an overview of statistical methods applied to cpr data

Progress in Oceanography 58 (2003) 235–262www.elsevier.com/locate/pocean

An overview of statistical methods applied to CPR data

G. Beaugranda,∗, F. Ibanezb, J.A. Lindleya

a Sir Alister Hardy Foundation for Ocean Science, The Laboratory Citadel Hill, Plymouth PL1 2PB, UKb Observatoire oceanologique, Laboratoire d’Oceanologie de Villefranche, BP 28, 06230 Villefranche-Sur-Mer, France

Abstract

Since the beginning of the Continuous Plankton Recorder (CPR) survey in 1931, information on the abundance ofa large number of plankton species or taxa has been obtained on a monthly basis in the northern North Atlantic. Themany different ecological issues in which the survey has been involved have led to the application of a range ofstatistical methods. In this paper, we review some of the methods applied to the CPR data by presenting new and up-to-date analyses. Special attention is devoted to multivariate analysis, which has been used extensively to extract infor-mation from the CPR database. Results obtained from recently applied geostatistical methods on CPR data are thenconsidered. An example of a time series decomposition by the use of Eigenvector filtering is presented to illustratetime-series analysis. 2003 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

2. The descriptive period of the CPR survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

3. Multivariate analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2373.1. Ordination in reduced space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2383.1.1. Standardised Principal Component Analysis (PCA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2383.1.2. Centred PCA at diel and seasonal scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2433.1.3. Three-mode Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2443.1.4. Non-metric multidimensional scaling (MDS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

3.2. Cluster analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2473.2.1. Seriation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2473.2.2. Cluster Analysis and ordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

3.3. Indicator-value method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

4. Geostatistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

∗ Corresponding author. Tel.:+44-1752-633133; fax:+44-1752-600015.E-mail address: [email protected] (G. Beaugrand).

0079-6611/$ - see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.pocean.2003.08.006

236 G. Beaugrand et al. / Progress in Oceanography 58 (2003) 235–262

4.1. Spatial interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2504.2. Semi-variograms and cumulative semi-variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

5. Time series analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2545.1. Cumulative sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2545.2. Eigenvector filtering (EVF) and power spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2545.3. Maximum entropy spectral and cross-spectral analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

1. Introduction

Since the start of the Continuous Plankton Recorder (CPR) monitoring survey in 1931, large amountsof data have been accumulated. At present, information on the abundance of more than 450 species ortaxa has been gathered. A total of some 178,000 CPR samples were collected by the year 2000, comprising~2 million entries and ~80 million data-points in the database. This programme has become the largestplankton monitoring programme in the world, considering both its wide spatial coverage and long time span.

The CPR survey has been involved in the investigation of many ecological issues. Biogeographicalstudies have been conducted showing spatial distribution throughout the North Atlantic Ocean and shelfseas of more than 250 species such as Calanus finmarchicus and Calanus helgolandicus (Colebrook,Glover & Robinson, 1961a; Edinburgh Oceanographic Laboratory, 1973). Recently, the mapping protocolhas been improved using the Lambert conical projection (Planque, 1996) and mapping techniques such askriging and the inverse squared distance interpolation method (Planque, 1996; Planque & Ibanez, 1997;Beaugrand, Reid, Ibanez, & Planque, 2000a). A number of investigations have allowed a better characteris-ation of seasonal cycles and of spatial changes for many taxa (Glover, 1957; Colebrook, 1979; Colebrook,1984). Other works have examined long-term changes in phytoplankton and zooplankton in relation tohydro-meteorological forcing (Colebrook, 1981; Colebrook, 1982a; Colebrook, 1991; Taylor, Colebrook,Stephens, & Baker, 1992; Reid, Edwards, Hunt, & Warner, 1998a; Edwards, John, Hunt, & Lindley, 1999).Recent results using this large dataset indicate that year-to-year changes in standing stock, production andcommunity structure of plankton may be related to the North Atlantic Oscillation (NAO) and climatechange (Fromentin & Planque, 1996; Reid & Planque, 2000; Beaugrand, Ibanez, & Reid, 2000b; Beaugrand,Reid, Ibanez, Lindley, & Edwards, 2002a). Other studies on diel vertical migration of some calanoid cope-pods (Hays, Proctor, John, & Warner, 1994; Hays, 1995; Hays, 1996; Hirst & Batten, 1998), spatial andtemporal changes in the diversity of copepods (Beaugrand & Edwards, 2001; Beaugrand, Ibanez, & Lindley,2001), monitoring of non-indigenous species (Edwards, John, Johns, & Reid, 2001a), and unusual events(Lindley et al., 1990; Edwards, John, Hunt & Lindley, 1999; Edwards, Reid, & Planque, 2001b; Edwards,Beaugrand, Reid, Rowden, & Jones, 2002) have been undertaken and have led to a better understanding ofthe ecology of many species, exceptional events and the functioning of North Atlantic pelagic ecosystems.

The many issues in which the CPR data have been used have involved the deployment of numerousstatistical analyses, of which only a limited number can reasonably be presented in this paper. Since moststatistical analyses found in classical statistical manuals can be used on the CPR data, only those methodsthat have often been applied to the CPR dataset and for which it was possible to include a clear exampleassociated with a particular ecological issue are emphasised in this review. Moreover, the importance ofscales of variability, as stressed by many authors (e.g. Levin, 1992; Angel, 1994; Mann & Lazier, 1996;Haury & McGowan, 1998; Lundberg, Ranta, Ripa, & Kaitala, 2000) is also addressed as this is as importantas the analyses themselves.

237G. Beaugrand et al. / Progress in Oceanography 58 (2003) 235–262

2. The descriptive period of the CPR survey

Until 1964, geographical distribution, annual and year-to-year variability of species or taxa sampled bythe CPR survey were mainly investigated by the use of graphs, contour diagrams or maps (Lucas, 1941;Lucas, 1942; Rees, 1952; Glover, 1952). Most statistical analyses were restricted to one dimension. Despitethat, results were immediately meaningful and good progress was made in describing the biogeography ofspecies around the United Kingdom (Lucas, 1940; Robinson, 1961; Colebrook, John, & Brown, 1961b).The spatial distribution of Centropages hamatus and Ceratium fusus is shown in Fig. 1, based on datacollected during the period 1948–1956 (Colebrook, John & Brown, 1961b; Robinson, 1961). This showsthe coastal distribution of Centropages hamatus, whereas the dinoflagellate Ceratium fusus has a widerdistribution, occurring in both oceanic and neritic waters (Fig. 1). This way of presenting the spatial distri-bution of plankton (on gridded charts of 1° of latitude by 2° of longitude), described by Colebrook, John &Brown, 1961b) was used to produce the first atlas of plankton in the North Atlantic Ocean (EdinburghOceanographic Laboratory, 1973). Seasonal cycles of plankton around the British Isles were also investi-gated. For example, Rae and Rees (1947) presented the seasonal cycle of Temora longicornis and thegroup Para-Pseudocalanus spp. This way of investigating CPR results is still used today, although theapplication of multivariate statistics has radically changed the way in which information is extracted fromthe CPR dataset.

