Baseline study Fish, fry and commercial fishery Nysted Offshore ...

Bio/consult as Page 83
Figur.3.10.1. Steps in a multivariate analysis based on calculations of a “distance” between every pair
of samples (dis-similarity).
The first step is to calculate “distance” between the samples based on an appropriate
metric. There are a number of different measures of distance available with each their
qualities. A commonly used measure for distance in between samples in investigations
of benthic fauna is the Bray-Curtis similarity, which principally function as an index of
the ratio between the number of common species and the total number of species. The
ratio is typically weighed with one of parameters attached to a single species, e.g.
biomass or abundance. If that index of similarity is scaled as percentage the similarities
will be in the range from 0 to 100 representing from totally different to identical. Using
a proper transformation of the raw data, it is possible to increase or decrease the weight
of different parameters, such as the presence of rare species, in the calculation of the
similarity index. The final product is an N*N distance matrix, which provides all the
mutual distances between the studies N samples.
The second step is a more complex set of single steps.
• A graphic presentation of the similarities as a Multi-Dimensional Scaling plot or
MDS-plot. MDS is a complex mathematical method to construct a map of the
samples in a certain number of dimensions. The purpose of the map is to place the
samples on the map in accordance with the calculated distances in similarity. If
sample A is more like sample B than C then A should be closer to B than to
sample C.
• Test of the similarity between two different distance matrixes. This test is part of
the detective work to identify the responsible factors affecting the composition of
species and their abundance in the samples. To identify the cause similar MDSplots
of the chemical parameters can be made and compared to the MDS-plot of
the biological parameters. A match between the set of maps would indicate that
the chemical parameters was responsible for or affected the biological data.
• Test of independence in the matrix of similarities to factors grouping the data
material. The tests are similar to the test used in an analysis of variance. In the
actual study, time and place are the factors and the tests are performed as
SEAS. Baseline study – Fish, fry and commercial fishery Dok. nr. 2148-03-001-rev3 2P.doc