1417
Application of a generalized additive model (GAM) to reveal
relationships between environmental factors and distributions
of pelagic fish and krill: a case study in Sendai Bay, Japan
Hiroto Murase, Hiroshi Nagashima, Shiroh Yonezaki, Ryuichi Matsukura, and Toshihide Kitakado
Murase, H., Nagashima, H., Yonezaki, S., Matsukura, R., and Kitakado, T. 2009. Application of a generalized additive model (GAM) to reveal
relationships between environmental factors and distributions of pelagic fish and krill: a case study in Sendai Bay, Japan. – ICES Journal of
Marine Science, 66: 1417– 1424.
A generalized additive model (GAM) was applied to fishery-survey data to reveal the influences of environmental factors on the distribution patterns of Japanese anchovy (Engraulis japonicus), sand lance (Ammodytes personatus), and krill (Euphausia pacifica).
Echosounder and physical-oceanographic data were collected in Sendai Bay, Japan, in spring 2005. A hierarchical model was used
with two spatial strata: (i) presence and absence of each species; and (ii) biomass density of each species, given its presence; and
six environmental covariates (surface water temperature, salinity, and chlorophyll, and near-seabed water temperature, salinity, and
depth). The results indicate non-linear responses of the two indices to the environmental covariates. In addition, the biomasses estimated by the GAMs were comparable with estimates based on conventional, stratified-random sampling for each species. GAMs are
very useful for (i) investigating the effects of environmental factors on the distributions of biological organisms, and (ii) predicting the
distributions of animal densities in unsurveyed areas.
Keywords: abundance estimation, distribution model, echosounder, ecosystem, fish, GAM, habitat model, marine ecology.
Received 7 August 2008; accepted 10 February 2009; advance access publication 17 April 2009.
H. Murase: The Institute of Cetacean Research, 4-5 Toyomi-cho, Chuo-ku, Tokyo 104-0055, Japan. H. Nagashima: Miyagi Prefecture Fisheries
Technology Institute, 97-6 Sodenohama, Watanoha, Ishinomaki, Miyagi 986-2135, Japan. S. Yonezaki: National Research Institute of Far Seas
Fisheries, 5-7-1 Orido, Shimizu-ku, Shizuoka 424-8633, Japan. R. Matsukura: Graduate School of Environmental Science, Hokkaido University,
3-1-1 Minato-cho, Hakodata, Hokkaido 041-8611, Japan. T. Kitakado: Tokyo University of Marine Science and Technology, 4-5-7 Konan,
Minato-ku, Tokyo 108-8477, Japan. Correspondence to H. Murase: tel: þ81 3 3536 6576; fax: þ81 3 3536 6522; e-mail: [email protected].
Introduction
Knowledge of the abundances and dynamics of target fish populations is basic to effective fishery management. It is also important to know how environmental factors affect the distributions
of such populations. In 1991, ICES held a workshop on the applications of spatial techniques to acoustic-survey data, where spatialstatistical methods were discussed (ICES, 1993). One of the
methods considered was a generalized additive model (GAM). A
GAM is a non-parametric, regression technique not restricted by
linear relationships, and it is flexible regarding the statistical distribution of the data (Swartzman et al., 1995). GAMs have been
applied to acoustic datasets to investigate relationships between
environmental factors and horizontal distributions of herring in
the Northeastern Atlantic (Maravelias, 1997; Maravelias and
Reid, 1997; Bailey et al., 1998; Maravelias et al., 2000a, 2000b),
and walleye pollock in the Bering Sea (Swartzman et al., 1994,
1995). GAMs have also been used to depict the effects of environmental factors on the vertical distribution of various fish
(Swartzman, 1997; Swartzman et al., 1999; Taylor and Rand,
2003; Winter et al., 2007). However, there have been few applications of GAMs to create maps of the horizontal distribution of
fish (Beare et al., 2002). Moreover, GAMs have not been used commonly on echosounder data to estimate the biomasses of
# 2009
commercially fished species and the measurement of the associated uncertainty of the estimate. A stratified, random-sampling
method (Jolly and Hampton, 1990) is often used to estimate
biomass and its associated uncertainty, but it does not account
for the effects of environmental variables. GAMs, however, are
flexible enough to model relationships between biomasses and
variables describing their environments.
