


In this update I focused on three sampling strategies: 1) the default simple random sample, 2) stratification with annual sample sizes allocated to strata based on the Bethel Algorithm, and 3) stratification with annual sample allocated equally among strata. The Bethel Algorithm requires specification of the maximum CV of the mean catch of the species sampled. The algorithm outputs the actual stratum specific sample size where the sum across all strata is the total annual sample size. Since the target of our sampling effort is not specifically to estimate the mean catch within some minumum amount of precision, it is unclear exactly how to specify mean catch CV. Additionally, because we want to be able to examine different total annual sample sizes within the range of available effort (total annual sample sizes), I chose to use the output of the Bethel Algorithm to compute the proportions of the annual sample size among strata.

Results below use the Bethel Algorithm allocation with a target of the maximum of mean catch CV of 0.05 for each of the 8 species. This produced Bethel allocation proportions of: 37%, 3%, 6%, 29%, and 23% for each stratum 1-5, respectively. As is readily apparent, the allocation proportion for each stratum 1-5 under equal allocation is 20%. If the allocation among strata is proportional to size as is the expectation for the simple random sampling proces, the proportions for each stratum 1-5 are: 29%, 7%, 7%, 37%, and 20%, respectively. Generally relative to a proportional allocation, the Bethel Algorithm allocates greater sampling effort to stratum 1, lesser sampling effort to strata 2 and 4, and similar sampling effort to strata 3 and 5.

Sampling Process

Gray triggerfish, black sea bass, red porgy, gag grouper, red snapper, scamp grouper, vermillion snapper, and red grouper were annually sampled in each of 12 years among 1,500 samples during the first 6 years and 750 samples during the last 6 years. Annual samples were chosen from the sampling universe by simple random samples, stratified samples with Bethel Allocation, or stratified samples with equal allocation. Each species sampled had a simulated true declining trend.

Estimation Results

I computed indices for each replicate sample (n=1000), species, observation method (trap and video), and sample type (Figures 2-9). Each model used latitude, longitude, and depth for both the negative binomial and binomial portions of the zero inflated error structure.

Figure 2 Grey triggerfish true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 2 Grey triggerfish true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 3. Black sea bass true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 3. Black sea bass true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 4. Red porgy true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 4. Red porgy true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 5. Gag grouper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 5. Gag grouper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 6. Red snapper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 6. Red snapper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 7. Scamp grouper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 7. Scamp grouper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 8. Vermillion snapper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 8. Vermillion snapper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 9. Red grouper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).
Figure 9. Red grouper true abundance trend (red line) and 1000 replicate index trends from chevron trap sampling (gray lines) and video sampling using Sumcount (blue lines) and for simple random sampling (Left), stratified sampling with Bethel allocation (Center), and stratified sampling with equal allocation (Right).

Evaluation Process

I computed annual coefficients of variation for each species, observation method (trap and video), and sampling method (Figures 10-17). Note the increase in the CV during the second half of the timeseries owing to the reduction in annual sample size. Additionally, there is not a consistent or notable apparent shifting in the relative magnitude of CV among methods between the first and second halves of the timeseries. This suggests that CV under smaller sample size is not generally improved for one sampling method versus the others.

Figure 10. Grey triggerfish coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 10. Grey triggerfish coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 11. Black sea bass coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 11. Black sea bass coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 12. Red porgy coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 12. Red porgy coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 13. Gag grouper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red). Note different scales on the y-axes.
Figure 13. Gag grouper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red). Note different scales on the y-axes.
Figure 14. Red snapper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 14. Red snapper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 15. Scamp grouper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red). Note different scales on the y-axes.
Figure 15. Scamp grouper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red). Note different scales on the y-axes.
Figure 16. Vermillion snapper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 16. Vermillion snapper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red).
Figure 17. Red grouper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red). Note different scales on the y-axes.
Figure 17. Red grouper coefficients of variation for simple random sampling (Blue), stratified sampling with Bethel Allocation (Black), and stratified sampling with Equal Allocation (Red). Note different scales on the y-axes.


I computed performance scores based on average annual CV for each species and summed across all species for the chevron trap index and the video index (Figure 18-19). The relative degree of difference among sampling methods for the chevron trap indices is larger than for the video indices. For the species that have relatively low CV in the chevron trap indices (grey triggerfish, black sea bass, red porgy, red snapper, and vermillion snapper) there is really very little difference among sampling methods. Similarly and considering the video sampling indices, there is very little difference in total CV scores and individual species CV among the different sampling methods. The largest difference is for red grouper.

Figure 18. Chevron trap index CV scoring.
Figure 18. Chevron trap index CV scoring.
Figure 19. Video index CV scoring.
Figure 19. Video index CV scoring.

Preliminary Conclusion and Possible Next Steps

Considering these results, stratified sampling does not appear particularly beneficial in improving the precision of indices for important assessed species. I question whether these findings are significant enough to publish or recommend a change of sampling design.

I would like to hear your thoughts on these results and preliminary conclusion as well as any suggestions of things to try next in order to determine a better stratification strategy. If you have other ideas about how to improve the operational, observation, or estimation models I would like to hear those suggestions as well.