Northeast Fisheries Science Center Reference Document 97-01 

Preliminary Results 

of a Spatial and Temporal Analysis 

of Haddock Distribution 

Applying a Generalized 

Additive Model 

by 

Loretta O'Brien 

National Marine Fisheries Serv., Woods Hole, MA 02543 

U.S. DEPARTMENT OF COMMERCE 

National Oceanic and Atmospheric Administration 

National Marine Fisheries Service 

Northeast Region 

Northeast Fisheries Science Center 

Woods Hole, Massachusetts 

January 1997 
The Northeast Fisheries Science Center Reference Document series comprises informal reports produced by the 

Center for timely transmission of results obtained through work at various Center laboratories. The reports are reviewed 

internally before publication, but are not considered formal literature. The National Marine Fisheries Service does not 

endorse any proprietary material, process, or product mentioned in these reports. To obtain additional copies of this 

report, contact: Research Communications Unit, Northeast Fisheries Science Center, Woods Hole, MA 02543-1026 

(508-495-2260). 

This report may be cited as: O'Brien, L. 1997. Preliminary results of a spatial and temporal analysis of haddock 

distribution applying a generalized additive model. Northeast Fish. Sci. Cent. Ref Doc. 97-01; 43 p. Available from: 

National Marine Fisheries Service, 166 Water St., Woods Hole, MA 02543-1026. 
Table of Contents 

ABSTRACT ................................................... 1 

INTRODUCTION ............................................... 1 

METHODS .................................................... 1 

Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

Model Description and Application ............................... 2 

RESULTS ..................................................... 3 

DISCUSSION .................................................. 4 

ACKNOWLEDGEMENTS ......................................... 5 

LITERATURE CITED ............................................ 6 

APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 

LIST of TABLES 

Table 1. Annual pseudo-R2 values for models 1 and 2, the difference in R2 between the 

models, and the number of fish captured and number of stations with bottom 

temperature recorded for Georges Bank-Gulf of Maine haddock (strata 13-40), 1963-

1994. A formulation of Model 1, without the year effect is preSented as 1963-1994. 

Table 2. Stratified mean number per tow and coefficient of variation (CV) for observed and 

GAM fitted catch numbers for Georges Bank-Gulf of Maine haddock (strata 13-40), 

1963-1994. 

LIST of FIGURES 

Figure 1. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

bottom temperature and average depth for 1963. 

Figure 2. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

III 
bottom temperature and average depth for 1965. 

Figure 3. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

bottom temperature and average depth for 1969. 

Figure 4. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

bottom temperature and average depth for 1970. 

Figure 5. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

bottom temperature and average depth for 1975. 

Figure 6. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

bottom temperature and average depth for 1980. 

Figure 7. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

bottom temperature and average depth for 1985. 

Figure 8. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

bottom temperature and average depth for 1989. 

Figure 9. Interpolated observed and GAM fitted catch numbers of haddock and corresponding 

bottom temperature and average depth for 1994. 

Figure 10. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95% confidence intervals (dotted line), autumn 1963. Y-axis is 

scaled to zero, rugplot along x-axis indicates number of observations. 

Figure 11. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95 % confidence intervals (dotted line), autumn 1965. Y-axis is 

scaled to zero, rugplot along x-axis indicates number of observations. 

Figure 12. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95% confidence intervals (dotted line), autumn 1969. Y-axis is 

scaled to zero, rugplot along x -axis indicates number of observations. 

Figure 13. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95% confidence intervals (dotted line), autumn 1970. Y-axis is 

scaled to zero, rugplot along x-axis indicates number of observations. 

Figure 14. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95% confidence intervals (dotted line), autumn 1975. Y-axis is 

scaled to zero, rugplot along x-axis indicates number of observations. 

iv 
Figure 15. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95 % confidence intervals (dotted line), autumn 1980. Y-axis is 

scaled to zero, rugplot along x-axis indicates number of observations. 

Figure 16. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95 % confidence intervals (dotted line), autumn 1985. Y-axis is 

scaled to zero, rugplot along x-axis indicates number of observations. 

Figure 17. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95% confidence intervals (dotted line), autumn 1989. Y-axis is 

scaled to zero, rugplot along x-axis indicates number of observations. 

Figure 18. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) 

for model 1 with 95 % confidence intervals (dotted line), autumn 1994. Y-axis is 

scaled to zero, rugplot along x-axis indicates number of observations. 

Figure 19. Stratified mean number per tow for observed and GAM fitted catch numbers for 

haddock, 1963-1994. 

Figure 20. Stratified mean number per tow with standard errors for observed and GAM fitted 

catch numbers for haddock, 1963-1994. 

Figure 21. Stratified mean number per tow with standard errors for observed catch numbers 

for haddock, 1963-1994. 