Sendai Bay is located in the northeastern part of Japan, where
there are strong seasonal changes in the location of the Subarctic,
western-boundary current. In this area, the cold, low-salinity water
of the Oyashio Current converges with the warm, high-salinity
water of the subtropical, western-boundary Kuroshio Current.
Distributions of animals in Sendai Bay change markedly with the seasonal changes in oceanographic conditions. In spring, when the
influence of the Oyashio is strong, krill (Euphausia pacifica) and
sand lance (Ammodytes personatus) are the dominant pelagic
species in the bay. Japanese anchovy (Engraulis japonicus) start
migrating from south to north at this time, and some early migrant
anchovy are observed in the bay. These three species are important
for the commercial fishery there (Nagashima, 2000, 2007; Taki,
2002). For these reasons, Sendai Bay is an ideal region to test the
applicability of GAM-based, spatial modelling to reveal relationships
between environmental factors and the distributions of these species.
International Council for the Exploration of the Sea. Published by Oxford Journals. All rights reserved.
For Permissions, please email: [email protected]
1418
In this paper, GAMs are applied to an acoustic and
physical-oceanographic dataset to: (i) examine the effects of
environmental variables (e.g. oceanographic conditions) on the
distributions of Japanese anchovy, sand lance, and krill; (ii)
predict their spatial distributions; and (iii) estimate their biomasses.
Methods
The survey was conducted in Sendai Bay from 11 to 25 April 2005,
as a part of the coastal component of the Japanese Whale Research
Programme in the western North Pacific—Phase II (JARPN II).
The survey area was stratified into seven blocks (A–G block)
based on seabed depth (Figure 1) and a zigzag track line covered
each one. In each block, the surveyed distance divided by the
square root of the survey area was larger than 6, the number
needed for precise estimates of biomass according to Aglen
(1989). Acoustic and oceanographic surveys were conducted
with the trawler RV “Takuyo maru” (Miyagi prefecture, 120
GT). Track lines were run at 9 knots. A 38- and 120-kHz echosounder system (Simrad EK500) was used for the acoustic
survey. The data were recorded with the aid of Echoview (Sonar
Data Co., Ltd, Australia). The EK500 was calibrated before the
survey using a copper sphere and following the methods of
Foote (1982). A trawlnet with a mouth opening 7 m wide by
3.5 m high, and with a 3-mm liner codend, was used to validate
the species of target echoes in the survey area. Trawls were conducted in the blocks where scatterer densities were high.
Representative echoes were selected, based on knowledge gathered
during surveys of this area since 1999. Oceanographic conditions
from the sea surface to 1 m above the seabed were recorded by
CTD casts at 42 stations. Sea-surface temperature (SST), salinity,
and chlorophyll a concentration were recorded every minute
along the track line.
H. Murase et al.
Identification of the species contributing echoes was based on
the differences of mean volume-backscattering strength (Sv )
measured at 120 and 38 kHz (DSv120 – 38) and the Sv at 120 kHz.
Ranges of these values were calculated, based on the results of targeted trawls. Respective ranges of Sv and DSv120 – 38, which indicate
these three species, were: krill, 270 to 245 dB and 10 to 20 dB;
adult Japanese anchovy, 250 to 235 dB and 210 to 5 dB; and
adult sand lance, 270 to 250 dB and 210 to 10 dB.
Nautical-area-backscattering coefficients (sA) were calculated
with the aid of Echoview for each species, for every 0.1 nautical
mile transect distance, from the sea surface to the seabed.