3. Multivariate analyses

While graphical presentation of CPR data is useful, it soon became clear that the huge mass of multidi-mensional information provided by the Survey had to be sorted and reduced according to its relevance.For most techniques reviewed in this paper, no mathematical expressions are given in the text and readersare referred to specialised books (e.g. Jolliffe, 1986; Legendre & Legendre, 1983; Legendre & Legendre,

Fig. 1. Spatial distribution of the calanoid copepod Centropages hamatus (a) and the dinoflagellate Ceratium fusus (b) for the period1948–1956 around the British Isles. From Colebrook, Glover & Robinson (1961a) and Robinson (1961).


1998) and other references cited in the text. Table 1 lists the types of multivariate analyses that have beenapplied to CPR data.

3.1. Ordination in reduced space

This type of multivariate analysis has been applied extensively to CPR data. It consists of representingthe relationships between objects and observations in a reduced number of dimensions (Legendre & Legen-dre, 1998). Principal Component Analysis (PCA) is an example. This ordination method has greatly helpedin the extraction of relevant information in many types of tables derived from the CPR dataset (Table 2).Non-metric multidimensional scaling (Shepard, 1962; Kruskal, 1964) and three-mode Principal ComponentAnalysis (Jolliffe, 1986) are other techniques that have been applied more recently.

3.1.1. Standardised Principal Component Analysis (PCA)Following Williamson (1961) and Cassie (1963), who were among the first to apply Principal Component

Analysis in plankton ecology, Colebrook (1964) started to analyse data on abundance from the CPR usingmultivariate techniques. Standardised PCA was first applied by him to examine the main patterns of varia-bility in the distributions of 22 different taxa around the United Kingdom (Fig. 2). He used eigenvectors(Fig. 2(a)) to investigate the relationships between the species and principal components to examine thespatial distribution of groups of species (Fig. 2(c)–(d)). Fig. 2(a) illustates the separation between neriticand southern species along the first axis, while the second axis separates northern oceanic and intermediatespecies. The 22 taxa were classified into five species associations (northern and southern oceanic, northern

Table 1Types of multivariate analysis performed on CPR data

Multivariate techniques Ecological goal Authors

Standardised PCA See Table 2 See Table 2Centred PCA See Table 2 See Table 2Seriation Examination of the relations between species Colebrook (1964), Colebrook and

based on their annual fluctuation in abundance Robinson (1964), Colebrook (1969)Cluster Analysis. Single linkage Grouping of species or taxa Lindley (1987), Lindley andagglomerative (nearest-neighbour) Williams (1994)clustering methodCluster Analysis. Hierarchical Clustering of pixels or geographical areas to Planque and Ibanez (1997),agglomerative flexible clustering identify regions with similar year-to-year or Beaugrand, Reid, Ibanez & Planque,technique (Lance & Williams, 1967) annual patterns in the abundance of species 2000a)Cluster Analysis. Complete linkage Partition of the North Atlantic Ocean based on the Beaugrand, Ibanez, Lindley & Reid,agglomerative clustering diel and seasonal pattern of diversity of calanoid 2002b)

copepodsIndicator-value method (Dufrene & Determination of species associations based on the Beaugrand, Ibanez, Lindley & Reid,Legendre, 1997) relative abundance and presence of species in 2002b)

distinct areas in the North AtlanticNon-metric multidimensional scaling Ordination of species or taxa based on the Lindley (1987)Lindley and Williams

similarity of their spatial distribution (1994)Mantel correlogram Study of relationships between the size of spatial Planque and Ibanez (1997)

structures and their temporal variabilityGeneralised additive models Spatial and temporal modelling of the abundance Beare & McKenzie, 1999a, 1999b)

of speciesThree-mode PCA Analyses of biological tables structured in space Beaugrand, Reid, Ibanez & Planque,

and time. Evaluation and quantification of the 2000a)interactions between biology, space and time


Table 2Diversity of matrices on which principal component analysis has been performed

Tables Correlation/ Ecological goal Authorscovariance matrix

Standardised Matrix area × taxa taxa × taxa Identification of species assemblages. Colebrook (1964,PCA Examination of the relations between species. 1984)

Geographical locations of species associations.Standardised Matrix years × Areas × areas Extraction of major patterns of year-to-year Colebrook (1978,PCA geographical areas variability in the abundance of species and its 1982b, 1986)

variation in space.Standardised Matrix years × taxa taxa × taxa Examination of the relationships between Colebrook (1978,PCA species on the basis of their year-to-year and 1982b) Reid et al.,

long-term changes in a region. 1998b) Reid andBeaugrand (2002)

Standardised Buys-Ballot table Months-total Determination of the relationships between the Colebrook (1979)PCA geographical areas × copepods-colour timing of the amplitude and the duration of the

months-total index × Months- spring bloom for total copepods andcopepods-colour total copepods- phytoplankton (eigenvectors). Examination ofindex colour index spatial changes in the characteristics of the

seasonal cycle (principal components).Standardised Table geographical Months × months Investigation of the relationships between Colebrook (1981,PCA areas × months months for species such as Temora longicornis 1982a, 1984)

and Acartia clausii and examination of thespatial coherence of the seasonal cycle.

Standardised Table months × taxa taxa × taxa Investigation of the relationships between Colebrook (1984)PCA months and ordination of species according to

their main pattern of seasonality.Standardised Table years × Months × months Relationships between the seasonal cycle and Colebrook (1985a)PCA months the year-to-year variability of species.Standardised Matrix months × Pixels × pixels Determination of seasonal cycle of C. Planque, Hays, IbanezPCA for table map pixels of the finmarchicus and investigation of its spatial and Gamble (1997)with missing abundance of variation.data C.finmarchicusCentred PCA Buys-Ballot table Pixels × pixels Determination of seasonal and diel patterns of Beaugrand et al.

months-2-hour the diversity of calanoid copepods. (2001)period × pixels for Quantification of the two scales of variability atdiversity of calanoid a mesoscale resolution in the North Atlantic.copepods Examination of the spatial variation of the

diversity of calanoids at diel and seasonalscales.

and southern intermediate, and neritic) and their locations (see Fig. 2(b)–(d)) were in part explained bythe effect of temperature and its seasonal variability, and also salinity.

