Recent Results

Following input from our last meeting, I incorporated the sampling design currently used in the SERFS survey (e.g., selecting 5 stations nearest, but more than 200m, from each point identified in a random sampling process), added sampling from the video survey, and added a stratified sampling design. I used strata defined from the multivariate regression tree analysis based on chevron trap catches shown below in Figure 1 (n=7). Annual sample size was allocated to each of the strata equally, so long as each stratum had at a total number of sampling stations greater than or equal to the stratum specific sample size. In the case of 1,500 annual samples, each strata was allocated approximately 214 samples. All strata contained more than 214 sampling stations except for stratum 6 which only has 121 sampling stations. Therefore, all stations within stratum 6 were sampled, and the remaining 214-121=93 samples were reallocated among the remaining strata randomly according to a multinomial process. The probability of assigning remaining samples to each strata (1-5 and 7) was computed as the number of sampling sites within each stratum divided by the total number of sampling sites in strata 1-5 and 7.

Here are the 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            lat>=29.7&d>=38.5                                                                                  1525

5            d>=29.5&lat>=29.7&d<38.5&lon<(-78.91)                                               307

6            d>=29.5&d<38.5&lon>=(-78.91)&lat>=33.99                                           121

7            d>=29.5&lat>=29.7&d<38.5&lon>=(-78.91)&lat<33.99                            369

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

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 annual simple random samples (SRS), annual diversity weighted random samples (DIV), or stratified samples (Stratified). Each species sampled had a 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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.
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 (SRS, Left), diversity weighted random sampling (DIv, Center). and Stratified random sampling.

Evaluation Process

I computed annual coefficients of variation for each species, observation method (trap and video), and sampling schema (Figures 10-17). Note the increase in the CV during the second half of the timeseries owing to the reduction in annual sample size

Figure 10. Grey triggerfish coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 10. Grey triggerfish coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 11. Black sea bass coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 11. Black sea bass coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 12. Red porgy coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 12. Red porgy coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 13. Gag grouper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 13. Gag grouper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 14. Red snapper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 14. Red snapper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 15. Scamp grouper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 15. Scamp grouper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 16. Vermillion snapper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 16. Vermillion snapper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 17. Red grouper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).
Figure 17. Red grouper coefficients of variation for simple random sampling (SRS, Blue), diversity weighted random sampling (DIV, Black), and stratified random sampling (Stratified, Red).

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).

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.