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The copepod communities of the north
and south Pacific central gyres and the
form of species-abundance distributions
MARK WILLIAMSON1* AND JOHN A. MCGOWAN2
1
5DD, UK AND 2INTEGRATIVE OCEANOGRAPHY
92093-0227, USA
DEPARTMENT OF BIOLOGY, UNIVERSITY OF YORK, YORK YO10
OCEANOGRAPHY,
9500 GILMAN DRIVE, LA
JOLLA, CA
DIVISION, SCRIPPS INSTITUTION OF
*CORRESPONDING AUTHOR: [email protected]
Received April 8, 2009; accepted in principle September 18, 2009; accepted for publication November 4, 2009
Corresponding editor: Roger Harris
Epiplanktonic copepods were sampled on 10 cruises in the Pacific central gyres, 7 in
the north gyre and 3 in the south gyre, between 1964 and 1973. These gyres are the
largest biomes, stable, ancient, down-welling, oligotrophic and with little temporal
variation. The data from each cruise were standardized to numbers per 103 m3; no
data from the south gyre cruises has been published before. The structure of the
communities was analysed with species-abundance curves and ordination. One
hundred and eighty-two species were found in all, 118–158 per cruise, 73 in all
cruises. Double-centred ordination of those 73 showed three distinct sets of cruises:
south (Isaacs-Kidd net), north (Isaacs-Kidd net) and north (bongo net). The distance
in species-space between the north and south gyres is the same but orthogonal to the
distance between samples collected by the two nets! Sixteen species abundance distributions (SADs), from 10 cruises and 6 combinations of them, were used to test the
hypotheses that such distributions are mildly platykurtic and increasingly left-skew
with increasing sample size. All SADs were sigmoidal on rank abundance plots of
the log abundance, and agreed with the hypotheses, clarifying the mathematical
form. Such replicated, large sample, SADs are rare.
I N T RO D U C T I O N
The north and south Pacific central gyres are among the
world’s largest ecosystems, notable also for their species
richness, low productivity, and stability. In the 1960s,
‘70s and ‘80s the Scripps Institution of Oceanography
(SIO) ran a series of research ship cruises to a standard
central point in each gyre, known as the Climax areas
after the name of some of the cruises. This was, as
Venrick (Venrick, 1982) said of the north area, “an oligotrophic environment selected for study because of its
great age, large size, and temporal and spatial stability”;
the stability and lack of seasonality is shown by much
work from SIO (e.g. also Hayward and McGowan,
1979; Reid et al., 1978). The areas are therefore excellent
places for the study of the structure of ecological
communities. Although much has been published about
the north Climax area, around 288N 1558W, an area
about 88 or 900 km north of the [big] island of Hawaii
(e.g. Hayward et al., 1983; McGowan and Walker, 1979,
1985; Venrick, 1982, 1990; Venrick et al., 1987), very
little has been published about the south area around
258S 1558W, about 38 or 350 km south of the Îles
Maria, the westernmost of the Austral Island, or about
the comparison of the north and south areas.
Physically, the present form of the gyres will have
been established early in the tertiary, when the Pacific
gained, roughly, its present shape and size and its position relative to the poles, tens of millions of years ago.
In contrast, the age of most of the species will probably,
from evolutionary and palaeobiological work, be
doi:10.1093/plankt/fbp119, available online at www.plankt.oxfordjournals.org. Advance Access publication December 1, 2009
# The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: [email protected]
JOURNAL OF PLANKTON RESEARCH
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measured only in millions of years. Hayward and
McGowan (Hayward and McGowan, 1979) give some
information about chaetognaths, pteropods, heteropods,
squid, fish, amphipods, euphausiids and copepods.
Here we consider the community of the epipelagic
copepods, the most abundant taxon.
The north and south communities are found in two
of the largest provinces in Longhurst’s (Longhurst,
1998) system of marine biogeography, the North Pacific
Tropical Gyre Province (NPTG) and the South Pacific
Subtropical Gyre Province (SPSP), separated by about
228 of latitude (about 2500 km) by, in the east, the
North Pacific Equatorial Counter current Province
(PNEC) and the Pacific Equatorial Divergence Province
(PEQD) and, in the west, the Western Pacific Warm
Pool Province (WARM). Much information on the distribution of planktonic species across the Pacific provinces can be found in other papers from the SIO
group (McGowan, 1971; Reid et al., 1978). The gyres
are very stable. As Miller (Miller, 2004) says “The key
feature of the central gyres is water column stability”
and Longhurst (Longhurst, 1998) notes that SPSP is
“the most uniform and seasonally stable region of the
open oceans” as well as being “the least well-described
region of the ocean”. The low productivity of the gyres
is nowadays obvious in many satellite images of the
world’s oceans. Many oceanographers have considered
the plankton of the gyres in general to be species rich.