The ‘simplification’ of multidimensional space by this method proved satisfactory and led to the extensiveuse of standardised PCA on CPR data. Examples of studies that used this method of ordination are summar-ised in Table 2. Standardised PCA was much used to extract the main patterns of year-to-year and long-term changes in the community structure of phytoplankton and zooplankton, typically in CPR StandardAreas (Colebrook (1978; Colebrook, 1982a). In most of the CPR Standard Areas, Colebrook (1978, 1982a)reported a declining trend of about 70% for zooplankton taxa and 60% for phytoplankton taxa. As thesechanges were detected consistently throughout a large geographical region, and were shown to be correlatedwith westerly weather, Colebrook (1986) argued that these changes were being triggered by meteorologi-cal forcing.


Fig. 2. Principal Component Analysis on a matrix of geographical rectangles × species or taxa (22) in the eastern North Atlantic.(a) Scatter diagrams for the first two eigenvectors. Each point on this diagram represents one species. Five species groups wereidentified by examination of the first three eigenvectors. The points were clustered on the basis of the ecological knowledge of theauthor. (b)–(d) Maps of the distribution of the first three principal components. From Colebrook, Glover & Robinson (1961a).

This type of PCA was re-applied in 1998 (Reid, Planque, & Edwards, 1998b) and 2001 (Reid & Beaug-rand, 2002), and an example is presented for a set of zooplankton taxa in the North Sea (Fig. 3). A totalof 28 taxa (Table 3), which were abundant and did not have a high frequency of zeros during the period1958–1999, were selected. Scatter plots of the first two eigenvectors are shown (Fig. 3(a)) as well as long-term changes in the associated principal components (Fig. 3(b) and Fig. 3(c)). Groups of years have beendistinguished by a Cluster Analysis (Lance & Williams, 1967; hierarchical agglomerative flexiblealgorithm) are indicated. The first principal component (Figs. 3(b), 30.2% of the total variance) showsthere was a period of high values from 1962 to 1976 followed by one of low values from 1983 for both


Fig. 3. (a) Ordination by PCA of the 28 species or taxa listed in Table 3 in the plane of the two first principal components (50.5%of the total variability). (b) Year-to-year changes in the first principal component. (c) Year-to-year changes in the second principalcomponent. Periods detected by a Cluster Analysis using the flexible algorithm of Lance and Williams (1967) are indicated. Overall,there is a good temporal connection with the exception of the years 1958 (period 1), 1975 (period 2), 1991 (period 5), 1993 (period 5).


Table 3List of species used in a PCA to examine long-term change in zooplankton community structure in the North Sea with normalisedeigenvectors 1 and 2. The correlation between each species or taxon and the corresponding principal components is indicated by (r).The coefficient of determination (r2) indicates the contribution of a species to the first two axes. Numbers (column 1) correspond tothose shown in Fig. 3

Identification number names of taxa eigenvector 1 eigenvector 2

r r2 r r2

1 Calanus I-IV 0.497 0.247 0.763 0.5832 Pseudocalanus elongatus Adult �0.401 0.161 0.667 0.4453 Para-Pseudocalanus spp. �0.604 0.365 0.688 0.4744 Temora longicornis �0.708 0.501 �0.043 0.0015 Acartia spp. �0.529 0.280 �0.032 0.0016 Centropages typicus �0.623 0.388 �0.081 0.0067 Centropages hamatus �0.445 0.198 0.061 0.0038 Oithona spp. �0.270 0.073 0.844 0.7139 Corycaeus spp. �0.743 0.552 �0.208 0.04310 Calanus Total Traverse 0.500 0.250 0.784 0.61411 Podon spp. �0.547 0.300 �0.283 0.08012 Evadne spp. �0.517 0.267 0.289 0.08313 Limacina retroversa �0.234 0.054 0.724 0.52414 Lamellibranchia larvae �0.538 0.289 0.396 0.15615 Chaetognatha Traverse �0.632 0.399 0.541 0.29316 Cyphonautes larvae �0.571 0.326 0.420 0.17617 Echinoderm larvae �0.607 0.369 0.004 0.00018 Larvacea �0.571 0.326 �0.334 0.11119 Calanus finmarchicus 0.616 0.379 0.719 0.51720 Calanus helgolandicus �0.633 0.401 �0.138 0.01921 Decapoda larvae �0.789 0.622 �0.094 0.00822 Euphausiacea Total 0.688 0.474 0.452 0.20423 Chaetognatha Eyecount �0.515 0.265 0.503 0.25324 Harpacticoida Total �0.580 0.336 0.002 0.00025 Metridia Total Traverse �0.482 0.233 0.421 0.17726 Copepod nauplii �0.425 0.181 �0.334 0.11227 Cirripede larvae �0.249 0.062 �0.278 0.07728 Euphausiacea calyptopis 0.367 0.135 0.055 0.003

cold-water mixed oceanic and neritic species (e.g. Euphausiacea and C. finmarchicus), which were posi-tively related to the first axis. A strong increase was detected during a cold period between 1978–1982(see Fig. 3(a) and Table 3). For species negatively related to the first axis, the long-term changes showedthe inverse pattern with an increasing trend followed by a significant decrease during the cold period (seeFig. 3(a) and Table 3). This pattern of variability was followed by the warmer-water, neritic or pseudo-oceanic species such as C. helgolandicus, Temora longicornis, Corycaeus spp. and decapod larvae.

The second principal component (Fig. 3(c), 20.32% of the total variance) displays a decreasing trendfor temperate neritic and pseudo-oceanic taxa such as Para-Pseudocalanus spp., Oithona spp., Limacinaretroversa and colder-water taxa such as Calanus finmarchicus. These opposing trends led to a change inthe ecosystem of the North Sea with a decrease in indicators of cold water and an increase in warmer-water pseudo-oceanic and neritic taxa. This confirms the trend discovered by Beaugrand, Reid, Ibanez,Lindley & Edwards (2002a), who found an increase in the abundances of warm-temperate and temperatespecies, which was associated with decreases in colder-water species. These changes have been linked tothe climatic warming observed in the North-East Atlantic in recent decades.


