Fig. 1.—Diagrammatic representation of the influence of 
three factors on one species. 
for one than for another. At the same time a species 
may be influenced by a factor or set of factors which af- 
fect it only. These will be referred to as specific factors. 
This relationship is diagrammed in Fig. 2. Even in this 
relatively simple community with uncorrelated factors, 
the complexity is evident. 
COMMON 
FACTORS 
SPECIES 
SPECIFIC 
FACTORS 
Fig. 2.—Diagrammatic representation of the influence of 
three specific and four common factors on three species. 
If two species share a common factor or factors, the 
changes in their populations will be correlated. For 
example, if two species are both limited by rainfall and 
rainfall is increased, both populations will increase. 
However, if one species is only slightly dependent on 
rainfall and the other strongly so, the changes will be 
disproportionate and the correlation less. As a simple 
principal rule, the correlations among a group of species 
making up a community are determined by the species’ 
mutual association with a group of common factors. 
In essence, factor analysis takes a matrix of correla- 
tion coefficients among a set of variables and reduces it 
to a series of mathematical common factors that ac- 
count for the correlations among the variables. 
TECHNIQUES 
The procedures carried out in this paper are calcu- 
lation of the correlation matrix, estimation of commu- 
nalities (the amount of variance caused by factors com. 
mon to other species), factoring of the matrix using 
the principal axis method, rotation to a specified hypoth. 
esis (transformation of the numbers to other biologically 
meaningful numbers), calculation of factor scores, anc 
the formulation of the so-called specification equation: 
for each species to serve as a model of the community 
If all of the above steps except the factoring of the 
calculated correlation matrix are skipped, the result i 
a form of factor analysis normally referred to as prin 
cipal components analysis. 
Principal Components Analysis 
Mathematically, factor analysis resolves a correla 
tion matrix (a covariance matrix can also be used i 
some cases) into a n x k factor matrix where the num 
ber of factors, k, is usually smaller than n, the numbe 
of variables (in this case species). This factor matri 
has the characteristic that when multiplied by its trans 
pose (rows and columns interchanged) it restores th 
original correlation matrix. In matrix notation 
R= ViVou 
where R is the correlation matrix, V, the factor matri 
and V,’ the transposed factor matrix. Basically th 
problem is to resolve the correlation matrix into 1 
latent roots and vectors (also referred to as eigenvaluc 
and eigenvectors) . 
Principal components analysis assumes that all « 
the variance of each species can be accounted for by 
set of factors common to all of the other species in tl 
community and lumps variance due to specific facto 
and error factors in with the common factors. In tl 
actual computation, the loadings (weights) of the fir 
factor on each species (the latent vector or eigenvector 
are calculated in such a way as to remove the maximuw 
amount of variance from the matrix as can be explaine 
by one factor. The effects of this factor are then sul 
tracted from the correlation matrix. A second fact 
is then calculated from this reduced correlation matri 
and so forth until the reduced correlation matrix co 
sists of essentially all zeros. 
These calculations have been carried out on da 
given by Hunter (1966). Hunter measured the speci 
populations of Drosophila at several sites in Colombi 
principally near Bogota. I have analyzed her data f 
“Pine Woods,” a government-protected pine forest ne 
Bogota. The census was carried out from Septemb« 
1961 to December, 1963 (28 months) by sweeping 
net over bait. In Hunter’s table for Pine Woods, t 
figures for each month are lumped, and the abundan 
of each species expressed as a percentage of the to’ 
Drosophila community. In cases where a species ft 
quency was less than 1 percent, it is listed only as presé! 
In my analysis when a species is listed as “present,” 
have considered it to be absent because individuals 
that species made up less than 1 percent of the tot 
Of the 11 species listed by Hunter, I have analyz 
only 10 because the 11th, “dreyfust 22,” was very ra 