Theoretical target strength (TS) vs. log-length relationships were
derived for krill and sand lance at 120 kHz, based on the distortedwave Born approximation model (Stanton and Chu, 2000):
TS ¼ 50.7 log(LT) 2 150.4
and
TS ¼ 49.3 log(LS) 2 160.2,
respectively (R. Matsukura, unpublished data), where total length
(LT) and standard length (LS) are in millimetres. For Japanese
anchovy, TS ¼ 20 log(TL) 2 72.5, where TL is in centimetres
nautical mile22) of
(Iversen et al., 1993). Biomass densities (r, t P
the three species were estimated as r ¼ ðsA =ð4psbs ÞÞfi Wi ,
where sbs is the backscattering cross-sectional area (=10(0.1TS)),
fi the frequency, and Wi the weight of the ith length class. As a reference value to evaluate the performance of the GAMs, biomasses of
the three species and their variances were estimated based on the
stratified, random-sampling method of Jolly and Hampton (1990).
Interactions between the biomasses of the three species and
environmental factors were investigated at a longitudinal–latitudinal scale of 3000 3000 , i.e. the grid-cell size. Six environmental
factors [sea surface water temperature (8C), salinity (psu), chlorophyll a concentration (mg m23), and near-seabed (1 m above
seabed) water temperature, salinity, and depth (m)] were used as
covariates in the spatial modelling. In the survey area, Japanese
anchovy was typically distributed in a near-surface layer, whereas
Figure 1. (a) Survey area in Sendai Bay, Japan, with a contour map of surface-water temperature. The area was divided into seven blocks
(A– G) to estimate the biomasses of krill, Japanese anchovy, and sand lance using a stratified, random-sampling method. Depths of isobaths
are indicated. (b) Contour map of near-seabed water temperature.
1419
GAM–estimates of fish and krill distributions
krill and sand lance were distributed in both near-surface and
near-seabed layers. The value of each environmental factor in
each grid cell was estimated using kriging methods with the aid
of a GIS, Marine Explorer (Environmental Simulation
Laboratory, Japan).
A hierarchical-spatial structure with two strata (first stratum:
presence and absence of a biological organism; second stratum:
biomass density r given its presence) was developed. The
two-strata GAMs were used to estimate biomasses and create distribution maps of fish and krill and to examine the effects of
environmental factors on their distributions. A GAM with a binomial error distribution that had a logistic-link function was
assumed for the first stratum. A GAM with either a Gamma
error distribution with the log-link function or a Gaussian error
distribution with identical link function was used for the second
stratum modelling. In the case of the GAM with a Gaussian
error distribution and the identical link function, natural logarithms of r were used as dependent variables. All environmental
covariates were considered initially for both strata. When the
number of observations was few, data for that covariate were
pooled into groups of either positive or negative values.
Smoothness parameters were estimated with generalized crossvalidation (GCV).
Effective covariates were selected following Wood (2001).
Covariates were deleted from the models if the following three criteria were met: (i) the estimated degrees of freedom was close to 1;
(ii) the confidence interval was zero everywhere; and (iii) the GCV
score decreased when the term was dropped. Models with the
lowest GCV scores were selected. However, if the use of a selected
model resulted in: (i) unrealistically large biomasses relative to
those predicted by the stratified, random-sampling method, or
(ii) convergence errors in the estimation of uncertainty of
biomass, the covariates were deleted until approximate significance levels of all smoother terms were ,0.001. Wood (2001)
indicated that the deletion of terms is sometimes subjective, and
that if the deletion of a term results in a small change in the
GCV score, the term should be deleted.
This GAM-based analysis used the “mgcv” package (version
1.30-27) of the R program (R Development Core Team, 2007).
“Deviance explained” (analogous to variance in a linear
regression), adjusted r2, and GCV scores were calculated. The
shapes of the functional forms for the selected covariates were
plotted. When the slopes of the functional forms are positive,
the covariates are related positively to the dependent variables,
or vice versa. Selected models allowed prediction of r in unsurveyed cells. Biomass density for each species was estimated as the
product of the results from the two strata. The coefficient of variation, CV of r, was estimated using a parametric bootstrap with
1000 iterations, assuming lognormally distributed errors. GAMestimated r was compared with the echosounder-estimated r.
