THE USE O F STATISTICS IN PHYTOSOCIOLOUY
73
We are indebted to Professor W. T. Williams, of this Department, for
the following logical definition, which we shall here adopt : “If we have
a set of sites such that for every site in the group there is at least one
other site with which it has one or more species in common, and if this
group cannot be divided into two or more groups such that all the sites
of any one group have no species in common with those of another, then
the vegetation may be said to be continuous. MoreoGer, if in any group of
sites which is continuous in this sense, a linear or cyclic order of species
can be found such that every site is defined by an uninterrupted segment
of this order, the vegetation can be said to be progressively continuous;
if not, it will be said to be diffusely continuous, in which the diffuseness
itself can take various forms.”
With such a definition, most phytosociological data are likely to be
continuous to a greater or lesser degree, except in such cases as the
sites to be compared have been taken only from widely disparate
ecological situations with no transitions between : such a situation can
easily be tested, and needs no elaborate statistical analysis. A more
generally useful concept than continuity and discontinuity, therefore,
is that of the degree of heterogeneity between the different sites. I n fact,
the equation of heterogeneity with discontinuity we believe to have
been the cause of much of the present confusion among ecologists ; as
we have here defined the terms, though a discontinuous set of sites
must be heterogeneous, a heterogeneous set of sites need not be discontinuous.
Further, there seems to be a common misconception that classification is only properly applicable to “discontinuous” data, while ordination
techniques are more appropriate to continuous systems. In contrast, it
cannot be too strongly emphasized that there is no a priori reason why
the use of either method should be restricted in this way: continuous
systems can be efficiently classified if classification is desired, while
“discontinuous” (i.e. markedly heterogeneous) systems can be ordinated if ordination is thought more useful for the immediate purpose
in hand. Moreover, there is in principle no reason why classification and
ordination techniques should be mutually exclusive : classified units
can be ordinated, and ordinated units classified. Which method to
adopt at a given stage of the investigation is entirely a matter for the
user, irrespective of any subjective concept of the “real” nature of
vegetation.
The relative efficiency of the two approaches can most easily be compared by considering methods of ordination fist. Here we must first
distinguish between “ordination” of the species/site information on
external axes directly related to the environment (as in Whittaker’s
“gradient analysis”, to be mentioned in Section IIIF), and structuring
73
We are indebted to Professor W. T. Williams, of this Department, for
the following logical definition, which we shall here adopt : “If we have
a set of sites such that for every site in the group there is at least one
other site with which it has one or more species in common, and if this
group cannot be divided into two or more groups such that all the sites
of any one group have no species in common with those of another, then
the vegetation may be said to be continuous. MoreoGer, if in any group of
sites which is continuous in this sense, a linear or cyclic order of species
can be found such that every site is defined by an uninterrupted segment
of this order, the vegetation can be said to be progressively continuous;
if not, it will be said to be diffusely continuous, in which the diffuseness
itself can take various forms.”
With such a definition, most phytosociological data are likely to be
continuous to a greater or lesser degree, except in such cases as the
sites to be compared have been taken only from widely disparate
ecological situations with no transitions between : such a situation can
easily be tested, and needs no elaborate statistical analysis. A more
generally useful concept than continuity and discontinuity, therefore,
is that of the degree of heterogeneity between the different sites. I n fact,
the equation of heterogeneity with discontinuity we believe to have
been the cause of much of the present confusion among ecologists ; as
we have here defined the terms, though a discontinuous set of sites
must be heterogeneous, a heterogeneous set of sites need not be discontinuous.
Further, there seems to be a common misconception that classification is only properly applicable to “discontinuous” data, while ordination
techniques are more appropriate to continuous systems. In contrast, it
cannot be too strongly emphasized that there is no a priori reason why
the use of either method should be restricted in this way: continuous
systems can be efficiently classified if classification is desired, while
“discontinuous” (i.e. markedly heterogeneous) systems can be ordinated if ordination is thought more useful for the immediate purpose
in hand. Moreover, there is in principle no reason why classification and
ordination techniques should be mutually exclusive : classified units
can be ordinated, and ordinated units classified. Which method to
adopt at a given stage of the investigation is entirely a matter for the
user, irrespective of any subjective concept of the “real” nature of
vegetation.
The relative efficiency of the two approaches can most easily be compared by considering methods of ordination fist. Here we must first
distinguish between “ordination” of the species/site information on
external axes directly related to the environment (as in Whittaker’s
“gradient analysis”, to be mentioned in Section IIIF), and structuring