Figure 22. Stratified mean number per tow with standard errors for GAM fitted catch numbers 

for haddock, 1963-1994. 

LIST of APPENDICES 

Appendix Table A. Summary of GAM statistics for model 1. 

v 
ABSTRACT 

The temporal and spatial trends in the distribution of haddock, Melanogrammus aeglejinus, 

from Nova Scotia and south, were examined using a generalized additive model (GAM). 

Spatial (latitude and longitude) and environmental (depth and temperature) covariates were 

used as predictor variables for the response variable (abundance). The preferred depth was 

less than 100m and the preferred bottom temperature was between 8 ° - 12 ° C. Estimates of 

mean abundance using the model results were more precise than the estimates normally 

derived from observed catch numbers. 

INTRODUCTION 

Data collected on annual groundfish surveys provide information on the spatial distribution of 

species and the environmental conditions at the time of capture. Typically, analyses of these 

data have been done using generalized linear models (GLMs), often with the addition of 

covariates. An alternative to a GLM is a generalized additive model or GAM (Hastie and 

Tibshirani 1986, Swartzman et al. 1992) that models the nonlinearity of the predictor 

variables. A GAM can be utilized as a predictive model or as an exploratory method to 

suggest possible transformations of the data or appropriate parametric models, such as a GLM. 

In this paper, a GAM was applied to catches of haddock, Melanogrammus aeglejinus, to 

explore trends in abundance related to spatial and environmental covariates. A step-wise GAM 

was performed to determine the best fitting model prior to applying the final GAM to the entire 

data set. Abundance indices of stratified mean number per tow and the associated variances were 

estimated for both the sample and fittes catch numbers. 

METHODS 

Data from the NEFSC bottom trawl research surveys, described by Azarovitz (1981), were 

used in the analyses. Catch of haddock, in numbers, were obtained from the autumn surveys 

for the offshore strata only, from 1963-1994. Stations where haddock were not caught, ('zero 

tows'), were also included. The latitude, longitude, average depth, and bottom temperature 

observations recorded at each station were also used in the analysis. The range of occurrence 

of haddock within the 31 year time series defined the area of the study and was delineated by 

63°W to 75°W longitude and 37"N to 45°N latitude. Catch numbers were adjusted for vessel 

and gear differences using the coefficients of 0.82 and 1.49, respectively, for the appropriate 

years (NEFSC 1991). Only acceptable tows were included (station type-haul-gear code of 136 

1 
or less), and stations without a bottom temperature observation were deleted. 

Abundance indices of stratified mean number per tow, and the associated variances were 

estimated for both the observed and fitted values of catch number using the same methodology 

currently implemented by the NEFSC (Cochran 1977). The indices were derived from 

offshore strata 13-40, which is different from the NEFSC estimate derived from strata 13-25 

and 29-30 presented in the current assessment (O'Brien and Brown 1995). 

Model Description and Application 

A GAM is a nonparametric analog to a GLM and can be described as: 

where the usual linear function of a covariate, ~ jX j is replaced with J; , an unspecified smooth 

function. As in the GLM, it is necessary to specify the underlying error distribution of the model 

and the link function which relates the response variable to the predictors. The error distribution 

used for this application of the GAM is a Poisson, which is appropriate for describing random 

occurrences and count data (Zar 1974, Sokal and Rohlf 1981). The link function is the log of the 

response variable, which is catch in numbers. The candidate predictor variables are the spatial 

variables latitude and longitude, and the environmental variables depth and bottom temperature. 

The GAM, in addition, requires specification of the smooth function using a scatterplot smoother 

such as loess, running mean, or a smooth spline. The scatterplot smoother used in this application 

is the cubic B-spline. The resulting 'smooth' characterizes the trend of the response variable as a 

function of the predictor variables. The degree of smoothing in a scatterplot smooth is controlled 

by the span, which is the proportion of points contained in each neighborhood (the set of x values 

within a defined distance of Xi ). In S-PLUS, the software used for this analysis, the smooth 

functions of the GAM are solved by an iterative process of smoothing the partial residuals called 

the Gauss-Seidel iterative method or backfitting (Hastie 1992). The algorithm separates the 

parametric from the nonparametric part of the fit, and fits the parametric part using weighted 

linear least squares within the backfitting algorithm. 

As an example, in a multiple predictor model with 2 variables, given an estimate i , (x,) , 

f 2 (x 2) is estimated by smoothing the residual of y - i 1 (x,) on X2 • With the estimate 

i2 (x2 ) , an improved estimate of i , (x,) is obtained by smoothing y-i2 (x2 ) on x,. 

