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5 Analytical Methods

5.1 Validation

The validation phase of this project sought to provide a robust basis for the selection of a final set of environmental variables with which to define the classifications. In particular, we aimed to explore correlations between the candidate environmental variables and both species and communities using a variety of biological datasets and a mixture of analytical techniques. The latter included clustering combined with analysis of variance (ANOVA), Generalised Additive Models (GAM), classification and regression trees (CART), canonical correspondence analysis (CCA), and analysis of correlation of biological and environmental spaces (BVSTEP). It was considered that general agreement among multiple statistical methods would provide confidence in the final choice of environmental variables.

5.1.1 EEZ analysis

Table 3 summarises the statistical methods used for each of the EEZ biological datasets. The methods are discussed briefly below. A complete description of the validation analyses is contained in Image et al. (2003).

Classification of community data, followed by use of ANOVA to test the magnitude of environmental differences between groups, was used with both the fish and benthic datasets. In the classification phase, sampling stations were grouped on the basis of biological similarity measured using the Bray-Curtis distance measure (Digby and Kempton 1987). When used with presence/absence data this compares numbers of species in common between sites, with distances ranging from 1 (no taxa in common between sites) to 0 (all species in common). Cluster analyses were performed on the resulting biological distance matrices using hierarchical agglomerative, group-average linkage (Clarke and Warwick 2001). Membership of sample stations in fish and invertebrate community groups was defined by pruning the cluster dendrogram at a level of similarity that produced 10 and 20 groups. Analysis of variance (ANOVA) was then used to assess the magnitude of environmental differences between the biological groups. Although the use of biological groups as treatments might be considered unconventional, the ANOVA F-ratios provide an indication of which environmental variables co-varied most strongly with variation in biological composition. Because we were not interested in the actual statistical significance of the calculated F-ratios, any violation of the normality assumptions of ANOVA were considered to be unimportant.

Table 3: Summary of the statistical methods used for each data type

Dataset

Classification and ANOVA

GAM

CART

CCA

BVSTEP

Chlorophyll a

 

Yes

Yes

 

Yes

Fish species

   

Yes

   

Fish community

Yes

 

Yes

Yes

Yes

Benthic species

   

Yes

   

Benthic community

Yes

 

Yes

Yes

Yes

The relationships between the environmental variables and the concentration of chlorophyll, and the probability of occurrence of 12 fish and 10 benthic species, were analysed using generalised additive models. In this approach the abundance or probability of occurrence was modelled as a function of smoothed responses to a set of environmental variables. Both the marginal contribution of each variable and the order in which it was fitted gave an indication of its importance, while the overall abilities of the environmental factors to predict the biological responses were assessed using cross-validation procedures (Image et al. 2003).

A regression tree analysis was used to examine correlations between the environmental variables and chlorophyll concentration, and classification trees were used to relate environment to the presence/absence of both fish and benthic species. Classification trees were used to assess the environmental relationships of the fish and invertebrate community groups defined by the numerical classifications described above.

Canonical correspondence analysis (CCA) as described by Francis et al. (2002) was used to explore relationships between environment and the composition of both fish and benthic communities. Because CCA is sensitive to the presence of rare species (Ter Braak and Smilauer 1998), only species occurring in 1% or more of the stations were included in these analyses.

The multivariate routine BVSTEP (Clarke & Warwick 2001) was used to compare dissimilarity matrices generated for combinations of environmental variables with the matrix generated for taxa data (using Bray-Curtis dissimilarities). Spearman's correlation coefficient (rho) quantified the correlation between biological and environmental space and enabled comparisons to be made between alternative definitions of environmental space (i.e. defined using different combinations of environmental variables). Forward stepwise selection was used and new variables were added into the model only if they increased the correlation coefficient by > 0.001.

5.1.2 Hauraki analysis methods

Techniques similar to those used for the EEZ were used to model individual species, namely multiple regression based on generalised linear models (GLM), logistic regression (based on presence/absence data) and general additive models (GAM) (Table 4). Two multivariate procedures were used to identify environmental variables that most affected community composition (CCA and BVSTEP). Forwards selection was used for both procedures and new variables were only added into the model if they increased the correlation coefficients by ≥ 0.05.

