The Rapid Appraisal of the Status of Fisheries

Rapfish is a new multi-disciplinary rapid appraisal technique for evaluating the sustainability of fisheries. Fisheries may be defined flexibly, from a broad scope such as all the fisheries in a country or lake, down to a narrower scope such a single jurisdiction, a target species, a gear type or even individual vessels. A set of fisheries may be compared, or the time trajectories of individual fisheries may be plotted.

Ordinations of sets of attributes are performed using multi-dimensional scaling (MDS). Normally this is in two dimensions and the MDS is followed by rotation to an orientation adopted as a convention (horizontal). Ordinations are bounded by reference points that simulate the best and worst possible fisheries using extremes of the all attribute scores, and these hypothetical 'good' and 'bad' fisheries define the extremes and the orientation of the horizontal axis. Fisheries are given a score of 0% to 100% along this axis. A second set of fixed reference points constructed from two half-way scores stabilizes the vertical dimension of the plot. Further constructed reference 'fisheries' with randomly allocated attribute scores define the size of differences among fisheries that might be regarded as significant.

Separate Rapfish ordinations may be performed using sets of pre-defined attributes in ecological, economic, technological, social and ethical disciplines (or 'fields' or 'components of sustainability'). More fields may be added as required for particular analyses. A combined ordination may also be performed, providing an unweighted conflation of the fields.

Within a field, attributes are chosen to reflect sustainability, and although intended to remain fixed so that different analyses may be compared, attributes may be refined or substituted as improved information becomes available. Most attributes are scored on a ranked scale, for example a five point scale from zero to 4. Intermediate scores are permitted because all scores are normalized before ordination. Scores given to a particular fishery should be justified. Candidate attributes whose extreme scores cannot be unequivocally regarded as 'good' or 'bad' should be dropped from the analysis. Discussion of attributes in a workshop venue makes explicit the values that define a particular field.

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Summary of Rapfish Procedure

Validation of the Rapfish Technique using Simulated Fishery Data

The rapid appraisal of fisheries method using Multidimensional Scaling (MDS) depends upon the position of actual fisheries relative to the constructed 'good' or 'bad' fisheries, or a trajectory of a fishery in time moving towards or away from these reference points. The trajectory from good to bad should be monotonic. It would be useful to superimpose later Rapfish analyses on previous ones. This section investigates both of these problems using data from three simulated test fisheries.

Testing Monotonicity

The progression from 'good' to 'bad' must be monotonic for the evaluation of status to be credible. To test this, I simulated fisheries with ten attributes, each scored on a scale from zero to 4. The 'good' fishery (100%) and 'bad' (0%) fishery had all 4s or all zero scores respectively. I then simulated a fishery whose scores improved progressively by one unit in one attribute at a time. There is a large number of such fisheries following alternate paths one step at a time from 'bad' to 'good'

First, I checked which MDS options gave the best results for this procedure. MDS scores from five different variants of the method are shown in Figure 1. The clearest monotonic trajectory is shown by the MDS using Euclidean distance squared, normalization by attribute using Z scores and, in Figure 1, using the ordinal data MDS option.

Figure 2a shows the results from a Rapfish ordination of two simulated fisheries (small and large circles). Both of the trajectories are encouragingly monotonic. In this case the SPSS option for ratio data has been used, giving a more linear plot. The slightly greater width of the step sizes at the edge of the plot reflects, in part, the normalization of attribute scores, and partly the greater range of score possibilities in the centre of the plot. The two fisheries follow slightly different tracks because they differed in the scores with which they moved from bad to good. Note that, at the centre of the plot, a large number of possible combinations lead to the same total score and hence position on the x axis. The number of possible ways of achieving the same total score diminish as one approaches the 'good' and 'bad' locations, and each of those has only one possible set of scores (all good or all bad). The random ("ugly") fisheries are represented by the cross in the centre of the plot - they are normally distributed and the size of the arms of the cross is proportional to the 95% confidence limits on their standard errors. The cross has been displaced slightly vertically to make it visible: in fact it lies almost precisely at the centre of the ordination.