Smoothing is continued until y-i,(X, ) onx2 is i 2 (X2 ) and y-i2 (X2 ) on Xl is i,(x, ). 

The fitting of the GAM is an iterative looping process involving the scatterplot smooth, the 

backfitting algorithm, and the local scoring algorithm, which is a generalization of the Fisher 

scoring procedure in a GLM. Each iteration of the local scoring algorithm produces a new 

2 
working response and weights that are directed back to the backfitting algorithm which produces 

a new additive predictor using the scatterplot smoother (Hastie 1992, Hastie and Tibshirani 

1986, Stat. Sci. 1993, Swartzmanetal.1992). 

A step-wise GAM was performed to determine the best fitting model based on the criteria of the 

lowest Akaike Information Criterion (AIC) test statistic. AIC is a function of both the log 

likelihood function and the effective number of parameters being estimated. The AIC in the 

step-wise GAM (Hastie 1992) is calculated as: 

AIC = D + 2df<l> , 

where D=Deviance (residual sums of squares), 

df = effective degrees of freedom, and 

<l> = dispersion parameter (variance). 

The deviance estimated in the model, analogous to the residual sums of squares, is a measure of 

the fit of the model. The model with the lowest AIC is considered to have the best number of 

parameters to include in the final model. The spatial variables, latitude and longitude, and both 

the linear and the smooth functions for depth and temperature were among the possible 

variables in the step-wise GAM. A pseudocoefficient of determination, R', was estimated as 1.0 

- the ratio of the deviance of the model to deviance of the null model (Swartzman et al. 1992). 

The effect of the environmental variables alone on abundance was examined by running a second 

model that did not include the spatial variables and comparing the R' values for the two models. 

RESULTS 

The step-wise GAM indicated that the model with the lowest AlC was: 

Catch number = Intercept + s(average depth) + s(bottom temperature) + latitude + longitude, 

where s is a smoothing spline. This model, modell, was used to run the GAM for the entire 

time series and model 2 used the same formulation without the spatial variables. 

Distribution plots of observed and fitted catch numbers from model 1 for selected years, 

generally about every 5 years, are presented in Figures 1-9. The catch number, temperature, 

and depth data are interpolated in the plots to provide contour representation. The effect of 

the spatial and environmental variables on the distribution of abundance can be seen by 

comparison of the plots of observed and fitted catch numbers. In the earlier years, when the 

distribution of haddock was more widespread there is a noticeable shift in the fitted relative to 

the observed (1963,1965) abundance. In the latter years (1989,1994) when the population is 

relatively smaller, with a highly contracted range, there is little difference between the 

observed and fitted abundance. 

Plots in Figures 10-18 represent the contribution of average depth and bottom temperature to 

3 
the fitted additive predictor. The curves are drawn by connecting the points of the fitted 

values for each function against its predictor. The y-scale is not of importance given that there 

is an intercept in the model; the fitted values are adjusted to average zero (Hastie 1992). In all 

years, abundance is negatively correlated with depth and the preferred depth is generally less 

than 100 m. The preferred bottom temperature varied between years but was generally around 

80 _120 C. 

The pseudocoefficient of determination, or R2, for each model and for the difference between 

models, is presented in Table 1. Modell always has an R2 greater than model 2, indicating 

that model 1 is the better fitting model as previously determined by the AlC in the step-wise 

GAM. Small differences in R2 between the two models indicates little additional information 

is provided by including latitude and longitude in the model (1963, 1969, 1977, 1987, 1990). 

When R2 is greater than 50% in model 2 (1969,1977, 1987, 1990), the enviromnent appears 

to influence the spatial distribution of haddock. When the difference in R2 is large between the 

two models (1983, 1994), some factor other than depth and temperature is most likely 

influencing the spatial distribution. 

The observed and GAM fitted stratified mean number per tow index follow the same trend 

and, in general, the GAM fitted mean is less than the observed mean (Table 2, Figure 19). 

The GAM fitted index has a lower variance than that of the observed (Figures 20-22), which is 

also evident in the consistently lower coefficients of variation (Table 2). 

A summary output of model 1 for the years corresponding to Figures 1-9 is presented in 

Appendix A. 

DISCUSSION 

The time series of distribution plots clearly indicates how the relative size and distribution of 

the haddock stock has declined and contracted, respectively, over time (Figures 1-9). The 

variability in R2 values over the time series indicates that factors other than depth and 

temperature are influencing the spatial distribution of haddock. If depth and temperature 

preferences are different among age classes, variable recruitment and the age structure of the 

stock may be influential factors. Surficial sediment is also a likely spatial characteristic 

influencing distribution of haddock, particularly for juveniles avoiding predation. 