For instance, Margalef (Margalef, 1969) “[in plankton]
diversity is negatively correlated with productivity”,
Venrick (Venrick, 1982) “High diversity in an oligotrophic environment appears to be characteristic of
pelagic systems” and Pierrot-Bults (Pierrot-Bults, 1997)
“there seems to be an inverse relationship between productivity and biological diversity [of macrozooplankton]”. Angel (Angel, 1991) quantified this for a transect
along 208W in the North Atlantic and found that, for
values at 108 intervals, the maximum diversity for fish,
ostracods, decapods and euphausiids was each at 208N,
at the edge of the unproductive North Atlantic gyre,
with a decline towards the equator.
The species richness of these ecosystems has been
insufficiently considered in the literature on macroecology, the study of statistical patterns in the abundance,
distribution, biomass and diversity of individual organisms or species (Belgrano and Brown, 2002). Discussions
of the polar-tropical gradient in species richness often
conclude that diversity is greatest where there is more
productivity. For instance, Field et al. (Field et al., 2009)
from a meta-analysis of 393 cases in which they examined six hypotheses (not including stability) concluded
that climate and productivity were important, particularly in terrestrial habitats. The gyres are a strong
counter-example. Oceanographers have often ascribed
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this to stability, variously defined. For instance,
Slobodkin and Sanders (Slobodkin and Sanders, 1969)
opined that “species diversity is greater in higher predictability areas” and Lewontin commented in the discussion of that paper “for you, a high predictability
environment is one with a high serial autocorrelation
just with a low variation”. Williamson (Williamson,
1977) suggested that the stability was the common
factor behind the species richness of tropical rain forests
and the deep-sea benthos. Leigh et al. (Leigh et al.,
2004) in an important collective review of diversity in
tropical rain forests conclude “. . . diversity is higher and
temperature and rainfall are less seasonal . . . pest
pressure is higher, maintaining higher tree diversity,
where winter is absent” and “tree diversity is highest
where environmental conditions vary least”.
Studying the communities of the gyres is therefore
important in understanding global biodiversity patterns.
McGowan and Walker (McGowan and Walker, 1979,
1985, 1993) noted the similarity in community structure
between samples for different cruises to the north area
and that the north and south communities are surprisingly similar “most species . . . maintained the same relative positions [in the rank order of abundance] in both
gyres”. Here we extend those studies to compare and
contrast the epipelagic copepod communities found on
10 cruises, 7 to the north area and 3 to the south. Data
from the south gyre are given here for the first time,
data from the north gyre are wider than those given
before and the results are all new.
The structure of communities can be studied at
various levels of complexity. McGill et al. (McGill et al.,
2007) distinguish between three levels of complexity,
low, such as the number of species, intermediate, particularly species abundance distributions (SADs) and
high, particularly ordination. Here we present results at
all three levels. At the high level, correlations and ordination are used to clarify the similarity of the two gyres
and to indicate which sets of data should be used and
combined for species abundance plots. That allows the
use, at the intermediate level, of the 10 cruises and 6
natural combinations of them giving 16 SADs, “the
most basic description of [the structure of ] an ecological
community” and “a major stepping stone to understanding communities” (McGill et al., 2007).
Nevertheless, the mathematical form of SADs is not
agreed by ecologists. Statistical distributions can be
characterized by their moments, though this approach
has not been used for SADs. From Williamson and
Gaston (Williamson and Gaston, 2005), where the data
were purely terrestrial, it is possible to hypothesize that
well-sampled SADs will be platykurtic (a function of the
fourth moment), and will change from right-skew to
left-skew (a function of the third moment) as the sample
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size increases. This large marine set of SADs is well
suited to testing these hypotheses. At the lowest level of
complexity, the number of species per cruise and per
gyre is merely part of the statistical description of the
species abundance curves.
METHOD
Samples of planktonic copepods were collected either
with bongo nets (McGowan and Brown, 1966) or with
an Isaacs-Kidd midwater trawl (Isaacs and Kidd, 1953)
modified to be a plankton net. We refer to the latter as
an Isaacs-Kidd net; it is called an IKPT (Isaacs-Kidd
plankton trawl) in the cruise reports. Both had 505 mm
mesh nylon, the bongo net a pair of nets with a 0.78 m2
total mouth opening, the Isaacs-Kidd net a 7.78 m2
mouth opening. The water column was sampled uniformly from the surface to 300 m with balanced day
and night samples at each station. The results we report
here are per cruise, summed over the water column,
over day and night and over stations (all close together)
in each cruise. The basic data are expressed as counts
per species per 103 m3. Further details can be found in
McGowan and Walker (McGowan and Walker, 1979,
1985) and in the cruise reports (e.g. Scripps Institution of
Oceanography, 1975). The taxonomy is that used at the
time, which involved a morphological species concept.
We have merely updated the names.
