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RH-12-2008
Thesis for the degree of Master of Science in Environment and Natural
Resources
Robustness of three hierarchicalagglomerative clustering
techniques for ecological data
Warsha Singh
Faculty of Natural Sciences
Department of Mathematics
October 2008
A thesis submitted in partial ful�llment of the requirements for the degree of Master
of Science in Environment and Natural Resources at the University of Iceland.
Robustness of three hierarchical agglomerative clustering techniques for ecological
data
Warsha Singh
Science Institute Report: RH-12-2008
c© Warsha Singh 2008
Committee in charge:
Dr. Gunnar Stefánsson (Department of Mathematics, University of Iceland)
Dr. Einar Hjörleifsson (Marine Research Institute of Iceland)
Moderator:
Dr. Erla Björk Ornolfsdóttir (Marine Research Center Breiðafjörður)
iii
iv
Contents
Abstract xv
Acknowledgement xvi
1 Introduction 1
1.1 Purpose of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Statistical Theory 11
2.1 Hierarchical agglomerative clustering . . . . . . . . . . . . . . . . . . 11
2.1.1 Average linkage (UPGMA) . . . . . . . . . . . . . . . . . . . . 12
2.1.2 Complete linkage . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 Ward's linkage . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Non-Metric Multidimensional Scaling (NMDS) . . . . . . . . . . . . . 13
3 Methodology 15
3.1 Icelandic Ground�sh Survey . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Hierarchical cluster analysis - Species Assemblages . . . . . . . . . . . 17
3.3.1 Analysis I: Correlation distance . . . . . . . . . . . . . . . . . 17
3.3.2 Analysis II: Bray-Curtis distance . . . . . . . . . . . . . . . . 18
3.3.3 Data Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Comparison of the hierarchical clustering techniques . . . . . . . . . . 22
3.5 Comparison of hierarchical clustering with non-metric multidimen-
sional scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.6 Fish Assemblages in relation to environmental variables . . . . . . . . 23
3.7 Habitat analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.8 Heatmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
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vi CONTENTS
4 Results 25
4.1 Comparison of the three hierarchical clustering techniques . . . . . . 25
4.1.1 Analysis I: Correlation distance . . . . . . . . . . . . . . . . . 25
4.1.2 Analysis II: Bray-Curtis distance . . . . . . . . . . . . . . . . 26
4.2 Sample size e�ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.1 Analysis I: Correlation distance . . . . . . . . . . . . . . . . . 36
4.2.2 Analysis II: Bray-Curtis distance . . . . . . . . . . . . . . . . 37
4.3 Data Aggregation (smoothing) e�ect . . . . . . . . . . . . . . . . . . 50
4.3.1 Analysis I: Correlation distance . . . . . . . . . . . . . . . . . 50
4.3.2 Analysis II: Bray-Curtis distance . . . . . . . . . . . . . . . . 50
4.4 Comparison of hierarchical clustering with non-metric multidimen-
sional scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 Fish Assemblages in relation to environmental variables . . . . . . . . 57
4.5.1 Analysis I: Correlation distance . . . . . . . . . . . . . . . . . 57
4.5.2 Analysis II: Bray-Curtis distance . . . . . . . . . . . . . . . . 58
4.6 Habitat Classi�cation . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.6.1 Analysis I: Correlation distance . . . . . . . . . . . . . . . . . 71
4.6.2 Analysis II: Bray-Curtis distance . . . . . . . . . . . . . . . . 71
4.7 Heatmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5 Discussion 77
5.1 Fish Assemblages and species-environment relationships . . . . . . . . 82
6 Main considerations and recommendations 85
A Appendix 89
List of Figures
3.1 Icelandic ground�sh survey area within the 500 meter contour line,
outlining the statistical rectangles and the locations of the stations . . 16
3.2 Distribution of the data (a) before and (b) after transforming to
fourth root and scaling to zero mean and variance 1, for four abundant
species in the survey, as labelled. The histogram shows the number
of �sh per tow collections. . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Distribution of the data (a) before and (b) after transforming to
fourth root and standardising by range, for four adundant species
in the survey, as labelled. The histogram shows the number of �sh
per tow collections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1 Dendrogram of species assemblage for the Icelandic Ground�sh (IGF)
survey from 1998-2007 using (a) Average linkage and (b) Complete
linkage, with correlation dissimilarity measure. Data consists of species
abundance in numbers, fourth root transformed and scaled to 0 mean
and variance 1, comprising of all tow collections. The rectangles high-
light the clusters with AU > 0.9. The AU values are used for interpre-
tation are indicated in blue and the cluster number (edge) is marked
in green. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Dendrogram of species assemblage using Ward's linkage with corre-
lation dissimilarity measure. Data consists of species abundance in
numbers fourth root transformed and scaled to 0 mean and variance
1. The rectangles highlight the clusters with AU > 0.9. . . . . . . . . 29
vii
viii LIST OF FIGURES
4.3 Dendrogram of species assemblage using (a) Average linkage and (b)
Complete linkage, with correlation dissimilarity measure. Data con-
sists of mean species abundance in numbers by stations, fourth root
transformed and scaled to 0 mean and variance 1. The rectangles
highlight the identi�ed species assemblages for comparison. . . . . . . 30
4.4 Dendrogram of species assemblage using Ward's linkage with correla-
tion dissimilarity measure. Data consists of mean species abundance
in numbers by stations, fourth root transformed and scaled to 0 mean
and variance 1. The rectangles highlight the identi�ed species assem-
blages for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.5 Dendrogram of species assemblage using (a) Average linkage and (b)
Complete linkage with Bray-Curtis dissimilarity measure. Data con-
sists of species abundance in numbers, fourth root transformed and
standardised by range. The rectangles highlight the clusters with AU
> 0.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.6 Dendrogram of species assemblage using Ward's linkage with Bray-
Curtis dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and standardised by range. The
rectangles highlight the clusters with AU > 0.9. . . . . . . . . . . . . 33
4.7 Dendrogram of species assemblage using (a) Average linkage and (b)
Complete linkage with Bray-Curtis dissimilarity measure. Data con-
sists of mean species abundance in numbers by stations, fourth root
transformed and standardised by range. The rectangles highlight the
identi�ed species assemblages for comparison. . . . . . . . . . . . . . 34
4.8 Dendrogram of species assemblage using Ward's linkage with Bray-
Curtis dissimilarity measure. Data consists of mean species abun-
dance in numbers by stations, fourth root transformed and standard-
ised by range. The rectangles highlight the identi�ed species assem-
blages for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.9 Dendrogram of species assemblage using Average linkage with corre-
lation dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and scaled to 0 mean and variance
1, comprising of (a) 50% random subsample and (b) 25% random
subsample of the total tow collections. The rectangles highlight the
clusters with AU > 0.9. . . . . . . . . . . . . . . . . . . . . . . . . . . 38
LIST OF FIGURES ix
4.10 Dendrogram of species assemblage using Average linkage with corre-
lation dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and scaled to 0 mean and variance
1, comprising of 10% random subsample of the total tow collections.
The rectangles highlight the clusters with AU > 0.9. . . . . . . . . . 39
4.11 Dendrogram of species assemblage using Complete linkage with cor-
relation dissimilarity measure. Data consists of mean species abun-
dance in numbers by stations, fourth root transformed and scaled
to 0 mean and variance 1, comprising of (a) 50% random subsam-
ple and (b) 25% random subsample of the total tow collections. The
rectangles highlight the clusters with AU > 0.9. . . . . . . . . . . . . 40
4.12 Dendrogram of species assemblage using Complete linkage with corre-
lation dissimilarity measure. Data consists of mean species abundance
in numbers by stations, fourth root transformed and scaled to 0 mean
and variance 1, comprising of 10% random subsample of the total tow
collections. The rectangles highlight the clusters with AU > 0.9. . . . 41
4.13 Dendrogram of species assemblage using Ward's linkage with corre-
lation dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and scaled to 0 mean and variance
1, comprising of (a) 50% random subsample and (b) 25% random
subsample of the total tow collections. The rectangles highlight the
clusters with AU > 0.9. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.14 Dendrogram of species assemblage using Ward's linkage with corre-
lation dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and scaled to 0 mean and variance
1, comprising of 10% random subsample of the total tow collections.
The rectangles highlight the clusters with AU > 0.9. . . . . . . . . . 43
4.15 Dendrogram of species assemblage using Average linkage with Bray-
Curtis dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and standardised by range, com-
prising of (a) 50% random subsample and (b) 25% random subsample
of the total tow collections. The rectangles highlight the clusters with
AU > 0.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
x LIST OF FIGURES
4.16 Dendrogram of species assemblage using Average linkage with Bray-
Curtis dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and standardised by range, com-
prising of 10% random subsample of the total tow collections. The
rectangles highlight the clusters with AU > 0.9. . . . . . . . . . . . . 45
4.17 Dendrogram of species assemblage using Complete linkage with Bray-
Curtis dissimilarity measure. Data consists of mean species abun-
dance in numbers by stations, fourth root transformed and standard-
ised by range, comprising of (a) 50% random subsample and (b) 25%
random subsample of the total tow collections. The rectangles high-
light the clusters with AU > 0.9. . . . . . . . . . . . . . . . . . . . . 46
4.18 Dendrogram of species assemblage using Complete linkage with Bray-
Curtis dissimilarity measure. Data consists of mean species abun-
dance in numbers by stations, fourth root transformed and standard-
ised by range, comprising of a 10% random subsample of the total
tow collections. The rectangles highlight the clusters with AU > 0.9. 47
4.19 Dendrogram of species assemblage using Ward's linkage with Bray-
Curtis dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and standardised by range, com-
prising of (a) 50% random subsample and (b) 25% random subsample
of the total tow collections. The rectangles highlight the clusters with
AU > 0.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.20 Dendrogram of species assemblage using Ward's linkage with Bray-
Curtis dissimilarity measure. Data consists of species abundance in
numbers, fourth root transformed and standardised by range, com-
prising of 10% random subsample of the total tow collections. The
rectangles highlight the clusters with AU > 0.9. . . . . . . . . . . . . 49
4.21 Dendrogram of species assemblage using (a) Average linkage and (b)
Complete linkage with correlation dissimilarity measure. Data con-
sists of mean species abundance in numbers by statistical subrectan-
gles, fourth root transformed and scaled to 0 mean and variance 1.
The rectangles highlight the clusters with AU > 0.9. . . . . . . . . . 51
LIST OF FIGURES xi
4.22 Dendrogram of species assemblage using Ward's linkage with correla-
tion dissimilarity measure. Data consists of mean species abundance
in numbers by statistical subrectangles, fourth root transformed and
scaled to 0 mean and variance 1. The rectangles highlight the clusters
with AU > 0.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.23 Dendrogram of species assemblage using (a) Average linkage and (b)
Complete linkage with Bray-Curtis dissimilarity measure. Data con-
sists of mean species abundance in numbers by statistical subrectan-
gles, fourth root transformed and standardised by range. The rect-
angles highlight the clusters with AU > 0.9. . . . . . . . . . . . . . . 53
4.24 Dendrogram of species assemblage using Ward's linkage with Bray-
Curtis dissimilarity measure. Data consists of mean species abun-
dance in numbers by statistical subrectangles, fourth root transformed
and standardised by range. The rectangles highlight the clusters with
AU > 0.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.25 Multidimensional scaling using Bray-Curtis distance measure for (a)
the full data set (comprising all tow collections) (b) data aggregated
by statistical sub-rectangle. Species abundance in numbers was fourth
root transformed and standardised by range. . . . . . . . . . . . . . . 56
4.26 Geographical distribution of the 40 species analysed for this study,
labelled accordingly. The bubble plot shows the mean abundance of
species by statistical subrectangles averaged across years. The size of
circles are proportional to the square root of the mean abundance. . . 67
4.27 Weighted average depths and standard deviations for the 40 species
analysed. A-D refers to the identi�ed �sh assemblages from Ward's
hierarchical clustering based on correlation distance. . . . . . . . . . . 68
4.28 (a) Box and whisker plot for the mean depths of species in the iden-
ti�ed �sh assemblages from Ward's hierarchical clustering based on
correlation distance (b) Tukey test results showing the signi�cant dif-
ference between the identi�ed �sh assemblages (c) Box and whisker
plot for the mean depths of species in the identi�ed �sh assemblages
from Ward's hierarchical clustering based on Bray-Curtis distance
(d) Tukey test results showing the signi�cant di�erence between the
identi�ed �sh assemblages from (c) . . . . . . . . . . . . . . . . . . . 69
xii LIST OF FIGURES
4.29 Weighted average depths and standard deviations for the 40 species
analysed. A*-C* refers to the identi�ed �sh assemblages from Ward's
hierarchical clustering based on Bray-Curtis distance. . . . . . . . . . 70
4.30 De�nition of areas in Icelandic waters using Ward's hierarchical clus-
tering. The data consist of species abundance in numbers transformed
to fourth root. Clustering was based on (a) correlation distance with
data scaled to 0 mean and variance 1 (b) Bray-Curtis distance with
data standardised by range. . . . . . . . . . . . . . . . . . . . . . . . 73
4.31 Species composition of de�ned clusters from the habitat classi�cation
using Correlation distance measure and Ward's linkage. The species
codes are outlined in Table 4 in the Appendix. . . . . . . . . . . . . . 74
4.32 Species composition of de�ned clusters from the habitat classi�cation
using Bray-Curtis distance measure and Ward's linkage. The species
codes are outlined in Table 4 in the Appendix. . . . . . . . . . . . . . 75
4.33 A heatmap showing the species-area association for the Icelandic
Ground�sh (IGF) survey from 1998-2007 using Average linkage hi-
erarchical clustering with correlation dissimilarity measure. The x-
axis shows the dendrogram of areas (statistical rectangles) and y-axis
shows the dendrogram of species assemblage. Data consists of species
abundance in numbers, fourth root transformed and scaled to 0 mean
and variance 1. The colours range from blue (low ratios) to red (high
ratios) indicating the strength of associations. . . . . . . . . . . . . . 76
A.1 De�nition of areas in Icelandic waters using (a) Average (b) Com-
plete hierarchical clustering with correlation distance. Data consists
of species abundance in numbers, transformed to fourth root and
scaled to 0 mean and variance 1. . . . . . . . . . . . . . . . . . . . . . 91
A.2 De�nition of areas in Icelandic waters using (a) Average (b) Com-
plete hierarchical clustering with Bray-Curtis distance. Data consists
of species abundance in numbers, transformed to fourth root and
standardised by range. . . . . . . . . . . . . . . . . . . . . . . . . . . 92
List of Tables
2.1 Parameter Values for the clustering algorithms used in this study . . 12
4.1 Cophenetic Correlation Coe�cient for Analysis I (Correlation dis-
tance) and II (Bray-Curtis distance) . . . . . . . . . . . . . . . . . . . 27
4.2 Agglomerative Coe�cient for Analysis I (Correlation distance) and
II (Bray-Curtis distance) . . . . . . . . . . . . . . . . . . . . . . . . . 27
A.1 The common and Latin names of the fourty most common species
analysed for this study with the codes used for analysis. . . . . . . . . 90
xiii
Abstract
Although, cluster validity has been a subject of interest and importance in the �eld
of molecular genetics for some decades now, substantive guidelines are not readily
available for the choice of the appropriate clustering algorithms for ecological data.
This study tested the robustness of three common hierarchical agglomerative clus-
tering methods, Average, Complete and Ward's linkage, for identi�cation of species
assemblages. The Icelandic ground�sh survey data for the period 1998-2007 was used
for this study, taking the fourty most abundant species into consideration. The ob-
jective criteria used for cluster validity or e�ciency was the Cophenetic Correlation
Coe�cient (CPCC) and the Agglomerative Coe�cient (AC). In order to test the
reliability of the clusters bootstrap resampling technique was used to generate the
probability for the clusters. Furthermore, to examine the stability and consistency
of the linkage methods, their performances across di�erent sample sizes and levels
of data smoothing were tested. Two modes of data analyses based on a di�erent
combination of data standardisation and distance measure; (1) Correlation distance
on data scaled to zero mean and one variance and (2) Bray-Curtis distance on data
standardised by range, showed that Ward's clustering technique was the most robust
and suitable for this data set. It generated consistent well-de�ned clusters with high
probabilities and gave high values of CPCC and AC. The assemblages were also
ecologically meaningful when related to two environmental parameters, depth and
geographical distribution. A veri�cation of the hierarchical clusters with Non-metric
Multidimensional Scaling also gave similar species groupings. The Complete linkage
was unstable generating inconsistent results across di�erent sample sizes and data
smoothing. The Average linkage maximised CPCC but was sensitive to the way the
data were standardised. The CPCC criterion of cluster validity was not seen as a
very reliable and adequate measure in this study.
Subsequently, the main species assemblages o� the Icelandic waters, covered by
the survey, were de�ned. Biological interpretations of the �sh assemblages showed
xiv
LIST OF TABLES xv
that the spatial structure of the environmental gradients around Iceland played a
role in characterising the �sh assemblages. A de�nition of areas around Iceland led
to a separation along the north-south gradient, according to the bathymetric and
hydrographic conditions, which further showed some di�erentiation along depth.
Furthermore, the use of a visualisation technique, the heatmap, was introduced for
exploring community patterns.
Acknowledgment
I would like to acknowledge the Marine Research Institute of Iceland for making the
data on the Icelandic ground�sh survey available for this study. My sincere gratitude
goes to Dr. Gunnar Stefánsson of the Department of Mathematics, University of
Iceland and Dr. Einar Hjörliefsson of the Marine Research Institute of Iceland for
their technical guidance and continued valuable support throughout this study and
for their constructive comments in strengthening this study.
I am immensely and forever grateful to the co-ordinating team of the United
Nations University Fisheries Training Programme, Dr. Tumi T'omasson, Mr. Þor
Ásgeirsson and Ms. Sigridur Kr. Ingvarsdóttir for giving me this opportunity to
be a part of this Masters Programme in Environment and Natural Resources at the
University of Iceland. I would also like to acknowledge the continued support and
encouragement from Dr. Brynhildur Davidsdóttir (Co-ordinator for the Masters
Programme).
I thank Mr. Sigurdur þor Jóonsson of the Marine Research Institute of Iceland
for providing his technical assistance with the statistical software R.
xvi
1Introduction
The shift toward ecosystem based �sheries management has resulted in numerous
studies, carried out world-wide, to determine �sh assemblages. This new approach
entails starting �sheries management at the ecosystem level rather than at sin-
gle species level (Pikitch et al., 2004). An initial step toward understanding the
ecosystem- or multispecies-based approaches is to understand the mechanisms of
the biological communities in space and time, including their correlation with the
environment (Sousa et al., 2005; Jaureguizar et al., 2006). Hence, the identi�cation
of �sh assemblages and their relation to environmental variables may be seen as
one probable measure of potential interactions between the species (Francis et al.,
2002). The term �sh assemblage refers to a group of species that coexist at a
geographical scale because of similar habitat preferences or biological interactions
(Jaureguizar et al., 2003; Mahon et al., 1998). Because these assemblages poten-
tially characterise geographical areas or environmental gradients, they are consid-
ered an appropriate indicator for habitat complexity (Noss, 1990). The patterns
of species assemblages are commonly de�ned using multivariate analysis, inferring
species-environment relationships. Nonetheless, not much attention is given to the
reliability of the methodology that is applied which is the main topic of the present
study.