The abundance indices derived from the GAM fitted catch numbers provide a more precise 

estimate compared to the observed catch numbers. Depth and temperature clearly influence 

the abundance of haddock, and additional predictor variables, such as bottom type, may 

further increase the precision of the estimate. 

As is the case in preliminary, developmental work, this analysis could be improved and the 

model extended. The lack of temperature observations at some stations contributed to the loss 

4 
of data in different years. This additional catch data can be incorporated into the GAM by 

using a supplemental temperature database. Application of the bootstrapping procedure to the 

GAM results would provide another approach to assess the significance of the smooth 

functions. The model could also be extended by transfo=ing the predictor variables, 

investigating the interaction ofthe predictor variables, or by adding other covariates such as 

bottom sediment type, age classes, or length groups. 

The GAM may be more informative for species that are inherently more coherent, such as 

schooling fish, e.g., herring or mackerel (Swartzman et al. 1994), or more aggregated species 

such as scup. Also, application of the GAM to a multi-species complex or group in the 

northwest Atlantic, such as flounders or gadids, would provide insight into the factors that 

influence spatial trends in distribution between species ( Swartzman et al. 1992). 

ACKNOWLEDGEMENTS 

I would like to acknowledge the assistance of D. Sheehan, P. Rago, and S. Wigley in 

completing this project. 

5 
LITERATURE CITED 

Azarovitz, T.R. 1981. A brief historical review of the Woods Hole Laboratory trawl survey 

time series. In: Doubleday, W.G. and D. Rivard(eds). Bottom trawl survey. Can. 

Spec. Tech. Pub!. Fish. Aquat. Sci. 58:62-67. 

Cochran, W.J. 1977. Sampling techniques. John Wiley and Sons. New York. 428 p. 

Hastie, T.J. 1992. Generalized additive models in Chambers,I.M and TJ. Hastie (eds), 

Statistical models in S. Wadsworth and Brooks, Pacific Grove. 

Hastie,T. and R. Tibshirani. 1986. Generalized additive models. Chapman and Hall, 

London. 335 p. 

Northeast Fisheries Science Center. 1991. Report of the 12th NE Regional Stock Assessment 

Workshop (12th SAW) Spring 1991. 

O'Brien, L. and R.W. Brown. 1995. Assessment of the Georges Bank haddock stock for 

1994. NEFSC CRD 95-13. 

Sokal, R.R. and FJ. Rohlf. 1981. Biometry. W.H. Freeman and Company, San Francisco. 

859p. 

Statistical Sciences, Inc. S-PLUS for Windows Reference Manual, Version 3.1 Seattle: 

Statistical Sciences, Inc., 1993. 

Swartzman, G., C.Huang, and S.Kaluzny. 1992. Spatial analysis of Bering Sea groundfish 

survey data using generalized additive models. Can. J. Fish. Aquat. Sci. 49: 1366-

1378. 

Swartzman, G., W. Stuetzle, K. Kulman, and M. Powojowski. 1994. Relating the distribution 

of pollock schools in the Bering Sea to environmental factors. ICES J. Mar. Sci,. 51: 

481-492. 

Zar, J.H. 1984. Biostatistical Analysis. Prentice-Hall, Inc. Englewood Cliffs. 718 p. 

6 
TabLe 1. AnnuaL pseudo-Rz vaLues for modeLs 1 and 21, the difference in R2 between the modeLs, and the 

number of fish captured and number of stations with bottom temperature recorded for Georges Bank-GuLf of 

Maine haddock (strata 13-40), 1963-1994. A formuLation of ModeL 1, without the year effect is presented as 

1963-1994. 

