Final Technical Report: - Southwest Fisheries Science Center - NOAA

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Encounter Rate and Group Size Models For each species or species group, we built separate models of cetacean encounter rate (number of sightings per unit of effort on the transect) and group size (number of individuals per sighting). In preparation for building the models, the cetacean sighting data and environmental data were summarized into segments of on-effort transect. Encounter rate models were built using all transect segments, regardless of whether they contained sightings. Group size models were built on only the subset of segments that contained sightings. Cetacean sighting data are essentially count data with relatively more zeroes than expected from a standard Poisson distribution. Therefore, we modeled encounter rate as a quasipoisson distribution with variance proportional to the mean and a logarithmic link function. The natural logarithm of segment length was included as an offset term to standardize each sample for effort. Cetacean group sizes can be highly variable, spanning up to three orders of magnitude. Estimating the mean group size associated with each line segment involved three steps. First, we computed an estimate of group size for each observer for each sighting based on the observer’s best, high, and low estimates of group size. Second, we computed the arithmetic mean of all observer’s group size estimates for each sighting. <strong>Final</strong>ly, we computed the arithmetic mean group size of all sightings in each line segment. This three-step process resulted in non-integer group size estimates. Given the wide range of cetacean group sizes and the fact that the group size estimates are continuous data, we constructed lognormal GAMs for group size, using the natural logarithm of group size as the response variable and an identity link function. It was necessary to apply a bias-correction factor to the group size predictions from the GAMs because the models were built in log space and then the results were transformed back to arithmetic space, converting the group size estimate to a geometric mean in the process (Finney 1941, Smith 1993). The ratio estimator was used to correct for this back-transformation bias (Smith 1993). Density Computations To estimate cetacean density, the encounter rate and group size model results were incorporated into the standard line-transect equation: where, n/L = encounter rate (number of sightings per unit length of transect), S = expected (or mean) group size, 18
ESW = effective strip width (one-sided), or 1/f(0), where f(0) is the sighting probability density at zero perpendicular distance g(0) = probability of detecting an animal on the transect line. Estimates of f(0) and g(0) were derived from previously published studies, as described in Section 3.5. 3.3.2 CART Tree-based Models We also applied Classification and Regression Trees (the CART algorithm in S-PLUS) to build a regression tree using the encounter rate data, but we found that the method was not appropriate for two reasons. First, it was not able to handle the zero-rich dataset. Second, the predictions were categorical not continuous, constrained to fall into one of the categories of observed encounter rate. Other methods of machine learning may perform better or provide additional insights for cetacean-habitat modeling, and further investigation is warranted. 3.4 Model Scale: Resolution and Extent The results of spatial modeling often depend on the scale used. A pattern or relationship seen at one scale may be entirely different if viewed at a different scale (Wiens 1989). The choice of scales within a model must be appropriate to the questions being asked and the variation of the object being modeled. One aspect of scale is spatial resolution, which refers to the physical dimension of the smallest unit being studied. In the case of cetacean line-transect surveys, resolution refers to the length of the transect segments for which densities are estimated. The number of sightings of a species or the group size within each segment is the response variable (or dependent variable) which is predicted by the model. The predictor variables (or independent variables) used in the model to predict cetacean density would ideally be measured on the same scale, but may be measured on a smaller scale (in which case values can be averaged) or on a larger scale (in which case values can be interpolated). We examined the effect of resolution on models of cetacean encounter rates and group sizes by building models using a range of segment sizes. Specifically, we examined spatial resolutions from 2 to 120 km in both the ETP and the CCE. Habitat is expected to be more spatially heterogeneous in the CCE. A detailed description of the modeling technique used in both ecosystems can be found in Redfern et al. (2008). Another aspect of scale is extent, which refers to the maximum area being studied. Our study areas encompass what are considered to be two distinct ecosystems: the eastern tropical Pacific and the California Current. We explored the effect of extent by comparing models that 19
Page 1 and 2: U N I R A P E D T T E M D S E N TA
Page 3: C O L A N IO T A N U N C I EA .S. D
Page 6 and 7: This report was prepared under cont
Page 8 and 9: Table of Contents Acronyms and Abbr
Page 10 and 11: C.1 Journal Publications ..........
Page 12 and 13: Figure 18. Encounter rate models bu
Page 14 and 15: List of Tables Table 1. Summary of
Page 16 and 17: Appendix B, Table B-6. Summary of m
Page 18 and 19: Acknowledgements This project was f
Page 20 and 21: 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 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 72 and 73: 4.2.4 Conclusions Regardings Modeli
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
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Table 14. Starting and final AIC va
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Table 17. Ratios of observed to pre
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species represented in the acoustic
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0.29 (Risso’s dolphin) to 3.20 (n
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Figure 25. Sample 2005 validation p
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Table 18. (continued) 1991 1993 Nor
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Blue whales had the greatest deviat
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Table 20. Abundance (number of anim
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Table 22. Proportion of deviance ex
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Figure 27. Average density (AveDens
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Table 23. Effective degrees of free
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We attempted to build encounter rat
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5.0 Conclusion The field of predict
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6.0 Transition Plan The models of c
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needed to ensure that the SDSS rema
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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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