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

Spring 1962 CAKONICAL DISTRIBUTION 205
tion. In particular, it does not discriminate be- octa~eor so, a necessary consequence of the low
tween singletons (say) of species that occur as G value of the Species-Abundance curve.
singletons every year and of species that occur
only once in 10 years.
Hicks (1935). Breeding birds near Wesferville,
If we therefore retain the names of the birds Ohio
and make this distinction, we can distinguish be-
~~i~ also is a 10 year count, in the course of
tween 'pecies that 'lavea':' chance of
which 86 spKies were observed, though the averin
any One year and that 'lave One age for a single year was 63 or less. In Figure
chance in 4 or one in 8. This produces Figure
21 we give the graph, on the same basis as ~ i ~ .
19, where, so to speak, we get a peep behind the
ABVIDUIGES.R\IRS PER W
FIG.19. Birds of "Keotoma," a typical year reconstructed
from a knowledge of what species were present
in each of 10 years. I Species Curve)
M
LOG, (INDIVIDUALS PER SPECIES)
veil. Although the curve as drawn lies reasonably
well among the observed points, which generally
alternate above and below it, there could be some
argument that a better curve might be one skewed
to the right, descending abruptly and terminating
at abundance 16. JVe shall not debate the point,
but merely note that the number of species involved
(N) is 56 excluding the cowbird, that o is
1.73octaves as against the canonical expectation of
3.37, and I/N is less than 3. The canonical
expectation in a complete universe would give
I/mN = 5000 or thereabouts. We may also note
that the individuals curve Figure 20 continues
past its own crest into its descending limb for an
Ln 2/2ae
MODE OF
SPEUES CURVE 2.15 OCTAVES MOW ff MOIV- CURVE
are A am 1.0 z a s P
ABVHMHCES, PAIRS PER SPECIES PER YEAR
FIG20. The "individuals" curve for an average year
at "Neototna." The observed termination is well beyond
the crest, as it should be for a negatively-contagious or
over-regularized distribution.
SCALE OF OCTAVES
SCALE OF OCTAVES
FIL.21. Top, Hicks. Breeding Birds near Westerville,
Central Ohio. Ten year count. Center, Walkinshaw.
Breeding Birds near Battle Creek, Michigan.
Ten year count. Bottom, Williams. Breeding Birds near
Cleveland, Ohio. Fifteen year count.
19, except that I have used the accumulated totals
for the 10 years and have not struck an average by
dividing this result by 10. The value of 5 is
almost exactly 2.0 octaves, the average value of
I/N is about 3.5 for a single year, and there is
a suggestion of skewness, as expected.
IValkins~zaw(1947). Breeding birds on 83 acres
of brushy fields
This is another 10 year count. Some 31 species
were accumulated. The distribution is graphed