Year ModeL 2 ModeL 1 Di fference Fish Stations Catch stations 

w/temperature wlo temperature 

1963 0.39 0.45 0.06 21105 131 1 

1964 0.36 0.48 0.12 15501 118 2 

1965 0.35 0.54 0.19 10712 123 5 

1966 0.24 0.54 0.30 ?622 100 4 

1967 0.28 0.44 0.16 2952 102 18 

1968 0.30 0.51 0.21 1979 85 11 

1969 0.53 0.62 0.09 1751 80 14 

1970 0.20 0.50 0.30 1676 109 3 

1971 0.32 0.53 0.21 2507 120 1 

1972 0.50 0.67 0.17 3695 104 4 

1973 0.54 0.63 0.09 3318 91 6 

1974 0.32 0.53 0.21 2052 89 5 

1975 0.21 0.45 0.24 5898 129 0 

1976 0.59 0.74 0.15 7496 80 3 

1977 0.54 0.62 0.08 9867 130 3 

1978 0.06 0.38 0.32 7712 199 8 

1979 0.42 0.59 0.17 18171 169 9 

1980 0.11 0.39 0.28 8266 111 7 

1981 0.40 0.71 0.31 3995 91 1 

1982 0.60 0.73 0.13 3054 73 12 

1983 0.46 0.81 0.35 3231 67 27 

1984 0.55 0.80 0.25 1206 39 94 

1985 0.49 0.66 0.17 598 30 54 

1986 0.58 0.79 0.21 798 35 20 

1987 0.65 0.70 0.05 3464 32 41 

1988 0.71 0.88 0.17 301 15 30 

1989 0.53 0.74 0.21 317 22 24 

1990 0.93 0.99 0.06 88 4 40 

1991 0.41 0.69 0.28 1155 39 1 

1992 0.31 0.49 0.18 760 62 9 

1993 0.58 0.81 0.23 1292 52 5 

1994 0.41 0.90 0.49 2145 33 8 

mean Mean Difference TotaL TotaL 

1963-1994 0.16 0.29 0.13 152684 2664 

Model 2: Catch number = s(average depth) + s(bottom temperature) 

ModeL 1 : Catch number s(average depth) + s(bottom temperature) + Latitude +Longitude 

7 
Table 2. Stratified mean number per tow and coefficient of variation (CV) for observed and GAM 

fitted catch numbers for Georges Bank-GuLf of Maine haddock (strata 13-40), 1963·1994. 

OBSERVED GAM FIT 

------------- -------------

Year Mean CV Mean CV 

1963 145.77 0.16 127.38 0.04 

1964 180.46 0.19 154.83 0.06 

1965 101.56 0.15 89.78 0.08 

1966 33.11 0.19 32.88 0.07 

1967 16.17 0.31 14.50 0.04 

1968 6.17 0.39 6.12 0.07 

1969 3.45 0.31 6.71 0.22 

1970 8.08 0.55 6.80 0.09 

1971 4.13 0.22 6.14 0.10 

1972 10.85 0.21 10.64 0.17 

1993 15.98 0.35 9.44 0.18 

1974 4.23 0.24 4.47 0.08 

1975 30.74 0.24 23.91 0,05 

1976 70.78 0.48 53.79 0.26 

1977 23.41 0.33 21. 77 0.16 

1978 25.30 0.20 28.05 0.04 

1979 57.07 0.59 48.45 0.15 

1980 28.75 0.23 37.79 0.07 

1981 13.38 0.31 12.52 0.11 

1982 5.36 0.32 6.95 0.27 

1983 7.97 0.38 8.40 0.21 

1984 3.42 0.40 5.90 0.11 

1985 10.77 0.38 11.22 0.28 

1986 6.58 0.52 5.62 0.30 

1987 4.91 0.36 3.16 0.05 

1988 2.57 0.66 4.10 0.55 

1989 6.33 0.46 6.76 0.33 

1990 1.77 0.52 1.78 0.50 

1991 6.98 0.38 7.21 0.14 

1992 4.39 0.30 3.94 0.14 

1993 6.33 0.30 6.62 0.20 

1994 10.34 0.56 10.28 0.35 

8 
Observed Catch Numbers 1963 

-74 -72 -70 -68 -66 -64 

GAM Fit Catch Numbers 1963 

·74 -72 -70 -68 -66 -64 

Figure 1. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1963. 

9 
Temperature (C) 1963 

-74 -72 -70 -68 -66 -64 

Average Depth (m) 1963 

-74 -72 -70 -68 -66 -64 

Figure 1 (Continued). Interpolated observed and GAM fitted catch numbers of haddock 

and corresponding bottom temperature and average depth for 1963. 

10 
OJ 

f') 

OJ 

f') 

-74 

-74 

Observed Catch Numbers 1965 

-72 -70 -68 -66 -64 

GAM Fit Catch Numbers 1965 

-72 -70 -68 -66 -64 

Figure 2. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1965. 

11 
m 

C0 

m 

C0 

-74 

-74 

Temperature (C) 1965 

-72 -70 -68 -66 -64 

Average Depth (m) 1965 

-72 -70 -68 -66 -64 

Figure 2 (Continued). Interpolated observed and GAM fitted catch numbers of haddock 

and corresponding bottom temperature and average depth for 1965. 

12 
co 

C0 

-74 

-74 

Observed Catch Numbers 1969 

o 200 .:100 

-72 -70 -68 -66 -64 

GAM Fit Catch Numbers 1969 

-72 -70 -68 -66 -64 

Figure 3. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1969. 

13 
OJ 

C'0 

OJ 

C'0 

-74 

-74 

Temperature (C) 1969 

-72 -70 -68 -66 -64 

Average Depth (m) 1969 

-72 -70 -68 -66 -64 

Figure 3 (Continued). Interpolated observed and GAM fitted catch numbers of haddock 

and corresponding bottom temperature and average depth for 1969. 