Hierarchical cluster analysis is widely applied for assemblage studies. This
method is based on identifying objects with similar characteristics and grouping
them together such that objects within the group are more similar than objects
in di�erent groups. Cluster analysis can be used to identify species assemblages,
1
2 Chapter 1 Introduction
and di�erent sites and times having similar community structures (Clarke and War-
wick, 2001). The output is a tree-like structure called a dendrogram with the x-axis
showing the objects and the y-axis indicating the level of similarity or dissimilarity
of the groupings. Similarity between the clusters diminishes moving from lower to
upper levels. Hierarchical clustering is sub-divided into agglomerative and divisive
methods. Agglomerative methods are most commonly used (Clarke and Warwick,
2001). In the basic description given by Quinn and Keough (2002), the procedure
starts with calculating a matrix of dissimilarity between the objects or variables and
two objects which are most similar cluster together to form a new object replacing
the merged pair. The dissimilarity between the new set of objects is re-calculated
and again the most similar objects are merged. The process continues until all the
objects are linked in a cluster. Dissimilarity indices (also called distance) measure
how di�erent the objects are (how far apart the objects are in multidimensional
space) and is calculated for every possible pair of objects. This is the basis for the
formation of a cluster. For continuous variables dissimilarity measures include Eu-
clidean (squared normal distance), Manhattan, Canberra, Minkowski, Bray-Curtis,
Kulczynski and Chi-square (Quinn and Keough, 2002). A variety of agglomerative
clustering methods exist depending on which technique or linkage method is used
to fuse the objects during the clustering process. Some of the common ones include
Single linkage, Complete linkage, Average linkage and Ward's hierarchical cluster-
ing method. The divisive method is opposite to the agglomerative, starting with a
single cluster which contains all the objects and splitting it up into smaller groups
(Clarke and Warwick, 2001) and two-way indicator species analysis (TWINSPAN)
is a common method in this class (Quinn and Keough, 2002) .
For the most part, hierarchical clustering techniques lack a completely stable
output and an objective measure for evaluating the outcomes obtained (Cao et al.,
2002a; Nemec and Brinkhurst, 1988) introducing subjectivity into the interpreta-
tion of the classi�cations (Mahon et al., 1998). Generally, prior to clustering the
grouping properties of the data set are unknown and the number of expected clus-
ters cannot be assigned beforehand. In other words, it is an unsupervised process
(�unsupervised learning�) and it is generally di�cult to judge whether the resulting
classi�cation patterns and the number of groups are acceptable. Additionally, the
function of the clustering algorithms are susceptible to the properties of the data
and the assumptions made for the de�nition of the groups (Halkidi et al., 2002b;
Kovács et al., 2005). Another drawback is that once a cluster is formed it cannot
Introduction 3
be broken down later in the process and an inaccurate cluster formed early in the
process will therefore in�uence the classi�cation that follows (Quinn and Keough,
2002). Consequently, evaluation and validation of clustering techniques are an es-
sential part of cluster analysis (Legendre, 1998). Comparing outcomes from a few
techniques can also ensure consistency and plausibility of the results as di�erent
clustering algorithms could lead to di�erent results for the same data set (Jakoniene
and Lambrix, 2007). Naturally, if there really is a strong association in the data,
di�erent methods should produce similar results (Quinn and Keough, 2002).
The results of hierarchical classi�cation depend on the choice of the clustering
technique (linkage method) and the initial dissimilarity index used to calculate the
pairwise dissimilarity between objects, thus one should be wary of their choices. The
purpose of the analysis, the nature of the data and the standardisations of the data
all play a role in determining the optimum clustering technique used (Quinn and
Keough, 2002) taking note that the choice of linkage method is more critical than the
choice of the dissimilarity measure (Vakharia and Wemmerlöv, 1995). For ecological
studies, the group mean (or Average) linkage technique also known as unweighted
pair-groups method using arithmetic averages (UPGMA) based on Bray-Curtis dis-
similarity has been a prominent technique for some decades, as noted by Clarke and
Ainsworth (1993) and also falls within the recommendation of Quinn and Keough
(2002). When data are in the form of species abundance the problem of "double
zeros� normally exists, that is, a species can be absent from two sites. �If a species is
absent from two sites, then these two sites are either both above or both below the
optimal niche value for that species, or one above and one below that value� (Leg-
endre, 1998). Thus clear indications about the ecological preferences of the species
cannot be reached in these circumstances and ecological conclusions should not be
drawn. Therefore, dissimilarity coe�cients that do not classify sampling units as
similar because they have no species in common are recommended. Coe�cients of
this type are called asymmetric as they treat zeros in a di�erent way and skip double
zeros altogether when computing dissimilarities (Legendre, 1998). Bray-Curtis is an
asymmetrical quantitative coe�cient where the comparison excludes double zeros
which makes it preferable for ecological studies (Legendre, 1998). Bray-Curtis is one
such asymmetric coe�cient together with others such as Kulczynski and Canberra.
On the other hand, Euclidean and Chi-square are also good measures of dissimi-
larity if the data do not have zeros (Quinn and Keough, 2002). Other reasons as
to why Bray-Curtis coe�cient is preferred is, the inclusion of a third sample does
4 Chapter 1 Introduction
not a�ect the similarity between two initial samples and its value is unchanged by
inclusion and exclusion of a species which is jointly absent from two samples (Clarke
and Warwick, 2001). If the data are �rst normalised then the use of correlation as a
dissimilarity measure may be appropriate for species associations (Legendre, 1998).
Correlation distance is used more in analysis of species than sites since it incor-
porates a type of row standardization (Clarke and Warwick, 2001). This however
does not remove the problem of double-zeros but the problem can be minimised by
eliminating rare species from the analysis (Legendre, 1998).
The ecological literature has a vast number of studies on �sh assemblages rang-
ing across various types of �sheries and habitats. Some of the analyses of demersal
�sh assemblages in the Northern region include; Galician continental shelf and up-
per slope, north-west Spain (Fariña et al., 1997); eastern Norwegian sea (Bergstad
et al., 1999); north-east Newfoundland/Labrador shelf (Gomes and Richard, 1995);
Flemish Cap (González-Troncoso et al., 2006); Faroe Banks (Magnussen, 2002); east
coast of North America (Mahon et al., 1998); west and east Greenland continen-
tal shelf and slope (Rätz, 1999) and Portuguese continental margin (Sousa et al.,
2005). Most of these studies relate the spatial and temporal patterns of species
assemblages to possible environmental variables that could explain these structures.
To ensure consistency of the results, output from at least two multivariate analyti-
cal techniques are generally compared in most studies. For example, Mahon et al.
(1998), Medina et al. (2007) and González-Troncoso et al. (2006) compare PCA to
hierarchical clustering. Francis et al. (2002); Sousa et al. (2005) compare CA and
hierarchical clustering and Lee and Sampson (2000) look at DCA and hierarchical
clustering. Some of the studies such as Brazner and Beals (1997) and Massuti and
Moranta (2003), among others, try to complement results obtained from clustering
with MDS. All these studies report consistent results from the di�erent techniques
used. However cluster validation or comparison of techniques was not the underlying
objective of these studies. With some exceptions, justi�cation is not provided on the
choice of techniques used. Generally such studies are more focused on the biological
aspects of analysis and interpretation rather than the reliability of the techniques
used. It is therefore not clear in general whether consistency is a general feature or
only present between the two methods chosen in each of those analyses.
Numerous studies have focused on testing the e�ciency and stability of various
hierarchical clustering techniques and in turn trying to determine the best linkage
method for the data set being evaluated. Some of these include Datta and Datta
Introduction 5
(2003); Gauch Jr and Whittaker (1981); Hennig (2007); Loganantharaj et al. (2006);
Milligan and Cooper (1987); Scheibler and Schneider (1985) and references therein.
Quinn and Keough (2002) and Cao et al. (1997a) also give further citations. The
majority of other studies on cluster validation are based on non-ecological data.
Studies such as Scheibler and Schneider (1985) used Monte Carlo tests to examine
the accuracy of a wide range of hierarchical and non-hierarchical clustering, show-
ing that Ward's linkage was the most robust among the hierarchical classi�cation
techniques examined. Some recent studies as Hennig (2007) use simulation studies
to test stability of clustering techniques also, based on external validation criteria
such as Jaccard's coe�cient.
Cluster validation studies are fairly limited in the �eld of ecology. One study
conducted by Cao et al. (1997a) compared the performance of three hierarchical
linkage methods, UPGMA, Complete and Ward's linkage, and TWINSPAN on river
benthic community data. Contrary to the general recommendation they found that
Ward's clustering technique produced the best result. Nonetheless, the choice of
dissimilarity measure also plays a role. Ward's linkage needs Euclidean distance
(Vakharia and Wemmerlöv, 1995) and this distance measure is known to strongly
overweight abundant species, even after data transformation (Cao et al., 1997a). In
their study Cao et al. (1997a) broaden the use of Wards linkage and apply it to
a new dissimilarity measure, namely CY dissimilarity measure, proposed by Cao
et al. (1997b). Ward's technique has generally been applied and recommended for
non-ecological studies. Since ecological patterns in multivariate data are normally
not known a priori this poses some di�culties in assessment of patterns. This short-
coming has been addressed by some studies through the use of simulated data. One
such study by Gauch Jr and Whittaker (1981) compared hierarchical classi�cation
for simulated community data and �eld data. They showed that UPGMA did not
perform very well in separating the predetermined plant communities in compari-
son to TWINSPAN and Complete linkage. On the contrary, Belbii and McDonald
(1993) found that �exible-UPGMA performed better than TWINSPAN when tested
on simulated community data.
Even though there are some studies which suggest that sampling e�ort could have
a signi�cant e�ect on the multivariate analyses, this has seldom been investigated
(Cao et al., 2002a,b). Cao et al. (2002a) investigated the e�ect of sampling e�ort on
the similarity/dissimilarity measures as opposed to the clustering technique, with
the justi�cation that these are fundamental to cluster analysis. Their study illus-
6 Chapter 1 Introduction
trated that increasing sampling e�ort signi�cantly improved the site separation in
techniques such as cluster analysis and ordination, since more samples improve the
estimate of the similarity between objects resulting in a clearer separation between
groups. Additionally, decreasing sampling e�ort or insu�cient sampling can have an
e�ect on the observed community structure as fewer species are caught and recorded
in smaller sample sizes (Riecken, 1999). As such, to test the e�ect of sample sizes
on the observed ecological communities appears worthwhile.
The two important aspects of cluster validation involve testing the e�ciency and
the stability of a method. Validation techniques used for testing e�ciency, or the
goodness-of-�t of the clustering, can be broadly classi�ed into external, internal and
relative criteria. A concise account of these are given by Halkidi et al. (2002b,a). In
short, an external criterion for cluster validation involves comparing the clustering to
a prede�ned structure. Statistical indices such as the Rand Statistic, Jaccard coe�-
cient, Hurbert's statistic and Folkes and Mallow Index are used for this criterion. A
relative criterion is based on certain assumptions and parameters and involves com-
paring the obtained classi�cation to other clustering schemes. Some of the statistics
used in this criterion are the Dunn family of indices, modi�ed Hurbert's statistic,
Davies-Bouldin index among others (Halkidi et al., 2002a). An internal criterion on
the other hand relies on the inherent features of the data to evaluate the clustering
structure (Halkidi et al., 2002b) such as the initial dissimilarity patterns between
the objects. This is particularly useful if no prior information about the de�nitions
in the data are available. One such criterion is the Cophenetic Correlation Coe�-
cient (CPCC), also referred to as a matrix correlation or the standardized Mantel
statistic, proposed by Sokal and Rohlf (1962). The hierarchical clustering proce-
dure produces a total dissimilarity matrix known as the cophenetic matrix. The
correlation between this cophenetic matrix and the original dissimilarity matrix on
which the clustering was carried out is the CPCC (Lessig, 1972). A high correla-
tion shows that the clustering technique did not distort much information contained
in the original dissimilarity matrix. This criteria of cluster validation has been
applied in several studies for evaluating clustering e�ciency (Farris, 1969). Such
evaluations also include Gauch Jr and Whittaker (1981); Li (1990); Rodrigues and
Diniz-Filho (1998). However some studies such as Farris (1969); Rohlf and Fisher
(1968); Phipps (1971) have questioned the reliability of this index of cluster validity.
Another criterion is the agglomerative coe�cient (AC), proposed by Kaufman and
Rousseeuw (1990). This criterion is based on the clustering structure itself found by
Introduction 7
the clustering algorithm and is normally used to assess the strength and quality of
the clustering (Rodrigues and Diniz-Filho, 1998; Hasan and Masumoto, 1999; Lesage
et al., 1999).
The second aspect of cluster validation, stability, normally refers to whether the
clusters remain constant irrespective of changes in the initial data set, such as taking
subsamples or adding noise to the data (Hennig, 2007). Perhaps one of the disad-
vantages of hierarchical cluster analyses is to verify that the clusters are not just a
result of random e�ects. This has been, in some ways, overcome by the bootstrap
technique. Bootstrapping is used to assess the uncertainty in hierarchical clustering
by determining the probabilities of the obtained clusters. The stability and con-
sistency of a cluster can therefore also be tested using the bootstrap (Hennig and
Mathematik-SPST, 2005; Efron et al., 1996). Bootstrapping has also been applied in
a variety of ways to assess the reliability of clusters (Efron et al., 1996; Handl et al.,
2005; McKenna, 2003; Kerr and Churchill, 2001; Shimodaira, 2002; Suzuki and Shi-
modaira, 2004). The majority of such work has been done in the �eld of molecular
genetics, some in a rather elaborate manner, and studies such as Bolshakova et al.
(2005) have developed speci�c software for cluster validation of DNA microarray
data. This software can be used to validate a range of clustering techniques and
incorporates various validation indices. However, bootstrapping of cluster analysis
is somewhat less seen among the numerous ecological studies conducted.
Given the drawbacks of cluster analysis which have been outlined earlier, ordi-
nation techniques such as MDS are sometimes preferred. An ordination is like a
map of the objects in more than two dimensions, where the placement of the ob-
jects represents their similarity. Multidimensional scaling (MDS), also referred to
as non-metric multidimensional scaling (NMDS), is like clustering, based on simi-
larities or dissimilarities between the objects. The procedure �scales objects based
on a reduced set of new variables derived from the original variables� (Quinn and
Keough, 2002). Other ordination techniques include Principal Co-ordinates Analy-
sis and Correspondence Analysis (CA), Canonical Correspondence Analysis (CCA),
Detrended Correspondence Analysis (DCA) and Principal Components Analysis
(PCA) which is the longest-established ordination method (Clarke and Warwick,
2001). Ordination gives a more informative display when samples do not portray a
strong grouping (Clarke and Warwick, 2001). Clarke and Warwick (2001) suggest
that cluster analysis be used in conjunction with ordination, even if the samples
are strongly grouped. Gauch and Whittaker 1981 argue that in community ecology,
8 Chapter 1 Introduction
data are relatively continuous with samples relatively evenly spaced and the data are
not naturally clustered. Consequently, clustering may impose clusters which are not
intrinsic to the data. Therefore they suggest that non-hierarchical and ordination
techniques have advantages over hierarchical techniques in such cases. NMDS is nor-
mally recommended as one of the best ordination techniques (Quinn and Keough,
2002; Clarke and Warwick, 2001; Clarke and Ainsworth, 1993) due to its �exibility.
It can be applied in conjunction with a wide range of dissimilarity measures and does
not rely on any particular response model between species and underlying ecological
gradients (Legendre, 1998).
Examining complex patterns in community structures can be considerably de-
manding and complex. When the data are extensive and structures are abstract,
a clear visualisation of patterns in a graphical format can be particularly bene�cial
for understanding and interpretation. The heatmap is one such visualisation tech-
nique that is a useful data exploratory tool and has been applied widely in the �eld
of genetics for studying patterns in complex DNA microarray data (Pryke et al.,
2006; Hastie et al., 2001; Zhang et al., 2003; Eisen et al., 1998; Quackenbush, 2007).
This conceptualisation deals with assigning colours to each data point that �quan-
titatively and qualitatively re�ects the original experimental observations� (Eisen
et al., 1998) which is much more interpretable and informative than reading num-
bers. Visualisation can also be used as a measure of quality of the solutions (Pryke
et al., 2006). Although applied extensively in taxonomical studies, ecologists have
refrained from the use of these visualisation techniques for exploring community
structures. Here an attempt is made to give an informative representation of the
species-area relationship through a heatmap.
1.1 Purpose of the study 9
1.1 Purpose of the study
Hierarchical agglomerative cluster analyses have been widely applied in the �eld of
ecology. However, the robustness of the techniques used are seldom examined. The
primary emphasis of this study was to address the methodological and statistical
aspects of clustering procedures. Secondarily, the biological aspects of the estimation
of �sh assemblages were also addressed.
The robustness of three hierarchical agglomerative clustering techniques namely,
Average linkage or Unweighted Pair-Group Mean Average (UPGMA), Complete link-
age and Ward's linkage were examined for identi�cation of �sh assemblages. These
are the most commonly used linkage methods in ecology. This study was based on
Icelandic ground�sh survey data for the period 1998 to 2007.
The objective criteria used for assessing the cluster validity or e�ciency was
the Cophenetic Correlation Coe�cient (CPCC) and the Agglomerative Coe�cient
(AC). In order to test the reliability of the clustering methods, the probability values
for the clusters were determined through bootstrap resampling. As a measure of the
stability and consistency of the methods, their performances were examined across
di�erent sample sizes and di�erent levels of data smoothing (data aggregation) .
As a secondary aim, it was explored if di�erent data standardisation methods
and dissimilarity measures played a signi�cant role in determining multivariate pat-
terns, in this context the species assemblages. Thus the above analyses were carried
out using two modes of data analysis. These were a di�erent combination of (1)
data transformation and standardisation and (2) the dissimilarity measure used to
obtain the matrix of dissimilarities before the clustering. For each mode of data anal-
ysis, relative comparisons were made between the three linkage methods in order to
determine which hierarchical agglomerative clustering technique was conditionally
most robust, thus potentially most suitable for the data being studied. Furthermore,
NMDS was used as an external subjective criterion to compare and verify the �sh
assemblages obtained from hierarchical cluster analysis.
