The Canonical Distribution of Commonness and Rarity: Part I F. W ...

Spring 1962 CANONICAL DISTRIBCTIO~T 209
It was, I think, hlacArthur's original view that
a genuine "community" might correspond approximately
with his predictions, while fortuitous
aggregations would more likely come close to the
lognormal. This presents us with the problem of
defining a genuine community. Superficially one
might imagine that a heronry or a colony of gulls
and terns and cormorants like Belknap's is a "community"
since in some sense the birds "attract"
one another in much the same way as human communities
are brought together. But we see from
Fig. 17 and from the data in Tables XI and XII,
that it is precisely such communities that depart
most from the MacArthur prediction. We should
have to define a community as a group of persons,
animals, or plants that insist on holding their
fellows at arm's length, or that are repelled by one
another.
Margaret Perner's breeding birds at Cleveland,
Ohio
Since the MacArthur formula seems more appropriate
to territorial species that1 others, I
thought we might examine one instance in more
detail, and for that purpose use Perner's ( 1955)
data on 25 species of nesting birds. This time
we plot simply the nests per species as ordinate
SCALE OF OCTAVES (Indtv!duak per Spectes>
against ordinal rank (of increasing commonness)
FIG.22. The MacArthur distribution for 5, 10, 100, as abscissa (Figure 23), and the 3IacArthur preand
1OOO species. diction is plotted on the same graph. The de-
It lies at an distance
partures of the observations from the prediction
the pints .re not random, but systematic. so that this aggre-
for gregarious or cololliall~-nesting birds and for
the "contagious" plant communities. Since the does not agree well with prediction.
effects of contagion may be expected to smooth
out, and die out, with very large areas or very
gation of species, tho~lgl~ negatively contagious,
Otlzcr pecztlarities of the Species-Area clrmre for
large ensembles of species, in the overall picture,
satnples
while the MacArthur distribution, even for 1000
species (see Fig. 22) gives a 3-value not much
Samples, especially small ones, have a number
higher than for 100 species, the distribution would
oi peculiarities, partly because they are sarrlples
not apply to such aggregrations oi species, as Macand
therefore likely to be incomplete or truncated
Arthur himself has said.
distributions, and partly because they are small,
I therefore suggest somewhat tentatively that
especially in numbers of species. and therefore
the MacArthur distribu.tion is not the norm, and
likely to be affected by contagion, positive or negathat
the frequent agreement of Icohn's diagrams tive. JVhereas the Species-Area curves for isotherewith
is due to the cone-shells being somewhat
lates can be understood comparatively easily, those
over-regularized in their spacial distribution. lye
for samples may present greater difficulties. Even
may note here Kohn's own comment that in a
in the matter of graphing the plots there are
~iumher of his diagrams "common species are
problems, and in interpreting the results there are
too common and rare ones too rare" to agree with
worse uncertainties.
the ?.lacLlrthur prediction. This statement
JIcthods
amounts to saying that the logarithmic standard
a~tdprobleuu of plottitzg the
deviation of abundances is too high, which means
Species-Area cztrves
that his points (not those I have plotted in Fig. This subject is almost a monopoly of plant
17) are often above the RiacArthur line. perhaps ecologists. who set out "quadrats" of various
approaching the canonical line.
sizes and count the species in the quadrats. They