14 
CD 

C0 

CD 

C0 

-74 

-74 

Observed Catch Numbers 1970 

-'- -' 

o 100 250 

-72 -70 -68 -66 -64 

GAM Fit Catch Numbers 1970 

"" 

o 20 40 

-72 -70 -68 -66 -64 

Figure 4. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1970. 

15 
o 

'<T 

o 

'<T 

CXJ 

C0 

-74 

-74 

Temperature (C) 1970 

-72 -70 -68 -66 -64 

Average Depth (m) 1970 

-72 -70 -68 -66 -64 

Figure 4 (Continued). Interpolated observed and GAM fitted catch numbers of haddock 

and corresponding bottom temperature and average depth for 1970. 

16 
co 

C0 

Observed Catch Numbers 1975 

r---- §JO~o -~p 

Q 200 • 400 

-74 -72 -70 -68 -66 -64 

GAM Fit Catch Numbers 1975 

o 100 200 

-74 -72 -70 -68 -66 -64 

Figure 5. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1975. 

17 
Temperature (C) 1975 

-74 -72 -70 -68 -66 -64 

Average Oepth (m) 1975 

-74 -72 -70 -68 -66 -64 

Figure 5 (Continued). Interpolated observed and GAM fitted catch numbers of haddock 

and corresponding bottom temperature and average depth for 1975. 

18 
co 

r:0 

-74 

-74 

Observed Catch Numbers 1980 

-72 -70 

2~.o 

_~lD~ 

o 600 1400 

-68 -66 

GAM Fit Catch Numbers 1980 

o 100 250 

-72 -70 -68 -66 

-64 

-64 

Figure 6. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1980. 

19 
Temperature (C) 1980 

-74 -72 -70 -68 -66 -64 

Average Oepth (m) 1980 

-74 -72 -70 -68 -66 -64 

Figure 6 (Continued). Interpolated observed and GAM fitted catch numbers of haddock 

and corresponding bottom temperature and average depth for 1980. 

20 
N 

'<t 

o 

'<t 

N 

'<t 

o 

'<t 

co 

('<') 

-74 

-74 

Observed Catch Numbers 1985 

o 40 100 

-72 -70 -68 -66 -64 

GAM Fit Catch Numbers 1985 

o 40 80 

-72 -70 -68 -66 -64 

Figure 7. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1985. 

21 
Temperature (C) 1985 

-74 -72 -70 -66 -64 

Average Depth (m) 1985 

-74 -72 -70 -68 -66 -64 

Figure 7 (Continued). Interpolated observed and GAM fitted catch numbers of haddock 

and corresponding bottom temperature and average depth for 1985. 

22 
Observed Catch Numbers 1989 

o 20 60 

-74 -72 -70 -68 -66 -64 

GAM Fit Catch Numbers 1989 

a 20 40 

-74 -72 -70 -68 -66 -64 

Figure 8. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1989. 

23 
N 

'<t 

o 

'<t 

N 

'<t 

o 

'<t 

<Xl 

«) 

-74 

-74 

Temperature (C) 1989 

5 10 20 

-72 -70 -68 -66 -64 

Average Depth (m) 1989 

o 100 250 

-72 -70 -68 -66 -64 

Figure 8 (Continued) Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1989. 

24 
Observed Catch Numbers 1994 

- --' 

o 600 

-74 -72 -70 -68 -66 -64 

GAM Fit Catch Numbers 1994 

o 400 800 

-74 -72 -70 -68 -66 -64 

Figure 9. Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1994. 

25 
N 

"<T 

o 

"<T 

co 

C"") 

N· 

"<T 

o 

"<T 

co 

C"") 

-74 

-74 

Temperature (C) 1994 

6 10 16 

-72 -70 -68 -66 -64 

Average Depth (m) 1994 

-72 -70 -68 -66 -64 

Figure 9 (Continued) Interpolated observed and GAM fitted catch numbers of haddock and 

corresponding bottom temperature and average depth for 1994. 

26 
\ 

'" \ 

50 

Figure 10. 

Haddock 1963 

\ 

'" - \ 

100 150 200 250 4 6 8 10 12 14 

Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) for model 1 with 95% confidence 

intervals (dotted line), autumn 1963. Y-axis is scaled to zero, rugplot along x-axis indicates number of observations. 
Haddock 1965 

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Figure 11. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) for model 1 with 95% confidence 

intervals (dotted line), autumn 1965. Y-axis is scaled to zero, rugplot along x-axis indicates number of observations. 
Haddock 1969 