Results
Contour maps of the surface and near-seabed water temperatures
are presented in Figure 1. Generally, both surface water and nearseabed water temperatures were high in coastal areas and low
offshore. However, the distribution of surface water temperatures
was heterogeneous compared with near-seabed temperatures.
Target-identification trawls were conducted at six stations
(Table 1). Echoes from krill and sand lance were each identified
at three stations. Because there was no opportunity to identify
Table 1. Summary of target trawls.
Total
Block Station #
Positions
catch (kg)
0.87
B
1
388050 N 1418080 E
2
C
1
388030 N 1418220 E
2
388130 N 1418260 E
0.65
2.4
D
1
378580 N 1418320 E
3.3
2
388000 N 1418450 E
F
1
37–518N 1418160 E
1.5
Species (% in
total catch)
Sand lance (100)
Krill (100)
Sand lance (100)
Krill (100)
Krill (100)
Sand lance (94.4)
Figure 2. Distributions of krill (top), Japanese anchovy (middle), and
sand lance (near-seabed) observed along the track line by the
echosounder (left) and predicted by GAMs (right). Circles in the
plots on the left represent observed densities (t nautical mile22).
Contours of biomasses (t) estimated by GAMs are drawn in the plots
on the right.
echoes of Japanese anchovy during the survey, their identification
was based on previous results (Nagashima, 2006).
Krill were found in all the blocks, whereas Japanese anchovy
and sand lance were found only in Blocks B, C, E, and F, and in
B– F, respectively (Figure 2). Initially, GAMs were calculated
using data from all the blocks. However, because a convergence
error was encountered when estimating uncertainty in the estimate of biomass, GAMs were recalculated using only blocks
with a species present. Selected GAMs for each species are
1420
H. Murase et al.
Table 2. Selected GAM-based, spatial models for krill, Japanese anchovy, and sand lance.
Krill
Parameter
Family
Link function
Adjusted r2
Deviance explained (%)
GCV score
Covariates
Near-seabed temperature
Near-seabed salinity
SST
Sea surface salinity
Sea surface chlorophyll a concentrations
Depth
First stratum
Binomial
Logit
0.86
81.0
0.27
Japanese anchovy
Second
stratum
Gamma
Log
0.15
22.2
3.39
First stratum
Binomial
Logit
0.06
13.9
0.49
Second
stratum
Gaussian
Identity
0.29
35.0
2.91
Sand lance
First stratum
Binomial
Logit
0.23
19.1
1.13
Second
stratum
Gamma
Log
0.07
27.6
2.62
d.f.
p-value
d.f.
p-value
d.f.
p-value
d.f.
p-value
d.f.
p-value
d.f.
p-value
8.34
7.37
8.65
8.84
8.96
8.69
,0.001
,0.001
,0.001
,0.001
,0.001
,0.001
6.43
2.57
3.43
–
4.41
7.87
,0.001
,0.001
,0.001
–
,0.001
,0.001
–
1.81
3.08
8.55
8.64
1.07
–
,0.01
,0.1
,0.001
,0.001
,0.001
–
–
–
–
–
6.86
–
–
–
–
–
,0.001
–
–
–
–
6.96
5.22
–
–
–
–
,0.001
,0.001
7.30
–
–
–
5.36
8.66
,0.001
–
–
–
,0.001
,0.001
Approximate significance levels (p-value) and degrees of freedom (d.f.) are displayed for each of the covariates.
summarized in Table 2. Selected covariates differed among the
various species.
The shapes of the functional forms for selected covariates of the
first and second strata are illustrated in Figures 3 –5. These indicate
that the three species displayed non-linear responses to the
covariates. For instance, krill presence is related non-linearly to
near-seabed temperature, whereas its biomass density exhibits a
monotonic, negative response. Functional forms of near-seabed
salinity were similar for both the first and the second strata for
krill. All environmental covariates were selected for both the first
and the second strata for krill, except for sea-surface salinity in
the second stratum. “Deviance explained” for the first and the
second strata was 81.0 and 22.2%, respectively.