Some further details of the sampling show that we
sampled enough water to get reliable counts, though
these details are not otherwise relevant or useful in
interpreting the results. No net, as is well known,
samples randomly so we only claim to be studying the
epiplanktonic copepods caught by two types of net with
the same mesh. The mesh was chosen to avoid clogging
on long hauls. Microzooplankton biomass was also
recorded at every station on some cruises from pump
samples, in sizes .363 m, .103 m and .35 m. Both
nets were towed at the same speed of about 1.5 knots;
the Isaacs-Kidd net had a 10 m bridle, the bongo none
at all. Both had depth meters and flow meters. The
Isaacs-Kidd tows were oblique hauls down to 300 m
and back. The bongo nets were opening – closing and
samples were taken in contiguous depth bands
(McGowan and Walker, 1979) and the counts then combined to make composite 0 – 300 m samples. On each
cruise, there were typically six stations each with, for
Isaacs-Kidd, a day and night sample of 1 h each
making 12 samples per cruise, for bongo 4 samples over
24 h, again of 1 h each, making 24 composite samples
per cruise. Each Isaacs-Kidd sample was 11 000 m3,
making ca. 132 k m3 per cruise. For the bongo nets,
each depth sample was for ca. 900 m3, so ca. 4500 m3
per composite sample, making ca. 108 k m3 per cruise.
Each sample, taking each of the pair of bongo nets as
one sample, was examined and counted. As usual, this
was done by aliquots where each aliquot contained at
least a thousand copepods and in all totalling no less
than a quarter of the whole sample. Replicate counts of
samples had 85 –92% similarity (McGowan and Walker,
1979). The minor differences in the quantity of water
examined per cruise were avoided by expressing the
results as copepods per 1000 m3. This gives us reliable
counts down to one per 10 k m3 per cruise and one per
100 m3 over the set of 10 cruises or better.
The names and dates of the cruises are in Table I.
There are three bongo cruises, all in the north Pacific,
and four Isaacs-Kidd cruises in the north and three in
the south. That is 10 cruises in three sets which, with
the set of all cruises, make 16 cruise sets. All samples
were taken in the Climax areas around 288N 1558W
and 258S 1558W. Many other measurements were of
course taken on the cruises. Here we only also use some
productivity and Secchi disc data from the Climax II
cruise which sampled in both the north and the south.
Table I: Basic information on the cruises and the community structures found
Cruises
Area
Net
Dates
Number of
species
Number of
individuals
log10 mean
Variance
Skewness
Kurtosis
Climax I
Ursa major
Zetes
Climax II
Aries IX
Cato I
SoTow
Climax II
Cato II
Aries III
North
North
North
North
North
North
North
South
South
South
Bongo
Bongo
Bongo
Isaacs-Kidd
Isaacs-Kidd
Isaacs-Kidd
Isaacs-Kidd
Isaacs-Kidd
Isaacs-Kidd
Isaacs-Kidd
20 –27 September 1968
11 –18 September 1964
11 –13 January 1966
26 August –10 September 1969
25 September –5 October 1971
19 –25 June 1972
29 January –4 February 1973
3 –9 October 1969
27 July –5 August 1972
15 –22 March 1971
158
152
146
138
149
132
143
122
134
118
12 474
12 952
9299
8988
5303
4907
5115
4296
3281
2785
0.817
0.816
0.676
0.761
0.454
0.638
0.543
0.568
0.263
0.286
0.925
0.798
0.804
0.699
0.686
0.624
0.749
0.774
0.734
0.780
20.019
0.134
0.372
0.135
0.508
0.363
0.377
0.278
0.450
0.400
20.762
20.603
20.576
20.666
20.334
20.630
20.612
20.750
20.204
20.575
The number of individuals is the number per 103 m3, the log10 mean is the mean of the log10 abundance of each species and the variance, skewness
and kurtosis are also of the log10 abundance. The north area is around 288N, 1558W, and the south area is around 258S, 1558W.
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The statistical methods used are standard. Most of the
analyses were done on the log10 of the abundances as
these are population data. The hypotheses to be tested
related to the third and fourth moments. Skewness
(from the third moment) and kurtosis (from the fourth)
were measured by g1 and g2. We provide more detail on
these terms in the Appendix. The one principal component analysis (PCA) reported here is double centred.
Usually, principle component analyses use either the
correlations of rows (or columns) or the covariances of
rows (or columns). In the latter, the row (or column)
means are standardized to zero; in the former, in
addition, the row (or column) variances are also standardized to unity (Digby and Kempton, 1987, equations 3.3
and 3.4). Formally, the transformation here is yij ¼
xij 2xi. 2x.j þ x., where the dots refer to means. There
can be advantages in having the principal components
from a row analysis exactly comparable to the principal
components from a column analysis and that can be
done by standardizing row and column means simultaneously to zero (Williamson, 1972; Digby and
Kempton, 1987, equation 3.7), i.e. doing a double
centred ordination. Williamson (Williamson, 1987), for
example, uses this technique to analyse plankton data
from the Irish Sea giving exactly comparable principal
component descriptions of the annual cycle by time and
by species (and the effect throughout the community of
an invasive species). With that technique here, the analysis by cruises is an exact counterpart of the analysis by
species, the two analyses have the same eigen values.
