84
J. M. LAMBERT A N D M. B. DALE
decided. The ranking method originally suggested by Williams and
Lambert is only appropriate to monothetic classifications, and Dale
(1964) has suggested an alternative numerical method based on
information statistics which, though computationally more cumbersome,
might prove to be more applicable in certain circumstances.
I n any situation, there is in principle no reasoh why coincidences
should not occur between a given group of species and more than one
group of sites, or between a given group of sites and more than one
group of species. However, although such aggregates may. be indistinguishable on one axis, they are distinguishable on the other and may
therefore be separately defined by reference to that axis. For instance,
an area of grassland might well contain one group of species exclusive
to grazed sites, another which is graze-tolerant but not codned to
pastures, and a third which is normally found in meadows but can just
survi(P-e under grazing ; conversely, any of these groups of species could
occur over a variety of Werent soils, but associated in each case with a
different subsidiary flora. Any one group of sites may thus bear anumber
of different noda, while any one group of species may form different
noda across a range of sites.
Once the noda have been obtained, they represent abstractions from
the data which can then be used as phytosociological units in their
own right; by whatever method they are eventually obtained, their
value clearly lies in their double definition in terms of both species and
sites. However, to be useful as independent “vegetation-units”, they
still require to be characterized for identification purposes as economically as possible. The simplest characterization is to define and identify
each nodum by reference to the single species and site carrying most
information concerning the unit in question, so that each is uniquely
represented by a single species/site coincidence. But the decision must
then be made as to the nature of the information actually required by
the user. For instance, the extraction of the “characteristic” species
and site could be made by reference solely to the information contained
within each nodum itself; this will give maximum information about the
internal composition of any particular nodum, but none about its
interrelationships with other units. Alternatively, the information
could be derived from the sets of species and sites from which each
nodum was directly obtained; this method will incorporate information
about the lateral relationships of any one nodum with others of similar
site- but different species-groups, and of similar species- but different
site-groups, respectively, but some information concerning the composition of the nodum may correspondingly be lost. Again, another
method (and the one actually used so far) is to derive the information
from the immediate parent populations of species and sites fiom which
J. M. LAMBERT A N D M. B. DALE
decided. The ranking method originally suggested by Williams and
Lambert is only appropriate to monothetic classifications, and Dale
(1964) has suggested an alternative numerical method based on
information statistics which, though computationally more cumbersome,
might prove to be more applicable in certain circumstances.
I n any situation, there is in principle no reasoh why coincidences
should not occur between a given group of species and more than one
group of sites, or between a given group of sites and more than one
group of species. However, although such aggregates may. be indistinguishable on one axis, they are distinguishable on the other and may
therefore be separately defined by reference to that axis. For instance,
an area of grassland might well contain one group of species exclusive
to grazed sites, another which is graze-tolerant but not codned to
pastures, and a third which is normally found in meadows but can just
survi(P-e under grazing ; conversely, any of these groups of species could
occur over a variety of Werent soils, but associated in each case with a
different subsidiary flora. Any one group of sites may thus bear anumber
of different noda, while any one group of species may form different
noda across a range of sites.
Once the noda have been obtained, they represent abstractions from
the data which can then be used as phytosociological units in their
own right; by whatever method they are eventually obtained, their
value clearly lies in their double definition in terms of both species and
sites. However, to be useful as independent “vegetation-units”, they
still require to be characterized for identification purposes as economically as possible. The simplest characterization is to define and identify
each nodum by reference to the single species and site carrying most
information concerning the unit in question, so that each is uniquely
represented by a single species/site coincidence. But the decision must
then be made as to the nature of the information actually required by
the user. For instance, the extraction of the “characteristic” species
and site could be made by reference solely to the information contained
within each nodum itself; this will give maximum information about the
internal composition of any particular nodum, but none about its
interrelationships with other units. Alternatively, the information
could be derived from the sets of species and sites from which each
nodum was directly obtained; this method will incorporate information
about the lateral relationships of any one nodum with others of similar
site- but different species-groups, and of similar species- but different
site-groups, respectively, but some information concerning the composition of the nodum may correspondingly be lost. Again, another
method (and the one actually used so far) is to derive the information
from the immediate parent populations of species and sites fiom which