Final Technical Report: - Southwest Fisheries Science Center - NOAA

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4.2.4 Conclusions Regardings Modeling Approaches Three additional features of the mgcv gam algorithm distinguish it from the S-PLUS counterpart and make it the preferred algorithm for future work. First, the predict.gam function in mgcv does not require the original dataset in order to make predictions from a parameterized GAM. This is in contrast to the S-PLUS predict.gam algorithm, which will produce a run-time error and stop working if the original dataset is not in the working directory. The practical consequence of this restriction is that a model developer working in the S-PLUS environment must provide both the original data and the GAM model object to anyone interested in making predictions from the model. The second desirable feature of mgcv gam is its ability to construct a variety of multidimensional smooth terms. Incorporating tensor product smooths improved the predictive performance of the ETP eastern spinner dolphin and Cuvier’s beaked whale encounter rate models, as discussed further in Section 4.8. <strong>Final</strong>ly, the developer of the mgcv package is very active in the field of statistics and is constantly updating and improving the package. The differences between GLMs and S-PLUS GAMs for a given dataset were surprisingly little based on a comparison of ASPE, explained deviance, the predictor variables and associated degrees of freedom in the final models, the shape of the smoothing splines for each predictor variable, and visual examination of geographic contour plots of predicted density. Greater differences in statistical details (but not in geographic contour plots of predicted densities) were observed between GLMs and GAMs constructed using mgcv because the GLMs and S-PLUS GAMs were constrained to a maximum of three degrees of freedom per term, whereas the mgcv gam function allowed higher degrees of freedom. As evident from the comparison between simple and complex mgcv gam models in Tables 10 and 11, however, and the outcome of the SWFSC Cetacean Experts’ Workshop, greater complexity frequently does not result in better models. Two lessons emerged from this model comparison exercise: 1. It is worthwhile to compare models built using a variety of tools. Choice of the “preferred” tool is likely to be case-specific, but it is best to be fully aware of the advantages and disadvantages of alternative modeling methods and algorithms. 2. Model evaluation should encompass a suite of model evaluation techniques. It was rare that all model evaluation techniques pointed to the same model to be the best model. Quantitative statistics such as the observed-to-predicted ratios provide nice summaries, but they lose spatial accuracy. Visual examination of geographic contour plots maintain spatial details, but it is difficult to quantify concordance between observations and predictions or between plots derived from different models. 50
Table 10. Comparison of the simple and complex encounter rate GAMs for the ETP. All models were built using the gam algorithm in the R package mgcv. The term gam.method refers to the numerical method used to optimize the smoothing parameter estimation criterion for the gam. Splines were either cubic regression splines with shrinkage (cs) or thin plate regression splines with shrinkage (ts). The gamma parameter determines the penalty for model complexity, with larger values of gamma resulting in greater penalty. Also shown are the total effective degrees of freedom (EDF), the sum of the absolute value of the deviance in the ratio of observed to predicted number of sightings, the explained deviance, and the average squared prediction error (ASPE) for the best model re-fit using all data from 1986-2006 (or 1998-2006 for offshore spotted dolphins). If a single model outperformed all others, the corresponding elements of the table show "NA" for the type of model that was not considered any further. Model Total Guild Type gam.method Spline gamma EDF sum(abs(1-R)) Explained Deviance ASPE Offshore spotted dolphin Simple perf.magic cs 1.400 6.914 1.443 0.104 0.044 Complex outer ts 1.000 42.143 1.303 0.116 0.044 Eastern spinner dolphin Simple perf.magic cs 1.000 32.200 1.947 0.252 0.018 Complex NA NA NA NA NA NA NA Whitebelly spinner dolphin Simple perf.magic cs 1.000 22.627 2.070 0.165 0.007 Complex NA NA NA NA NA NA NA Striped dolphin Simple perf.magic cs 1.000 22.533 1.149 0.086 0.048 Complex outer ts 1.400 53.388 1.048 0.094 0.048 Rough-toothed dolphin Simple perf.magic cs 1.000 8.914 1.355 0.155 0.010 Complex outer cs 1.000 60.560 0.745 0.180 0.010 Short-beaked common dolphin Simple perf.magic cs 1.400 16.733 1.599 0.162 0.020 Complex perf.outer cs 1.000 59.646 1.494 0.183 0.020 Bottlenose dolphin Simple perf.magic ts 1.400 14.240 1.806 0.163 0.029 Complex perf.outer ts 1.000 51.457 1.475 0.178 0.029 Risso's dolphin Simple perf.magic cs 1.000 14.238 2.196 0.088 0.011 Complex outer cs 1.000 59.795 1.797 0.111 0.011 51
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U N I R A P E D T T E M D S E N TA
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C O L A N IO T A N U N C I EA .S. D
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This report was prepared under cont
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Table of Contents Acronyms and Abbr
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C.1 Journal Publications ..........