Furthermore, after the identi�cation of the most robust linkage method, it was
important to examine if the species assemblages obtained from that method were
ecologically meaningful. Thus the identi�ed assemblages were examined in rela-
tion to two environmental variables, depth and geographic distribution. These two
variables were hypothesised to be in�uential in determining the species associations.
A classi�cation of the �shing areas was also carried out to determine similar
10 Chapter 1 Introduction
habitats. This was carried out in line with the two modes of data analysis and
the three linkage methods in order to examine the consistency of the outcomes. A
visualisation technique, the �heatmap�, was then used to give a more informative
display of the patterns in the community structures by giving a pairwise display of
the two classi�cations of species and areas (statistical rectangles).
2Statistical Theory
2.1 Hierarchical agglomerative clustering
All hierarchical agglomerative clustering procedures begin with an initial dissimi-
larity matrix between the objects. At the start of the agglomerative process each
object is considered as a separate class or cluster. For a set of N initial objects,
the �rst clustering will result in N-1 clusters, the next N-2 and so on until only one
cluster contains all the objects, with objects which are most similar fusing together
at each step. How the distance between the new cluster and the remaining objects is
computed is determined by the clustering algorithm being used (Gordon, 1999). A
general equation proposed by Lance and Williams (1967) and outlined in Scheibler
and Schneider (1985), describes how the various hierarchical algorithms compute
this distance:
dhk = αidhi + αjdhj + βdij + λ |dhi − dhj| (2.1)
where:
dij denotes the Euclidean distance between the entities i and j which have been
combined to form a new cluster k
dhk denotes the Euclidean distance between a remaining entity h and the new cluster
k
αi, αj, β and λ are parameters that depend on the clustering method being used and
are outlined in Table 1 below for the three methods considered here.
11
12 Chapter 2 Statistical Theory
Cluster Method αi αj β λAverage ni
nk
nj
nk0 0
Complete 0.5 0.5 0 0.5Ward's nh+ni
nh+nk
nh+nj
nh+nk
−nh
nh+nk0
Table 2.1: Parameter Values for the clustering algorithms used in this study
where:
ni is the number of entities in cluster i of preceding partition
nj is the number of entities in cluster j of preceding partition
nk is the number of entities in the new cluster k (nk = ni + nj)
nh is the number of remaining entities for which the distance to cluster k has to be
recomputed (one less than the number of clusters after the merger).
The output from the analyses are represented as hierarchical tree or dendrograms.
A general description of the three methods evaluated in this study is given below.
2.1.1 Average linkage (UPGMA)
In this method after two objects with the least dissimilarity fuse together an arith-
metic average of the dissimilarity of this new cluster and the rest of the objects are
calculated. This leads to a reduction in the size of the original dissimilarity matrix.
The procedure then continues with the dissimilarity matrix being correspondingly
reduced. When the average between an object and a cluster is calculated, the
method gives equal weights to the members of the clusters when averaging, thus is
called unweighted. Thus, in the progressive reduction of the dissimilarity matrix,
only relationships between groups are considered, which are given equal weighting
and this leads to loss of information about the relationships between pairs of objects
(Legendre, 1998).
2.1.2 Complete linkage
The fusion of the clusters depends on the most distant pair of objects as opposed to
the closest. An object can join a cluster only when it is linked to all objects present
in the cluster. Two clusters can only fuse when all members from the �rst cluster
are related to all objects from the second cluster, hence it becomes more di�cult
2.2 Non-Metric Multidimensional Scaling (NMDS) 13
for objects to join a cluster. This however creates clusters with clear discontinuities
(Legendre, 1998).
2.1.3 Ward's linkage
This method is also referred to as Ward's minimum variance method. The procedure
minimizes the sum of squares to form clusters, thus it is also referred to as the
incremental sum of squares method. The procedure initially considers each object
as a cluster on its own so the distance of the object to its cluster centroid is 0.
The centroid of a cluster is the average of the coordinates of the objects in the
cluster. As the clusters form, the centroids move away from actual object coordinates
and the sum of squared distances between the objects and the centroids increases.
The distance of the object to its cluster centroid is calculated using the Euclidean
distance formula. At each clustering step, the cluster identi�ed for fusion is the one
that minimizes the sum of squared distance over all objects. The dendrogram is
normally represented in squared distances.
2.2 Non-Metric Multidimensional Scaling (NMDS)
The process begins with an ordination (scaling) of the objects in full-dimensional
space and then represents them in few dimensions while the distance relationships
between objects are retained as much as possible. The main objective of NMDS
is to plot dissimilar objects far apart in the ordination space and similar objects
close to one another. An initial distance matrix is calculated using an appropriate
distance measure for the data. A con�guration of the objects is constructed in a
speci�ed dimension which goes through an iterative algorithm to calculate a matrix
of �tted distances in the ordination space, using Euclidean distance mostly. The
solution depends on the initial positions of the objects so the choice of the original
dissimilarity measure is important. The �tted distances are then compared to the
original distances through regression and the corresponding scatter plot is known as
the Shepard Diagram. The goodness-of-�t of the regression is evaluated by the use
of the sum of squares from the regression analysis. These are known as the stress
values and the �t is considered good if the stress value is less than 0.01 (Legendre,
1998).
14 Chapter 2 Statistical Theory
Stress =
√√√√∑h,i(dhi − d̂hi)2∑
h,i d2hi
(2.2)
where:
dhi are the �tted distance values
d̂hi are the values forecasted by the regression between dhi and dhi (original distances)
3Methodology
3.1 Icelandic Ground�sh Survey
The Icelandic ground�sh survey was instigated in 1985 and has been conducted in
March every year since by the Marine Research Institute. The survey area which
consists of the Icelandic continental shelf inside the 500 meters depth contour, is
divided into statistical rectangles. Each statistical rectangle represents one half
degree latitude and one degree longitude, on which the strati�cation scheme is based.
Statistical rectangles are further divided into 4 subrectangles. The strati�cation
system in the survey design, used to de�ne the locations of tows (stations) was
based on the density of cod found in the area. These density patterns, estimated by
statistical rectangles, were calculated from catch data from commercial and research
vessels prior to the survey design. For analysis, the survey area is divided into a
northern and southern area and ten strata based on biological and hydrographic
considerations. The allocation of stations to strata is directly proportional to the
area of the stratum and its estimated cod density (Pálsson et al., 1989). Figure 3.1
shows the survey area, the statistical rectangles and the approximate locations of
the stations.
The sampling scheme can be classi�ed as semi-random strati�ed (Pálsson et al.,
1989) as half the stations were randomly chosen by the research team of the institute
whereas the other half was chosen by �shermen who had knowledge and experience
of �shing and the �shing grounds. The design however is systematic since the same
stations are covered every year (Pálsson et al., 1989). Five commercial vessels are
15
16 Chapter 3 Methodology
Figure 3.1: Icelandic ground�sh survey area within the 500 meter contour line,outlining the statistical rectangles and the locations of the stations
leased every year to carry out the survey within the restricted time frame of 2-3
weeks. Emphasis is placed on standardizing the �shing methods as far as possible.
The towing speed is �xed at 3.8 knots over the bottom and the towing distance is
4.0 nautical miles.
3.2 Data
The survey targets all major commercial demersal �sh species within the survey
area. The criterion used for identifying the species to be included in the current
analysis was the frequency of occurrence of the species in the overall number of
samples. Species which appeared in greater than 5% of the total number of samples
were analysed. This comprised 40 species. Rare species were excluded as they could
confuse patterns in multivariate analysis if left in the similarity matrix since they
typically have only single sporadic occurrences at variable sites, without apparent
structure (Clarke and Warwick, 2001).
Data for the period 1998-2007 were analyzed. The raw data used for analy-
sis consisted of abundance in numbers by species, year, station, statistical square,
3.3 Hierarchical cluster analysis - Species Assemblages 17
sub-square, depth, latitude and longitude of the stations. The original matrix of
abundance had species arranged in columns and each row corresponded to a single
tow.
The data were appropriately standardized (for each method) and transformed
before analysis. For data on species abundance standardizing reduces the strong
weighting and in�uence of few highly abundant species. It is important to make all
species have similar importance so that uncommon species also contribute to the
dissimilarities. Standardization also reduces the e�ect of di�erent total abundance
in di�erent sampling units which is important when comparing sites.
3.3 Hierarchical cluster analysis - Species Assem-
blages
The data analyses consisted of two main parts (Analysis I and II), based on di�erent
data standardisations and dissimilarity measures and are described below.
3.3.1 Analysis I: Correlation distance
For this distance measure, the data were �rst transformed to fourth root and then
scaled to mean 0 and variance 1 before carrying out the analysis. The distribution of
the data, before and after transformation are outlined in Figure 3.2, for four abun-
dant species. The dissimilarity measure used was 1 - Correlation. This coe�cient
best measures linear relationships between standardized (zero mean and unit vari-
ance) variables (Quinn and Keough, 2002). Since the data were centered (zero
mean), the Uncentered Pearsons Correlation Coe�cient was used, subsequently
modi�ed to dissimilarity by subtracting from 1:
1−
n∑i=1
xijxik√√√√ n∑i=1
x2ij
n∑i=1
x2ik
where xij and xik represents the abundance of jth and kth species at site i.
18 Chapter 3 Methodology
3.3.2 Analysis II: Bray-Curtis distance
The second distance measure tested was the Bray-Curtis. The data were transformed
to fourth root and standardized by range which is one suitable standardisation for
this distance measure (Quinn and Keough, 2002). The Bray-Curtis measure of
dissimilarity could not be applied to earlier data standardisation as it does not
accept negative values (Quinn and Keough, 2002) which are generated when the
data are scaled. Figure 3.3 outlines the distribution of the data before and after
transformation for four abundant species. The Bray-Curtis coe�cient compares two
species in terms of their minimum abundance at each site:
100
∑pi=1 2min(xij, xik)∑p
i=1(xij + xik)(3.1)
where xij and xik represents the abundance of jth and kth species at site i.
The dissimilarity coe�cient is calculated by subtracting similarity from 100.
3.3.3 Data Analyses
The statistical software R was used to carry out all the analyses.
For each mode of analysis (Analysis I: Correlation distance and II: Bray-Curtis
distance) the three hierarchical clustering methods; Average, Complete and Ward's
were applied. For each method three levels of data aggregation were tested; (i) raw
data including all stations and years, (ii) data aggregated by station by taking an
average across years and (iii) data aggregated by subrectangles by taking an average
across years and stations.
The e�ect of sample size was tested by taking subsamples of the data. A total
of 5352 tows were available initially. Subsamples of 50%, 25% and 10% of the
original tow collection were taken. These subsamples were generated randomly
while maintaining the design and relative station density of the survey. Clustering
was done on each subsample for the two modes of analyses.
The cluster analysis was carried out using the Pvclust routine under package
Pvclust to assess the uncertainty in the clustering through bootstrap resampling
technique. A thousand bootstrap replications were run for each cluster. Two types
3.3 Hierarchical cluster analysis - Species Assemblages 19
of probability values are computed in parallel by the routine i.e. approximately
unbiased (AU) p-value and bootstrap probability (BP) value. The AU p-value is
generated through multiscale bootstrap resampling and has asymptotic superiority
in bias over the BP value (Suzuki and Shimodaira, 2006). The BP value of a cluster,
which is calculated by the ordinary bootstrap resampling, is the frequency that it
appears in the bootstrap replicates. A detailed account of these computations are
given by Shimodaira (2008).
In R the Bray-Curtis measure of dissimilarity is implemented using the routine
vegdist in package vegan.
20 Chapter 3 MethodologyC
od a
Frequency
020
0050
00010002000300040005000
b
Frequency
−2
02
46
020040060080010001200
Had
dock
a
Frequency
010
000
2500
0
010002000300040005000
b
Frequency
−2
02
4
02004006008001000
Red
fish
a
Frequency
020
000
4000
0
010002000300040005000
b
Frequency
−2
02
46
020040060080010001400
Long
rou
gh d
ab
a
Frequency
020
0050
00010002000300040005000
b
Frequency
−2
02
4
020040060080010001200
Figure3.2:
Distributionof
thedata
(a)beforeand(b)aftertransformingto
fourth
root
andscalingto
zero
meanand
variance
1,forfour
abundant
speciesinthesurvey,aslabelled.
The
histogramshow
sthenumberof�shpertowcollections.
3.3 Hierarchical cluster analysis - Species Assemblages 21C
od a
Frequency
020
0050
00010002000300040005000
b
Frequency
0.0
0.4
0.8
050010001500
Had
dock
a
Frequency
010
000
2500
0
010002000300040005000
b
Frequency
0.0
0.4
0.8
02004006008001000
Red
fish
a
Frequency
020
000
4000
0
010002000300040005000
b
Frequency
0.0
0.4
0.8
0500100015002000
Long
rou
gh d
ab
a
Frequency
020
0050
00010002000300040005000
b
Frequency
0.0
0.4
0.8
050010001500
Figure3.3:
Distributionof
thedata
(a)beforeand(b)aftertransformingto
fourth
root
andstandardisingby
range,for
four
adundant
speciesin
thesurvey,as
labelled.
The
histogram
show
sthenumber
of�shper
towcollections.
22 Chapter 3 Methodology
3.4 Comparison of the hierarchical clustering tech-
niques
One objective criterion used for comparison was the Cophenetic Correlation Coef-
�cient (CPCC). The CPCC is a simple correlation coe�cient between the original
dissimilarity matrix and the cophenetic matrix which is the total dissimilarity matrix
produced after clustering i.e. the distance at which two objects become members of
the same cluster. This correlation therefore measures how well the clustering was
able to maintain the original dissimilarity in the data. The Pearson's correlation
coe�cient was used here. In order to test the e�ect of di�erent sample sizes, the
correlation was calculated between the cophenetic matrix for the various reduced
sample sizes and the original dissimilarity matrix for all samples.
Another objective criterion used was the agglomerative coe�cient (AC) which
basically measures the clustering structure found by a technique. �For each ob-
servation i, its dissimilarity to the �rst cluster it is merged with is divided by the
dissimilarity of the merger in the �nal step of the algorithm, denoted by m(i). The
AC is the average of all 1 - m(i)� (Maechler et al., 2005). The value ranges from 0
to 1 and the higher the AC the better. The AC was however not used to compare
results for di�erent sample sizes as the coe�cient tends to increase with the number
of observations. In R, AC is computed using the routine agnes in package cluster.
The de�nition of the clusters and their probability values were noted and com-
pared. The signi�cance of the clusters were set at 0.9 for the AU p-value of the
clusters.The dendrograms were also visually compared for the presence of similar
clusters across the di�erent data smoothing and sample sizes.
Independent comparisons were made for Analysis I (Correlation distance) and
Analysis II (Bray-Curtis distance) to examine which clustering method performed
relatively better, for the two modes of analysis. The most robust method was then
identi�ed.
3.5 Comparison of hierarchical clustering with non-
metric multidimensional scaling
A non-statistical approach was used to validate the results from the hierarchical ag-
glomerative clustering. This was done by comparing it with non-metric multidimen-
3.6 Fish Assemblages in relation to environmental variables 23
sional scaling (NMDS). The Kruskal's non-metric multidimensional scaling routine
isoMDS under package MASS was used. The procedure does not accept negative
values for initial dissimilarities, hence it could not be applied to data scaled to 0
mean and 1 variance. Thus the comparison could only be made with Analysis II:
Bray-Curtis dissimilarity measure on fourth root transformed data scaled by range.
NMDS plots the clusters on an ordination diagram to look for groupings. These
identi�ed groups were then compared with the clusters formed by the hierarchical
clustering. The stress values were used to examine the goodness-of-�t.
3.6 Fish Assemblages in relation to environmental
variables
After the comparisons of the clustering techniques and the identi�cation of the most
robust linkage method, some biological interpretations were made on the identi�ed
species assemblages, for both Analysis I and II. It was tested if the identi�ed �sh
community structures could be related to two environmental variables, depth and
geographic location of species.
For each species, weighted average depths d and standard deviations sd were
calculated by:
d =
∑nsds∑ns
(3.2)
and
sd =
√∑ns(ds − d)2∑
ns
(3.3)
where ns represents the abundance in numbers for species and ds represents the
depth at station s.
A one-way Analysis of Variance (ANOVA) was carried out to examine any sig-
ni�cant variability in mean depths among the identi�ed �sh assemblages. A Tukey
multiple comparison test was then undertaken to determine between which treat-
ment levels (assemblages) the actual di�erences lay.
Furthermore, the geographic distribution of each species was mapped. This was
24 Chapter 3 Methodology
done by generating a bubble plot which shows the mean abundance of each species,
averaged across all years, by statistical sub-rectangles. The sizes of the circles are
proportional to the square root of the mean abundance. Any relationship between
this and the identi�ed assemblages was then examined in a non-statistical manner.
3.7 Habitat analysis
This part of the analysis entailed carrying out a classi�cation of the areas within the
Icelandic continental shelf. The areas were de�ned as the statistical subrectangles.
An average of the species abundance in numbers, was calculated by each subrectangle
generating a species-subrectangle matrix. This was essentially a transpose of the
species-site matrix used for species assemblages. Clustering was then carried out
on these data to determine the hierarchical classi�cation of the areas. Classi�cation
was carried out using the three hierarchical linkage methods, for the two distance
measures described above (Analysis I: Correlation distance and II: Bray-Curtis).
The classi�cations obtained were mapped for clarity. For each identi�ed cluster of
areas, its species composition was also determined.
In a previous analysis described in Stefánsson and Pálsson (1997) it was inferred,
based on the bathymetric and hydrographic structure of the Icelandic continental
shelf, that some de�nition between the north and south areas and some depth di-
visions should be observed. The e�ciency of the techniques were based on this
hypothesis.
3.8 Heatmap
A heatmap was generated using the heatplot routine in package made4 ). This plots
hierarchical dendrograms of objects and variables, in this context sites and species
respectively, in a two-way rearrangement. The data were transformed to fourth root
and scaled to mean 0 and variance 1 for this analysis. Here the default settings
were used, which is clustering based on correlation dissimilarity and Average linkage
(Culhane et al., 2005). This generated an image with a spectrum of colours indicat-
ing the strength of associations between the species and their corresponding areas
of occurrence.
4Results
4.1 Comparison of the three hierarchical clustering
techniques
4.1.1 Analysis I: Correlation distance
The results from the objective criteria for assessing the clustering techniques, CPCC
and AC, are outlined in Tables 4.1 and 4.2 respectively. Overall it was seen that
Average linkage gave the highest CPCC (0.82), followed by Complete (0.79) then
Ward's (0.76), although Complete linkage performed poorly with the full data set
(0.67). The AC was the highest for Ward's linkage (0.82) followed by Complete
(0.62) then Average (0.49).
The hierarchical clustering yielded by Average and Complete linkage, Figures
4.1a and 4.1b respectively, produced clusters at high dissimilarity levels. Ward's
linkage, however, gave well-de�ned clusters forming at lower levels of dissimilarity.