R E S U LT S
Basic statistics
The basic results are given in Table I which gives, as
well as the cruise data, the number of species and the
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total number of copepod individuals per 103 m3. The
other statistics in that table are presented below. Note
that the number of species is greatest in the North
Pacific bongo samples, about 150, and least in the
South Pacific Isaacs-Kidd ones, about 125, with the
North Pacific Isaacs-Kidd samples between at about
140. The species composition is remarkably similar over
all sets, as will be shown below. The total number of
species in all samples was 182 (Table II). Similarly, the
number of individuals is more than twice as great in the
North Pacific in bongo nets than in Isaacs-Kidd nets,
and, among the Isaacs-Kidd samples, 50– 100% more
individuals in North Pacific than in the South. The
differences in the number of species between the three
sets is significant in a one-way ANOVA at P ¼ 0.007,
for the individuals at P ¼ 0.002.
The possible effects of season and year were examined for all the population variables in Table I with
plots, correlations and regressions of varying complexity.
The lack of seasonality is a feature of the gyres as was
mentioned in the Introduction, so it is no surprise that
no indication of a seasonal effect could be found here.
With only 10 cruises distributed non-randomly over the
year, those were not strong tests, but adequate to show
that seasonality could be ignored in our analyses. All
systems show year to year fluctuations, with cumulative
variance increasing with time in accordance with the
reddened spectrum (Williamson, 1988), including the
North Pacific gyre (Sheridan and Landry, 2004). Here
the bongo cruises are all earlier than the Isaacs-Kidd
cruises, but each set covers several years and the sets are
contiguous. It would be surprising if there were a
sudden shift coinciding with the change of nets. The
only population variable in Table I with a significant
(P ¼ 0.004) negative regression with years is the number
of individuals. Examination of that shows it essentially
to be the result of the north – south difference; regressing just the north cruises produces an insignificant
Table II: Basic statistics for groups of cruises
Cruises
Number of species
log10 mean
North bongo, 3
168
North IK, 4
166
South IK, 3
150
North all, 7
172
IK all, 7
177
All cruises, 10
182
Venrick (1990) north gyre phytoplankton, by log10 (relative abundance in %)
shallow association
244
deep association
231
Variance
Skewness
Kurtosis
0.402
0.282
0.229
0.216
0.176
0.153
0.890
0.760
0.911
0.784
0.800
0.839
0.019
0.105
0.276
20.006
0.096
20.094
20.580
20.448
20.641
20.433
20.418
20.296
21.977
21.913
1.320
1.418
0.615
0.356
20.250
20.330
The numbers in the cruises column are the numbers of cruises summed; see Table I. IK refers to samples from Isaacs-Kidd plankton nets, bongo to
those from bongo nets. log10 mean is the mean of the logarithm of the species abundances after they have been averaged across the cruises
specified. Variance, skewness and kurtosis refer to those logarithmic numbers.
The Venrick means translate to ca. 0.01%, but the volume sampled is not defined.
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result. So, as with seasonally differences, yearly differences can be ignored in our analyses.
Overall, there were only 2 – 13 individuals per m3,
showing the oligotrophy of the gyres. In contrast,
Williamson (Williamson, 1961) reports around 900 individual copepods, in a mere 10 species, per m3 in the
summer plankton of the northern North Sea. His data
were from Small Hardy Plankton Indicator samples
with a ca. 350 mm mesh.
The completeness of the samples may be judged in
Fig. 1 which gives the abundance of each of the 182
species against the number of cruises it was found in.
There is a sharp decline in the distribution of abundances with every cruise missed, particularly so for
those found on only one cruise. Rather few species of
the community we are sampling, copepods caught with
two particular nets, are likely to be missing and those
very rare. We return to that point when considering,
below, the mathematical form of SADs.
Principal component analysis
Although the results in the paragraphs above indicate
that there are three sets of cruises in our data, distinguished by hemisphere and by net, a PCA brings out,
as usual, more interesting detail. As we were working in
logarithmic numbers, it is confined to those 73 species
found on every cruise (Fig. 1). Using zero data in multivariate studies is dangerous and undesirable, leading to
difficulties such as the horse-shoe effect. All species,
though, are used in the SADs described below.
The PCA is, as described in methods, double
centred, removing the known effects of the differences
in abundance between cruises and between species.
Fig. 1. Abundance of species, on a log10 scale, against the number of
cruises in which they were found. The abundance in each cruise was
standardized to numbers per 103 m3. The numbers here are the sum
over all 10 cruises so are log10 of the numbers per 104 m3.