Table 4: Analysis types carried out on the different Hauraki Gulf biological datasets

Data type

GLM

Logistic regression

GAM

CCA

BVSTEP

Chlorophyll

Yes

 

Yes

   

Large zooplankton

Yes

 

Yes

   

Microzooplankton

Yes

 

Yes

   

Fish

 

Yes

Yes

Yes

Yes

Benthic macrofauna

Yes

Yes

Yes

Yes

Yes

5.2 Classification procedure

The values of each of the chosen environmental variables for each grid cell were used as input for a two-stage multivariate classification process. In the first stage we used ALOC (Belbin 1995), a non-hierarchical clustering strategy designed for use with very large datasets, to amalgamate grid cells into up to 300 clusters (i.e. each cluster is a class). The Gower metric (Sneath and Sokal 1973) was used as the measure of environmental distance. The Gower metric is defined as:

The Gower distance (D) between two objects in a multivariate space (in this case two grid cells described by various environmental variables) is the sum of the absolute difference between the objects for each of the variables divided by the total variation (ie. the range in that variable).

where D is the environmental distance between points j and k, which are described by a set of variables xi, i = 1, 2, ... n. Therefore, xij is the value of variable xi at site j. This distance measure incorporates implicit range standardisation of each variable. Therefore, all variables have equal weight and contributed equally to the definition of environmental distance. In the second stage, relationships between the 300 clusters were defined using their average environmental conditions as input to a sequential agglomerative clustering technique, again using the Gower metric. The classification results comprised a table of group membership of all grid cells from the 2 to 30 class level of the classification hierarchy. In order to map the final classification at any hierarchical level this table was imported into a desktop geographic information system and linked to the classification grid.

5.3 Classification definition

5.3.1 Complicating factors

During the development of the Marine Environment Classification, the steering group agreed that the aim of the classification was to divide environmental space into units that maximise discrimination of variation in biological composition. The classification's discrimination of biotic composition is influenced by:

  1. including variables that have functional linkages with, or at least are correlated with, variation in biological composition
  2. transformation of variables to increase their correspondence with biological composition
  3. increasing the weighting of variables where there is clear evidence of their dominant role in driving, or correlation with, variation in biological composition.

While the validation analyses described above were informative for choosing a set of environmental variables for use in the classification phase, the results were relatively uninformative regarding how best to combine these variables to define classification units. We therefore sought a more objective means of tuning the classification that would guide our selection of environmental variables so as to maximise the ability of the resulting classification to discriminate variation in biological composition. Three issues needed to be carefully considered and addressed in deciding how to best define such a classification.

First, in deciding which variables should be included in the classification, we were aware that the relative importance of some environmental variables was dependent at least in part upon the geographic scale and/or location at which this was assessed. In large measure, this reflects the markedly different geographic scales over which different environmental factors vary. For example, some environmental variables show relatively continuous variation throughout the EEZ (e.g. depth, annual mean solar radiation and wintertime sea surface temperature), while others remain relatively invariant over large areas but show pronounced changes in particular locations (e.g. orbital velocity, SST gradient and slope). As a consequence, any techniques used for deciding either which variables to include in the classification, or what weightings and/or transformations should be applied to them, had to be performed at more than one spatial scale. In practical terms, our aim was to produce a classification that gave good discrimination at higher classification levels of global variation (i.e. at the scale of the whole area being classified) in broadly varying factors such as depth and mean annual solar radiation, while also separating at more detailed classification levels variation in factors such as tidal current and orbital velocity that are important at more local scales in particular locations.

Second, while the classification procedure treats equally any given interval of change in a variable regardless of its value, rates of biological turnover (i.e. change in biological composition) do not necessarily remain constant along environmental gradients. For example, the classification treats changes in depth in steps of say 10 m independently of the depth at which they occur, so that 10-20 Ξ 110-120 Ξ 5010-5020. By contrast, examination of fish trawl data suggests that turnover in fish community composition with increasing depth is relatively rapid in shallow waters but becomes progressively more muted in deeper water. This observation suggests that the discriminatory power of a classification could be increased by use of transformations of input variables that make the relationship between a variable and biological turnover more linear. Another useful feature of transformations is their ability to mute the influence of extreme values of variables that are highly skewed. For example, the distributions of the tidal current and orbital velocity variables were highly skewed with a small part of the environmental domain comprising extremely high values of these variables relative to the mean. If left untransformed, the extreme values in the distributional tails of these variables can unduly influence the classification while variation at lower levels is largely ignored.

