74
J. M. LAMBERT AND M. B . DALE
of the species/site data on purely internal axes. To avoid confusion,
we shall here restrict the term to the latter situation.
As indicated earlier (IIIA), the raw data themselves are already
crudely ordered, in that the sites can be displayed as points along axes
representing the species. The assumption now is that the existence of
relationships between the species may allow reduction, on some predetermined efficiency criterion, in the number of species-axes required
to accommodate the sites. The results of ordination are thus a set of
new and simpler axes, on which the sites can then be replotted in a
more convenient form. If enough new axes are used, the data may be
completely redescribed; and the sites specified, in terms of these new
axes; but since each axis is now associated with a value indicating the
variability in the total population which it represents, those axes with
little information-value can be rejected and the situation correspondingly simplified. This form of ordination, known as “principal component analysis”, is thus mainly a method for efficient description and
display: it requires no assumption of common structure in the population analysed, and any suggestion as to the meaning of the axes is
purely a matter of subjective hypothesization.
A more sophisticated approach, however, is to assume that new
axes can be found which will reiate to some more fundamental structure. The sites are now thought of as being informed by underlying
factors-such
as differences in the soil-varying
over the whole
area; the species will be responding to these in groups, and if groups
can be found they can be used to generate hypotheses concerning the
ecological properties of the sites. But the species are also responding
to-aspects of the environment to which they alone are sensitive individually; variation of this sort will give no information about the area as a
whole and is better eliminated. As the result of such elimination, the
sites can be eventually ordinated on new axes describing only-the
common variation.
Methods of this sort, which seek to remove the variation due to
individual interests, are known under the general title of “factor
analysis”. The term involves a variety of techniques, and the computation involved is usually formidable. At the start, either the number of
axes, or the common variance of each species, must be estimated, a
difficulty which is resolved only by iterative procedures for approximating the required values. Moreover, if the underlying structure is
assumed t o contain correlated factors, rotation of axes is permissible
subject to further constraints, and this involves additional computation.
Unlike component analysis, which uses all the information about the
species and makes no assumption of any “common” variation, factor
analysis is primarily concerned with extracting common information
J. M. LAMBERT AND M. B . DALE
of the species/site data on purely internal axes. To avoid confusion,
we shall here restrict the term to the latter situation.
As indicated earlier (IIIA), the raw data themselves are already
crudely ordered, in that the sites can be displayed as points along axes
representing the species. The assumption now is that the existence of
relationships between the species may allow reduction, on some predetermined efficiency criterion, in the number of species-axes required
to accommodate the sites. The results of ordination are thus a set of
new and simpler axes, on which the sites can then be replotted in a
more convenient form. If enough new axes are used, the data may be
completely redescribed; and the sites specified, in terms of these new
axes; but since each axis is now associated with a value indicating the
variability in the total population which it represents, those axes with
little information-value can be rejected and the situation correspondingly simplified. This form of ordination, known as “principal component analysis”, is thus mainly a method for efficient description and
display: it requires no assumption of common structure in the population analysed, and any suggestion as to the meaning of the axes is
purely a matter of subjective hypothesization.
A more sophisticated approach, however, is to assume that new
axes can be found which will reiate to some more fundamental structure. The sites are now thought of as being informed by underlying
factors-such
as differences in the soil-varying
over the whole
area; the species will be responding to these in groups, and if groups
can be found they can be used to generate hypotheses concerning the
ecological properties of the sites. But the species are also responding
to-aspects of the environment to which they alone are sensitive individually; variation of this sort will give no information about the area as a
whole and is better eliminated. As the result of such elimination, the
sites can be eventually ordinated on new axes describing only-the
common variation.
Methods of this sort, which seek to remove the variation due to
individual interests, are known under the general title of “factor
analysis”. The term involves a variety of techniques, and the computation involved is usually formidable. At the start, either the number of
axes, or the common variance of each species, must be estimated, a
difficulty which is resolved only by iterative procedures for approximating the required values. Moreover, if the underlying structure is
assumed t o contain correlated factors, rotation of axes is permissible
subject to further constraints, and this involves additional computation.
Unlike component analysis, which uses all the information about the
species and makes no assumption of any “common” variation, factor
analysis is primarily concerned with extracting common information