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Figure 18. Encounter rate models bu
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List of Tables Table 1. Summary of
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Appendix B, Table B-6. Summary of m
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Acknowledgements This project was f
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of these choices as possible and us
Page 22 and 23: Although our models include most of
Page 24 and 25: 2.0 Background The Navy and other m
Page 26 and 27: comparison is based on a separate s
Page 28 and 29: Figure 1. Transects (green lines) s
Page 30 and 31: used to evaluate the ability of sum
Page 32 and 33: 3.1.5 Mid-trophic Sampling with Net
Page 34 and 35: variable. Interpolated maps of the
Page 36 and 37: Table 2. Variogram model results. A
Page 38 and 39: “number of individuals” as the
Page 40 and 41: Encounter Rate and Group Size Model
Page 42 and 43: were built separately for each of t
Page 44 and 45: Expanding models to the entire U.S.
Page 46 and 47: Table 4. Summary of the weighted ef
Page 48 and 49: Consistent with Barlow and Forney (
Page 50 and 51: incorporation of geographic coordin
Page 52 and 53: overwhelming majority of “Bryde
Page 54 and 55: the genera Ziphius and Mesoplodon.
Page 56 and 57: Table 7. Geographically stratified
Page 58 and 59: above, and the data themselves, are
Page 60 and 61: (hereafter “summer”). SWFSC has
Page 62 and 63: avoid these problems, we decided to
Page 64 and 65: Figure 9. Thermocline depth (m) obs
Page 66 and 67: Attempts to adjust search parameter
Page 68 and 69: CAMMS 1991 PODS 1993 ORCAWALE 1996
Page 70 and 71: 4.2 Modeling Framework : GLM and GA
Page 74 and 75: Table 10 cont. Comparison of the si
Page 76 and 77: Table 11 cont. Comparison of the si
Page 78 and 79: Figure 15. The transect lines used
Page 80 and 81: A) Striped dolphin 10 km B) Short-b
Page 82 and 83: dependent. For example, the number
Page 84 and 85: Figure 19. Predicted average densit
Page 86 and 87: ecosystem, eastern spinner dolphins
Page 88 and 89: Table 13. Variables selected for mo
Page 90 and 91: Table 14. Starting and final AIC va
Page 92 and 93: Table 17. Ratios of observed to pre
Page 94 and 95: species represented in the acoustic
Page 96 and 97: 0.29 (Risso’s dolphin) to 3.20 (n
Page 98 and 99: Figure 25. Sample 2005 validation p
Page 100 and 101: Table 18. (continued) 1991 1993 Nor
Page 102 and 103: Blue whales had the greatest deviat
Page 104 and 105: Table 20. Abundance (number of anim
Page 106 and 107: Table 22. Proportion of deviance ex
Page 108 and 109: Figure 27. Average density (AveDens
Page 110 and 111: Table 23. Effective degrees of free
Page 112 and 113: We attempted to build encounter rat
Page 114 and 115: 5.0 Conclusion The field of predict
Page 116 and 117: 6.0 Transition Plan The models of c
Page 118 and 119: needed to ensure that the SDSS rema
Page 120 and 121: Administrative Report LJ-07-02. NOA
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Forney KA, Barlow J (1993) Prelimin
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Redfern JV, Barlow J, Ballance LT,
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Appendix A: Detailed Model Results
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Table A-1 (continued) Blue whale 19
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Figure A-1a. Striped dolphin 108
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Figure A-1c. Risso’s dolphin 110
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Figure A-1e. Northern right whale d
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Figure A-1g. Sperm whale 114
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Figure A-1i. Blue whale 116
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Figure A-1k. Baird’s beaked whale
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Figure A-2. Predicted average densi
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Figure A-2b. Short-beaked common do
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Figure A-2d. Pacific white-sided do
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Figure A-2f. Dall’s porpoise 126
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Figure A-2h. Fin whale 128
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Figure A-2j. Humpback whale 130
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Figure A-2l. Small beaked whales 13
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Table B-2. Summary of model validat
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Table B-10. Summary of model valida
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Figure B-1. Predicted yearly and av
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Figure B-1. b) Eastern spinner dolp
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Figure B-1. c) Whitebelly spinner d
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Figure B-1. d) Striped dolphin 168
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Figure B-1. e) Rough-toothed dolphi
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Figure B-1. f) Short-beaked common
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Figure B-1. g) Bottlenose dolphin 1
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Figure B-1. h) Risso’s dolphin 17
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Figure B-1. i) Cuvier’s beaked wh
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Figure B-1. j) Blue whale 180
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Figure B-1. k) Bryde’s whale 182
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Figure B-1. l) Short-finned pilot w
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Figure B-1. m) Dwarf sperm whale 18
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Figure B-1. n) Mesoplodon beaked wh
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Figure B-1. o) Small beaked whales
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Figure B-2. Predicted average densi
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Figure B-2. (cont.) c) Whitebelly s
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Figure B-2. (cont.) g) Bottlenose d
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Figure B-2. (cont.) k) Bryde’s wh
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Figure B-2. (cont.) o) Small beaked
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Ferguson MC (2005) Cetacean Populat
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Barlow J, Kahru M, Mitchell BG (In
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Memorandum NMFS-SWFSC-374, U.S. Dep
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