When the entire data set was used, this technique classi�ed the species into 2 distinct
signi�cant groups (AU > 0.9; edge 37 & 38 in Figure 4.2). Edge refers to the
cluster number which is marked in green in the �gures. A few signi�cant groups of
species were produced by the Average and Complete linkage. Overall, the probability
of clustering was lower for the Complete linkage in comparison to the other two
methods. The AU p-values were used for comparison which are illustrated in blue
in the �gures.
Clustering on the full data set provided inconsistent species assemblages across
25
26 Chapter 4 Results
the three hierarchical clustering techniques. However, with some data smoothing,
i.e. averaging the species abundance by stations and across years, the results were
more consistent and comparable among the three clustering methods. Essentially
four main species assemblages could be identi�ed and these are portrayed in Figures
4.3a, 4.3b and 4.4 for Average, Complete and Ward's linkage respectively. Species
such as altantic wol�sh, moustache sculpin, lump�sh, long rough dab and snake
blenny were inconsistent in clustering, among the three linkage methods.
4.1.2 Analysis II: Bray-Curtis distance
For this analytical method also, it was seen that Average linkage gave the highest
CPCC (0.87), followed by Complete (0.74) then Ward's (0.61) (Table 4.1). The AC
was the highest for Ward's (0.75) linkage followed by Complete (0.62) then Average
(0.44) (Table 4.2).
When the clustering was carried out on the full data set, the Average (Figure
4.5a) and Complete linkage (Figure 4.5b) produced clusters at high dissimilarity
levels. The Complete linkage did not give a clear de�nition of clusters in particular.
Ward's linkage gave well de�ned clusters (Figure 4.6). The results among the three
linkage techniques was not consistent. With smoother data, the clustering structure
improved for Average and Complete linkage and the results across the three clus-
tering techniques were relatively more consistent. Similar groups of species could
be identi�ed. The results from Average and Complete linkage were similar (Figures
4.7a, 4.7b) except Average linkage produced some outlying observations. However
the clustering structure between the constituent groups of species was di�erent for
Ward's linkage (Figure 4.8).
4.1 Comparison of the three hierarchical clustering techniques 27
Data Average Complete Ward's
I II I II I IIFull data set 0.82 0.87 0.67 0.74 0.75 0.61Aggregated by stations 0.82 0.84 0.79 0.74 0.76 0.64Aggregated by subrectangles 0.81 0.83 0.79 0.79 0.75 0.6650% Subsample 0.80 0.83 0.74 0.79 0.75 0.6925% Subsample 0.80 0.83 0.75 0.68 0.75 0.6510% Subsample 0.78 0.82 0.70 0.61 0.66 0.63
Table 4.1: Cophenetic Correlation Coe�cient for Analysis I (Correlation distance)and II (Bray-Curtis distance)
Data Average Complete Ward's
I II I II I IIFull data set 0.49 0.44 0.62 0.62 0.82 0.75Aggregated by stations 0.66 0.55 0.75 0.65 0.90 0.83Aggregated by subrectangles 0.70 0.61 0.77 0.63 0.91 0.85
Table 4.2: Agglomerative Coe�cient for Analysis I (Correlation distance) and II(Bray-Curtis distance)
28 Chapter 4 Results(a)
deepwater redfishpolar cod
polar sculpinatlantic sculpin
artic rocklinggreenland halibutesmark's eelpout
lycodes spatlantic poacherlongfin snailfish
codspotted wolffish
thorny skatesnake blenny
long rough dabvahl's eelpout
witchfourbeaded rockling
haddockwhiting
monkfishlemon sole
blue whitingblueling
greater argentinetusk
megrimnorway pout
lingnorway haddock
saitheredfish
skatedogfish
atlantic wolffishmoustache sculpin
lumpfishhalibutplaice
dab
0.20.40.60.81.0
Dissimilarity
9797
9299
9999
9897
9910
094
100
9910
098
9910
010
098
6010
010
010
061
6989
5793
100
100
7673
4993
6485
75
83au
9910
086
9710
010
098
9799
100
100
100
9910
097
100
100
100
9856
100
9910
033
6982
7291
100
100
6467
5790
4860
65
61bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
37
38ed
ge #
(b)
megrimnorway pout
lingnorway haddock
tusksaithe
redfishwitch
fourbeaded rocklinghaddock
whitingmonkfish
lemon soleatlantic wolffish
moustache sculpinthorny skate
codspotted wolffish
lumpfishhalibutplaice
dabdeepwater redfish
blue whitingblueling
greater argentineskate
dogfishsnake blenny
long rough dabvahl's eelpout
polar codgreenland halibutesmark's eelpout
lycodes spatlantic poacherlongfin snailfish
polar sculpinatlantic sculpin
artic rockling
0.20.40.60.81.01.21.4
Dissimilarity
9974
9210
010
080
9896
9910
099
100
100
100
100
9797
9610
063
9710
096
8897
5154
6153
9849
4755
6279
9190
78
au
9910
086
9910
010
098
9799
100
9910
010
010
010
092
9310
098
6192
100
9784
96
6848
7830
7955
4236
2918
1414
23
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
25
2627
2829
3031
3233
3435
3637
38
edge
#
Figure4.1:
Dendrogram
ofspeciesassemblagefortheIcelandicGround�sh
(IGF)survey
from
1998-2007using(a)Average
linkage
and(b)Com
pletelinkage,withcorrelationdissimilarity
measure.Dataconsists
ofspeciesabundancein
numbers,
fourth
root
transformed
andscaled
to0meanandvariance
1,comprisingof
alltowcollections.The
rectangles
highlight
theclusterswithAU>0.9.
The
AUvalues
areused
forinterpretation
areindicatedin
blue
andtheclusternumber
(edge)
ismarkedin
green.
4.1 Comparison of the three hierarchical clustering techniques 29
witchfourbeaded rockling
haddockwhiting
monkfishlemon sole
halibutplaice
dabmegrim
norway poutsaithe
redfishtuskling
norway haddockblueling
greater argentineblue whiting
deepwater redfishskate
dogfishpolar cod
atlantic poacherlongfin snailfish
greenland halibutlycodes sp
atlantic sculpinartic rockling
esmark's eelpoutpolar sculpin
long rough dabsnake blennythorny skate
vahl's eelpoutatlantic wolffish
moustache sculpinlumpfish
codspotted wolffish
0123456
Dissimilarity
9910
099
7010
099
9471
6510
074
100
3264
9663
5576
6190
5366
100
7493
8599
9597
9688
9892
8698
90
94
94
au
9996
100
6999
100
9268
5110
069
100
100
4575
4258
4351
3942
5199
4461
8093
7888
7380
8848
5289
42
72
72
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
37
38
edge
#
Figure4.2:
Dendrogram
ofspeciesassemblageusingWard'slinkage
withcorrelationdissimilarity
measure.Dataconsists
ofspeciesabundancein
numbersfourth
root
transformed
andscaled
to0meanandvariance
1.The
rectangles
highlight
theclusters
withAU>0.9.
30 Chapter 4 Results
(a)
tuskblue whiting
bluelinggreater argentine
lingnorway haddock
megrimnorway pout
saitheredfish
haddockfourbeaded rockling
whitingwitch
plaicedab
halibutmonkfish
lemon soleskate
dogfishmoustache sculpin
atlantic wolffishlumpfish
vahl's eelpoutlong rough dab
snake blennycod
spotted wolffishdeepwater redfish
polar codthorny skateartic rocklingpolar sculpin
atlantic sculpingreenland halibutesmark's eelpoutatlantic poacherlongfin snailfish
lycodes sp
0.20.40.60.81.01.2
Dissimilarity
9893
9681
9398
8487
9798
9883
9987
9995
9699
8474
8999
9999
8497
9473
8192
7280
8685
8378
78
78
au
9575
9761
8598
7188
8610
098
8198
6399
7488
9974
6357
9210
097
4288
4829
2569
1763
3362
4153
53
53
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
37
38
edge
#
(b)
tusksaithe
redfishling
norway haddockmegrim
norway poutblue whiting
bluelinggreater argentine
long rough dabsnake blenny
fourbeaded rocklingwhiting
witchhalibutplaice
dabhaddockmonkfish
lemon soleskate
dogfishmoustache sculpin
atlantic wolffishlumpfish
codspotted wolffish
thorny skatevahl's eelpout
greenland halibutesmark's eelpoutatlantic poacherlongfin snailfish
lycodes sppolar sculpin
atlantic sculpinartic rockling
deepwater redfishpolar cod
0.00.51.01.5
Dissimilarity
9987
9698
8898
8486
100
8199
9989
8275
8688
7887
7892
9391
9563
8983
9477
8594
81
84
77
91
81
8081
au
9575
9795
7198
7188
100
8198
9885
5689
5864
5574
5564
3262
9757
4843
4965
2749
18
42
40
14
22
3131
bp
12
34
56
78
910
1112
1314
1516
1718
1920
21
2223
2425
2627
2829
3031
32
33
34
35
36
3738
edge
#
Figure4.3:
Dendrogram
ofspeciesassemblageusing(a)Average
linkage
and(b)Com
pletelinkage,withcorrelationdis-
similarity
measure.Dataconsists
ofmeanspeciesabundancein
numbersby
stations,fourth
root
transformed
andscaled
to0meanandvariance
1.The
rectangles
highlight
theidenti�edspeciesassemblages
forcomparison.
4.1 Comparison of the three hierarchical clustering techniques 31
codspotted wolffish
thorny skatevahl's eelpout
deepwater redfishpolar cod
greenland halibutesmark's eelpoutatlantic poacherlongfin snailfish
lycodes sppolar sculpin
atlantic sculpinartic rocklingblue whiting
bluelinggreater argentine
lingnorway haddock
megrimnorway pout
tusksaithe
redfishmoustache sculpin
atlantic wolffishlumpfish
long rough dabsnake blenny
haddockfourbeaded rockling
whitingwitchskate
dogfishplaice
dabhalibut
monkfishlemon sole
02468
Dissimilarity
9892
9697
9597
8285
9982
9999
8582
9798
9389
7994
8010
098
7895
9651
9997
9480
8275
8557
78
83
63
au
9577
9794
8198
7188
100
8098
9963
5797
9466
8361
6970
100
9442
8774
3293
8963
3454
4448
28
32
29
26
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
35
36
37
38
edge
#
Figure4.4:
Dendrogram
ofspeciesassemblageusingWard'slinkage
withcorrelationdissimilarity
measure.Dataconsists
ofmeanspeciesabundancein
numbersby
stations,fourth
root
transformed
andscaled
to0meanandvariance
1.The
rectangles
highlight
theidenti�edspeciesassemblages
forcomparison.
32 Chapter 4 Results
(a)
polar codpolar sculpin
atlantic sculpinartic rockling
greenland halibutlycodes sp
esmark's eelpoutatlantic poacherlongfin snailfish
deepwater redfishblueling
greater argentineblue whiting
snake blennyhalibutplaice
dabnorway pout
lingmegrim
monkfishfourbeaded rockling
whitingwitch
moustache sculpinlumpfish
atlantic wolffishthorny skate
codlong rough dab
haddockredfish
spotted wolffishvahl's eelpout
saithetusk
lemon solenorway haddock
skatedogfish
0.00.20.40.60.81.0
Dissimilarity
5610
0
100
100
100
100
8710
087
9886
100
8184
100
6793
6373
8210
054
8954
6687
58
7558
100
75
7779
7573
86
100
57au
5510
0
100
100
100
100
8710
091
9992
100
8582
9965
9663
2767
100
5079
5989
7748
9254
100
81
9287
8182
90
100
59bp
12
34
5
67
89
1011
1213
1415
1617
1819
2021
2223
2425
2627
2829
3031
3233
3435
36
3738
edge
#
(b)
snake blennymoustache sculpin
lumpfishspotted wolffish
vahl's eelpoutpolar sculpin
esmark's eelpoutatlantic sculpin
artic rocklingdeepwater redfish
polar codatlantic poacherlongfin snailfish
greenland halibutlycodes sp
halibutplaice
dabnorway pout
lingmegrimblueling
greater argentineblue whiting
fourbeaded rocklingmonkfish
whitingwitchtusk
atlantic wolffishthorny skate
codlong rough dab
haddockredfishsaithe
lemon solenorway haddock
skatedogfish
0.00.20.40.60.81.0
Dissimilarity
5610
0
100
100
100
100
8589
9991
9286
100
8354
5894
9191
6490
5742
9292
9175
9493
80
9183
7781
6686
7986
au
5410
0
100
100
100
100
8691
9893
8085
9979
5261
7996
7049
6952
6768
55
9627
6647
26
3324
5826
6924
1224
bp
12
34
5
67
89
1011
1213
1415
1617
1819
2021
2223
2425
2627
2829
30
3132
3334
3536
3738
edge
#
Figure4.5:
Dendrogram
ofspeciesassemblageusing(a)Average
linkage
and(b)Com
pletelinkage
withBray-Curtis
dissimilarity
measure.Dataconsistsofspeciesabundancein
numbers,fourth
root
transformed
andstandardised
byrange.
The
rectangles
highlight
theclusters
withAU>0.9.
4.1 Comparison of the three hierarchical clustering techniques 33
moustache sculpinpolar sculpin
esmark's eelpoutatlantic sculpin
artic rocklingpolar cod
atlantic poacherlongfin snailfish
greenland halibutlycodes sp
spotted wolffishvahl's eelpout
lumpfishhaddock
redfishatlantic wolffish
thorny skatecod
long rough dabdeepwater redfish
bluelinggreater argentine
blue whitingskate
dogfishhalibutplaice
dabnorway pout
lingmegrim
saithetusk
lemon solenorway haddock
snake blennymonkfish
fourbeaded rocklingwhiting
witch
0.00.51.01.52.02.53.03.5
Dissimilarity
5410
010
010
010
010
085
9299
8787
7199
9390
6693
8394
7764
8678
7973
9381
8372
7678
94
7467
84
65
80
74
au
5310
010
010
010
010
087
9199
9275
6499
8894
6295
5897
5067
9758
5773
9540
4865
5560
99
4028
58
36
52
40
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
35
36
37
38
edge
#
Figure4.6:
Dendrogram
ofspeciesassemblageusingWard'slinkage
withBray-Curtisdissimilarity
measure.Dataconsists
ofspeciesabundancein
numbers,fourth
root
transformed
andstandardised
byrange.
The
rectangles
highlight
theclusters
withAU>0.9.
34 Chapter 4 Results
(a)
dogfishskate
dabgreenland halibut
lycodes spartic rockling
atlantic sculpinpolar sculpin
esmark's eelpoutatlantic poacherlongfin snailfish
deepwater redfishpolar cod
snake blennymoustache sculpin
tusknorway haddock
saitheredfish
atlantic wolffishlumpfishhaddock
thorny skatelong rough dab
vahl's eelpoutcod
spotted wolffishfourbeaded rockling
whitingwitch
plaicehalibut
monkfishlemon sole
megrimling
norway poutblue whiting
bluelinggreater argentine
0.00.20.40.60.8
Dissimilarity
100
100
100
100
100
5710
066
100
9582
100
7399
8082
9866
7976
8288
8984
8590
9276
6997
6789
99
63
75
64
5655
au
100
100
9910
010
054
100
4710
094
9310
0
6098
4657
9778
4634
6780
4454
4171
8222
2288
2268
99
17
56
26
2323
bp
1
23
45
67
89
1011
12
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
33
34
35
36
3738
edge
#
(b)
artic rocklingesmark's eelpout
polar sculpinatlantic sculpin
atlantic poacherlongfin snailfish
greenland halibutlycodes sp
deepwater redfishpolar cod
megrimling
norway poutblue whiting
bluelinggreater argentine
skatedogfish
atlantic wolffishlumpfishhaddock
thorny skatelong rough dab
moustache sculpinvahl's eelpout
codspotted wolffish
saitheredfish
tusknorway haddock
halibutmonkfish
lemon soleplaice
dabsnake blenny
fourbeaded rocklingwhiting
witch
0.00.20.40.60.81.0
Dissimilarity
100
100
9986
9454
9410
093
69
7470
8095
9854
8779
8488
8597
8779
8982
8583
8792
88
9390
8189
9595
91
au
100
100
100
7797
5597
100
9437
8361
5292
9757
6386
3480
3199
3167
8036
5468
7654
33
9430
7330
4648
82
bp
1
23
45
67
89
10
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
31
3233
3435
3637
38
edge
#
Figure4.7:
Dendrogram
ofspeciesassemblageusing(a)Average
linkage
and(b)Com
pletelinkage
withBray-Curtis
dissimilarity
measure.Dataconsists
ofmeanspeciesabundancein
numbersby
stations,fourth
root
transformed
and
standardised
byrange.
The
rectangles
highlight
theidenti�edspeciesassemblages
forcomparison.
4.1 Comparison of the three hierarchical clustering techniques 35
atlantic poacherlongfin snailfishatlantic sculpin
artic rocklingesmark's eelpout
polar sculpingreenland halibut
lycodes spdeepwater redfish
polar codatlantic wolffish
lumpfishhaddock
thorny skatelong rough dab
moustache sculpinvahl's eelpout
codspotted wolffish
blue whitingblueling
greater argentinesaithe
redfishtusk
norway haddockmegrim
lingnorway pout
skatedogfish
snake blennyfourbeaded rockling
whitingwitch
halibutmonkfish
lemon soleplaice
dab
01234
Dissimilarity
100
100
9793
6298
8394
7310
073
7175
9995
9081
9789
100
7360
9271
9796
100
9896
7369
9297
7662
5365
97
au
100
100
100
9155
100
100
9429
100
8660
5699
9778
3197
8110
021
1788
6379
8510
096
6154
2992
96
387
870
96
bp 12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
33
3435
3637
38
edge
#
Figure4.8:
Dendrogram
ofspeciesassemblageusingWard'slinkage
withBray-Curtisdissimilarity
measure.Dataconsists
ofmeanspeciesabundancein
numbersby
stations,fourth
root
transformed
andstandardised
byrange.
The
rectangles
highlight
theidenti�edspeciesassemblages
forcomparison.
36 Chapter 4 Results
4.2 Sample size e�ect
4.2.1 Analysis I: Correlation distance
For this part, Average linkage performed well down to a subsample of 25% with some
minor changes in the clustering structure of the species. On the other hand, Com-
plete linkage gave unstable results but Ward's linkage performed well down to 10%
subsample. Two main observations can be made in all three cases. The probability
values decreased with smaller sample size leading to many clusters being insigni�-
cant and the CPCC for all linkage techniques generally decreased with decreasing
sample size (Table 4.1). Some more detailed observations for the three clustering
methods are outlined below.