It analyses the interaction variance between species and
cruises. On the first two components, accounting for
56% of that variance, the three sets are very apparent.
It is also apparent that the interpretation is easier with a
458 rotation of the axes to C1 þ C2 and to C12C2,
where Cn is the nth principle component. In Fig. 2, the
first of those comes out as a north– south axis, the
second as a net axis and the three groups of cruises are
clearly distinct.
These rotated, derived, axes are independent of each
other, orthogonal. They also have the same variance!
Recall that var(a þ b) ¼ var(a) þ var(b) þ 2.covar(a,b)
and that var(a 2 b) ¼ var(a) þ var(b)22.covar(a,b),
where var is short for variance. As the components are
orthogonal, uncorrelated, the covariance terms are
zero, so var(C1 þ C2) ¼ var(C12C2). The two derived
components, for the north– south difference and the net
difference each account for 28% of the variance; the
distance, measured in species/cruise space, between
areas in two gyres 5000 km apart is the same as the distance between two plankton nets with the same mesh.
Figure 2 shows the results for this analysis by cruises;
Table III gives the component scores by species.
Species abundance distributions
As emphasized by McGill et al. (McGill et al., 2007), all
SADs plotted arithmetically show a hollow curve, with
a few abundant species and many rare ones, and that is
the only generalization that they could make about such
Fig. 2. A rotated principal component plot from the double-centred
analysis of the log10 abundance of the 73 spp. found in every cruise.
The three north-bongo cruises, the three south-Isaacs-Kidd cruises
and the four north-Isaacs-Kidd cruises each form a distinct cluster.
The abscissa is the sum of components 1 and 2, the ordinate the
difference of them; so the plot is a 458 rotation of the first two
components and the variance is the same on both axes.
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Name
Plankton net
component
Mesocalanus lighti
Corycaeus (Corycaeus) clausi
Candacia bispinosa
Euaugaptilus filigerus
Sapphirina metallina
Heterorhabdus papilliger
Euchaeta pubera
Heterorhabdus spinifrons
Euaugaptilus hecticus
Undeuchaeta plumosa
Corycaeus (Agetus) flaccus
Haloptilus paralongicirrus
Pleuromamma abdominalis
Lucicutia paraclausi
Heterorhabdus subspinifrons
Nannocalanus minor
Lophothrix latipes
Corycaeus (Urocorycaeus) lautus
Scolecithrix fowleri
Mesocalanus tenuicornis
Neocalanus gracilis
Euchirella amoena
Lucicutia gemina - L. flavicornis
Phaenna spinifera
Pleuromamma gracilis
Euchaeta media
Racovitzanus levis
Copilia mediterranea
Euchirella curticauda
Family Heterorhabdidae
Euchirella messinensis
Corycaeus sp.
Aegisthus mucronatus
Scolecithricella vittata
Pleuromamma piseki
Candacia longimana
Haloptilus longicornis
Copilia vitrea
Pleuromamma xiphias
Lucicutia clausi
Centropages sp.
Xanthocalanus dilatus
Haloptilus ornatus
Haloptilus mucronatus
Aetideus acutus
Nullosetigera helgae
Corycaeus (Urocorycaeus) furcifera
Family Augaptilidae
Augaptilus longicaudatus
Corycaeus (U.) longistylis
Copilia sp.
Chiridius poppei
Corycaeus (Corycaeus) speciosus
Scaphocalanus sp.
Lucicutia sp.
Chirundina streetsi
Oithona robusta
Scottocalanus sp.
Clausocalanus sp.
Scolecithrix bradyi
Candacia ethiopica
Gaetanus minor
22.512
22.106
21.828
21.737
21.336
21.288
21.2481
21.208
21.185
21.012
20.866
20.865
20.788
20.744
20.715
20.678
20.652
20.602
20.565
20.553
20.465
20.453
20.436
20.431
20.409
20.353
20.318
20.314
20.269
20.258
20.218
20.127
20.125
20.096
20.051
20.043
20.004
0.049
0.051
0.058
0.080
0.134
0.189
0.210
0.244
0.264
0.325
0.327
0.343
0.345
0.403
0.406
0.423
0.466
0.499
0.503
0.509
0.525
0.535
0.655
0.734
0.811
20.868
20.596
20.275
20.204
20.943
20.633
21.341
20.461
20.258
21.956
20.210
20.504
21.044
0.646
20.001
20.211
20.287
20.669
0.211
0.622
20.130
20.102
1.891
20.930
0.441
20.730
0.187
20.372
20.575
20.916
21.530
0.949
0.169
0.740
0.457
20.411
20.003
20.244
21.117
0.592
20.561
0.725
0.066
20.029
0.150
20.954
2.861
0.067
20.199
20.415
20.626
20.830
20.090
20.035
1.459
20.613
3.242
21.025
1.701
1.220
21.499
20.827
Continued
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Table III: Continued
Table III: The principal component scores for
the two derived components shown in Fig. 2
N-S
component
NUMBER
Name
Coplilia quadrata
Sapphirina sp.