Third, unless explicitly altered, the multivariate classification procedure that we used places equal weight on all environmental variables. Although intuitively this suggests that all variables make an equal contribution, in practice the contribution made by variables at different classification levels will largely reflect their spatial variability. Thus, variables that change in a continuous fashion over the whole domain (e.g. for the EEZ wintertime SST and mean annual solar radiation, for the Hauraki Gulf, SST phase and SST annual amplitude) will tend to dominate the definition of classes at higher levels (i.e. a small number of classes) of the classification. By contrast, more spatially patchy variables (e.g. tidal current, mean orbital velocity in both classifications) will tend to determine class boundaries at lower levels of the classification (i.e. a large number of classes).

One way to improve the ability of an environmental classification to discriminate variation in biological composition is to alter the default contributions of different variables to more closely match their varying degree of influence on biological patterns. For example, most of the validation analyses indicated that depth has a stronger correlation with biological variation than other variables. This suggests that a judicious increase in the weighting given to depth has the potential to increase the correspondence between classification classes and biological patterns. The subsequent increase in the influence of the weighted variable on class definition can be clearly seen in Figure 10, where an increase in the weighting given to depth is reflected in the class boundaries showing a higher correspondence with variation in bathymetry. However, as weighting increases the contribution of the weighted variable at all levels of the classification hierarchy, care has to be taken to insure that the weighted variable does not overly dominate the classification outcome at the expense of other variables. This, in particular, may result in more locally important variables making insufficient contribution at finer levels of classification detail.

The problem of how best to weight the variables used in a classification is also inextricably linked to the problems caused by their inter-correlation. When two variables are correlated, the component that is common to both is effectively given a double weighting while the unique component of each variable may make only a small contribution relative to the common component. One possible solution to this problem is to use the Mahalanobis distance measure (Mahalanobis 1936) rather than the Gower metric (Gower 1971) because this distance measure automatically corrects for inter-variable correlations and calculates site to site distances based on the uncorrelated components. However, use of the Mahalanobis measure also requires the normalisation of variables, a procedure that we were reluctant to implement given the advantages of transformation as a tool to maximise the matching of environment to biological turnover as discussed above.

Figure 10: Comparison of two pilot EEZ classifications at the 6 (top), 10 (centre) and 25 (bottom) class levels

Note: Both classifications are defined using the same eight variables but with different weightings of depth. The classifications on the left have a double weighting of depth and the classifications on the right have a triple weighting of depth. The 1000-metre depth contours are shown as black lines. Environmental classes are discriminated by colour.

Maps of the EEZ showing distribution of classes using two different classification methods and three different levels of resolution (i.e. defined by the number of classes). Classification methods differed in their weighting of depth.

5.3.2 Method used for tuning the classifications

Given that our overall objective was to define an environmental classification that maximises discrimination of variation in biological character (see above), we used Mantel tests (Mantel 1967) to refine the final mix of variables used for the classification. These allowed us to objectively explore the effects of including or excluding, and transforming and/or weighting the different candidate variables on the subsequent measurement of environmental differences between different sets of sample sites (= environmental distances). Matrices containing environmental distances created using particular combinations of variables were compared with equivalent matrices describing biological distance for the same test sites, and the degree of correlation (r) between these two measures of 'distance' was calculated. Using this process, we sought to find a combination of variables, weightings, and transformations that would maximise the correlation between measures of environmental and biological distances between different sets of sample sites.

Test sites for this process were selected from the same biological datasets as the earlier validation analyses. Measures of biological distance for the community datasets were defined using the Bray-Curtis distance measure. Because of the length of the biological gradients described by these datasets, a large proportion of sites had no species in common resulting in many of the individual dissimilarities having the maximum possible value for this measure, i.e. a value of one. An estimate of the true biological distances for these pairs of sites was recalculated using a flexible shortest path adjustment method (De'ath 1999). This involved recalculating any dissimilarities above a nominated limit (e.g. 0.9) using sites with lower dissimilarities as stepping stones and allowing dissimilarities greater than one to be estimated. Because the chlorophyll concentration data was univariate, the Euclidean distance measure was used.

In order to better understand the relative importance of spatial scale and different geographic contexts we carried out Mantel tests at two scales of analysis. Tests were performed for sites distributed across the entire EEZ and for geographic sub-samples of the biological datasets that were constrained to a smaller spatial scale defined by a tile covering approximately one sixteenth of the spatial extent of each biological dataset. The fish trawl dataset was the only one large enough to allow a multi-scale analysis for the Hauraki Gulf and when these analyses were performed, no significant differences in correlation were found; therefore these results are not shown here. For the EEZ data, the results of the spatial sub-samples were averaged to provide an overall result, while variability among subsamples indicated the degree to which the definition of environmental space was dependent on the geographic context.