Average linkage
The 50% subsample gave very similar assemblage groupings to the total sample
size. Three clusters were identi�ed at a dissimilarity of 1 (edge 34, 36 & 37 in Figures
4.1a and 4.9a). The 25% subsample gave similar results except the species group
containing blue whiting, blue ling and greater argentine clustered with a di�erent
group of species (Figure 4.9b). At a subsample of 10%, the clusters containing cod
and greenland halibut (edge 36; Figure 4.10) were similar however the clustering for
the rest of the species changed. The probability values decreased with decreasing
sample size. The CPCC decreased from 0.82 for the largest sample to 0.78 for the
smallest sample. (Table 4.1).
Complete linkage
Data aggregated by stations were used to compare the sample sizes in this case
as it gave relatively more consistent results. Additionally, the results obtained from
these were similar to the results obtained from the other two clustering techniques
therefore this was considered more reliable for comparison. Reducing the sample
size had an e�ect on the assemblages obtained from this method. Even though the
results from 25% subsample were similar (Figures 4.3b & 4.11b), the 50% subsample
gave some inconsistent results, such as, the cluster containing cod (edge 34; Figures
4.11a) had a di�erent clustering structure. At 10% subsample the clustering was
4.2 Sample size e�ect 37
signi�cantly di�erent (Figure 4.12). The probability values decreased with decreas-
ing sample size. The CPCC decreased from 0.79 for the largest sample to 0.70 for
the smallest sample (Table 4.1).
Ward's linkage
For the 50% and 25% subsamples the results were similar with lump�sh, skate
and dog�sh being exceptions (Figures 4.2, 4.13a, & 4.13b). At 10% subsample
snake blenny was an exception to the general clustering structure (Figure 4.14).
The probability values of the clusters decreased signi�cantly with fewer samples.
The CPCC values were consistent down to 25% subsample at 0.75 but decreased to
0.66 with a further reduction in the sample size (Table 4.1).
4.2.2 Analysis II: Bray-Curtis distance
For this distance measure, Average and Ward linkage performed relatively better
than Complete linkage.
Average linkage performed consistently at 50% subsample, some species were
unstable in clusters (Figures 4.5a and 4.15a). Some inconsistencies were observed at
25% subsample however the overall structure was similar (Figure 4.15b) but changed
considerably at 10% sample size (Figure 4.16).
Complete linkage performed consistently at 50% subsample, some species were
unstable in clusters (Figures 4.7b and 4.17a). The assemblages were considerably
di�erent at 25% and 10% subsample (Figures 4.17b & 4.18).
Ward's linkage performed relatively well at 50% and 25% subsample, with some
exceptions (Figures 4.6, 4.19a and 4.19b). At 10% subsample the assemblages were
considerably di�erent (Figure 4.20).
Here again, the CPCC values decreased gradually with decreasing sample size for
all techniques (Table 4.1) and the probability values of the clusters also decreased.
38 Chapter 4 Results
(a)
codspotted wolffish
thorny skatesnake blenny
long rough dabvahl's eelpout
deepwater redfishpolar cod
polar sculpinatlantic sculpin
artic rocklingatlantic poacherlongfin snailfish
lycodes spgreenland halibutesmark's eelpout
skatedogfish
witchfourbeaded rockling
haddockwhiting
monkfishlemon sole
blue whitingblueling
greater argentinetusk
megrimnorway pout
lingnorway haddock
saitheredfish
atlantic wolffishmoustache sculpin
lumpfishhalibutplaice
dab
0.20.40.60.81.0
Dissimilarity
99
9684
6199
9710
095
7398
9096
8294
9293
9910
093
100
6465
9396
6458
7591
9910
0
6695
6783
7976
68
70
au
100
9678
5010
092
100
9679
9986
100
7789
9692
100
100
9610
038
2175
8935
3954
9210
099
3688
3575
2733
27
38
bp
1
23
45
67
89
1011
1213
1415
1617
1819
2021
2223
2425
2627
2829
30
3132
3334
3536
37
38
edge
#
(b)
polar codpolar sculpin
atlantic sculpinartic rockling
esmark's eelpoutatlantic poacherlongfin snailfish
greenland halibutlycodes sp
codspotted wolffish
thorny skatevahl's eelpout
long rough dabsnake blenny
atlantic wolffishmoustache sculpin
lumpfishhalibutplaice
dabdogfish
skatedeepwater redfish
blue whitingblueling
greater argentinemonkfish
lemon solewitch
fourbeaded rocklinghaddock
whitingtusk
saitheredfish
megrimnorway pout
lingnorway haddock
0.20.40.60.81.0
Dissimilarity
9997
9995
6696
9895
6710
075
100
100
6880
8277
7879
5898
8171
6269
100
8271
9895
79
8083
8587
8082
80
au
9891
100
8768
9510
090
6810
064
100
100
7373
4742
4741
5710
043
4542
5699
7069
9781
62
5545
2841
1623
25
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
31
3233
3435
3637
38
edge
#
Figure4.9:
Dendrogram
ofspeciesassemblageusingAverage
linkage
withcorrelationdissimilarity
measure.Dataconsists
ofspeciesabundancein
numbers,fourth
root
transformed
andscaled
to0meanandvariance
1,comprisingof
(a)50%
random
subsam
pleand(b)25%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusterswith
AU>0.9.
4.2 Sample size e�ect 39
dogfishskate
greater argentineblue whiting
tusksaithe
redfishfourbeaded rockling
haddockmonkfish
whitingwitch
bluelingmegrim
norway poutling
norway haddockhalibutplaice
lemon soledab
lumpfishpolar sculpin
deepwater redfishatlantic sculpin
artic rocklingesmark's eelpout
polar codgreenland halibut
lycodes spatlantic poacherlongfin snailfishatlantic wolffish
moustache sculpinsnake blenny
long rough dabthorny skate
vahl's eelpoutcod
spotted wolffish
0.00.20.40.60.81.01.2
Dissimilarity
6582
9287
9974
6761
9210
079
6678
9784
9069
8184
7075
8497
8875
8777
9178
8083
8380
7880
7385
86
au
5357
8179
9749
6644
8810
040
4015
9656
6518
5164
2810
6176
1628
7342
5134
935
1735
1626
1939
38
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
3738
edge
#
Figure4.10:Dendrogram
ofspeciesassemblageusingAverage
linkage
withcorrelationdissimilarity
measure.Dataconsists
ofspeciesabundancein
numbers,fourth
root
transformed
andscaled
to0meanandvariance
1,comprisingof10%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusters
withAU>0.9.
40 Chapter 4 Results
(a)
tusksaithe
redfishling
norway haddockmegrim
norway poutblue whiting
bluelinggreater argentine
haddockwhiting
witchfourbeaded rockling
long rough dabsnake blenny
monkfishlemon sole
halibutplaice
dabskate
dogfishlumpfish
atlantic wolffishmoustache sculpindeepwater redfishgreenland halibutesmark's eelpout
polar sculpinartic rockling
codspotted wolffish
thorny skatevahl's eelpout
polar codatlantic sculpin
lycodes spatlantic poacherlongfin snailfish
0.00.51.01.5
Dissimilarity
8588
8178
9694
9887
9194
6585
7952
8790
9275
6668
7388
8081
7374
4795
8176
8280
7982
71
88
8586
au
7096
5569
9685
9833
9189
5012
8753
6058
7438
1442
66
2456
35
3366
8142
162
3547
15
23
3535
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
35
36
3738
edge
#
(b)
tuskblue whiting
bluelinggreater argentine
saitheredfish
lingnorway haddock
megrimnorway pout
long rough dabsnake blenny
fourbeaded rocklinghaddock
whitingwitchskate
dogfishplaice
dabhalibut
monkfishlemon sole
lumpfishatlantic wolffish
moustache sculpincod
spotted wolffishthorny skate
vahl's eelpoutesmark's eelpout
polar sculpinatlantic sculpin
artic rocklingdeepwater redfish
polar codatlantic poacherlongfin snailfish
greenland halibutlycodes sp
0.00.51.01.5
Dissimilarity
9187
8788
7599
9199
7580
9899
9083
8864
8483
7571
9355
8679
8976
6879
7176
8364
6572
72
7165
65
au
7470
8281
7499
5799
5741
9696
8847
5240
5539
4532
2129
4857
8824
1113
928
1121
1510
8
410
9
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
35
3637
38
edge
#
Figure4.11:Dendrogram
ofspeciesassemblageusingCom
pletelinkage
withcorrelationdissimilarity
measure.
Data
consists
ofmeanspeciesabundancein
numbersby
stations,fourth
root
transformed
andscaled
to0meanandvariance
1,comprisingof
(a)50%
random
subsam
pleand(b)25%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusters
withAU>0.9.
4.2 Sample size e�ect 41
(a)
dabmonkfish
lemon soleling
norway haddockfourbeaded rockling
haddockwhiting
witchtusk
saitheredfishdogfishmegrim
norway poutblueling
greater argentineblue whiting
lumpfishatlantic wolffish
moustache sculpinhalibutplaice
long rough dabsnake blennypolar sculpin
codthorny skate
vahl's eelpoutskate
artic rocklingspotted wolffishatlantic sculpin
polar codatlantic poacherlongfin snailfish
greenland halibutlycodes sp
deepwater redfishesmark's eelpout
0.00.51.01.5
Dissimilarity
9786
9110
092
9673
9586
9165
7792
7295
7182
9479
7977
7664
6081
7579
87
9685
70
6290
8786
70
80
71
au
9161
5810
070
7834
7735
5215
3072
2482
2944
8510
1222
1518
1416
226
39
05
3
32
21
1
9
1
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
31
3233
3435
36
37
38
edge
#
Figure4.12:Dendrogram
ofspeciesassemblageusingCom
pletelinkage
withcorrelationdissimilarity
measure.
Data
consistsof
meanspeciesabundancein
numbersby
stations,fourth
root
transformed
andscaled
to0meanandvariance
1,comprisingof
10%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusters
withAU>0.9.
42 Chapter 4 Results
(a)
polar sculpinatlantic sculpin
artic rocklingpolar cod
greenland halibutesmark's eelpout
lycodes spatlantic poacherlongfin snailfish
thorny skatesnake blenny
long rough dabvahl's eelpout
codspotted wolffishatlantic wolffish
moustache sculpindeepwater redfish
blue whitingblueling
greater argentinemegrim
norway poutling
norway haddocktusk
saitheredfish
witchfourbeaded rockling
haddockwhiting
monkfishlemon sole
skatedogfish
lumpfishhalibutplaice
dab
0123456
Dissimilarity
9797
9299
9797
9895
9910
010
010
010
098
100
100
9999
9899
100
100
9998
8486
9910
097
8486
9280
6492
78
9191
au
9910
086
9910
010
098
9710
010
010
010
010
096
100
100
100
9896
9910
010
098
9968
8999
100
9990
7873
3655
7338
6666
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
3738
edge
#
(b)
polar sculpinatlantic sculpin
artic rocklingpolar cod
greenland halibutesmark's eelpout
lycodes spatlantic poacherlongfin snailfish
thorny skatesnake blenny
long rough dabvahl's eelpout
codspotted wolffishatlantic wolffish
moustache sculpinmegrim
norway poutsaithe
redfishtuskling
norway haddockdeepwater redfish
bluelinggreater argentine
blue whitingskate
dogfishwitch
fourbeaded rocklinghaddock
whitingmonkfish
lemon solelumpfish
halibutplaice
dab
0123456
Dissimilarity
9799
6696
7299
9883
8295
100
8910
010
085
5676
7510
010
079
7258
7786
9957
100
7199
6681
9379
8378
8080
au
9610
077
9672
100
9981
100
9610
089
100
100
6855
7350
9910
071
4581
7360
9867
100
7998
8575
7876
6951
7575
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
3738
edge
#
Figure4.13:Dendrogram
ofspeciesassemblageusingWard'slinkage
withcorrelationdissimilarity
measure.Dataconsists
ofspeciesabundancein
numbers,fourth
root
transformed
andscaled
to0meanandvariance
1,comprisingof
(a)50%
random
subsam
pleand(b)25%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusterswith
AU>0.9.
4.2 Sample size e�ect 43
tusksaithe
redfishdogfish
greater argentineblue whiting
skatebluelingmegrim
norway poutling
norway haddockhalibutplaice
lemon soledab
haddockmonkfish
whitingwitch
fourbeaded rocklingsnake blenny
polar codgreenland halibut
lycodes spatlantic poacherlongfin snailfish
polar sculpinatlantic sculpin
artic rocklingdeepwater redfishesmark's eelpout
codspotted wolffishlong rough dab
thorny skatevahl's eelpout
lumpfishatlantic wolffish
moustache sculpin
01234567
Dissimilarity
6977
9287
8371
7299
9410
090
100
7794
9078
8050
8187
7582
7890
8384
9291
8579
7492
8789
6881
65
65
au
5544
7479
5767
5195
8710
051
9950
7974
5032
2116
1828
4942
7548
2025
237
508
48
257
46
6
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
37
38
edge
#
Figure4.14:Dendrogram
ofspeciesassemblageusingWard'slinkage
withcorrelationdissimilarity
measure.Dataconsists
ofspeciesabundancein
numbers,fourth
root
transformed
andscaled
to0meanandvariance
1,comprisingof10%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusters
withAU>0.9.
44 Chapter 4 Results
(a)
skateatlantic sculpin
artic rocklinglycodes sp
greenland halibutesmark's eelpout
polar sculpinatlantic poacherlongfin snailfish
deepwater redfishpolar cod
dogfishblue whiting
bluelinggreater argentine
snake blennyplaice
dabsaithe
norway haddockredfish
tuskmoustache sculpin
atlantic wolffishlumpfishhaddock
thorny skatelong rough dab
codspotted wolffish
vahl's eelpoutfourbeaded rockling
lingmegrimhalibut
monkfishlemon sole
norway poutwhiting
witch
0.10.20.30.40.50.60.70.8
Dissimilarity
100
8980
7984
8065
9310
070
9968
7364
8378
8069
7880
7780
9291
9378
9998
5880
5750
99
5060
6664
64au
9966
4252
6168
4695
100
59
9861
5947
5655
6448
6444
2923
7684
5416
9492
3173
1217
100
1826
2734
16bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
33
3435
3637
38ed
ge #
(b)
dogfishskate
polar coddeepwater redfish
lycodes sppolar sculpinartic rockling
atlantic sculpinatlantic poacherlongfin snailfish
greenland halibutesmark's eelpout
bluelingmegrim
greater argentineblue whiting
dabhalibutplaice
tusknorway haddock
saitheredfish
monkfishlemon sole
lingnorway pout
moustache sculpinatlantic wolffish
lumpfishhaddock
thorny skatelong rough dab
vahl's eelpoutcod
spotted wolffishsnake blenny
fourbeaded rocklingwhiting
witch
0.00.20.40.60.8
Dissimilarity
99
9493
8788
7998
8295
9399
9680
7399
9187
7252
7459
6069
6670
8569
6773
8681
6993
6790
89
8378
au
99
8993
6281
7196
6889
8095
8841
5393
6530
1840
4322
3566
136
318
4032
579
3145
1869
47
4678
bp
1
23
45
67
89
1011
1213
1415
1617
1819
2021
2223
2425
2627
2829
3031
3233
3435
36
3738
edge
#
Figure4.15:Dendrogram
ofspeciesassemblageusingAverage
linkage
withBray-Curtisdissimilarity
measure.
Data
consists
ofspeciesabundancein
numbers,
fourth
root
transformed
andstandardised
byrange,
comprisingof
(a)50%
random
subsam
pleand(b)25%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusterswith
AU>0.9.
4.2 Sample size e�ect 45
(a)
polar coddeepwater redfishgreenland halibut
skateartic rockling
atlantic poacheratlantic sculpin
polar sculpinesmark's eelpout
longfin snailfishlycodes sp
dogfishblue whiting
bluelinggreater argentine
snake blennyplaice
dabsaithe
tuskredfish
norway haddockmoustache sculpin
vahl's eelpoutspotted wolffish
codthorny skate
atlantic wolffishlumpfishhaddock
long rough dabhalibut
monkfishlemon sole
fourbeaded rocklingling
megrimwitch
whitingnorway pout
0.10.20.30.40.50.60.70.8
Dissimilarity
9967
8370
8980
9789
8076
9997
8977
9599
9184
9285
7110
087
8653
9079
6990
83
7785
85
8481
9292
93
au
9733
5246
5451
8432
4852
8680
5638
6387
6125
1212
2398
1311
2810
520
815
514
16
99
3024
23
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
33
3435
3637
38
edge
#
Figure4.16:DendrogramofspeciesassemblageusingAverage
linkage
withBray-Curtisdissimilarity
measure.Dataconsists
ofspeciesabundanceinnumbers,fourth
root
transformed
andstandardised
byrange,comprisingof10%random
subsam
ple
ofthetotaltowcollections.The
rectangles
highlight
theclusters
withAU>0.9.
46 Chapter 4 Results
(a)
deepwater redfishpolar cod
lycodes spgreenland halibutesmark's eelpout
atlantic sculpinartic rocklingpolar sculpin
atlantic poacherlongfin snailfish
fourbeaded rocklingsnake blenny
atlantic wolffishlumpfishhaddock
thorny skatelong rough dab
moustache sculpincod
spotted wolffishvahl's eelpout
plaicehalibut
monkfishlemon sole
saithenorway haddock
redfishtusk
norway poutwhiting
witchling
megrimblue whiting
bluelinggreater argentine
dabskate
dogfish
0.00.20.40.60.81.0
Dissimilarity
100
8890
7861
9881
9870
6468
9958
8477
8667
9073
6291
7989
8592
9182
68
7883
83
9974
8572
87
91
94au 99
6855
5446
9573
100
5052
4997
5360
5670
51
5769
6887
2668
2388
3168
43
5927
11
9860
137
11
9
83bp
12
34
56
78
910
1112
1314
1516
17
1819
2021
2223
2425
2627
28
2930
31
3233
3435
36
37
38ed
ge #
(b)
skatemegrim
lingnorway pout
bluelinggreater argentine
blue whitingdogfish
dabplaice
halibutmonkfish
lemon soledeepwater redfish
polar sculpinartic rockling
atlantic sculpinatlantic poacherlongfin snailfish
polar codlycodes sp
greenland halibutesmark's eelpout
snake blennyfourbeaded rockling
whitingwitchtusk
norway haddocksaithe
redfishmoustache sculpin
codspotted wolffish
vahl's eelpoutthorny skate
long rough dabhaddock
atlantic wolffishlumpfish
0.00.20.40.60.81.0
Dissimilarity
98
9490
9084
9789
9389
93
8692
7892
9891
8463
8092
6771
9667
9960
67
9285
7886
6693
95
9281
9695
au
98
9093
6478
9577
8065
53
4676
5567
9248
4327
5049
6414
7022
8835
8
5133
224
157
23
1119
99
bp
1
23
45
67
89
10
1112
1314
1516
1718
1920
2122
2324
2526
27
2829
3031
3233
34
3536
3738
edge
#
Figure4.17:Dendrogram
ofspeciesassemblageusingCom
pletelinkage
withBray-Curtisdissimilarity
measure.Data
consistsofmeanspeciesabundancein
numbersby
stations,fourth
root
transformed
andstandardised
byrange,comprising
of(a)50%
random
subsam
pleand(b)25%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
the
clusters
withAU>0.9.