Acartia sp.
Oithona setigera
Gaetanus miles
Scolecithricella sp.
Euchirella sp.
Aetidius giesbrechti
Scolecithrix danae
Neocalanus robustus
Copilia mirabilis
N-S
component
0.883
0.999
1.031
1.170
1.333
1.354
1.445
1.626
2.017
2.667
3.244
Plankton net
component
20.633
20.367
2.406
1.376
20.034
0.862
20.614
0.653
0.122
2.008
1.054
The scores are in rank order for the north-south component. “sp.”
means a morphological but unidentified species, different from any in
the same genus that have been identified to species.
curves. So it is true too of all the SADs here; an
example is given in Fig. 3 of McGowan and Walker
(McGowan and Walker, 1985) which plots the combined
data of all the north gyre cruises. But McGill et al.
(McGill et al., 2007) also note “[after] log-transforming
. . . more variability in shape occurs” so for that reason,
as well as for the reason, noted above, that, as population data vary multiplicatively, they should always be
examined statistically in the logarithmic form as well as
in other ways. Indeed, the fact that logarithmic population data are well behaved statistically is part of the
explanation of why most species, considered arithmetically, are rare. McGill et al. (McGill et al., 2007) say that
the frequency of rarity on an arithmetic scale is “surprising, counterintuitive and therefore informative”. On
a logarithmic scale, most species are middlingly
common, while abundant and rare species are unusual.
Maybe that result is intuitive, suggesting that the detail of
the logarithmic distribution is where the information is.
SADs in large samples are usually lognormal-like, sigmoidal in a rank abundance plot, though they are not,
and cannot be, exactly lognormal (Williamson and
Gaston, 2005). Moments can be used to clarify what
mathematical shape they are, and here we hypothesize
that they are typically characterized by fourth moments
that make them slightly platykurtic, and with third
moments that change from giving right-skew to giving
left-skew as the sample size increases. We consider the
consequences of these hypotheses below, having tested
them first.
Here we have SADs from each of the 10 cruises.
From the both Table I and the PCA, it is reasonable to
add individuals across cruises to give, in addition, SADs
for bongo nets, north Isaacs-Kidd nets, south
Isaacs-Kidd nets, all north cruises, all Isaacs-Kidd
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cruises and all 10 cruises, another six in all (Table II).
Figure 3 shows the SADs as rank abundance plots for
the three sets of cruises in Fig. 2. The usual S-shaped
curve is very similar for all three; the vertical separation
reflects the differences in abundance between these sets,
noted above. To show that these S shapes differ from
the lognormal, a probability plot is helpful. Figure 4 is
one for the set of all cruises. The fit to a lognormal is
good except at the right-hand end. The most common
species are not common enough, as they cannot be
(Williamson and Gaston, 2005), to fit a lognormal.
The mild mis-fit to the lognormal is shown by skewness and kurtosis, the parameters of our hypotheses.
A lognormal has zero values for these two parameters.
Fig. 3. Rank abundance plots for, from top to bottom, all cruises (W),
the sum of the three north bongo cruises (A), three-fourth the sum of
the four north Isaacs-Kidd cruises (4), and the sum of the three south
Isaacs-Kidd cruises (5). The ordinate scale is the logarithm (base 10)
of the number of individuals per 3 103 m3.
Fig. 4. A probability plot of the species abundance distribution
(SAD) for the total sample, for all cruises combined. The fit to a
lognormal is good except at the right-hand end. The rearing up there
is characteristic of many large sample SADs and means that the most
common species are rarer than they would be were the distribution
lognormal.
In Tables I and II, it can be seen that skewness is positive (right skew) in all the cruises but one, but changes
to negative (left skew) in two of the largest combined
sets. This is shown graphically in Fig. 5, where there is
a consistent shift towards left-skew as the sample size
increases and with no indication of lower limit. Possibly,
this indicates that with even larger samples, some more
species would have been found, making the SAD even
more left skew. In contrast, kurtosis is negative ( platykurtic) in every SAD, a highly significant result irrespective of the significance of the individual values
(non-parametrically, using the signs, P ¼ 0.0000305,
two-tailed, assuming the samples are independent, or
parametrically, the mean ¼ 20.533 + 0.0403 (SEM),
t ¼ 13, P effectively zero, formally ca. 10238). The kurtosis reflects the shape of the right-hand end of the
probability plot, among other factors.
These same characteristics are found in the parameters we have calculated for two SADs for phytoplankton in the north gyre, for Venrick’s shallow and
deep associations (Venrick, 1990, Fig. 3). The phytoplankton was collected on another set of six cruises,
between 1973 and 1985 and the statistics for the two
SADs are also in Table II. Once again, they are platykurtic. They are right skew and possibly missing of the
order of 100 rare species each.