For Japanese anchovy, different covariates were selected for
models of the first and the second strata. For the first stratum,
they included SST, salinity, and chlorophyll a, and near-seabed salinity and depth. For the second stratum, only depth was selected.
“Deviance explained” for the first and the second strata was 13.9
and 35.0%, respectively.
For sand lance, the covariates for the first stratum included seasurface chlorophyll a and depth. The covariates for the second
stratum included sea-surface chlorophyll a, near-seabed temperature, and depth. The shape of the functional forms indicated that
biomass density of sand lance was positively related to near-seabed
temperature. The shapes of the functional forms for sea-surface
chlorophyll a were similar for the first and the second strata.
Although depth was selected for the first and the second strata,
the responses differed. The probability of presence peaked at
50 m, decreased down to 150 m, then increased towards
200 m. Biomass density peaked at 100 m and declined at both
shallow and deep seabed depths. “Deviance explained” for the
first and the second strata was, respectively, 19.1 and 27.6%.
Biomass estimates of krill, Japanese anchovy, and sand lance
based on GAMs were, respectively, 1.49 106 t (CV ¼ 0.07),
0.71 103 t (CV ¼ 0.48), and 7.54 103 t (CV ¼ 0.02). Of the
bootstrap seeds, 3% were discarded as outliers during the calculation of uncertainty in the krill-biomass estimate. For comparison, biomass estimates of krill, Japanese anchovy, and sand lance
based on the stratified, random-sampling method were, respectively, 1.56 106 t (CV ¼ 0.14), 1.32 103 t (CV ¼ 0.33), and
7.68 103 t (CV ¼ 0.19). The estimated values of r were similar
to the observed r, indicating that the models fitted the data well.
Predicted spatial distributions are illustrated in Figure 2. There
are large discrepancies in the cells with large observed r. In fact, r
estimated by GAMs tended to be underestimated in cells with high
observed r.
Discussion
The study demonstrated that GAM-based, spatial modelling could
be used to create plausible fish- and zooplankton-distribution
maps from acoustic-survey data. The resulting distribution maps
of krill, Japanese anchovy, and sand lance match the animal distributions observed by the echosounder along the track lines.
Although geostatistical methods, especially kriging, have often
been used to create animal-distribution maps using acousticsurvey data (Rivoirard et al., 2000, for reference), they do not
account for the effects of environmental factors on the distributions of such organisms. In contrast, GAMs can take account
of such factors by treating them as covariates.
Maravelias (1997) used two-strata GAMs (first stratum: presence and absence; second stratum: number of individuals given
presence) to study trends in abundance and geographic distribution of North Sea herring. In the current study, two-strata
GAMs were used to estimate biomasses, create distribution
maps, and explore the effects of environmental factors.
Unfortunately, the low values obtained for “Deviance explained”,
especially for Japanese anchovy and sand lance, indicate that
these GAMs need improvement before they can be applied successfully to predict biomasses of these species in Sendai Bay in
spring. The inclusion of different environmental covariates
might improve the results. For instance, because sand lance have
strong preferences for certain seabed types (Kobayashi et al.,
1995), the inclusion of seabed metrics as covariates might
improve these GAM results. It is therefore important to collect
data on potentially influential covariates.
Taki et al. (1996) and Taki and Ogishima (1997) used net
samples to demonstrate that distributions of E. pacifica are
related to water temperature ranging from 7 to 148C and salinity
,34 psu, and that their biomass was high at depths of 100–
150 m in April. Finer-scale interactions between animal
GAM–estimates of fish and krill distributions
1421
Figure 3. Smoothed fits of covariates modelling (a) the presence –absence and (b) the biomass density of krill. Tick marks on the x-axis are
observed datapoints. The y-axis represents the spline function. Dashed lines indicate 95% confidence bounds.