Simulated trajectories

Superimposing one Rapfish plot upon another

It would be useful if new fishery points could be overlaid on a single Rapfish ordination plot that has previously been completed. This would mean that the maximum of about 100 data points in MDS would not limit Rapfish analyses.

Without modification this is not possible, because small changes in the data can cause MDS ordinations to flip 180 degrees, forming approximate mirror images. In the horizontal dimension this problem is taken care of by always rotating so that 'Good' is at 90 degrees and 'Bad' at 270 degrees azimuth. But simulations show that a similar problem applies to the vertical dimension of the Rapfish plot. For example, Figure 5 shows an attempted overlay of Fishery B, ordinated separately (broken line) from its original analysis (solid line) in which it was included along with data from fisheries A and C. It is clear that there has been a vertical flip.

Figure 5. Two overlaid Rapfish ordinations of one of the three simulated fisheries, B, from Figure 3. Solid line shows original plot from analysis where all three simulated fisheries were included. Broken line shows plot from analysis in which fishery B data alone was included. There has been a vertical flip of the fishery position.

Figure 6. Two overlaid Rapfish ordinations of the three simulated fisheries from Figure 3. Solid line shows original plots from analysis. Broken lines shows plots from analysis that included twice as many random points. There has been vertical flip of the fishery positions.

Vertical flips in MDS can also be caused by trivial changes. For example, Figure 6 shows fisheries A, B and C from Figure 3 above (solid lines). When Rapfish is repeated with 40 instead of 20 random values included, the three fisheries flip positions vertically (broken lines). Note, however, that the scores along the sustainability axis, from 'Bad' (= 0%) to 'Good' (=100%), are not much affected by the vertical flip.

To overcome this problem, it is necessary to construct some additional 'mid-range' fixed reference points in the analysis. When these fixed reference points are included, Rapfish analyses produce plots that approximately overlay one another.

The first additional 'mid-range' reference point is constructed from half of the attributes being assigned a maximum (= 'Good') score and the other half a minimum (= 'Bad') score. The second additional reference point is constructed to have the opposite set of scores, a mirror image, as it were. All attributes set to one extreme score for the first reference point must be set to the opposite extreme in the other; there should be no overlap. There are a whole set of similar mid range points, but only two, one pair of opposites, need be chosen. These points define the extreme vertical extent at the centre of the Rapfish plot. By convention one of these reference points is chosen to always have a positive value. For the overlay of Rapfish plots to work, the same combination must be chosen for all analyses using this set of attributes.

Figure 7 shows some simulations in which the Rapfish ordination of Fishery B from Figure 5 (solid line) is ordinated in two further Rapfish analyses on its own and with various other mid-way points and random values. The overlays are shown by broken and thin solid lines lines. On the whole, individual points are quite close to their original positions and the plot has been flipped back by the adoption of the new 'mid-points' convention. But it is clear that the vertical position of two of the 21 individual points has 'flipped'. The circumstances in which these flips occur need further investigation, but the MDS algorithm is not sufficiently transparent to make this an easy task. The result is that we cannot be certain that overlays of individual points from a new analysis will be accurate in the y dimension, although the overall pattern of trajectory will be similar.

Figure 7. Two Rapfish ordinations overlaid on the original ordination of the simulated fishery B from Figure 3, where fisheries A and C were included with in the analysis (thick line). Broken and thin lines shows plots from analyses where fishery B data only was included with different set of mid-range reference points and random scores. Note that one of the mid-range points was fixed as positive by convention.

Foverlays of Fishery B (Figure 8) are very similar to the original, so that it ortunately, the time trajectory for the two is unlikely that an overlay would lead to misleading results on the 'good to bad' axis.

Figure 8.Plots on the 'Good' to 'Bad' axis of the overlay and original Rapfish scores from the simulated fisheries in Figure 7.