The copepod data of the different cruises not only
have very similar rank abundance plots, they have very
similar rank orders as was noted by McGowan and
Walker (McGowan and Walker, 1985, 1993). The correlations of the log abundances for every pair of cruises
are positive and significant at P , 0.001 (10 cruises, so
45 pairs). However, the correlations are stronger within
sets than between them. Within sets, the median
Fig. 5. The relationship between skewness and the number of species
in the sample. The regression, y ¼ 1.3220.00738x, has an r 2 of 0.56
and indicates that skewness would be more negative in yet larger
samples.
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DISCUSSION
Fig. 6. The relationship of log10 abundance of species caught in
Isaacs-Kidd nets in both the north and south gyres. The line is the
locus of species being twice as abundant in the north as the south.
correlations are 0.837, 0.687 and 0.780 for the south,
north Isaacs-Kidd and bongo sets, respectively.
Abbreviating those to s, n, b, the median between set
correlations for sn, sb, nb are 0.661, 0.526 and 0.638.
An example of these relationships, sn, is shown in
Fig. 6, with the locus of where the north abundance is
twice the south abundance. The similarity of the plankton communities in the north and south Pacific central
gyres is remarkably strong considering how far apart
they are.
Productivity (and transparency)
Productivity nowadays is often measured from satellite
images. That is not appropriate here both because there
were no satellite images at the time of the cruises and
the oceans have changed since, and also because the
chlorophyll maximum in the gyres is deep, around
100 m. Venrick (Venrick, 1982) notes “a persistent
chlorophyll maximum layer between 90 and 135 m”
while Venrick et al. (Venrick et al., 1987) graph the depth
and structure of the maximum. However, there are
comparable productivity measurements for north and
south in the Climax II cruise report (Scripps Institution
of Oceanography, 1975). Total water column productivity was measured, in mg C21 m22 12 h day, at
north and south Climax stations. For the north, the
range was 202.5 – 566.6, mean 364.6, and for the south,
the range was 64.5– 344.9, mean 120.9. The 3-fold
difference between the means is statistically significant
at P ¼ 0.005; the north Pacific gyre is, as is known from
much other data as well, appreciably more productive
than the south. This is also shown by the transparency
as measured by Secchi disc depth, in metres, on
the same cruise. For the north, it varied from 22 to
26, median 25, while in the south it was 28– 40,
median 33 metres.
The epipelagic copepod communities of the north and
south Pacific gyres show remarkable similarities and systematic differences. The similarities are shown in the
correlations between the samples of the 10 cruises
studied and the consistent pattern of the SADs. No consistent differences between years and months were
found. The major differences that were found are
brought out by the PCA of the 73 species found in
every cruise (Fig. 2). That analysis, and the correlations
over all species, brought out three groups: samples in
the north Pacific with bongo nets, samples in the north
Pacific with Isaacs-Kidd nets, samples in the south
Pacific with Isaacs-Kidd nets. The differences between
north and south are the same size, but orthogonal to
the differences between the nets. Differences between
the three groups can also be seen in the total abundances of individuals (Table I).
To what extent can these similarities and differences
be explained? That samples taken in the middle of one
gyre or the other are similar is not surprising; it is a
reflection of the reasons for choosing to study the gyres
in the first place, their size, homogeneity and stability.
That the south gyre should have a very similar community to the north is surprising but at this stage just
an interesting fact. The sampling positions were separated by 538 of latitude and the very different water
masses straddling about 228 across the equator,
Longhurst’s (Longhurst, 1998) PNEC and PEQD provinces. The similarities presumably result from similar
species interactions in the two hemispheres, but
whether these similarities are strengthened by exchanges
between the two hemispheres and at what scale and
timing has yet to be determined. As the southern gyre,
Longhurst’s (Longhurst, 1998) SPSP, is as he says “the
least well-described region of the ocean”, it is to be
expected that we need more information. The differences, particularly the differences in total abundances,
no doubt to some extent reflect the differences in productivity, the north being about three times as productive as the south during the Climax II cruise.
However, the distinctions found by the PCA are independent of abundance and of the SADs, as the species
and cruise means were standardized. We tested the
scores to see if there was any relationship to the recurrent groups found by McGowan and Walker
(McGowan and Walker, 1979) or the sets in the Atlantic
found by Beaugrand et al. (Beaugrand et al., 2002). We
found no relationship to either. The recurrent groups
are primarily groups of species with similar depth preferences and vertical migration patterns. The Atlantic
groups are biogeographic, from data collected by
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COPEPODS OF THE NORTH AND SOUTH PACIFIC CENTRAL GYRES
Continuous Plankton Recorders at a constant depth of
10 m and include many of the species studied here. The
scores in Table III might indicate what the differences
arise from, were more known of the biology of the
species. We have noted one possible clue. The species
that most distinguishes the south, the top species in
Table III, is Mesocalanus lighti. Mullin (Mullin, 1969) concluded “Calanus lighti is an epiplanktonic species largely
restricted to the Central Water masses of the North
Pacific and South Pacific” which perhaps suggest that it
is an oligotrophic specialist, adapted to, doing well, in
oligotrophic conditions. Maybe the more oligotrophic
the better. Perhaps that is the basis of the distinctions in
Table III, negative values indicating species favoured by
more oligotrophy, positive values by those favoured by
less. There are no data we know of to test that hypothesis properly.