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Figure 12. Scatterplot smooths of average depth (avedepth) and bottom lemperature (boltemp) for model 1 with 95 % confidence 

intervals (dolted line), autumn 1969. Y-axis is scaled 10 zero, rugplot along x-axis indicates number of observations. 
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Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) for model 1 with 95% confidence 

intervals (dotted line), autumn 1970. Y-axis is scaled to zero, rugplot along x-axis indicates number of observations. 
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Figure 14, Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) for model 1 with 95% confidence 

intervals (dotted line), autumn 1975, Y-axis is scaled to zero, rugplot along x-axis indicates number of observations, 
Haddock 1980 

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Figure 15. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) for model 1 with 95% confidence 

intervals (dotted line), autumn 1980. Y-axis is scaled to zero, rugplot along x-axis indicates number of observations. 
Haddock 1985 
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Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) for model 1 with 95 % confidence 

intervals (dotted line), autumn 1989. Y-axis is scaled to zero, rugplot along x-axis indicates number of observations. 
Haddock 1994 

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Figure 18. Scatterplot smooths of average depth (avedepth) and bottom temperature (bottemp) for model 1 with 95% confidence 

intervals (dotted line), autumn 1994. Y~axis is scaled to zero, rugplot along x~axis indicates number of observations. 
• 

Haddock 

Georges Bank and Gulf of Maine 

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60 65 70 75 80 85 90 95 

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Figure 19. Stratified mean number per tow for observed and GAM ,fitted catch numbers for haddock, 1963-1994. 
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80 85 90 

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95 

Figure 20. Stratified mean number per tow with standard errors for observed and GAM fitted catch numbers for haddock, 1963-

1994. 

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95 

Figure 21. Stratified mean number per tow with standard errors for observed catch numbers for haddock, 1963-1994. 
Haddock 

Georges Bank and Gulf of Maine 

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60 65 70 75 80 85 90 95 

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Figure 22. Stratified mean number per tow with standard errors for GAM fitted catch numbers for haddock, 1963-1994. 
Appendix TabLe A. Summary of GAM statistics for model 1. 

1963 

Summary of h63s2 

CaLL: gam(formuLa = form2, famiLy = poisson, data = h63, na.action = na.omit) 

Deviance ResiduaLs: 

Min lQ Median 3Q Max 

-23.70334 -9.257201 -3.4409120.130610660.68097 

(Dispersion Parameter for Poisson famiLy taken to be 

NuLL Deviance: 42950.02 on 180 degrees of freedom 

ResiduaL Deviance: 23480.34 on 170.0727 degrees of freedom 

Number of Local Scoring Iterations: 7 

DF for Terms and Chi-squares for Nonparametric Effects 

Df 

(Intercept) 1 

s( avedepth) 1 

s(bottemp) 1 

lat 1 

Ion 1 

1965 

Summary(h65s2) 

Npar Df Npar Chisq P(Chi) 

3.0 1195.835 0 

2.9 1110.979 0 

CalL: gam(formuLa = form2, family = poisson, data h65, na.action = na.omit) 

Deviance Residuals: 

Min 1Q Median 3Q Max 

-14.92645 -5.793921 -3.368031 1.277742 27.86504 

(Dispersion Parameter for Poisson family taken to be 

Null Deviance: 24432.84 on 188 degrees of freedom 

Residual Deviance: 11173.43 on 178.1817 degrees of freedom 

Number of LocaL Scoring Iterations: 6 

DF for Terms and Chi-squares for Nonparametric Effects 

Df 

(I ntercept) 1 

s(avedepth) 1 

s(bottemp) 1 

lat 1 

Ion 1 

1969 

SUlTlTlary(h69s2) 

Npar Df Npar Chisq P(Chi) 

3.0 148.3583 0 

2.8 686.6302 0 

Call: gam(formuLa = form2, famiLy = poisson, data = h69, na.action = na.omit) 

Deviance Residuals: 

Min lQ Median 3Q Max 

-14.16375 -1.774192 -0.8154677 -0.150751 26.97446 

(Dispersion Parameter for Poisson family taken to be 1 ) 

40 
Null Deviance: 7371.993 on 209 degrees of freedom 

ResiduaL Deviance: 2791.303 on 199.0142 degrees of freedom 

Number of LocaL Scoring Iterations: 7 

OF for Terms and Chi-squares for Nonparametric Effects 

of 

(Intercept) 1 

s(avedepth) 1 

s(bottemp) 1 

lat 1 

Ion 1 

1970 

SUlTlTlary{h70s2) 

Npar of Npar Chisq P(ChO 

3 92.7616 0 

3 869.5796 0 

CaLL: gam(formuLa = form2, famiLy = poisson, data h70, na.action = na.omit) 

Deviance ResiduaLs: 

