指導老師 王勝平 學生 賴冠宇

1. Incorporating spatial autocorrelation into the generallinear model with an application to the yellowfin tuna(Thunnus albacares) longline CPUE data 將空間自我相關與泛線性模式結合，並應 用在黃鰭鮪魚延繩釣的CPUE數據資料中。 指導老師 王勝平 學生 賴冠宇

2. Frame Introduction Results Methods Discussion Evaluation of the spatial-GLM CPUE Standard-GLM Standard Standard-GLM/HBM Case study Spatial-GLM Spatial-GLM/HBM

3. Introduction

4. CPUE • Often been utilized to obtain a relative index of the abundance • of a fish stock. • Affected by changes of year, season, area of fishing and various • environmental factors.

5. Standard • Many statistical methods have been used to ‘standardize’ them to • account for such variations. • generalized linear models (standard- GLM) • － the most commonly used • general additive models (GAM) • neural networks (NN) • regression trees (RT)

6. Standard Problem Thespatial autocorrelation brings a potentially major problem in standardizing the CPUEs by use of the standard-GLM, GAM, NN or RT. Solution Standardized CPUEs Relative indices of the abundance of the fish HBM ┼ Standard-GLM = Standard-GLM/HBM Habitat-based models More accurate Spatial autocorrelation┼　Standard-GLM/HBM= Spatial-GLM/HBM

7. Case study • Weuse these models to analyze data on the CPUE of yellowfin tuna (Thunnus albacares) of the Japanese longline fisheries in the Indian Ocean. • Finally • Evaluate the results of the spatial-GLMs

8. Introduction Methods

9. Methods • standard-GLM and spatial-GLMwere used to analyze the • Japaneseyellowfin tuna longline CPUE data in the Indian • Ocean. • Each method was employed with and without HBM. The data • were detailed in Nishida et al. (2003) and summarized in Table 1.

10. Methods

11. Standard-GLM The standard-GLM without HBM is of the form:

12. Standard-GLM

13. Standard-GLM • Following Bigelow and Nishida: • HBF(the number of hooks between two floats) was divided into six classes: • 5–6、7–9、10–11、12–15、16–20、21–25. • The Japanese tuna longline fisheries with 3–4 HBFSwordfish. • Excluded the data from this type of gear. • Also added the effects : • SST (sea surface temperature ) • TD (thermocline depth ) to the model. • May have affected the distribution and abundance of • yellowfin tuna.

14. Standard-GLM/HBM Standard- GLM/HBM :

15. Spatial-GLM Eq. (1) can be written as: The assumption of independent CPUE or ε in the standard-GLM, Eq. (3), is obviously violated for a fish population, for it ignores the spatial autocorrelation in the many features of the population. After all, fish move together with a positive spatial dependency. The more closely in space the observations are made, the more similar they are.

16. Spatial-GLM With the inherited positive spatial dependency, the error term ε = (ε1, . . . , εn) in Eq. (3) is no longer i.i.d., for cov(εi, εj) = σij ≥ 0, i is not equal to j:

17. Spatial-GLM

18. Spatial-GLM

19. Spatial-GLM/HBM LRT(likelihood ratio test)used for the spatial-GLM can be applied to the effective CPUE, as defined in Eq. (2), to yield the spatial-GLM/HBM. For both spatial-GLM and spatial-GLM/HBM, the spatial autocorrelation structure was modeled as covariograms, as defined in Eq.(5) In the spatial-GLM, three distancerelated parameters (sill, range and nuggets) were estimated, along with those in the standard-GLM.

20. A case study Four GLMs (standard-GLM, standard-GLM/HBM, spatial-GLM and spatial-GLM/HBM) were used to analyze yellowfin tuna CPUE data (1958–2001) of the Japanese longline fisheries in the Indian Ocean, together with some environmental factors. In the spatial-GLM and spatial-GLM/HBM, four distance models (Gaussian, exponential, linear, and spherical) were also examined.

21. Introduction Methods Results

22. Results

23. Results Of the four distance models, the Gaussian model had the best goodness-of-fit. The residuals from the standard-GLM were not i.i.d. (Fig3)

24. Results

25. Results

26. Results

27. Results

28. Results

29. Introduction Methods Results Discussion

30. Evaluation of the spatial-GLM Although the temporal trends in the CPUEs from the spatial-GLMs did not differ greatly from those from the standard-GLMs, the spatial-GLMs are preferred for analyzing the CPUE data on yellowfin tuna, especially if there is strong spatial autocorrelation among the data. This is because the spatial-GLMs took account of the spatial autocorrelation effectively and yielded more realistic estimates of the variances. This is not surprising, especially considering the semivariograms and covariograms from the standard-GLMs (Fig. 3).

31. Evaluation of the spatial-GLM A covariogram is a function of the distance between data points that measures how strong their spatial autocorrelation is. A positive spatial autocorrelation manifests itself in a decrease with distance to zero at some distance, where observations are no longer autocorrelated. The likelihood ratio tests (LRT) for spatial independence of H0: r = 0 showed that the test statistics were highly significant in all cases (Table 3). Therefore, the spatial-GLMs perform better in analyzing yellowfin tuna CPUE data than the standard-GLMs, if the data exhibit strong spatial autocorrelation.

32. Introduction Methods Results Discussion The end Thank You