3.1.2. Centred PCA at diel and seasonal scalesUntil recently, little attention has been devoted to the analysis of spatial changes in pelagic diversity

(Lindley, 1998; Beaugrand, Reid, Ibanez & Planque, 2000a) at all temporal scales. Studies have beencarried out to examine in more detail spatial patterns of pelagic biodiversity at diel and seasonal scales(Beaugrand, Ibanez & Lindley, 2001; Beaugrand, Ibanez, Lindley, & Reid, 2002b). PCA was used toidentify the spatial patterns in diversity (in terms of the number of taxa per CPR sample) of calanoidcopepods and to detect major seasonal and diel patterns of change across the northern North AtlanticOcean. Fig. 4 shows (left) the first four eigenvectors and (right) monthly and diel changes of the correspond-ing principal components from January to December based on 40 years of CPR sampling (1958–1997).They represent a total explained variance of 63.0%. The monthly and diel plot of the first principal compo-nent (Fig. 4, PC1, 47.8%) shows that strong diel variations occurred throughout the year. These diel changeswere more pronounced from April to October. Seasonal changes were also detected but were weaker thandiel changes. The value and intensity of diel variations were clearly detected during winter. As the firsteigenvector is only composed of positive values, high values (in red on the first map in Fig. 4) indicate

Fig. 4. Spatial, seasonal and diel changes in calanoid diversity in the northern North Atlantic. Mapping of the first four eigenvectorsand monthly and diel changes in the corresponding principal components (PC 1-4). The symbol above each graph indicates midnightand the dashed lines between them denote midday. Modified, from Beaugrand et al. (2001).


where monthly and diel changes were strongest. This pattern occurred predominantly in the south–westsector of the North Atlantic Drift Province (Longhurst, 1998).

PC2 (Fig. 4, 8.4%) shows that there were seasonal changes in species richness although diel changeswere still detectable in almost all months. The diel changes were weaker in summer than in spring, autumnand winter. The corresponding eigenvector has both negative and positive values. High negative valuesshould be negatively related to the signal displayed by PC2 and inversely related to high positive eigenvec-tor values. Thus, in the northern part of the North Atlantic Drift Province, the southern part of the AtlanticSubarctic Province and the North Sea there were large seasonal changes in diversity with high valuesoccurring mainly in summer and low diel changes. In contrast, regions south of 50°N had high values fordiversity, mainly in spring, and showed higher diel variations.

PC3 (Fig. 4, 4.6%) displays the contrast that exists between seasonal changes in diversity between spring,autumn and winter periods. High negative values of EV3 in the Bay of Biscay region indicate high diversityduring spring and the high positive values reflect high diversity during autumn and winter in the GulfStream extension region.

PC4 (Fig. 4, 2.2%) shows two seasonal maxima in March–April and in July–October. May, June andwinter months are characterised by a lower value. Examination of EV4 shows that this pattern occurs offthe Iberian coast.

Diel and seasonal changes were modelled by multiplying the first four principal components by theirrespective eigenvectors. Fig. 5 shows the seasonal and diel variability of calanoid diversity by re-estimationof the original matrix. The North Atlantic Drift Province (Longhurst, 1998) can be clearly divided intotwo parts; one to the south-west that is highly variable at a diel scale; the other to the north-east that ishighly variable on a seasonal scale. Consideration of these two scales of variability gave better discrimi-nation between regions, as a result of which new divisions of the North Atlantic Ocean and adjacent seaswere proposed and new hypotheses about factors that contribute to the regulation of pelagic diversitysuggested (Beaugrand, Ibanez & Lindley, 2001).

3.1.3. Three-mode Principal Component AnalysisThis numerical technique has recently been applied to CPR data to investigate long-term changes in the

community structure of pelagic ecosystems along the SA route. This route, which crosses the EnglishChannel, the Celtic Sea and the Bay of Biscay, was divided into twenty sections ranging in length from20 to 70 km, but which contained the same number of CPR samples (188 observations for each section,making a total of 3760 samples). Selecting the most common phytoplankton and zooplankton species, athree-way table of the annual mean abundance of each taxon for each section and for each year over theperiod 1979–1995 was constructed. In oceanography, methods that allow the analysis of such complextables are rare. A three-mode PCA was developed and applied in conjunction with cluster analysis(Beaugrand, Ibanez & Reid, 2000b). The calculation of a three-mode PCA is made in two stages. First,three ‘classical’ PCAs are performed on the matrices time-space x species (mode species), time-species xspace (mode space) and space-species x time (mode time). Secondly, a core matrix, which establishes theinterrelationships between each mode, is calculated from the three eigenvector matrices computed in thefirst step of the analysis. Fig. 6 presents the results of this analysis, showing the regions identified (Fig.6(a)) and the long-term changes from the three principal components, species-locations (Fig. 6(b), modetime), years-locations (Fig. 6(c), mode species) and species-time (Fig. 6(d), mode space). Five differentzones, corresponding to a distinct interannual variability in plankton abundance, were identified (Fig. 6(a)–(b)). The zones were also characterised by distinct physical processes. It was even possible to detect theeffects of the Ushant Front, which corresponded to zone 3. Significant negative correlations were detectedbetween the NAO index, air temperature and the first principal component in the English Channel. Thalas-sionema nitzschioides, Nitzschia delicatissima and various zooplankton taxa mainly present in the EnglishChannel showed interannual variability in abundance that differed from that in the Bay of Biscay (Fig.


Fig. 5. (a) Intensity of the diel variability (as a percentage) in the diversity of calanoid copepods in the North Atlantic Ocean. (b)Intensity of the seasonal variability (in percentage) in the diversity of calanoids. Redrawn, from Beaugrand et al. (2001).