In order to determine the level of statistical confidence for differences between definitions of environmental space, the datasets were randomly subsampled and the analyses replicated. For each subset, we computed Mantel r for two competing definitions of environmental space. We subtracted the two Mantel r values for each subset to obtain the values delta-r. We then tested the distribution of the delta-r values to determine if there was a significant difference between the competing definitions. For the fish trawl and chlorophyll datasets we took 100 random subsets of 300 sites each without replacement at both the full EEZ and the sub EEZ scale. We used paired t-tests to assess whether any departure of mean delta-r values from a value of zero were significant. For the shelf dataset the number of sites was too small (274 sites) to subsample without replacement. We therefore took 100 random subsets of the 274 sites with replacement (both within each subset and between subsets). After applying the Mantel test to the distance matrices formed using each of these samples, we ranked the 100 delta-r values and took the fifth and 95th values as an estimate of the 5% and 95% confidence bounds. We interpreted the mean delta-r value as significant if the 5% confidence bound did not encompass zero (a one-tailed test). Only the significant delta-r values are shown in the graphs in this report. Where a delta-r value was not statistically different from zero it has not been shown.

As discussed above, large parts of the range of many of the environmental variables were not sampled by the biological datasets. This restricted our ability to test the effect of classification decisions such as transforming and/or weighting variables. The tuning analyses therefore provided an indication of whether the classification's strength would be improved or weakened by different definitions of environmental space. However, the lack of biological representation meant that Mantel test alone could not be used to define the environmental space so that inspection of the mapped classification and expert judgements were also used to finalise the classification.

5.4 Statistical testing of classifications

The overall objectives of the testing component of the Marine Environment Classification project were to:

  1. assess the strength of environmental classifications for the Hauraki Gulf and the New Zealand region (i.e. their ability to discriminate variation in biological composition)
  2. typify the biological character for classes at one level from environment-based classifications for the Hauraki Gulf and the New Zealand region.

Information about biological distributions was derived from point-based surveys of species presence or abundance, with surveys generally focussed on particular functional groups (i.e. fish, benthic invertebrates, chlorophyll a). While in the previous phase these data were used to fine-tune the selection of environmental variables and their weighting and transformation, here we used the same data to assess the ability of the resulting environment-based classifications to summarise variation in ecosystem character.

ANOSIM (Clarke and Warwick 2001) was used to test the strength of the EEZ and Hauraki Gulf classifications (i.e. to assess the ability of these environment-based classifications to summarise variation in biological composition). The r-values calculated by ANOSIM indicated the average difference between ranked biological distances calculated for sites located in the same environmental classes, versus ranked distances calculated for sites in contrasting environmental classes. Values of r, therefore, indicated the degree to which points within the same environmental classes have closer biological similarity to each other than average levels of similarity occurring across the wider dataset. These analyses can be used to calculate either the global (i.e. overall) average difference in compositional distances taken across all classes or to make comparisons for sites occurring in particular pairs of classes. A brief graphical description of the ANOSIM test is provided in Appendix 4.

This ANOSIM analysis was complicated by the continuous nature of the environmental classifications, i.e. they are able to viewed at any level of detail from 1 to around 300 classes. The large number of sample points for some of the EEZ biological data sets also complicated the analyses so that subsets of biological sample points had to be randomly selected to prevent excessive memory demands for the analysis. However, despite this apparent plethora of biological data for some environmental classes, both the ANOSIM analyses and the subsequent description of the biological character for other classes were hampered by the very uneven sampling of classes by most of the biological sample sets, i.e. with the exception of the remotely sensed and hence spatially extensive chlorophyll data, a large proportion of classification classes at any particular classification level had either few biological sample points or lacked them altogether, particularly in the Hauraki Gulf.

As a consequence, we commenced our analysis by assessing the number of classes with adequate biological data (five or more sites) at each level of classification for both the EEZ and Hauraki Gulf and the significance of differences in biological composition between these classes. Results from these analyses were then used to identify one level of detail (20 classes) for both the EEZ and Hauraki classifications at which the significance of biological differences for all possible pair-wise combinations of classes was assessed. The average species composition of environmental classes at this level of classification detail was also summarised using MATLAB with frequencies of occurrence calculated for each fish species or invertebrate family. While chlorophyll data were available for 15 out of 20 classes in the EEZ classification, the number of classes at a 20-class level of classification for which adequate data were available from the biological data sets varied between three and eleven.