4.2 Sample size e�ect 47
(a)
polar coddeepwater redfish
atlantic poacheresmark's eelpout
longfin snailfishlycodes sp
artic rocklingatlantic sculpin
polar sculpinskate
greenland halibutdogfish
greater argentineblue whiting
saithetusk
redfishnorway haddock
witchwhiting
norway poutfourbeaded rockling
bluelingling
megrimhalibut
monkfishlemon sole
plaicedab
snake blennymoustache sculpin
vahl's eelpoutspotted wolffish
codthorny skate
atlantic wolffishlumpfishhaddock
long rough dab
0.00.20.40.60.81.0
Dissimilarity
9967
8580
8590
9883
7499
9574
92
8575
9683
9410
071
5290
7167
8567
9077
8648
5675
9183
9493
75
77au
9732
5151
5247
8643
5281
6138
36
4641
6820
6898
157
1547
98
6
3213
71
10
78
42
15
13bp
12
34
56
78
910
1112
13
1415
1617
1819
2021
2223
2425
26
2728
2930
3132
3334
3536
37
38ed
ge #
Figure4.18:Dendrogram
ofspeciesassemblageusingCom
pletelinkage
withBray-Curtisdissimilarity
measure.Data
consistsofmeanspeciesabundancein
numbersby
stations,fourth
root
transformed
andstandardised
byrange,comprising
ofa10%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusters
withAU>0.9.
48 Chapter 4 Results
(a)
lycodes spgreenland halibutesmark's eelpoutatlantic poacherlongfin snailfishatlantic sculpin
polar sculpinartic rockling
deepwater redfishpolar cod
atlantic wolffishlumpfishhaddock
thorny skatelong rough dab
moustache sculpinvahl's eelpout
codspotted wolffish
bluelinggreater argentine
blue whitingskate
dogfishtusk
norway haddocksaithe
redfishmegrim
lingnorway pout
snake blennyfourbeaded rockling
whitingwitch
dabplaice
halibutmonkfish
lemon sole
01234
Dissimilarity
9988
8988
8599
9076
9381
8674
9292
9884
8362
6787
6787
8168
8496
9570
9170
9186
9182
95
88
94
92
au
9991
9280
6296
8067
8165
4755
7967
9243
4625
6560
1344
3043
1178
7428
4817
5323
4615
29
11
36
51
bp 12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
35
36
37
38
edge
#
(b)
deepwater redfishpolar cod
atlantic sculpinartic rockling
lycodes spgreenland halibutesmark's eelpout
polar sculpinatlantic poacherlongfin snailfish
saithenorway haddock
redfishtusk
atlantic wolffishlumpfishhaddock
thorny skatelong rough dab
moustache sculpincod
spotted wolffishvahl's eelpout
skatedogfish
norway poutling
megrimblue whiting
bluelinggreater argentine
dabplaice
halibutmonkfish
lemon solesnake blenny
fourbeaded rocklingwhiting
witch
01234
Dissimilarity
100
8987
8069
9683
100
8083
6210
082
7981
7482
8576
9681
5673
9698
7979
9789
9066
7586
8180
77
86
87
au
9968
5252
5295
7010
063
5349
9959
6356
4467
5675
9041
6365
9389
7431
8174
6647
1685
3816
24
27
84
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
37
38
edge
#
Figure4.19:DendrogramofspeciesassemblageusingWard'slinkage
withBray-Curtisdissimilarity
measure.Dataconsists
ofspeciesabundancein
numbers,
fourth
root
transformed
andstandardised
byrange,
comprisingof
(a)50%
random
subsam
pleand(b)25%
random
subsam
pleof
thetotaltowcollections.The
rectangles
highlight
theclusters
withAU
>0.9.
4.2 Sample size e�ect 49
(a)
skategreenland halibut
artic rocklingatlantic poacheratlantic sculpin
polar sculpinesmark's eelpout
longfin snailfishlycodes sp
snake blennydeepwater redfish
polar codatlantic wolffish
lumpfishhaddock
long rough dabmoustache sculpin
vahl's eelpoutspotted wolffish
codthorny skate
dogfishblueling
lingmegrim
greater argentineblue whiting
plaicedab
fourbeaded rocklingwitch
whitingnorway pout
saithetusk
redfishnorway haddock
halibutmonkfish
lemon sole
01234
Dissimilarity
9969
8381
8783
9880
7398
9275
9292
8199
8910
073
7875
6488
9476
6984
6882
7395
5380
7779
70
83
83
au
9732
4954
5151
8642
5379
6038
4355
2079
3498
619
484
2765
211
213
116
293
73
72
9
6
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
37
38
edge
#
Figure4.20:DendrogramofspeciesassemblageusingWard'slinkage
withBray-Curtisdissimilarity
measure.Dataconsists
ofspeciesabundanceinnumbers,fourth
root
transformed
andstandardised
byrange,comprisingof10%random
subsam
ple
ofthetotaltowcollections.The
rectangles
highlight
theclusters
withAU>0.9.
50 Chapter 4 Results
4.3 Data Aggregation (smoothing) e�ect
4.3.1 Analysis I: Correlation distance
The level at which the data were aggregated had an e�ect particularly on Complete
linkage. With the full data set, the clusters were not very well-de�ned and the
de�nition improved with data smoothing, increasing the probability slightly also
(Figure 4.1b & Figure 4.3b & Figure 4.21b). The CPCC was considerably higher
for aggregated data then for the full data set. The CPCC for Average and Ward's
linkage did not show any considerable di�erence with data smoothing (Table 4.1).
The overall assemblage patterns for these two linkage methods were comparable,
across di�erent data aggregations, with some species being exceptions that moved
between the clusters. These are illustrated in Figures 4.1a, 4.3a & 4.21a for Average
linkage and Figures 4.2, 4.4 & 4.22 for Ward's linkage.
The dissimilarity levels at which the clusters formed was lower when the data
were aggregated by stations, for Average and Complete linkage. Further data aggre-
gation by subrectangles, did not result in any signi�cant changes in the clustering
levels. The AC values considerably increased when the data were aggregated by sta-
tions for all three linkage methods. However, no considerable changes were observed
when data were further aggregated by subrectangles (Table 4.2).
The probability of clustering generally decreased with data smoothing. Ward's
linkage performed well across all three data aggregation levels with the highest
probability of clustering with the full data set, indicating the greatest consistency
in generated clusters across bootstraps.
4.3.2 Analysis II: Bray-Curtis distance
The structure of assemblages were sensitive to data aggregation for all three link-
age techniques, in particular for Complete linkage. The probability of the clusters
increased with increased data smoothing for all three linkage techniques. These are
illustrated in Figures 4.5a , 4.7a and 4.21a for Average linkage; Figures 4.5b , 4.7b
and 4.21b for the Complete linkage and Figures 4.6 , 4.8 and 4.24 for the Ward's
linkage.
The CPCC increased for Complete and Ward's linkage but decreased slightly for
Average linkage (Table 4.1). The AC values increased with data smoothing for all
linkage techniques (Table 4.2) together with the probability values for the clusters.
4.3 Data Aggregation (smoothing) e�ect 51
(a)
halibutplaice
dablong rough dab
snake blennyfourbeaded rockling
haddockwhiting
witchskate
dogfishblue whiting
bluelinggreater argentine
monkfishlemon sole
lingnorway haddock
megrimnorway pout
tusksaithe
redfishmoustache sculpin
atlantic wolffishlumpfish
deepwater redfishthorny skate
vahl's eelpoutcod
spotted wolffishpolar cod
artic rocklingpolar sculpin
atlantic poacheratlantic sculpin
greenland halibutesmark's eelpout
longfin snailfishlycodes sp
0.00.20.40.60.81.01.2
Dissimilarity
9376
100
100
93
100
6199
9883
100
9677
7298
9984
7096
7081
9086
100
9259
9286
8191
8593
72
6087
80
81
80
au
8043
100
100
75
9965
9810
049
9893
4367
9499
7429
8757
7663
7410
082
4738
4453
7030
5552
1529
16
31
32
bp
12
34
5
67
89
1011
1213
1415
1617
1819
2021
2223
2425
2627
2829
3031
3233
3435
36
37
38
edge
#
(b)
moustache sculpinatlantic wolffish
lumpfishthorny skate
vahl's eelpoutcod
spotted wolffishatlantic sculpin
greenland halibutesmark's eelpout
longfin snailfishlycodes sp
polar sculpinartic rockling
deepwater redfishatlantic poacher
polar codblue whiting
bluelinggreater argentine
tusksaithe
redfishskate
dogfishmonkfish
lemon soleling
norway haddockmegrim
norway pouthalibutplaice
dabhaddock
whitingwitch
fourbeaded rocklinglong rough dab
snake blenny
0.00.51.01.5
Dissimilarity
9280
9999
8799
6410
099
9766
7496
7198
9760
9592
7278
84
9784
7166
95
8189
8476
77
9280
83
87
8685
au
8150
100
100
5599
6598
100
9367
4993
2494
9830
8282
5052
68
9638
6231
55
1325
2043
21
2249
18
24
2728
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
27
2829
3031
32
3334
35
36
3738
edge
#
Figure4.21:Dendrogram
ofspeciesassemblageusing(a)Average
linkage
and(b)Com
pletelinkage
withcorrelation
dissimilarity
measure.
Dataconsists
ofmeanspeciesabundancein
numbersby
statisticalsubrectangles,
fourth
root
transformed
andscaled
to0meanandvariance
1.The
rectangles
highlight
theclusters
withAU>0.9.
52 Chapter 4 Results
(a)
atlantic sculpingreenland halibutesmark's eelpout
longfin snailfishlycodes sp
polar sculpinartic rockling
vahl's eelpoutcod
spotted wolffishthorny skate
atlantic poacherpolar cod
deepwater redfishblue whiting
bluelinggreater argentine
tusksaithe
redfishmonkfish
lemon soleling
norway haddockmegrim
norway poutmoustache sculpin
atlantic wolffishlumpfish
long rough dabsnake blenny
fourbeaded rocklinghaddock
whitingwitch
halibutplaice
dabskate
dogfish
0246810
Dissimilarity
9385
100
100
8099
7199
100
9666
6497
6110
055
8292
9984
100
6967
9188
7194
7594
7589
8992
8494
93
94
87
au
8252
100
100
5199
6598
100
9366
4293
2099
3065
8293
7410
062
4581
7924
4745
7130
2353
2035
1716
15
33
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
3536
37
38
edge
#
Figure4.22:Dendrogram
ofspeciesassemblageusingWard'slinkage
withcorrelationdissimilarity
measure.Dataconsists
ofmeanspeciesabundancein
numbersby
statisticalsubrectangles,
fourth
root
transformed
andscaled
to0meanand
variance
1.The
rectangles
highlight
theclusters
withAU>0.9.
4.3 Data Aggregation (smoothing) e�ect 53
(a)
dogfishskate
polar coddeepwater redfish
polar sculpinartic rockling
atlantic poacheratlantic sculpin
lycodes spgreenland halibutesmark's eelpout
longfin snailfishblue whiting
bluelinggreater argentine
snake blennyplaice
dabmoustache sculpin
atlantic wolffishlumpfishhaddock
thorny skatelong rough dab
vahl's eelpoutcod
spotted wolffishmegrim
norway poutfourbeaded rockling
whitingwitch
lingnorway haddock
tusksaithe
redfishhalibut
monkfishlemon sole
0.00.20.40.60.8
Dissimilarity
99
6697
9980
7494
7991
8210
088
100
5768
6458
9472
6563
8266
7495
4678
8793
76
7195
96
8685
99
7974
au
100
7397
9959
6193
100
9655
9969
100
3824
5541
9120
3043
7111
4196
5220
8077
24
2670
95
4450
93
6684
bp
1
23
45
67
89
1011
1213
1415
1617
1819
2021
2223
2425
2627
2829
30
3132
33
3435
36
3738
edge
#
(b)
dogfishhalibut
monkfishlemon sole
tusksaithe
redfishnorway pout
lingnorway haddock
megrimblue whiting
bluelinggreater argentine
skateplaice
dabdeepwater redfish
artic rocklingpolar sculpin
esmark's eelpoutlongfin snailfish
polar codgreenland halibut
lycodes spatlantic poacheratlantic sculpinatlantic wolffish
lumpfishhaddock
thorny skatelong rough dab
moustache sculpinvahl's eelpout
codspotted wolffish
snake blennyfourbeaded rockling
whitingwitch
0.00.20.40.60.81.0
Dissimilarity
100
8596
9978
9697
9294
100
9087
8867
8197
7494
7982
6288
8286
8980
8890
5987
86
8867
83
7082
8283
au
100
8896
9951
9410
086
9499
8668
5564
4897
4778
7126
5027
2591
1969
1825
4511
34
9138
19
179
2121
bp
1
23
45
67
89
1011
1213
1415
1617
1819
2021
2223
2425
2627
28
2930
31
3233
34
3536
3738
edge
#
Figure4.23:Dendrogram
ofspeciesassemblageusing(a)Average
linkage
and(b)Com
pletelinkage
withBray-Curtis
dissimilarity
measure.
Dataconsists
ofmeanspeciesabundancein
numbersby
statisticalsubrectangles,
fourth
root
transformed
andstandardised
byrange.
The
rectangles
highlight
theclusters
withAU>0.9.
54 Chapter 4 Results
(a)
deepwater redfishpolar cod
greenland halibutlycodes sp
artic rocklingpolar sculpin
esmark's eelpoutlongfin snailfishatlantic poacheratlantic sculpinatlantic wolffish
lumpfishhaddock
thorny skatelong rough dab
moustache sculpinvahl's eelpout
codspotted wolffish
blue whitingblueling
greater argentineskate
dogfishmegrim
norway pouthalibut
monkfishlemon sole
lingnorway haddock
tusksaithe
redfishplaice
dabsnake blenny
fourbeaded rocklingwhiting
witch
01234
Dissimilarity
9897
9610
093
9210
010
089
9190
9162
6780
7199
7964
8164
9480
8077
6169
9496
7088
8390
86
90
94
94
88
au
100
9796
9981
9310
099
9369
8988
6064
4759
9974
2025
6183
1180
1733
3493
8915
8731
8138
44
43
80
87
bp
12
34
56
78
910
1112
1314
1516
1718
1920
2122
2324
2526
2728
2930
3132
3334
35
36
37
38
edge
#
Figure4.24:DendrogramofspeciesassemblageusingWard'slinkage
withBray-Curtisdissimilarity
measure.Dataconsists
ofmeanspeciesabundancein
numbersby
statisticalsubrectangles,fourth
root
transformed
andstandardised
byrange.
The
rectangles
highlight
theclusters
withAU>0.9.
4.4 Comparison of hierarchical clustering with non-metric multidimensional scaling 55
Summary
For both Analysis I: Correlation distance and Analysis II: Bray-Curtis distance,
the following holds for the linkage methods. Average linkage always gave the highest
CPCC followed by Complete then Ward's linkage. Complete linkage was the most
sensitive method, giving inde�nite patterns with full data set and with deviations
in sample size. Average and Ward's linkage were to some extent sensitive to data
aggregation but less so than Complete linkage and were more stable when sample size
was altered. The CPCC and the probability of clusters decreased with decreasing
sample size for all three linkage techniques.
Ward's linkage always gave the highest AC followed by Complete then Average
linkage. The AC always increased with data aggregation.
The Bray-Curtis distance measure worked better with aggregated data yielding
higher p-values for the clusters. The Correlation distance measure worked better
with the full data set for Ward's linkage. This was based on the reliability of the
clusters in terms of their probability values.
4.4 Comparison of hierarchical clustering with non-
metric multidimensional scaling
The NMDS ordination of species, with Bray-Curtis dissimilarity measure resulted
in a high stress of 8.87% in three dimensions, for the full data set. The ordination
was repeated for the two data aggregation levels and produced a stress of 7.85%
and 7.49% respectively. Ordination of the full data set did not produce any distinct
groupings (Figure 4.25a). With smoother data (aggregated by statistical subrect-
angles) four species groups could be identi�ed (Figure 4.25b) which were similar to
the outcome from the hierarchical clustering, particularly to Ward's linkage (Figure
4.24), on the same level of data aggregation .
56 Chapter 4 Results
(a)
−0.
50.
00.
5
−0.4−0.20.00.20.40.60.8
Str
ess
= 8
.87
cod
hadd
ock
saith
e
whi
ting
redf
ish
ling
blue
ling tu
sk
atla
ntic
wol
ffish
thor
ny s
kate
spot
ted
wol
ffish
mon
kfis
h
skat
edo
gfis
h
grea
ter
arge
ntin
e
halib
ut
gree
nlan
d ha
libut
plai
ce
lem
on s
ole
witc
h
meg
rim
dab
long
rou
gh d
ab
norw
ay p
out
blue
whi
ting
lum
pfis
hm
oust
ache
scu
lpin
atla
ntic
poa
cher
four
bead
ed r
ockl
ing
norw
ay h
addo
ck
deep
wat
er r
edfis
h
esm
ark'
s ee
lpou
t
long
fin s
nailf
ish
pola
r co
d
atla
ntic
scu
lpin
vahl
's e
elpo
ut
pola
r sc
ulpi
n
artic
roc
klin
g
snak
e bl
enny
lyco
des
sp
(b)
−0.
4−
0.2
0.0
0.2
0.4
0.6
−0.20.00.20.4
Str
ess
= 7
.49
cod
hadd
ock
saith
ew
hitin
gre
dfis
h
ling
blue
ling
tusk
atla
ntic
wol
ffish
thor
ny s
kate
spot
ted
wol
ffish
mon
kfis
h
skat
e
dogf
ish
grea
ter
arge
ntin
e
halib
ut
gree
nlan
d ha
libut
plai
ce
lem
on s
olew
itch
meg
rim
dab
long
rou
gh d
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Figure4.25:Multidimensional
scalingusingBray-Curtisdistance
measure
for(a)thefulldata
set(com
prisingalltow
collections)(b)data
aggregated
bystatisticalsub-rectangle.
Speciesabundancein
numberswas
fourth
root
transformed
andstandardised
byrange.
4.5 Fish Assemblages in relation to environmental variables 57
4.5 Fish Assemblages in relation to environmental
variables
4.5.1 Analysis I: Correlation distance
The classi�cations from Ward's linkage, carried out on the full data set, were related
to the two environmental variables, depth and geographic location, to examine pos-
sible ecological rationale for the assemblages obtained. Two discrete clusters were
obtained having high probabilities (AU > 0.9) (edge 37 & 38, Figure 4.2). These
clusters were further divided into two. Essentially, four species assemblages were
obtained. The �rst assemblage (A) comprised of halibut, plaice, dab, monk�sh,
lemon sole, witch, fourbeaded rockling, whiting and haddock clustering at AU=0.86.