6(c) and (d)). The first principal component in each mode was indicative of plankton abundance and showeda decrease between 1988 and 1991 in the English Channel (Fig. 6), a period that coincided with a highNAO index as well as the beginning of the 1989/1991 high-salinity anomaly (Becker & Dooley, 1995).Furthermore, especially in the northeast and central English Channel, higher abundances were observed attimes of negative or low NAO values. At times of high and positive NAO indices, westerly winds arestronger throughout this area, and this may lead to an increase in mixing, which could delay the onset of


Fig. 6. Interannual variability along the SA route. (a) Location of the SA route sampled by the CPR survey. The five regions detectedby the analysis are superimposed. (b) year mode. Variability of the first principal component (species-locations). The groups determ-ined from the cluster analysis are indicated for species on the ordinate and for locations on the abscissa. (c) species mode. Year-to-year variability in the first principal component (years-locations). The grey level indicates the intensity of the first component. Thegroups determined from the cluster analysis are indicated for years on the ordinate and for locations on the abscissa. (d) locationmode. Variability in the first principal component (species-years). The groups determined from the cluster analysis are indicated forspecies on the ordinate and for years on the abscissa. Redrawn, from Beaugrand, Ibanez & Reid, 2000b). Z1: northern eastern EnglishChannel; Z2: southern western English Channel; Z3: Ushant Front; Z4: Celtic Sea; Z5: Bay of Biscay. TN: Thalassionema nitzscho-ides; AC: Acartia spp.; CH: Calanus helgolandicus; PP: Para-Pseudocalanus spp.; ND: Nitzschia delicatissima; LI: Limacina spp.;CT: Centropages typicus; OI: Oithona spp.; CF: Ceratium fusus; CM: Ceratium macroceros; CC: Clausocalanus spp.

water column stabilisation essential for the seasonal increase in net primary production (Dickson, Meincke,Malmberg, & Lee, 1988).

3.1.4. Non-metric multidimensional scaling (MDS)MDS is a non-parametric ordination method that aims to project multidimensional space into a reduced

number of dimensions, generally two. This analysis, which can be applied with almost any coefficient ofassociation (see Legendre & Legendre, 1998), in contrast to PCA (Euclidean distance) or correspondenceanalysis (c2 distance), has been applied to CPR data by Lindley (1987); Lindley and Williams (1994), andEdwards (2000). The analysis presented here to illustrate the method is one that was performed by Lindleyand Williams (1994) but the dendrogram and MDS scatter plot for this tow were not presented in that


paper. Plankton was sampled by a Continuous Plankton and Environmental Recorder (CPER) betweenAberdeen and Grimsby in the North Sea along route LR. Four groups of plankton were recognised. Onegroup occurred mainly in samples from Areas A (Aberdeen end) and C (unstratified water near Grimsby),the second occurred mainly in samples from Area A with a few from Area B (Grimsby), the third andlargest group occurred throughout the tow, and the fourth was found mainly in Area B. MDS used inconjunction with cluster analysis (hierarchical agglomerative single-clustering method) made it possible toidentify three regions along the transect on the basis of their plankton composition (20 taxa wereconsidered). Fig. 7 shows a clear separation between station 21 situated in unstratified water and otherstations located in more stratified areas. The cluster analysis grouped the northern and southern stations.The stress coefficient for the MDS plot was 0.08 indicating that the projection of the multidimensionalspace into two dimensions was satisfactory. This was also confirmed by the cluster analysis.

3.2. Cluster analysis

Cluster analysis is a powerful multivariate tool that is used to group objects or descriptors. With theexception of probabilistic clustering methods (e.g. Clifford & Goodall, 1967), which necessitate a particularassociation coefficient (e.g. Goodall’s probabilistic coefficient), this technique can possibly be applied toalmost any distance or similarity matrix between objects or descriptors. The choice of the coefficient ofassociation depends on the type (e.g. quantitative, semi-quantitative or qualitative data) and nature(abundance of species or presence/absence) of data and the hypothesis that is under study (Legendre &Legendre, 1998). Results from cluster analysis are often represented by means of a dendrogram.

3.2.1. SeriationBefore cluster analysis techniques became available, relationships between objects or descriptors were

investigated by rearrangement of an association matrix. Colebrook (1964); Colebrook and Robinson (1964)and Colebrook (1969) applied this technique to study relationships between species and to detect speciesassociations based on their geographical variation in abundance or to examine geographical similarities inthe interannual variability of a species (e.g. Temora longicornis in the North Sea; Colebrook, 1969).

Fig. 7. Two-dimensional ordination of the 21 locations sampled by a Continuous Plankton and Environmental Recorder (CPER)between Aberdeen and Grimsby in the North Sea. A Bray-Curtis similarity coefficient was used and a cluster analysis was appliedto group locations on the scatter plot.


3.2.2. Cluster Analysis and ordinationLindley (1987) was one of the first to apply cluster analysis (single hierarchical agglomerative clustering

method) in conjunction with an ordination method. These two techniques were applied to investigate thedistribution of 36 species of decapod larvae around the British Isles. The resulting dendrogram demonstratedthe presence of seven groups of species, although the shape of the dendrogram clearly indicated a gradientin the distribution of larvae. The distributions of these decapods were explained by the interaction betweenlife histories of organisms and bathymetric depth, which is quite important in the ecology of benthicorganisms (Glemarec, 1973). The joint application of cluster analysis and an ordination method enables avisual inspection of the deformation of the projection of the multidimentional space into a two-dimensionalscatter plot to be visualised. This procedure has been recommended by several authors (e.g. Legendre &Legendre, 1998).

3.3. Indicator-value method

The recently proposed ‘ Indicator-value method’ (Dufrene & Legendre, 1997) has been applied to calanoidcopepods by Beaugrand, Ibanez, Lindley & Reid (2002b). This method enables species associations to beidentified. Several steps are necessary to detect such associations. If the goal is to identify indicator speciesin an area, a cluster analysis is first applied in order to identify the regions. Alternatively the regions canbe determined a priori if the area under investigation is already well known. This can be done using anytype of data (e.g. abundance, diversity, or abiotic factors). Then, a measure of specificity and of fidelitymust be calculated. The specificity Aij computes the ratio of the average abundance of species i in the pixelsof group j (Nindividualsij) to the sum of the mean abundance of the species i in all groups (Nindividualsi.).

Aij �Nindividualsij

Nindividualsi.

The fidelity Bij is the ratio of the number of pixels where the species i in the group j is present to thetotal number of pixels in this group.

Bij �Nsitesij

Nsites.j

The indicator value (INDVALij) is computed by multiplying the specificity and fidelity indices, as thesetwo quantities represent independent information.