1422
H. Murase et al.
Figure 4. Smoothed fits of covariates modelling (a) the presence –absence and (b) the biomass density of Japanese anchovy. Tick marks on
the x-axis are observed datapoints. The y-axis represents the spline function. Dashed lines indicate 95% confidence bounds.
distributions and environmental factors have been revealed
by GAMs (Swartzman, 1997; Swartzman et al., 1999; Winter
et al., 2007). In our results, the GAMs confirmed that krill
presence is related positively to near-seabed temperature, but
also revealed that its biomass density is related negatively to
temperature. Differences in the functional forms between the
first and the second strata suggest that the densities of krill
schools may be high in areas with high water temperature, and
low school densities may be found in areas with low water
temperature.
Previous qualitative studies have indicated that oceanographic
conditions have varying effects on the distributions of Japanese
anchovy, depending on the season (Nagashima, 2006). Because
April is the time of the early migration of Japanese anchovy
from the south to Sendai Bay, data from one year are insufficient
to assess any environmental linkages to their biomass or
distribution. However, a GAM analysis of a multiyear dataset
might reveal the environmental parameters that control the
timing of the northerly migration of Japanese anchovy.
Kobayashi et al. (1995) reported that the biomass of adult sand
lance was high in the central region of Sendai Bay, where the water
depth was 40 –70 m and the seabed was medium to large gravel.
Small sand lance (10– 13 cm) dominated where water depth was
40 –50 m, whereas large sand lance (.13 cm) dominated where
water depth was 50 –70 m. The amount of commercially caught
sand lance was related positively to the mean SST in March. The
shape of the functional forms of the near-seabed temperature for
the second stratum in our study also indicated a positive relationship between the biomass of sand lance and temperature.
Comparing the shapes of the functional forms between the first
and the second strata might differentiate the distribution patterns
of sand lance according to their length.
1423
GAM–estimates of fish and krill distributions
Relatively low CVs for krill and sand lance might have resulted
from accounting for covariates in the GAMs. The relatively high
CV for Japanese anchovy could have resulted from poor GAM performance when applied to data from patchily distributed animals.
The residuals indicate that it could be difficult to get GAMs to
predict cells with large biomasses.
The distribution maps produced with the GAMs are in good
agreement with the observed distributions of krill, Japanese
anchovy, and sand lance along the survey tracks. An objective criterion for evaluating such GAM maps is being sought. In addition,
for future work, many other predictive habitat-distribution
models could be considered (see Guisan and Zimmermann,
2000; Austin, 2002, 2007; Leathwick et al., 2006, for reviews).
The accuracies of the species-identification algorithms can be
improved (Nagashima et al., 2008). Other sources of measurement
uncertainty, such as those stemming from the calibration, targetstrength model, length-to-weight model, bubble attenuation,
signal thresholding, and survey-area definition, could also affect
the accuracy of the biomass estimation. The effect of these uncertainties on biomass estimation should also be investigated (Demer,
2004).
This study demonstrates that GAM-based, spatial modelling is
useful to create plausible distribution maps and to estimate
biomass, while considering environmental factors. Such
GAM-based methods could even be extended to studies of predator–prey relationships (Smout and Lindstrøm, 2007).
Acknowledgements
We thank the captain of RV “Takuyo-Maru”, Hiroaki Kimura, and
his crew who assisted us in collecting this valuable dataset. The
study was conducted as a part of the coastal component of
JARPN II; we thank coordinators Hidehiro Kato (Tokyo
University of Marine Science and Technology) and Yoshihiro
Fujise (the Institute of Cetacean Research) for their valuable comments on the survey. Kazushi Miyashita (Hokkaido University)
kindly provided critical comments on the acoustic-data analysis
methods. The survey was supported by the Fisheries Agency of
Japan, the Fisheries Research Agency of Japan, the Miyagi
Prefecture, and the Institute of Cetacean Research. We thank
these institutions for their support.
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Figure 5. Smoothed fits of covariates modelling (a) the presence–
absence and (b) the biomass density of sand lance. Tick marks on the
x-axis are observed datapoints. The y-axis represents the spline
function. Dashed lines indicate 95% confidence bounds.
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