The second assemblage (B) consisted of tusk, saithe, red�sh, ling, norway haddock,
megrim, norway pout, blueling, blue whiting, greater argentine, skate, dog�sh and
deepwater red�sh at AU=0.90. The third assemblage (C) was Altantic wol�sh,
moustache sculpin, thorny skate, vahl's eelpout, cod, spotted wol�sh, lump�sh,
long rough dab and snake blenny AU=0.98. The fourth assemblage (D) comprised
of greenland halibut, esmark's eelpout, polar sculpin, Altantic sculpin, lycodes sp.,
artic rockling, Altantic poacher, long�n snail�sh and polar cod AU=0.88. The latin
names for the �sh species are outlined in Table A.1 in the Appendix.
These assemblages could be related to environmental parameters such as depth
and geographic distribution of the species. The species that clustered together had
similar geographical distributions also. Assemblages A and B were characterised as
species found in the southern region (Figure 4.26). In relation to the mean depths of
the species, the �rst assemblage was de�ned as shallow to intermediate with depths
ranging from 50m - 200m. The second assemblage was de�ned as intermediate to
deep with a mean depth range of 180m - 340m. Assemblages C and D characterised
the northern region (Figure 4.26), where assemblage C was categorised as shallow
to intermediate with a 150m - 250m depth range and assemblage D was de�ned
as deep ranging between 280m - >400m. This relationship between depth and the
identi�ed assemblages is demonstrated in Figure 4.27 where the weighted depths
and standard deviations for each species are outlined and each species is assigned
to the respective cluster.
The box and whisker plot in Figure 4.28a shows the data on which a one-way
ANOVA was performed to investigate statistical di�erences in the mean depths of
58 Chapter 4 Results
the species comprising the assemblages. The ANOVA showed that the mean depths
at which the assemblages occurred were signi�cantly di�erent (F = 41.282, df:3, P
< 0.05). The Tukey multiple comparisons test showed that assemblages A, B and
D were signi�cantly di�erent from each other but assemblage B and C were not
signi�cantly di�erent (Figure 4.28b).
Average linkage gave similar assemblages when applied to data aggregated by sta-
tions, although some species from assemblage C became a part of assemblage D and
skate and dog�sh moved to cluster A (Figure 4.3a). Complete linkage gave similar
clusters with long rough dab, snake blenny, skate and dog�sh being exceptions. The
probability of the clusters were slightly lower than Average linkage (Figure 4.3b).
4.5.2 Analysis II: Bray-Curtis distance
Three assemblages were identi�ed by the Ward's linkage on data aggregated by sta-
tistical subrectangles. The �rst assemblage (A*) comprised of halibut, plaice, dab,
monk�sh, lemon sole, fourbeaded rockling, whiting, witch, tusk, saithe, red�sh, ling,
norway haddock, megrim, norway pout, blueling, blue whiting, greater argentine,
skate, dog�sh with an AU=0.94. The second assemblage (B*) comprised of cod,
spotted wol�sh, vahl's eelpout, moustache sculpin, long rough dab, thorny skate,
lump�sh, haddock and atlantic wol�sh with a probability of 0.94 and the third as-
semblage (C*) consisted of deepwater red�sh, polar cod, greenland halibut, lycodes
sp., artic rockling, long�n snail�sh, altantic poacher, atlantic sculpin, polar sculpin
and esmark's eelpout with an AU=0.88 (Figure 4.24).
The relationship between depth and the identi�ed assemblages is demonstrated
in Figure 4.29 where the weighted depths and standard deviations for each species
are outlined and each species is assigned to the respective cluster. The box and
whisker plot in Figure 4.28c shows the data on which a one-way ANOVA was per-
formed to see any statistical di�erences in the mean depths of the species comprising
the assemblages. The ANOVA showed that the mean depths at which the assem-
blages occurred were signi�cantly di�erent (F = 26.398, df:2, P < 0.05). The Tukey
multiple comparisons test showed that the di�erence lay between assemblage A and
C. Assemblages A and B were not signi�cantly di�erent (Figure 4.28d). The species
separated broadly into north and south divisions in relation to the geographic loca-
tion (Figure 4.26).
The Average linkage gave two signi�cant clusters when applied to data aggregated
4.5 Fish Assemblages in relation to environmental variables 59
by statistical subrectangles. One of the assemblages was similar to assemblage C*
de�ned above with a probability of 0.96. The rest of the species grouped together
with a probability of 0.99 with two outliers (Figure 4.23a). Complete linkage gave
two distinct groups, with a probability of > 0.80, according to the north and south
divisions except species such as whiting, witch and fourbeaded rockling grouped
with the cod cluster instead (Figure 4.23b).
60 Chapter 4 Results
63°
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Red
fish
4.5 Fish Assemblages in relation to environmental variables 61
63°
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4.5 Fish Assemblages in relation to environmental variables 63
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63°
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63°
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Mou
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he s
culp
in
64 Chapter 4 Results
63°
64°
65°
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28°
26°
24°
22°
20°
18°
16°
14°
12°
10°
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63°
64°
65°
66°
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28°
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24°
22°
20°
18°
16°
14°
12°
10°
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63°
64°
65°
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28°
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24°
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16°
14°
12°
10°
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Tho
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e
4.5 Fish Assemblages in relation to environmental variables 65
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Gre
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66 Chapter 4 Results
63°
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Lyco
des
sp.
4.5 Fish Assemblages in relation to environmental variables 67
63°
64°
65°
66°
67°
28°
26°
24°
22°
20°
18°
16°
14°
12°
10°
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pola
r co
d
Figure4.26:Geographicaldistribution
ofthe40
speciesanalysed
forthisstudy,
labelledaccordingly.
The
bubble
plot
show
sthemeanabundanceofspeciesby
statisticalsubrectangles
averaged
acrossyears.The
size
ofcirclesareproportional
tothesquare
root
ofthemeanabundance.
68 Chapter 4 Results
0
100
200
300
400
500
600
dab A
dogfish A
plaice A
lemon sole A
halibut A
whiting A
haddock A
atlantic wolffish C
lumpfish C
monkfish A
snake blenny C
witch A
saithe B
long rough dab C
fourbeaded rockling A
skate A
moustache sculpin C
norway pout B
thorny skate C
cod C
norway haddock B
redfish B
tusk B
ling B
vahl's eelpout C
megrim B
spotted wolffish C
polar cod D
polar sculpin D
blue whiting B
blueling B
atlantic poacher D
artic rockling D
greater argentine D
longfin snailfish D
atlantic sculpin D
deepwater redfish D
greenland halibut D
esmark's eelpout D
lycodes sp D
Depth (m)
Figure4.27:Weightedaveragedepths
andstandard
deviations
forthe40
speciesanalysed.A-D
refersto
theidenti�ed�sh
assemblages
from
Ward'shierarchicalclustering
basedon
correlationdistance.
4.5 Fish Assemblages in relation to environmental variables 69
(a)
A B C D
100
200
300
400
Assemblage
Dep
th
(b)
−100 0 100 200
D−
CD
−B
C−
BD
−A
C−
AB
−A
95% family−wise confidence level
Differences in mean levels of Assemblage
(c)
●●
●
A B C
100
200
300
400
Assemblage
Dep
th
(d)
−50 0 50 100 150 200
C−
BC
−A
B−
A
95% family−wise confidence level
Differences in mean levels of Assemblage
Figure 4.28: (a) Box and whisker plot for the mean depths of species in the identi�ed�sh assemblages from Ward's hierarchical clustering based on correlation distance(b) Tukey test results showing the signi�cant di�erence between the identi�ed �shassemblages (c) Box and whisker plot for the mean depths of species in the identi�ed�sh assemblages from Ward's hierarchical clustering based on Bray-Curtis distance(d) Tukey test results showing the signi�cant di�erence between the identi�ed �shassemblages from (c)
70 Chapter 4 Results
0
100
200
300
400
500
600
dab A*
dogfish A*
plaice A*
lemon sole A*
halibut A*
whiting A*
haddock B*
atlantic wolffish B*
lumpfish B*
monkfish A*
snake blenny A*
witch A*
saithe A*
long rough dab B*
fourbeaded rockling A*
skate A*
moustache sculpin B*
norway pout A*
thorny skate B*
cod B*
norway haddock A*
redfish A*
tusk A*
ling A*
vahl's eelpout B*
megrim A*
spotted wolffish B*
polar cod C*
polar sculpin C*
blue whiting A*
blueling A*
atlantic poacher C*
artic rockling C*
greater argentine A*
longfin snailfish C*
atlantic sculpin C*
deepwater redfish C*
greenland halibut C*
esmark's eelpout C*
lycodes sp C*
Depth (m)
Figure4.29:Weightedaveragedepths
andstandard
deviations
forthe40
speciesanalysed.A*-C*refers
totheidenti�ed
�shassemblages
from
Ward'shierarchicalclustering
basedon
Bray-Curtisdistance.
4.6 Habitat Classi�cation 71
4.6 Habitat Classi�cation
4.6.1 Analysis I: Correlation distance
The Average and Ward linkage yielded similar results. When the dendrogram of
subrectangles was split into 5 clusters, a separation along the north-west and south-
east gradient was obtained with clusters 1, 4 & 5 in the north and clusters 2 & 3 in
the south. The north and south areas further separated along the depth gradient
(Figure 4.30a). The output from Ward's linkage is presented here. The output from
Average linkage is given in Appendix; Figure A.1a. Whereas the outcome from the
Complete linkage was di�erent and is outlined in Appendix; Figure A.1b.
The species composition of the �ve clusters is delineated in Figure 4.31. Cluster
1 mainly comprised of greenland halibut, blue whiting, atlantic poacher, deepwater
red�sh, esmark's eelpout, long�n snail�sh, polar cod, atlantic sculpin, vahl's eelpout,
polar sculpin, artic rockling, lycodes sp. and some of altantic cod, thorny skate and
spotted wol�sh. Cluster 5 mainly comprised of atlantic wol�sh, lump�sh, moustache
sculpin, vahl's eelpout, cod, haddock, spotted wol�sh, tusk, long rough dab, snake
blenny and some of the species in cluster 1. Cluster 4 consisted of haddock, whiting,
thorny skate, plaice, witch, long rough dab, lump�sh, fourbeaded rockling, vahl's
eelpout, snake blenny and some cod. Cluster 3 consisted of haddock, atlantic wol�sh,
monk�sh, dog�sh, halibut, plaice, lemon sole, dab, lump�sh and moustache sculpin.
Cluster 2 contained haddock, saithe, whiting, red�sh, ling, blueling, tusk, monk�sh,
skate, dog�sh, greater argentine, halibut, lemon sole, witch, megrim, norway pout,
blue whiting, fourbeaded rockling, norway haddock. The species codes shown in
Figure 4.31 are outlined in Table A.1 in the Appendix.
4.6.2 Analysis II: Bray-Curtis distance
The Bray-Curtis distance with Ward's linkage showed a de�nition along the north
and south areas with some separation along the depth gradient within these areas
(Figure 4.30b). The Complete linkage also gave similar patterns (Appendix, Figure
A.2b). The Average linkage however gave a de�nition along the north and south
areas only but de�nition according to depth was not apparent (Appendix, Figure
A.2a). The species compositions for the di�erent clusters are delineated in (Figure
4.32).
72 Chapter 4 Results
4.7 Heatmap
A heatmap of the association between species and areas is shown in Figure 4.33.
The map shows a pair-wise display of two dendrograms which were generated us-
ing the Average linkage technique based on Analysis I: Correlation distance. The
species assemblage dendrogram is on the y-axis and the assemblage of areas den-
drogram is on the x-axis. The spectrum of colours ranging from blue (low ratios)
to red (high ratios) gave three main patches of high ratio colours indicating the
species-environment patterns. Thus it can be seen that the species relationships
were re�ected by the spatial relationships.
4.7 Heatmap 73
(a)
62°3
0'
63°
63°3
0'
64°
64°3
0'
65°
65°3
0'
66°
66°3
0'
67°
67°3
0'
29°
28°
27°
26°
25°
24°
23°
22°
21°
20°
19°
18°
17°
16°
15°
14°
13°
12°
11°
10°
clus
ter
1cl
uste
r 2
clus
ter
3cl
uste
r 4
clus
ter
5
(b)
62°3
0'
63°
63°3
0'
64°
64°3
0'
65°
65°3
0'
66°
66°3
0'
67°
67°3
0'
29°
28°
27°
26°
25°
24°
23°
22°
21°
20°
19°
18°
17°
16°
15°
14°
13°
12°
11°
10°
clus
ter
1cl
uste
r 2
clus
ter
3cl
uste
r 4
clus
ter
5
Figure4.30:De�nition
ofareasin
IcelandicwatersusingWard'shierarchical
clustering.
The
data
consistof
species
abundancein
numberstransformed
tofourth
root.Clusteringwas
basedon
(a)correlationdistance
withdata
scaled
to0
meanandvariance
1(b)Bray-Curtisdistance
withdata
standardised
byrange.
74 Chapter 4 Results
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
1
−1.00.5
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
2
−0.50.5
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
3
−0.50.5
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
4
−1.00.52.0
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
5
−0.50.5
Figure4.31:Sp
eciescompositionof
de�ned
clustersfrom
thehabitatclassi�cationusingCorrelation
distance
measure
and
Ward'slinkage.The
speciescodesareoutlined
inTable4in
theApp
endix.
4.7 Heatmap 75
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
1
−1.50.01.5
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
2
−0.50.5
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
3
−0.50.5
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
4
−0.50.5
cod
had
sai
whi
red
linbl
utu
sat
wth
osp
om
onsk
ado
ggr
aha
lgr
epl
ale
mw
itm
egda
blrd
nor
blw
lum
mou
atp
fou
noh
der
esm
los
pol
ats
vah
pos
art
sna
lyc
clus
ter
5
−1.00.52.0
Figure4.32:Sp
eciescompositionofde�ned
clustersfrom
thehabitatclassi�cationusingBray-Curtisdistance
measure
and
Ward'slinkage.The
speciescodesareoutlined
inTable4in
theApp
endix.
76 Chapter 4 Results
573320574611476619373620563513512562617618721375564424474672613663717667374668615718616714715664614671662568425422477423472571561716612426666376372475665511323361360362311673312310322318669570416575719370670319523625675624626623460410364365524366415462413414412463621527367569317461576411321674722622723525315316324473371720363526
deep
wat
er r
edfis
hpo
lar
cod
thor
ny s
kate
artic
roc
klin
gat
lant
ic p
oach
erpo
lar
scul
pin
atla
ntic
scu
lpin
gree
nlan
d ha
libut
esm
ark'
s ee
lpou
tlo
ngfin
sna
ilfis
hly
code
s sp
vahl
's e
elpo
utco
dsp
otte
d w
olffi
shsk
ate
dogf
ish
saith
ere
dfis
hm
onkf
ish
lem
on s
ole
ling
norw
ay h
addo
ckm
egrim
norw
ay p
out
tusk
blue
whi
ting
blue
ling
grea
ter
arge
ntin
em
oust
ache
scu
lpin
atla
ntic
wol
ffish
lum
pfis
hlo
ng r
ough
dab
snak
e bl
enny
witc
hfo
urbe
aded
roc
klin
gha
libut
dab
plai
ceha
ddoc
kw
hitin
g
−2
−1
01
23
4C
olum
n Z
−S
core
Col
or K
ey
Figure4.33:A
heatmap
show
ingthespecies-area
associationfortheIcelandicGround�sh
(IGF)survey
from
1998-2007
usingAverage
linkage
hierarchical
clustering
withcorrelationdissimilarity
measure.The
x-axisshow
sthedendrogram
ofareas(statistical
rectangles)andy-axisshow
sthedendrogram
ofspeciesassemblage.
Dataconsists
ofspeciesabundance
innumbers,fourth
root
transformed
andscaled
to0meanandvariance
1.The
coloursrangefrom
blue
(low
ratios)to
red
(highratios)indicating
thestrength
ofassociations.
5Discussion
A clustering algorithm will always generate a clustering structure even if no real
structure may be intrinsic to the data (Loganantharaj et al., 2006) and di�erent
clustering algorithms are likely to generate di�erent results from the same data set.
The problem becomes more complex when the choice of the dissimilarity measure
to be used is taken into consideration, and the data properties itself, which in turn
in�uence the e�ectiveness of the algorithm (Loganantharaj et al., 2006). This issue
becomes more di�cult as the number of variables increases. Cluster validity has
therefore been a subject of interest and importance in the �eld of molecular genetics
for some decades now. However, substantive guidelines are not available in regards
to the choice of the appropriate algorithms and distance metric for ecological data.
In the �eld of ecology the Average linkage technique is generally recommended in
conjunction with the Bray-Curtis distance measure (Clarke and Warwick, 2001;
Quinn and Keough, 2002).
A number of assessment criteria were used in this study to test the robustness
of the three hierarchical agglomerative clustering techniques that are commonly
applied in ecological studies, Average, Complete and Ward's linkage. According
to the internal criteria of cluster validity and e�ciency, CPCC, Average linkage
performed most e�ciently for both modes of data analyses (Correlation and Bray-
Curtis distance) and yielded the highest values for the coe�cient. In theory, this
would indicate that this linkage generated a classi�cation which was most similar
to the original dissimilarity patterns in the species and site matrix, since the CPCC
is a basic correlation between the two matrix of dissimilarities, that is prior to and
77
78 Chapter 5 Discussion
subsequent to the clustering. Thus by the de�nition of the CPCC criterion, the
overall performance ranking of the clustering methods were Average followed by
Complete then Ward's, although the CPCC for Complete and Ward's linkage were
not considerably lower. However, Complete linkage did not perform e�ciently when
applied to the full set of data.
On the other hand, based on the AC criterion which measures the caliber of the
clustering, Ward's linkage outperformed the Average and Complete linkage for both
modes of data analyses. The AC values for this method were always higher than
the other two techniques. Thus this clustering technique gave the highest quality
of clustered data set. This can be seen from the dendrograms that had well-de�ned
clusters forming at lower dissimilarity levels. Also, there were no outliers produced
by this technique. Ward's linkage is designed to give compact clusters that minimise
the loss of information based on the sums of squares criteria (Ward, 1963). Thus
from a di�erent perspective, this technique could impose clusters or patterns on a
data set which are not truly there (Gauch Jr and Whittaker, 1981). Average and
Complete linkage, on the other hand, gave clusters at high dissimilarity levels and
some species were always de�ned as outliers.