INDVALij � Aij � Bij � 100

Dufrene and Legendre (1997) retained the maximum indicator value for each species among all groups.This method has been used with CPR data to derive species assemblages from calanoid diversity (108taxa) (Beaugrand, Ibanez, Lindley & Reid, 2002b) as shown in Fig. 8. To take one example, the warm-temperate oceanic assemblage comprises 16 taxa. The boundary to this assemblage is quite sharp and itsgeographic coverage does not extend into water depths �200 m (Fig. 8(a)). The influence of the OceanicPolar Front at about 52–53°N on the latitudinal distribution of this association is strong between the Northw-est Corner (see Worthington, 1976) at 51°N, 44°W and the mid-Atlantic ridge. West of this, the latitudinalfront becomes meridional and the association extends to the north to about 58°N south of Iceland and55°N to the west of Ireland. To take another example, Fig. 8(c) and (d) shows a clear complementaritybetween the distribution of warm-water and cold-water species. At a lower level of distance in the dendrog-ram (not shown), warm-water species were divided into coastal, continental shelf, and pseudo-oceanicspecies (Fig. 9) while cold-water species were divided into cold-temperate, subarctic and arctic speciesassociations (Fig. 10). The subtropical and warm-temperate oceanic and pseudo-oceanic species associations


Fig. 8. Spatial distribution of calanoid copepod assemblages in the northern North Atlantic. The maps show the percentage ofoccurrence of taxa per pixel for each assemblage defined at the partition level of 1.152 of a dendrogram(not shown). Abundancedata were transformed into presence/absence data. Then, the percentage of present taxa per pixel for each assemblage was computed.An elevated percentage denotes a high degree of spatial aggregation of taxa inside an assemblage and vice versa. A blank pixelinside the survey area indicates the absence of species for a given group. (a) Warm-temperate oceanic species assemblage (16 speciesor taxa). (b) Bay of Biscay and southern European shelf-edge assemblage (4 species). (c) temperate neritic and pseudo-oceanic speciesassemblage (12 species or taxa) (d) cold-temperate, subarctic and arctic species assemblage (11 species or taxa). (e)–(f). Subtropicaland warm-temperate species assemblage (25 species). Redrawn from Beaugrand, Ibanez, Lindley & Reid (2002b).

were clearly detectable in the path of the Gulf Stream extension (Fig. 8(e) and (f)). These species assem-blages have been used to define in greater detail the ecosystems and ecotones of the North Atlantic Oceanand adjacent seas and to understand better the factors regulating diversity. Four modulating factors havebeen identified: 1. temperature, 2. hydrodynamics, 3. stratification, and 4. seasonal variability. These factorsare often linked, but they can act at different scales, and their contributions can vary geographically.Moreover, this study clearly detected the influence of warm currents on diversity and hence the functionalcharacteristics of ecotones west of Europe and in the Gulf Stream extension. Relationships between speciesassociations and water masses or currents are strong. These assemblages may, therefore, represent animportant environmental indicator for monitoring marine ecosystems and evaluating the impact of climatechange. Other techniques combining clustering methods and Bayesian probabilities, used recently by Anne-ville, Souissi, Ibanez, Ginot, Druart and Angeli (2002), could be used with the CPR data.


Fig. 9. Spatial distribution of calanoid copepod assemblages in the northern North Atlantic. Subdivision of the temperate neriticand pseudo-oceanic species assemblages (see Fig. 8(c)) at the partition level of 0.5 of the dendrogram (not shown). Data were codedin two states: 0 when the abundance of the taxa was less than half the mean. 1 when the abundance was more than half the mean.The percentage of species in one square was then calculated. This transformation allowed the main centres of the spatial distributionof taxa inside a group to be detected. Redrawn from Beaugrand, Ibanez, Lindley & Reid (2002b).

4. Geostatistics

4.1. Spatial interpolation

Selection of appropriate interpolation methods for spatial representation of plankton data is a key stagein making spatial and temporal comparisons of biological variables. The method selected should be rapidin calculation time and applicable to all species both rare and abundant. Many methods exist to interpolatedata (e.g. Lam, 1983). Two of the available methods have been used on CPR data. Planque (1996) appliedthe kriging procedure for the first time to CPR data. Kriging has the advantage that it takes into consider-ation spatial scales of change in ecological variability. This method allows a standard deviation of theinterpolation error to be derived, whereas this is less obvious in the case of the alternative inverse squareddistance method. Kriging was also used by Planque and Fromentin (1996) and has subsequently beenapplied successfully to abundant species and to the diversity of calanoid copepods (Planque & Ibanez,1997; Beaugrand, 1999). The total number of taxa identified per CPR sample has recently been mappedusing this procedure (Beaugrand, 1999). Fig. 11 shows monthly changes in the total number of taxa ident-ified per CPR sample. A clear contrast is seen between the total number of taxa in the eastern and westernnorthern North Atlantic. High values were found during winter off Canada and in the Bay of Biscay. Then,the number of taxa identified per CPR sample progressively extended northwards until September. The


Fig. 10. Spatial distribution of calanoid copepod assemblages in the northern North Atlantic. Subdivision of the cold-temperate,subarctic and arctic species assemblages (see Fig. 8(d)) at the partition level of 0.5 of the dendrogram, not shown. (a) cold-temperatespecies assemblage (4). (b) Subarctic species assemblage (4). (c) Arctic species assemblage (3). Redrawn from Beaugrand, Ibanez,Lindley & Reid (2002b).

use of kriging with CPR data is limited, however, by three main problems. First, there is the interpretationof the variogram and its approximation using a theoretical model. For each spatial interpolation, this stepmust be checked. Secondly, both geometric and zonal anisotropy must be corrected (Wackernagel, 1995).Thirdly, it is difficult to use kriging for rare species because of the high proportion of zeros in the matrices.In practice it is hard to verify all these parameters when a large number of maps is produced, so anothermethod, called inverse squared distance, has been applied (Beaugrand, Reid, Ibanez & Planque, 2000a;Planque & Batten, 2000). It is simpler than kriging and gives similar results when the radius of interpolationis relatively small (i.e less than 300 nautical miles). Fig. 12 shows the mean spatial distribution of sometaxa using this technique. There are considerable differences in the distribution patterns of the illustratedtaxa. The distribution of some taxa is complimentary (e.g. Euchaeta norvegica and the group Para-Pseudocalanus). In the case of Metridia lucens, a higher abundance is seen in the pelagic ecotones situatedwest of the British Isles and also along the path of the Gulf Stream extension and the North Atlantic


Fig. 11. Seasonal changes in the total number of taxa per CPR sample. Kriging was applied to interpolate the data spatially (period1958–1997, search radius = 200 nautical miles, neighbours between 5 and 15). Redrawn from Beaugrand (1999).

Current. Spatial interpolation techniques should be used with care in any application applied to the CPRdata because of the spatial and temporal heterogeneity of CPR sampling.

