THE USE O F STATISTICS I N PHYTOSOCIOLOGY
71
However, such data may also be considered homogeneous if the
quantitative measures of the separate species all show a unimodal (or
amodal) distribution across the sites : the sites are then statistically part
of a single population.
A t the other extreme, each site might contain an entirely different
set of species from all others; for instance, if one site lies in a field, one
in a wood, and a third at the margin of a lake, there could easily be no
overlap of species. In such a situation, the sites have no single property
in common, and the data are completely heterogeneous.
In quantitative data with, for the moment, no qualifative differences
between the sites, heterogeneity can occur if a similar set of values
obtains within any sub-set of the sites against a different pattern elsewhere. In qualitative data, if sub-sets of sites exist such that within a
sub-set some species are everywhere absent, then at least two sets of
species-axes are necessary to define the sites and the data can again be
considered heterogeneous. If the data contain both quantitative and
qualitative elements, as is usual with “quantitative” measures in
p4ytosociology, heterogeneity can derive from either or both elements.
Thus, although it is not impossible to obtain homogeneous data in the
presence of qualitative differences, it seems reasonable to assume that
overall homogeneity is unlikely to exist in practice. This assumption of
inherent heterogeneity in most phytosociological data in fact provides
their most important statistical property in the present context, since
it largely determines the nature of the most efficient methods available
for their analysis : it is the reduction of this heterogeneity t o an acceptable level, rather than the establishment of homogeneity, which
normally forms the basis of such methods.
The widespread occurrence of heterogeneity in most phytosociological
situations occasionally leads investigators to suggest, either that only
the “more important” species should be used for analysis, or that such
species should be weighted in some way to compensate for the qualitative differences between the sites. However, although there may
occasionally be grounds for weighting on some objective criterion
internal to the analysis (see p. 79), there appears no justification at all
for a priori weighting or selection. The occurrence together of certain
rare or inconspicuous species in certain of the sites could well prove a
powerful indication of phytosociological similarities of ecological importance, which could easily be obscured by concentration on the more
prominent species. For present purposes, therefore, the individual
species will be treated as initially all equally relevant to the situation
to be analysed, with no arbitrary assumptions as to their relative
importance.
Apart from questions of external weighting, however, there are
71
However, such data may also be considered homogeneous if the
quantitative measures of the separate species all show a unimodal (or
amodal) distribution across the sites : the sites are then statistically part
of a single population.
A t the other extreme, each site might contain an entirely different
set of species from all others; for instance, if one site lies in a field, one
in a wood, and a third at the margin of a lake, there could easily be no
overlap of species. In such a situation, the sites have no single property
in common, and the data are completely heterogeneous.
In quantitative data with, for the moment, no qualifative differences
between the sites, heterogeneity can occur if a similar set of values
obtains within any sub-set of the sites against a different pattern elsewhere. In qualitative data, if sub-sets of sites exist such that within a
sub-set some species are everywhere absent, then at least two sets of
species-axes are necessary to define the sites and the data can again be
considered heterogeneous. If the data contain both quantitative and
qualitative elements, as is usual with “quantitative” measures in
p4ytosociology, heterogeneity can derive from either or both elements.
Thus, although it is not impossible to obtain homogeneous data in the
presence of qualitative differences, it seems reasonable to assume that
overall homogeneity is unlikely to exist in practice. This assumption of
inherent heterogeneity in most phytosociological data in fact provides
their most important statistical property in the present context, since
it largely determines the nature of the most efficient methods available
for their analysis : it is the reduction of this heterogeneity t o an acceptable level, rather than the establishment of homogeneity, which
normally forms the basis of such methods.
The widespread occurrence of heterogeneity in most phytosociological
situations occasionally leads investigators to suggest, either that only
the “more important” species should be used for analysis, or that such
species should be weighted in some way to compensate for the qualitative differences between the sites. However, although there may
occasionally be grounds for weighting on some objective criterion
internal to the analysis (see p. 79), there appears no justification at all
for a priori weighting or selection. The occurrence together of certain
rare or inconspicuous species in certain of the sites could well prove a
powerful indication of phytosociological similarities of ecological importance, which could easily be obscured by concentration on the more
prominent species. For present purposes, therefore, the individual
species will be treated as initially all equally relevant to the situation
to be analysed, with no arbitrary assumptions as to their relative
importance.
Apart from questions of external weighting, however, there are