Conclusions

The conclusion from these simulations is that Rapfish ordinations using MDS are monotonic and reasonably superimposable provided that suitable reference points are included in the ordination. The 'Good' and 'Bad' reference points provide a fixed scale from 0% to 100% and a fixed orientation for the horizontal axis, guarding against horizontal flips in the raw MDS output. The mid-range reference points guard against vertical flips of the whole analysis, and enable approximate overlays to be made. At present, there is no guarantee that individual data points will overlay accurately in the vertical dimension. Inclusion of both sets of reference points, however, means that ordination scores along the horizontal axis from good to bad are well behaved.

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Leverage of Individual Attributes on Rapfish Ordinations

How much does each attribute influence the ordination scores of a fishery in the Rapfish technique? To answer this question, it proved necessary to adopt the full set of fixed reference points as discussed above, earlier attempts with only the two original fixed reference points at 'good' and 'bad' suffered from the MDS mirror image flipping problem (in about a quarter of cases).

Figure 9.Leverage of nine ethical attributes on sustainability scores (along the 'Good' to 'Bad' axis) and Y axis scores for a Rapfish analysis of East coast Canadian fisheries. leverage was calculated as standard errors of differences between scores obtained with and without the attribute)

Figure 10. Overall effect of leverage of nine ethical attributes on 18 Canadian east coast fisheries on sustainability scores (along the 'Good' to 'Bad' axis) and Y axis scores for a Rapfish analysis of East coast Canadian fisheries. Plot values were calculated as standard errors of differences between scores obtained with all nine attributes compared to total of scores successively without each of the attributes in turn.

We carried out a series of ordinations successively dropping each attribute out of the analysis. I used, as an example, data from an analysis of 18 fisheries from the east coast of Canada (Pitcher and Power in prep.). For each of the nine ethical attributes, we calculated the sum of squares of the differences of the x- and y- scores compared to those obtained with the full set of attributes. This provided a standard error expressing the leverage of each attribute. Figure 9 shows the results for nine ethical attributes used in this work. The standard errors for the horizontal sustainability axis are shown on the right, those for the vertical, y-axis on the left of the plot. There is an approximate three-fold variation in leverage, from about 2% to 6.5 % on the x axis, and from 0.2 to 0.6 of a standard deviation on the vertical axis. The two sets of leverages on the two axes are not correlated (r2=0.3). For example, for the 'adjacency' ethical attribute, this means that the sustainability score of fisheries is altered by about 13% with a likelihood of 95%. (twice standard error). For the attribute 'alternatives' the value is about 5%.

A similar calculation was carried out for the individual fisheries, to see which are most sensitive to the loss of attributes from the ordination. Figure 10 shows the results in order of influence of the sustainability score. For example, on the sustainability axis, the ordination positions of cod offshore, cod trawl, cod gillnet and scallop fisheries are influenced by 14 to 18% (twice the standard error) by the loss of an 'average' attribute in the analysis, while for fisheries like snow crab, shrimp and Bay of Fundy herring weir, the value is only about 3-6%.

We can ask how this variation from the individual attributes affects the plotted positions on the Rapfish ordination. Figures 11a and b show this for six example fisheries. Large circles show the ordination positions when all nine attributes are included in the analysis. Solid lines join the plotted positions of these fisheries when individual attributes are dropped from the analysis. Numbers indicate the attributes dropped at each point (their identity need not concern us for the purposes of this discussion). In this plot the vertical axis shows from -3 to +3 standard deviations, the normal extent of Rapfish positions. In all cases the position along the sustainability axis is affected by the loss of individual attributes far less than the vertical position on the y axis. The cod offshore fishery shows quite large changes, especially for attributes 3, 9 and 6. The other five fisheries shown as examples exhibit far less variation. Note that the polygons do not overlap, meaning that rank order of the three fisheries along the sustainability axis remains the same in all cases.

Figure 11.Rapfish plots showing the leverage of nine ethical attributes on 3 examples of Canadian east coast fisheries (11a, top), and three Canadian west coast fisheries (11b, bottom) on two-dimensional Rapfish plots. Solid points show the fishery positions when all nine attributes are included. Solid lines indicate the Rapfish scores when individual attributes (numbered points} are dropped from the analysis.

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