4.2. Semi-variograms and cumulative semi-variograms

Planque (1996) used experimental semi-variograms to investigate the spatial scale of variability of C.finmarchicus and C. helgolandicus. Semi-variograms were modelled using a spherical model. Importantyear-to-year variability was found in the shape of the experimental semi-variograms. This variance wasattributed to the sensitivity of the method to a small number of CPR samples. A clear spatial dependencyin the abundance of Calanus species was found within a range of about 400 km. C. helgolandicus exhibiteda more complex pattern from April to August, which was attributed to a multi-scale distribution pattern.In that case, spherical models were fitted to the experimental variograms to interpolate by kriging theabundance of the two species of Calanus for all months of the period 1958–1992. This same procedurewas then repeated in subsequent studies for different periods at different scales (Planque & Fromentin,1996; Fromentin & Planque, 1996). This technique probably helped to discover the well-known negative


Fig. 12. Mean spatial distribution of some key species or taxa in the North Atlantic Ocean. An inverse squared distance methodwas used with a research radius of 250 nm (neighbours between 5 and 15). Spatial interpolation was performed for each 2-monthand 2-hour period (144 maps). The mean of all maps was then calculated.

relationship between the state of the North Atlantic Oscillation and of C. finmarchicus (Fromentin &Planque, 1996).

However, classical experimental semi-variograms are highly sensitive to irregular distribution of obser-vations inside the spatial domain (Wackernagel, 1995; Sen, 1989). Sampling by the CPR survey is irregular,so an unbiased estimate of the experimental semi-variogram is difficult to obtain. Moreover, the choice ofdistance classes is quite arbitrary and may strongly influence the shape of the curve. This led Sen (1989)to propose a new way to evaluate the spatial dependence of observations for geological purpose. Theprinciple of Sen’s cumulative semi-variograms is to calculate for each sampling point a semi-variogrambased on geographical distances and dissimilarity between the particular sampling point and the others.Values for each semi-variogram are pooled, and then, as there are as many semi-variograms as there arepoints, it is possible to map the spatial dependence of the data. This gives an indication of the anisotropyof the regional variable and shows spatial changes in the scale of variability of the variable. Sen’s cumulat-ive semi-variograms were applied to CPR data by Beaugrand and Ibanez (2002). Fig. 13 shows the resultof applying the procedure to one month, using only data collected at night. The regional dependence in


Fig. 13. Application of Sen’s cumulative semi-variogram to show the spatial dependence of calanoid diversity in the northern NorthAtlantic. The value of the PCSV (Point Cumulative Semi-Variogram) was fixed at 1000. Blue indicates diversity changes at smallspatial scales, while red indicates that diversity varies at a larger spatial scale. Main surface currents are superimposed. Redrawnfrom Beaugrand and Ibanez (2002).

the path of the North Atlantic Current and in the north-eastern part of the North Atlantic Drift Province(see Longhurst, 1998) was low (400 km for a value of the Point Cumulative Semi-Variograms of 1000).This indicated that spatial variability in calanoid diversity varied at a small scale. The regional dependenceof diversity inside the two subtropical gyres was stronger (1200 km for a value of the Point CumulativeSemi-Variograms of 1000) and indicated a greater spatial variability in calanoid diversity.

5. Time series analysis

Objectives of this type of analysis are to describe and decompose time series and then develop modelsto enable future forecasting (Diggle, 1990). To date, most time series analyses used on the CPR datasethave been used to describe seasonal, year-to-year and long-term changes in the abundance of species.Then, correlation and cross-correlation techniques have been applied to identify environmental parametersresponsible for the observed trends (e.g. Fromentin & Planque, 1996). Time series analyses applied to theCPR data are presented in Table 4.

5.1. Cumulative sums

This technique is a simple method, which consists of graphically detecting local changes in a time seriesand assessing the intensity and duration of these changes (Ibanez, Fromentin, & Castel, 1993). This functionis calculated by subtracting for all values of the time series a reference number (i.e. the mean of the timeseries) and progressively pooling the residuals (Ibanez et al., 1993). This function was applied to theCPR data with the objectives of emphasising the relationships between community change and air surfacetemperature in the English Channel, the Celtic Sea and the Bay of Biscay (Beaugrand et al., 2000b, Fig.6). A clear relationship was detected between changes in community structure (Principal Component year-location from a three-mode Principal Component Analysis calculated on the three-dimensional table, years× locations × species) and air surface temperature in the English Channel and the Celtic Sea (Fig. 14).

5.2. Eigenvector filtering (EVF) and power spectra

The Eigenvector filtering method, also known as Principal Component Analysis of Processes (Ibanez &Etienne, 1991) or singular-spectrum analysis (Vautard, Yiou, & Ghil, 1992), was used on CPR data by


Table 4Examples of time series analyses used to interpret CPR data

Types of analyses Ecological goal or utility Authors

Box and Jenkins models Modelling of a time series and forecasting. Rothschild (1998)(AR.MA. ARMA. ARIMA)Multinomial logit model This kind of Generalized Additive Model was applied to analyse Beare & McKenzie (1999b)

the CPR data, using recorded values. This technique was utilised toreveal the seasonal, spatial and long-term variability in theabundance of species.

Cumulative sums Examination of local trends in a time series. Beaugrand, Reid, Ibanez &Planque (2000a)

Polynomial regression Determination of the trend in the abundance of Calanus Fromentin and Planque (1996)finmarchicus, C. helgolandicus and environmental parameters.Thistype of regression is used to de-trend the different time series andto take into account temporal autocorrelation in the calculation ofcorrelations (e.g. correlation between C. finmarchicus and the NAOindex).

Eigenvector filtering Decomposition of a signal. Smoothing of a time series and Colebrook (1978. 1982b)extraction of the trends. Emphasis of the major signal in the timeseries and quantification of temporal variability by the use ofeigenvalues (Ibanez & Dauvin, 1988; Ibanez & Etienne, 1991).

Power spectra Assessment of the scales of variability of a variable. Colebrook (1979)Maximum Entropy Spectral Assessment of the scales of temporal variability of a variable. This Colebrook (1981, 1982a,analysis was used on time series of sea-surface temperature, principal 1985b, 1991)

components and species abundance. This analysis is more adaptedto short time series and measures for which a higher degree oferror is expected than for classical spectral analysis (Legendre &Legendre, 1998).

Maximum entropy cross Examination of the common patterns of temporal variability for Colebrook (1985b, 1986,spectral analysis two pairs of variables (e.g. total copepods and sea-surface 1991)

temperature). This method uses both coherence and phase diagramsand determines relationships between variables for all possiblescales of variability.

Fig. 14. Cumulative sums of surface air temperature and the 2-dimensional principal component (years-locations) in the easternEnglish Channel. The figure shows the negative relationship between both variables. Redrawn from Beaugrand, Reid, Ibanez &Planque (2000a).


