70
J. M. LAMBERT AND M. B . DALE
111. METHODS OF ANALYSIS
A. THE STATISTICAL PROPERTIES O F PHYTOSOCIOLOOICAL
DATA
So far, the only assumption which we have made about the nature of
the vegetation to be analysed is that the plant component of the plant/
site system is composed of entities identifiable as species. We have
further decided that, for the purpose in hand, the species present at each
site shall be the properties we measure, either as a quantitative value
or, as recommended, on a purely qualitative presence-or-absence
system. On either basis, the raw data can now be displayed as a twodimensional matrix, with the individual sites along the top and the
species down the side: each column will show the species present in
each site, and each row will show the sites in which each species is
represented. From this, two other sets of matrices can be constructed,
one indicating relationships between all possible pairs of species (calculated over all sites), and the other indicating relationships between all
possible pairs of sites (calculated over all species).
We must now make a decision as to whether we are primarily
interested in a comparison of the sites on the basis of the species they
contain, or in a comparison of the species on the basis of the sites in
which they occur. At present, we will confine our attention to the
traditional phytosociological approach of comparing the sites in terms
of their floristic composition : we shall return to the other approacbin a
subsequent section (IIID).
From a statistical point of view, the raw data to be analysed are
already ordered to some extent, in that the sites can be represented
geometrically on a number of species-axes. Completely unordered data,
where relationships alone are known, are extremely rare in phytosociological work; the sole example we have encountered (G. A . Yarranton, unpublished) is one in which the number of times two species concur is known, but the number of separate occurrences of the species
across the sites is not recorded. Such data require special treatment for
analysis, which need not concern us here; instead, the more typical
partially ordered data, capable of immediate display on axes, will form
the starting point for subsequent discussion.
Theoretically, since any-species can be present in any site, it is possible
to conceive of a situation in which all sites contain all species; this might
occur, for instance, with a set of sites in poor heathland containing
only three species all of which are intimately intermingled. In quantitative data, if the quantities ofthe species are also equivalent, the sites
are clearly indistinguishable and the data completely homogeneous.
J. M. LAMBERT AND M. B . DALE
111. METHODS OF ANALYSIS
A. THE STATISTICAL PROPERTIES O F PHYTOSOCIOLOOICAL
DATA
So far, the only assumption which we have made about the nature of
the vegetation to be analysed is that the plant component of the plant/
site system is composed of entities identifiable as species. We have
further decided that, for the purpose in hand, the species present at each
site shall be the properties we measure, either as a quantitative value
or, as recommended, on a purely qualitative presence-or-absence
system. On either basis, the raw data can now be displayed as a twodimensional matrix, with the individual sites along the top and the
species down the side: each column will show the species present in
each site, and each row will show the sites in which each species is
represented. From this, two other sets of matrices can be constructed,
one indicating relationships between all possible pairs of species (calculated over all sites), and the other indicating relationships between all
possible pairs of sites (calculated over all species).
We must now make a decision as to whether we are primarily
interested in a comparison of the sites on the basis of the species they
contain, or in a comparison of the species on the basis of the sites in
which they occur. At present, we will confine our attention to the
traditional phytosociological approach of comparing the sites in terms
of their floristic composition : we shall return to the other approacbin a
subsequent section (IIID).
From a statistical point of view, the raw data to be analysed are
already ordered to some extent, in that the sites can be represented
geometrically on a number of species-axes. Completely unordered data,
where relationships alone are known, are extremely rare in phytosociological work; the sole example we have encountered (G. A . Yarranton, unpublished) is one in which the number of times two species concur is known, but the number of separate occurrences of the species
across the sites is not recorded. Such data require special treatment for
analysis, which need not concern us here; instead, the more typical
partially ordered data, capable of immediate display on axes, will form
the starting point for subsequent discussion.
Theoretically, since any-species can be present in any site, it is possible
to conceive of a situation in which all sites contain all species; this might
occur, for instance, with a set of sites in poor heathland containing
only three species all of which are intimately intermingled. In quantitative data, if the quantities ofthe species are also equivalent, the sites
are clearly indistinguishable and the data completely homogeneous.