The differences between the two nets are less surprising as there are numerous studies in the literature
showing different sampling properties of different nets,
sometimes quite large, sometimes effectively absent.
Wiebe and Benfield (Wiebe and Benfield, 2003) give
thorough comparisons of the nets used here and many
others; Rebstock (Rebstock, 2002) discussed those used
by the SIO. No net can take a truly random sample.
For these two nets, Hayward et al. (Hayward et al., 1983)
note “The estimates of biomass from the meter [bongo]
net were consistently about 3 times larger than the
[Isaacs-Kidd] plankton trawl” but do not comment on
the species composition. Note that this refers to all
species, not just copepods, and to biomass not individual abundance. As the PCA was of species found in all
samples, the differences in composition are merely in
small variations in catchability, reflected in the species
scores on the net axis (Table III). We have not been
able to find any associations with that order, so its
origin is unknown. But very little is known of the behaviour and kinetics, which would affect catchability, of
almost all the species.
The similarities of the SADs indicate that the shape
of the distribution is a robust characteristic of these
communities and indeed of others. To have so many
comparable SADs, all with over a hundred species, is
unusual (McGill et al., 2007) and therefore important,
allowing the testing of hypotheses. The SAD is quite
like a log-normal distribution, but its skewness varies
with sample size while the kurtosis is consistently negative, platykurtic. The lognormal has a kurtosis of zero,
while the commonest alternative, the gamma, has positive kurtosis when plotted on a logarithmic scale
(Johnson et al., 1994), so the distributions here are
neither of those, the most common candidates for the
mathematical form of the SAD. In particular, these
planktonic SADs have short right-hand tails; the most
common species are not as common as they would be
were the distribution either lognormal or gamma. The
change in skewness with change of sample size is not
just an effect of sampling because the larger samples
also encompass greater environmental heterogeneity.
The structure of the copepod communities found in
these cruises to the north and south Pacific central gyres
confirm the lognormal-like, with shortened right-hand
tail, SADs found in other communities, suggesting that
there is some general explanation for community
structure. The relationships between the cruises emphasize the extreme oligotrophy of the south gyre, the effect
of net design and the remarkable similarity, considering
their spatial separation, of the north and south
communities.
AC K N OW L E D G E M E N T S
This paper is dedicated to the memory of David
Cushing, friend of both of us and mentor to M.W.
when he was a planktologist. This paper depends on
eight closely written pages of notes compiled by Patricia
Walker, giving the averages per cruise for all species and
all cruises, with some other information. We are most
grateful for her meticulous work. We thank Larry
Crowder, Kevin Gaston, Michael Landry, Callum
Roberts and Elizabeth Venrick for helpful comments.
FUNDING
Support for the cruises came form the Marine Life
Research
Group
of
Scripps
Institution
of
Oceanography, the National Science Foundation (USA)
and the Office of Naval Research (USA).
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APPENDIX
M O M E N T S O F S TAT I S T I C A L
DISTRIBUTIONS
The jth moment of a distribution with n values xi,
around an arbitrary value c, is defined as
m j ¼ n1 Sn ðxi cÞ j ; i ¼ 1; . . . ; n; j ¼ 1; 2; . . . ; :
All distributions can be defined by their moments. In
practice, statistical distributions can be distinguished by
their first four. The first moment, m1, is taken around
the origin, i.e. with c ¼ 0, and so m1 is the mean. The
other moments are taken around the mean, with
c ¼ m1 ¼ x. The second moment, m2, is the variance,
s 2. The third moment measures skewness, essentially a
long tail either to the left or to the right. The fourth
moment measures kurtosis, or peakedness, either with a
flat top and short tails ( platykurtosis) or with a peaked
centre and long tails (leptokurtosis). Both the third and
fourth moments are changed by changing the scale so
are usually standardized. The standardizations used
here are the commonly used ones:
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for the third moment, for skewness
g1 ¼ m3/s 3, where s is the square root of the variance, which is negative for long left tails and positive
for long right ones, and
for the fourth moment, for kurtosis
g2 ¼ (m4/s 4)23, which is negative for platykurtic distributions, positive for leptokurtic ones.
For the Normal (Gaussian) distribution g1 ¼ g2 ¼ 0.
Further details and an on-line calculator can be
found at www.xycoon.com and at others web sites.
283