Colebrook, 1978, 1982a). He used this method to smooth and emphasise the trend of plankton time seriesand applied it directly to abundance data and to principal components (Colebrook, 1978). In more recentyears, EVF has seldom been used on CPR data. An application to the decomposition and quantificationof the scales of temporal variability in the diversity of calanoid copepods is presented in Fig. 15. A timeseries was built up for the North Sea (0°E–10°W, 50°N–60°N) from 1958 to 1999 with (× 42) the diversity(as the number of taxa per CPR sample) for each year, for daylight and dark periods (× 2) and for eachtwo-month period (× 6). Hence, the length of the time series was 504 (2 × 6 × 42). The lag chosen forthe Toeplitz matrix (autocovariance matrix) was 100. This lag was selected in order to eliminate long-termcycles and to emphasise the trend in the time series. The autocorrelation function (Fig. 15(a)) of the time

Fig. 15. Variability in the diversity of calanoid copepods from 1958 to 1999 for every two-month period and dark/daylight periods(504 points). (a) Autocorrelation function (99% and 95% confidence intervals are indicated). (b). Gain spectra assessed from theresults of the EVF.


series was high with a lag of one year between each maximum, which clearly showed the strong effectof seasonality on the diversity of calanoid copepods. The gain function was also calculated according tothe procedure described by Ibanez and Etienne (1991) (Fig. 15(b)). This function indicates the periodsemphasised by the corresponding eigenvectors of the EVF. A high value in the gain function for longperiods (infinity) indicates a trend while a high value for small periods can often be attributed to noise.The gain function (Fig. 15(b)) shows that the first two axes of the decomposition (S1 and S2, 24.9% and24.1% of the total variance of the time series, respectively) generated cycles with a period of about oneyear (the seasonal cycle). The third series (S3, 3.7%) emphasised the long-term variability of the timeseries, the fourth (S4, 2.8%) pointed out a cyclical trend with a period of approximately 16 years and thefifth series (S5, 2.8%) identified the day/night variation in diversity. Fig. 16 confirms the results of thegain function. Series 1 (the original time series reassessed by multiplying the first eigenvector by the firstprincipal component) and 2 (the original time series reassessed by multiplying the second eigenvector bythe second principal component) represented the seasonal cycle. Series 3 indicated the trend of the timeseries. This trend showed three peaks of high diversity in 1959, 1972 and 1990, which corresponded towarmer sea surface temperature. The low diversity in 1980 corresponds with the inflow of cold water intothe North Sea. Series 4 clearly shows a pseudo-cycle of about 16 years, evident from the gain function.

Fig. 16. Series recalculated from the data presented in Fig. 15 using the first five eigenvectors. As the use of the second eigenvectorgave a similar result to that of the first, it is not represented here. (a) first series: seasonal variability. (b) third series: long-term trend.(c) fourth series: cyclical variability (pseudo-period of about 16 years) with a slight influence of diel variability in diversity. (d) fifthseries: diel variability in the diversity of calanoid copepods.


Series 5 emphasised the day/night variation in diversity. Coefficients of variation calculated for each seriesindicated that the seasonal variability was more important than the year-to-year variability (Fig. 17). Thisresult confirms the observations on diel and seasonal variability made by Beaugrand, Ibanez and Lindley(2001). The result also shows that it is important to take seasonal variability into account in the examinationof calanoid copepod diversity. Diel variability is also important in relation to year-to-year variability andshould also be considered (Fig. 17). This may also apply to abundance data.

5.3. Maximum entropy spectral and cross-spectral analyses

Colebrook was the first to apply Maximum Entropy Spectral and Cross-Spectral analyses to CPR data(Colebrook, 1981, 1982b, 1985a, 1991). Colebrook and Taylor (1984) used these techniques to analysetemporal variability in the abundance of plankton sampled on a monthly basis and physical data such assea-surface temperature from 1948 to 1980. Maximum Entropy spectral and cross-spectral analyses wereused to determine the characteristic frequency of long-term variability in the abundance of plankton (firstprincipal component from a standardised PCA on the matrix years x species) and to examine similaritiesbetween plankton and physical variables around the British Isles. Using coherence and phase spectra, theseauthors identified a number of characteristic periods (e.g. 10–12 years, 5–6 years, 3–4 years). Wavelengthsof 3–4 years were associated with surface-heat exchange phenomena.

6. Conclusions

Considering the current number of years (43) and months (516) recorded from 1958 to 2000, for allspecies or taxa (about 450) and standard areas (33), about 7.7 million graphs would be needed to examineyear-to-year and long-term changes in the seasonal cycle of each species or taxon in all standard areas.More than ever, multivariate analyses need to be used to extract relevant information contained in the

Fig. 17. Quantification of temporal scales of variability in calanoid copepod diversity. The coefficient of variation was calculatedfor the first five series reconstructed from the EVF (see Fig. 16).


database. This review has emphasised how important statistical analyses have been, and are likely to con-tinue to be, in the interpretation of CPR data.

There is a clear need to develop techniques to improve the sorting of information in the CPR databaseand to evaluate relationships between biological and environmental data. Environmental parameters areavailable from the web (e.g. temperature, CZCS data, salinity, wind speed, wind direction). Environmentaltables could be gathered and compared with biological tables assembled from the CPR database. Techniquesso far not applied to CPR data (e.g. Redundancy Analysis or Canonical Correspondence Analysis) may beappropriate. Other techniques based on probability distribution (e.g. randomisation procedure for customiseddistributions, Poisson and Poisson-like distributions for rare species, Levy and log-Levy distributions forgeometrically fractal distributions, Bayesian techniques for regional variables) could also help to assessrelationships between biological and physical variables.

Acknowledgements

The authors are grateful to all past and present members and supporters of the Sir Alister Hardy Foun-dation for Ocean Science whose continuous efforts have allowed the long-term establishment and mainte-nance of the CPR dataset. We are particularly grateful to Philip C. Reid, Martin Edwards, BenjaminPlanque, Arnold Taylor and the two referees for advice and comments on the manuscript. The researchpresented was supported by the European Community Research Project No. MAS3-CT98-5058, the Nether-lands (contract RKZ595) and the French ‘Programme National en environnement cotier, theme: influencedes facteurs hydroclimatiques ou anthropiques sur la variabilite spatio-temporelle des populations et eco-systemes marins’ (PNEC art 4).

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an overview of statistical methods applied to cpr data

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