Min lQ Median 3Q Max 

·7.195061 ·2.322113 ·0.9872909 ·0.1218674 27.88095 

(Dispersion Parameter for Poisson famiLy taken to be 

NuLL Deviance: 5680.571 on 259 degrees of freedom 

Residual Deviance: 2827.305 on 249.1798 degrees of freedom 

Number of LocaL Scoring Iterations: 7 

OF for Terms and Chi-squares for Nonparametric Effects 

(J ntercept) 

s( avedepth) 

s(bottemp) 

lat 

Ion 

Of Npar Of Npar Chisq P(Chi) 

1 

1 3.0 175.5272 0 

1 2.9 354.7190 0 

1 

1 

1975 

SUlTlTlary(h75s2) 

Call: gam(formuLa = form2, family = poisson, data = h75, na.action = na.omit) 

Deviance Residuals: 

Min 1Q Median 30 Max 

·21.10518 -4.336802 -2.435916 -0.723532431.33545 

(Dispersion Parameter for Poisson family taken to be 

NulL Deviance: 20087.14 on 280 degrees of freedom 

ResiduaL Deviance: 10971.52 on 270.3134 degrees of freedom 

Number of Local Scoring Iterations: 7 

OF for Terms and Chi-squares for Nonparametric Effects 

Of Npar Of Npar Chisq P(Chi) 

(Intercept) 1 

s(avedepth) 1 2.9 3056.350 0 

s(bottemp) 1 2.8 849.076 0 

lat 1 

41 
Lon 1 

1980 

Surrmary{h80s2) 

Call: gam{formula = form2, family = poisson, data h80, na.action na.omit) 

Deviance Residuals: 

Min 1Q Median 3Q Max 

·18.26041 ·6.866505 ·2.713142 ·0.572909885.2113 

(Dispersion Parameter for Poisson famiLy taken to be 1 

NuLL Deviance: 34989.46 on 246 degrees of freedom 

ResiduaL Deviance: 21436.25 on 236.2112 degrees of freedom 

Number of Local Scoring Iterations: 9 

OF for Terms and Chi-squares for Nonparametric Effects 

(Intercept) 

sCavedepth) 

s(bottemp) 

lat 

lon 

Df Npar Of Npar Chisq P(Chi) 

1 

1 3.0 259.648 0 

1 2.8 1037.916 0 

1 

1 

1985 

Sunmary(h85s2) 

Call: gam(formuta = form2, family = poisson, data haS, na.action = na.omit) 

Deviance Residuals: 

Min 1Q Median 3Q Max 

·8.393346 ·2.069827 ·0.9312267 ·0.02706914 12.20916 

(Dispersion Parameter for Poisson famiLy taken to be 

NuLL Deviance: 2883.124 on 115 degrees of freedom 

Residual Deviance: 1030.41 on 105.223 degrees of freedom 

Number of LocaL Scoring Iterations: 7 

OF for Terms and Chi-squares for Nonparametric Effects 

Df Npar Of Npar Ch;sq peChi) 

( Intercept) 

s(avedepth) 

s(bottemp) 

lat 

lon 

1 

1 

1 

1 

1 

1989 

Surrmary(h89s2) 

2.9 

2.9 

166.3630 

231.3585 

o 

o 

CaLt: gam(formula form2, family = poisson, data ha9, na.action = na.omit) 

Deviance ResiduaLs: 

42 
Min 10 Median 30 Max 

-6.115248 ·0.8356205 -0.2329611 -0.016705468.019467 

(Dispersion Parameter for Poisson famiLy taken to be 1 

Null Deviance: 1607.183 on 120 degrees of freedom 

Residual Deviance: 407.267 on 110.1224 degrees of freedom 

Number of Local Scoring Iterations: 7 

DF for Terms and ChiMsquares for Nonparametric Effects 

(Intercept) 

s(avedepth) 

s(bottemp) 

Lat 

Lon 

Df Npar Df Npar Chisq P(Chi) 

1 

1 2.9 116.4413 0 

1 2.9 151.2236 0 

1 

1 

1994 

Summary(h94s2) 

CaLL: gam(formuLa = form2, family = poisson, data h94, na.action na.omit) 

Deviance Residuals: 

Min 1Q Median 30 Max 

-16.4313 -0.6643988 -0.0686757 -0.0002249396 14.96985 

(Dispersion Parameter for Poisson famiLy taken to be 1 

NuLL Deviance: 17354.96 on 279 degrees of freedom 

ResiduaL Deviance: 1780.679 on 269.1192 degrees of freedom 

Number of LocaL Scoring Iterations: 9 

DF for Terms and Chi-squares for Nonparametric Effects 

(Intercept) 

s{avedepth) 

s{bottemp) 

Lat 

Lon 

Df Npar Df Npar Chisq P(Chi) 

1 

1 2.8 2116.289 0 

1 3.0 937.258 0 

1 

1 

43