THE USE O F STATISTICS IN PHYTOSOCIOLOGY
75
and thus assumes that it exists; it will therefore tend to fail, in that
the results may be uninterpretable, in markedly heterogeneous situations. However, in both cases, the object of performing the analysis is
not only to place the sites in relation to one another, since the primary
data themselves contain such relative information if this is all that is
required. Both methods aim to simplify the situation by ordering the
axes in terms of information-content. In component analysis, the new
axes are mainly simplification constructs to show the nature of the
population; in factor analysis, the axes themselves are of primary importance since it is they which form the basis for hypothesis-generation.
It is these two interrelated sets of techniques which provide the
most fundamental mathematical approach to ordination so far available. Their exponents have beeq few, but two such studies deserve some
mention here. One is that of Goodall (1954b), who used a form of
principal component analysis (under the misnomer of factor analysis) in
a study of random samples from the Victorian mallee; however, his
attempts to interpret the ‘(factors” he obtained were unsuccessful
owing to marked heterogeneity in his data. Secondly, there is the
work of Dagnelie (1960), who used factor analysis for a variety of studies
of vegetation and environment, and obtained interpretable results ;
but his data consisted of selected stands, where at least some common
variation could be expected.
The massive computation involved in these formal methods has
probably been partly responsible for the development of more approximate methods by some workers. Thus Smensen (1948) employed
measures of similarity between sites to erect a single, grossly simplified,
ordination axis; and Bray and Curtis (1957) invented a method suggestive of component analysis, in which, however, the axes extracted
had no common origin nor any rigorous mathematical relation to each
other.
I n contrast to these crude approximations to a genuine mathematical
system, the literature is also beset with a number of empirical attempts
at ordination, most of which are so subjective in approach that they
do little more than extract an answer already built in by the use of
weighted data, biased selection of “important” species, and uncritical
use of inappropriate parameters. Moreover, it is far too frequently
assumed that the achievement of ordination by such methods provides
a demonstration that vegetation is essentially (‘continuous”. The further
assumption is then often made that classification is inappropriate, with
statements such as “differentiation is not sufficiently discrete to allow
classification on anything but an arbitrary basis” (Anderson, 1963,
p. 409). All classification is arbitrary in that the limits to the classes
are set by the investigator; but all ordination is equally arbitrary in
75
and thus assumes that it exists; it will therefore tend to fail, in that
the results may be uninterpretable, in markedly heterogeneous situations. However, in both cases, the object of performing the analysis is
not only to place the sites in relation to one another, since the primary
data themselves contain such relative information if this is all that is
required. Both methods aim to simplify the situation by ordering the
axes in terms of information-content. In component analysis, the new
axes are mainly simplification constructs to show the nature of the
population; in factor analysis, the axes themselves are of primary importance since it is they which form the basis for hypothesis-generation.
It is these two interrelated sets of techniques which provide the
most fundamental mathematical approach to ordination so far available. Their exponents have beeq few, but two such studies deserve some
mention here. One is that of Goodall (1954b), who used a form of
principal component analysis (under the misnomer of factor analysis) in
a study of random samples from the Victorian mallee; however, his
attempts to interpret the ‘(factors” he obtained were unsuccessful
owing to marked heterogeneity in his data. Secondly, there is the
work of Dagnelie (1960), who used factor analysis for a variety of studies
of vegetation and environment, and obtained interpretable results ;
but his data consisted of selected stands, where at least some common
variation could be expected.
The massive computation involved in these formal methods has
probably been partly responsible for the development of more approximate methods by some workers. Thus Smensen (1948) employed
measures of similarity between sites to erect a single, grossly simplified,
ordination axis; and Bray and Curtis (1957) invented a method suggestive of component analysis, in which, however, the axes extracted
had no common origin nor any rigorous mathematical relation to each
other.
I n contrast to these crude approximations to a genuine mathematical
system, the literature is also beset with a number of empirical attempts
at ordination, most of which are so subjective in approach that they
do little more than extract an answer already built in by the use of
weighted data, biased selection of “important” species, and uncritical
use of inappropriate parameters. Moreover, it is far too frequently
assumed that the achievement of ordination by such methods provides
a demonstration that vegetation is essentially (‘continuous”. The further
assumption is then often made that classification is inappropriate, with
statements such as “differentiation is not sufficiently discrete to allow
classification on anything but an arbitrary basis” (Anderson, 1963,
p. 409). All classification is arbitrary in that the limits to the classes
are set by the investigator; but all ordination is equally arbitrary in