An assessment of the uncertainty of the clusters, through bootstrapping showed
that Ward's linkage performed the best. When applied to the full data set for the
Correlation distance, it gave two distinct clusters with high probabilities. Thus some
con�dence could be placed in the clusters that were obtained. Average and Complete
linkage on the other hand, gave clusters with lower probabilities resulting in many
small signi�cant clusters. Thus the species were not grouping together with a high
likelihood. For Ward's linkage similar patterns were observed with aggregated data
except the likelihood (p-values) of the clusters were lower. This technique was also
robust across the decreasing sample sizes and performed well down to a subsample
of 10% with some anomalies. The clusters obtained were similar although their
probabilities were much lower. For Average linkage, aggregating the data formed
clusters at lower dissimilarity levels. However this reduced the probability of the
clusters. The linkage method worked well down to a sample size of 25% giving
similar species clusters.
The Complete linkage was observed to be the most unstable method. Irrespective
of the data analysis method used, it was sensitive to the di�erent levels of data
aggregation (smoothing) and the extent of the data used for clustering (sample
size). When the full set of data were used this technique did not perform well and
Discussion 79
gave unclear de�nition of clusters. With aggregated data the classi�cation was more
de�ned with high probability of clustering. Similarly as the samples were reduced
the patterns observed from the clustering were not coherent. This algorithm only
allows an object to merge with a cluster if it is similar to all objects already present
in the cluster (Legendre, 1998). Thus as a cluster is formed it is receding in space
from other clusters as its dissimilarity with the other groups increases (Cao et al.,
1997a). Hence a lot information in the data set could potentially a�ect the algorithm
in de�ning close groups which lead to an unstable outcome.
Generally, it seemed that a reduction in sample size reduced the information
about the species-site similarities in the data which resulted in lower bootstrap
probability values for the clusters. Even though the assemblages obtained were
similar for Ward's and Average linkage, for Correlation distance, the accuracy and
reliability of the clusters decreased with fewer samples.
Ward's linkage yielded similar species assemblages even with the Bray-Curtis
distance measure. However, this was when highly smooth data (aggregated by sub-
rectangles) were used. There distinct clusters, with similar species composition,
were obtained with high probabilities. Complete linkage also gave comparable re-
sults with some exceptions, when the outcome for data aggregated by stations for
Correlation distance and data aggregated by statistical subrectangles for Bray-Curtis
distance were compared. Average linkage on the other hand appeared sensitive to
the type of data standardisation and the distance measure that were used. This
method resulted in considerably di�erent species assemblages for the two modes of
data analyses. The Average clustering algorithm takes an average dissimilarity be-
tween two groups. All agglomerative methods inhabit a monotonic property, that
is the dissimilarity between the merged clusters increases monotonically with the
level of the merger. The average technique appears sensitive to the numerical scale,
on which the clustering dissimilarities are calculated from the initial dissimilarities,
since applying a monotonic function to averaging formula can have an e�ect on the
outcome (Hastie et al., 2001). Average linkage in combination with data standard-
ised by range and Bray-Curtis distance did not perform well in identifying species
assemblages for this data set. Clarke and Warwick (2001) recommend a row stan-
dardisation on untransformed data for Average linkage with Bray-Curtis distance
measure.
The general observation was that the Ward's linkage, when applied with Corre-
lation distance performed better with full data set. This was assessed in terms of the
80 Chapter 5 Discussion
accuracy and reliability of the clusters. On the contrary, with Bray-Curtis distance,
the method performed better with highly smooth data (aggregated by statistical
subrectangles). This could be related to the properties of the Bray-Curtis distance
measure which compares two species according to their minimum abundance at each
site.
Stability in cluster analysis is to a great extent dependent on the data set it-
self. Essentially if strong patterns are not present in the data then the clustering
algorithm might not give clear de�nitions and di�erent methods may give consid-
erable deviations in the patterns obtained (Hennig, 2007). The NMDS ordination
technique which is considered more reliable in �nding groups was used as an inde-
pendent technique to verify results from hierarchical cluster analyses. The NMDS
ordination showed roughly three groupings which were similar to the clusters ob-
tained from Ward's linkage, with Bray-Curtis distance and resulted in stress values
of approximately 0.075 in three-dimensions for data aggregated by statistical sub-
rectangles. Normally, results giving stress values of < 0.1 indicates a good ordination
with no real likelihood of misleading interpretation (Clarke and Ainsworth, 1993).
The Average technique has some desirable properties such as the maximisation
of the cophenetic correlation which makes it highly preferable in ecological studies
(Gauch Jr and Whittaker, 1981). As Cao et al. (1997a) point out, it has seldom been
assessed whether the classi�cation acquired from the Average linkage is ecologically
meaningful even though the technique is highly recommended. Cao et al. (1997a)
based their study on river samples with some predeterminations on site separation
from cluster analysis. They found that Ward's and Complete linkage were better
in site separation of the samples in comparison to Average linkage with Ward's
linkage performing better. Similar observations are made in this study. Gauch Jr
and Whittaker (1981) also showed that Average and Complete linkage were not as
adequate in recognising pre-determined plant communities as Ward's linkage and
other non-hierarchical clustering methods.
Since its formulation by Sokal and Rohlf (1962), the CPCC criterion of cluster
validity has been widely applied (Farris, 1969). However this criterion has been ques-
tioned and studies such as Farris (1969); Rohlf and Fisher (1968); Phipps (1971) have
deemed it inadequate. In this study the CPCC criteria was not adequate in identi-
fying the optimal clustering method either. As described earlier, it is a correlation
Discussion 81
between the initial dissimilarities and the �nal cophenetic dissimilarity obtained by
the clustering algorithm. The cophenetic dissimilarity is a restrictive measure since
it contains tied values i.e. out of the N(N − 1)/2 pair of dissimilarities only N − 1
values can be distinct (Hastie et al., 2001). Additionally, hierarchical classi�cations
of objects obey ultrametric inequality for distance hij (from classi�cation), �every
triple of objects (i, j, k) possesses the property that the two largest values in the set
hij, hik, hjk are equal� (Gordon, 1999). Comparing dissimilarities and ultrametric
distances seems ambiguous by measuring the strength of their linear relationship,
even more so when the ultrametric distance contains many tied values (Gordon,
1999). Besides, the signi�cance of CPCC cannot be tested since the cophenetic ma-
trix is dependent on the original dissimilarity matrix (Legendre, 1998). Thus the
nature of this cluster validity index is limiting.
Ward's linkage was identi�ed as the most robust method after assessing it against
the above criteria. This linkage method has been shown to be a robust method in
some non-ecological studies (Scheibler and Schneider, 1985; Milligan and Cooper,
1987). Its use in ecology has been restricted since it is normally used in conjunction
with Euclidean distance which appears unsuitable for species abundance data, as
noted earlier. This study showed that this linkage method performed well with
Correlation and Bray-Curtis distance metrics.
It was considered important that the validity and e�ciency of the linkage tech-
niques were not entirely based on only numeric indices. Clusters can be stable and
yet give meaningless results therefore it is important to complement the results by
some visual inspection and subject-based validation (Hennig, 2007). In the present
study, no pre-determinations could be made about the �sh assemblages. However,
as community structures may change along environmental gradients it was inferred
that the assemblages should be distributed according to some key environmental
variables, in this case geographic distribution and depth were considered in�uen-
tial parameters. Thus the obtained assemblages were related to these variables to
observe any meaningful ecological patterns.
82 Chapter 5 Discussion
5.1 Fish Assemblages and species-environment re-
lationships
The boreal �sheries are dominated by a few key species which strongly interact.
Generally highly dynamic environment, attributed to the oceanographic conditions,
in�uence the �sh stocks (Livingston and Tjelmeland, 2000). The assemblage pat-
terns of the fourty most abundant species in the Icelandic ground�sh survey area
were studied here. The focus was more on demersal species therefore pelagic species
such as capelin and herring were not considered in the study.
Bathymetric studies show that Iceland is situated on two ridges, the mid Atlantic
ridge running from south-west Reykjanes ridge to the north-east Jan Mayen ridge
and the Faroes-Greenland ridge going from south-east to north-west (Stefánsson and
Pálsson, 1997). The bathymetry largely in�uences the hydrography. Several water
masses are present in the Iceland shelf. The Irminger current, which is part of the
North Atlantic current, brings the warm saline Atlantic water to the south coast of
Iceland. To the North, the East Icelandic current is cold and fresh as it carries Artic
water, sea ice and icebergs from East Greenland Current. These largely a�ect the
atmosphere and oceanography around Iceland with warm conditions in the south
and the west, cold in the east, and variable conditions in the north (Valdimarsson
and Malmberg, 1999). Di�erent water masses have distinct thermal and oxygen
concentrations and temperature and salinity are highly variable as a result. This
leads to a natural separation in the habitat preferences of �sh species. Thus it
was inferred that the species occurring in the north and south areas should cluster
separately.
The species assemblage obtained by the Ward's linkage on Correlation distance
gave a separation along the geographic location (north and south) and depth gradient
within each region, as per the inference. Some con�dence could be placed in the
clusters obtained as the bootstrap generated high probability values for these clusters
and indicated that the assemblages were not entirely a result of random e�ects. High
probability values essentially indicate the accuracy of a cluster where �accuracy
means the certainty of the existence of a cluster� (Suzuki and Shimodaira, 2004).
Essentially, four �species assemblage areas� (Jaureguizar et al., 2006) were de-
�ned on the basis of the geographic distribution of the species. Species found in
the north clustered together (assemblages C and D). These formed two constituent
5.1 Fish Assemblages and species-environment relationships 83
groups, one containing the deepwater species such as Greenland halibut, that prefer
colder environmental conditions, and one containing species which are more dis-
persed within the area such as cod and the shallow range species such as lump�sh.
Species found in the south, that prefer warmer conditions, clustered into two assem-
blages, A and B. Assemblage A contained the shallow water species and assemblage
B was the group of species which were present in the intermediate to deep region.
Similar observations have been made by studies on demersal �sh assemblages in the
region (Bergstad et al., 1999; Colvocoresses and Musick, 1984; Fariña et al., 1997;
Gabriel, 1992; Rätz, 1999) where depth and geographic distribution were signi�cant
variables in explaining the �sh assemblages. A similar observation was made for
the analysis based on Bray-Curtis distance. Ward's linkage could be related to the
environmental gradients. Bottom temperature and salinity are other two potentially
important variables that could explain the variability in the �sh assemblages. How-
ever this has not been addressed in the present study since the primary focus of the
study was on the methodological aspects of identifying �sh assemblages.
Species assemblages are groups of species that tend to co-occur in space and time
because they have similar habitat preferences or because they interact biologically.
Nonetheless, association of species or co-occurrence does not necessarily imply that
the species are interacting (Legendre, 1998). This study showed assemblage patterns
in the data and it was seen that the environmental gradients, depth and geographic
properties, played a role in the structuring of the �sh assemblages. Thus the �sh
assemblages re�ected the habitat heterogeneity.
The deeper water species such as Greenland halibut, Altantic poacher, long�n
snail�sh and others that form part of this species group (assemblage D), have dis-
tinguished geographical locations and it was observed that this cluster of species
was always obtained irrespective of the data analysis and clustering methods used.
Whereas, most of the other species occur in a wide area and this could have confused
the multivariate patterns, leading to discrepancies in the classi�cations acquired with
di�erent approaches used for analysis.
The de�nition of areas around Iceland (habitat classi�cation) also led to a sep-
aration along the north-south gradient which further showed some di�erentiation
along depth. The de�nitions obtained were comparable to the previous study on
the de�nition of oceanic areas around Iceland in Stefánsson and Pálsson (1997),
which was in relation to identifying appropriate areas for Bormicon, a Boreal migra-
tion and consumption model for multispecies modeling. Similar observations were
84 Chapter 5 Discussion
made in this study, where the areas were approximately split according to the Bormi-
con area de�nitions (Stefánsson and Pálsson, 1997). The previous study was based
on hierarchical cluster analysis of some key species including cod, haddock, saithe,
red�sh, cat�sh, Greenland halibut, plaice, herring, capelin and shrimp showed some
consistency in the cluster of areas and the Bormicon strata. It was seen that this
independent study which took many species into consideration and di�erent hierar-
chical clustering methods, complemented the de�nitions of the Bormicon strata.
This study experimenting the use of heatmap in the �eld of ecology for pattern
recognition. The visual display showed some patterns in community structure. Es-
sentially three species-environment associations could be observed through the high
ratio (red) patches. These identi�ed the species characteristic of the northern area
and their corresponding habitats (statistical squares). The species in the southern
areas are divided into two according to depth. This basically gives a visual rep-
resentation that speci�c species groups characterise speci�c geographical locations.
It should be noted that the heatmap here was generated using the default settings
which was Average linkage hierarchical clustering with correlation distance mea-
sure. However, the heatmap routine in R can be used to de�ne speci�c clustering
techniques and distance measures for calculating the dendrograms.
6Main considerations and
recommendations
The Ward's linkage was the most robust hierarchical clustering method according to
this study and is recommended for any further studies based on the Icelandic ground-
�sh survey data. It generated consistent well-de�ned clusters with high probabili-
ties and gave high values of CPCC and AC. The assemblages were also ecologically
meaningful when related to two environmental parameters depth and geographical
distribution. It also performed well for the classi�cation of habitats, giving a de�-
nition as per the inference based on the bathymetric and hydrographic conditions
of the Icelandic continental shelf. Complete linkage worked well with aggregated
data, but was generally an unstable method. The Average technique appeared to be
sensitive to the type of data standardisation and distance measure used. The Bray-
Curtis distance metric in conjunction with Average linkage on data standardised by
range was not a suitable method of analysis for this data set. The �shing areas were
also not well-de�ned by this mode of data analysis.
The choice of the distance measure, data standardisation and clustering algo-
rithm is important and should be given more attention. As has been noted in prior
studies, the internal criteria for cluster validity CPCC was not adequate for this
study either.
Biological interpretations of �sh assemblages showed that the spatial structure
of the environmental gradients around Iceland played a role in characterising the
�sh assemblages. Further studies of this nature could relate the �sh assemblages
85
86 Chapter 6 Main considerations and recommendations
with other environmental variables such as temperature and salinity which could be
signi�cant parameters in explaining the variation in �sh assemblages. Examining
some spatial and temporal patterns in species assemblages could also be of interest.
Use of visualisation techniques such as heatmaps are recommended in the �eld
of ecology for displaying community patterns (species-habitat associations). Gen-
erating a heatmap based on Ward's linkage would be recommended for any further
studies of this nature.
Some limitations of the study need to be taken into consideration and some
appropriate recommendations are provided. More attention needs to be paid to
the initial sample selection criterion for analysis. Some pelagic and semi-pelagic
species such as blue ling and greater argentine were not excluded from the data
before analysis. This needs to be taken into consideration for any further studies
of this nature, if the emphasis needs to be on demersal species. In future this type
of analysis could also incorporate some details on the structural composition of the
major species by splitting the abundance values into juvenile (immature) and adult
(mature) prior to analysis.
The Icelandic ground�sh survey covers the �shing grounds down to 500m depth
as it was primarily designed for cod. As such, the variability of deep water species
such as Greenland halibut are relatively high in the survey. The autumn survey on
the other hand covers stations in deeper waters even though it has fewer stations.
However, this study indicated that a reduction in the sample size did not lead to any
major changes in the species assemblage patterns. Whether the high variability of
some deep water species in the spring survey, which are included in this assemblage
study, have an e�ect on the species associations could be examined by using the
data from the autumn survey.
Fisheries management is largely moving toward community analysis and identi-
fying potential management strategies to target �sh assemblages rather than single
species. These �ndings on species assemblages in relation to the particular envi-
ronmental conditions and the habitat de�nitions could be used for multi-species or
ecosystem based management purposes. Further research on temporal and spatial
variability and persistence of these assemblages would be recommended. Whether
these assemblages have functional relationships cannot be determined from this anal-
ysis. Some trophic studies in relation to habitat association within the de�ned
assemblages could be used to determine some functional associations between the
species. The de�nition of the speci�c geographical units having distinct species as-
Main considerations and recommendations 87
semblages relating to the bathymetry and hydrographic conditions, such as shown
here, could also be utilised for conservation purposes, for example if there were
intentions of setting up marine protected areas then these species-environment re-
lationships could be useful.
88 Chapter 6 Main considerations and recommendations
AAppendix
89
90 Chapter A Appendix
Common Name Latin Name Code
Cod Gadus morhua codHaddock Melanogrammus aegle�nus hadSaithe Pollachius virens saiWhiting Merlangius merlangus whiRed�sh Sebastes marinus redLing Molva molva linBlueling (European ling) Molva dipterygia bluTusk Brosme brosme tusAtlantic wol�sh Anarhichas lupus atwThorny skate (starry ray) Raja (Amblyraja) radiata thoSpotted wol�sh (leopard�sh) Anarhichas minor spoMonk�sh Lophius piscatorius monSkate Raja (Dipturus) batis skaDog�sh Squalus acanthias dogGreater argentine Argentina silus graHalibut Hippoglossus hippoglossus halGreenland halibut Reinhardtius hippoglossoides grePlaice Pleuronectes platessa plaLemon sole Microstomus kitt lemWitch Glyptocephalus cynoglossus witMegrim Lepidorhombus whi�agonis megDab Limanda limanda dabLong rough dab Hippoglossoides platessoides limandoides lrdNorway pout Trisopterus esmarki norBlue whiting Micromesistius poutassou blwLump�sh (lumpsucker) Cyclopterus lumpus lumMoustache sculpin Triglops murrayi mouAtlantic poacher Leptagonus decagonus atpFourbearded rockling Rhinonemus cimbrius fouNorway haddock Sebastes viviparus nohDeepwater red�sh Sebastes mentella derEsmark´s eelpout Lycodes esmarki esmLong�n snail�sh (sea tadpole) Careproctus reinhardti losPolar cod Boreogadus saida polAtlantic hookear sculpin Artediellus atlanticus atsVahl´s eelpout (checker eelpout) Lycodes vahli vahPolar sculpin Cottunculus microps posArctic rockling Onogadus argentatus artSnake blenny Lumpenus lampretaeformis snaLycodes sp. Lycodes eudipleurostictus lyc
Table A.1: The common and Latin names of the fourty most common species anal-ysed for this study with the codes used for analysis.
Appendix 91
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FigureA.1:De�nition
ofareasin
Icelandicwatersusing(a)Average
(b)Com
pletehierarchicalclustering
withcorrelation
distance.Dataconsistsof
speciesabundancein
numbers,transformed
tofourth
root
andscaled
to0meanandvariance
1.
92 Chapter A Appendix
(a)
62°3
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62°3
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FigureA.2:De�nition
ofareasin
Icelandicwatersusing(a)Average
(b)Com
pletehierarchicalclustering
withBray-Curtis
distance.Dataconsists
ofspeciesabundancein
numbers,transformed
tofourth
root
andstandardised
byrange.
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