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J. M. LAMBERT AND M. B . DALE
site-classification, sites with comparable sets of species are grouped
together, from which it can be postulated that roughly comparable
habitat conditions will obtain over the sites of any given site-group; in
“inverse” analysis, however, groups of species which occupy roughly
the same range of sites will be extracted, and the hypothesis now is that
the constituent species of each species-group w i l l have certain physiological/ecological properties in common.
Although there have been a number of contributions dealing with the
detection of associations between individual pairs of species (see
Greig-Smith, 1964, Chap. IV), few phytosociological analyses directed
at the formation of species-groups as the primary aim of the operation
have appeared in the literature so far. The somewhat empirical method
of Hopkins (1957) extracted “basic units” of reticulately-linked species
by using positive associations between species to erect the groups, but
concentrated more on the number of associations than on their relative
values; while Kershaw (1961) again extracted reticulately-linked
groups by using both positive and negative associations at different
block sizes of quadrats to calculate the overall co-variance of
species.
There is, however, in principle no reason why any of the more‘powerful hierarchical classificatory techniques already discpssed should not
be applied to the species as well as to the sites. The only example we
know of the independent use of the same hierarchical method for both
site- and species-classification is that of “association-analysis” used
normally for the sites and inversely for the’ species (Williams and
Lambert, 1961a). This method requires the use of a correlation-matrix
for the variables, which are necessarily brought to zero mean and unit
variance. Differences in “abundance” of the species are thus eliminated
from the normal analysis but remain in the inverse analysis, while
differences in “richness” of the sites are eliminated from the inverse
analysis but remain in the normal analysis ; but since both “abundance”
and “richness” are ecologically meaningful, this does not diminish the
interpretability of the results. ’
When methods of equal power are used for both normal and inverse
analyses, however, there is a further feature to be considered. Whereas
each site is an individual in its own right and floristically identical sites
could easily occur, each species is already an abstraction from taxonomic data and it is unlikely that any one species will have an exactly
comparable ecological range to any other. On a priori grounds, therefore, the degree of heterogeneity between the species could well be
considerably greater than that between the sites, and this must be
recognized in any cross-comparison of the results from the two independent analyses.
J. M. LAMBERT AND M. B . DALE
site-classification, sites with comparable sets of species are grouped
together, from which it can be postulated that roughly comparable
habitat conditions will obtain over the sites of any given site-group; in
“inverse” analysis, however, groups of species which occupy roughly
the same range of sites will be extracted, and the hypothesis now is that
the constituent species of each species-group w i l l have certain physiological/ecological properties in common.
Although there have been a number of contributions dealing with the
detection of associations between individual pairs of species (see
Greig-Smith, 1964, Chap. IV), few phytosociological analyses directed
at the formation of species-groups as the primary aim of the operation
have appeared in the literature so far. The somewhat empirical method
of Hopkins (1957) extracted “basic units” of reticulately-linked species
by using positive associations between species to erect the groups, but
concentrated more on the number of associations than on their relative
values; while Kershaw (1961) again extracted reticulately-linked
groups by using both positive and negative associations at different
block sizes of quadrats to calculate the overall co-variance of
species.
There is, however, in principle no reason why any of the more‘powerful hierarchical classificatory techniques already discpssed should not
be applied to the species as well as to the sites. The only example we
know of the independent use of the same hierarchical method for both
site- and species-classification is that of “association-analysis” used
normally for the sites and inversely for the’ species (Williams and
Lambert, 1961a). This method requires the use of a correlation-matrix
for the variables, which are necessarily brought to zero mean and unit
variance. Differences in “abundance” of the species are thus eliminated
from the normal analysis but remain in the inverse analysis, while
differences in “richness” of the sites are eliminated from the inverse
analysis but remain in the normal analysis ; but since both “abundance”
and “richness” are ecologically meaningful, this does not diminish the
interpretability of the results. ’
When methods of equal power are used for both normal and inverse
analyses, however, there is a further feature to be considered. Whereas
each site is an individual in its own right and floristically identical sites
could easily occur, each species is already an abstraction from taxonomic data and it is unlikely that any one species will have an exactly
comparable ecological range to any other. On a priori grounds, therefore, the degree of heterogeneity between the species could well be
considerably greater than that between the sites, and this must be
recognized in any cross-comparison of the results from the two independent analyses.