@) 
TaBLe 1.— Correlations among the frequencies of 10 species of Drosophila over a period of 28 months at Pines Woods (near 
Bogota, Colombia). 
Ms 8 
z : : % 3 
8 8 S$ 8 S 
& os a 8 rm op 
: E : s S 2 S 
S S 8 3 = & S a 8 : 
S 3 v & & s 8 5 S aS 
S : S s & S S 5 S 
S g, S 3 < & 5 § & & 
melanogaster 1.00 
pseudoobscura ay) 1.00 
bandetrantorum 34 6} 1.00 
“tripunctata 20” {0 46 Sy 1.00 
hydei -.08 —.09 .02 —.00 1.00 
immigrans 09 24 ES D7 = 18 1.00 
viracochi stil lies =(,() ey) sore. 02 1.00 
mesophragmatica —.42 1/9 = 30) =i 5) —.09 = DE = PAl 1.00 
brncict 43 45 61 .28 —.09 .05 —-Als5) —.41 1.00 
Zasict =a 18) = 20 lO BOW =O) 58 .O1 =I) = S 1.00 
The correlation matrix was calculated (Table 1) Taste 3.— Computed factor loadings from the principal 
using the Pearson product-moment correlation coeffi- components analysis on the 10 species of Drosophila. 
cient and factored using the principal axis method. The 
resulting factors are shown in Table 2, which also shows meas es ee 
melanogaster —.4750 —.3843 —.0687 
Ta BEC leulated fact f feels : pseudoobscura = O08 SDP .0020 
BLE | alculated lactors from the principal compon ie ee pe ~ 9002 ~ 9406 1279 
ents analysis. : 
“tripunctata 20” —.6886 .4540 —.1654 
Poe Cui hydei .0789 = O308 .7648 
; ; immigrans —.5498 .6897 —.0449 
Factor Variance Variance Percent wracoeh: 41171 0108 8662 
1 3.7991 37.9914 37.9914 mesophragmatica 9091 = Sys) =| 
2 1.9637 19.6365 57.5579 brnceict = 0233 — 448] —.1364 
3 1.5131 15.1310 72.6889 gasici —.0914 -8906 0226 
+ 0.9162 9.1621 81.8510 
: ee Dts Wares and factor 2 a loading of .03, factor 1 would be more 
7 0.994] D O414 97.2603 important to the variable than would factor 2. 
8 0.1728 Lo AAS 98.9885 R 
9 0.0971 0.9712 99.9596 orator | : | 
10 0.0040 0.0403 100.0000 The set of factors arrived at in the preceding section 
that the first three factors account for about 73 percent 
of the variance in the correlation matrix. The total 
1umber of factors extracted by the principal axis method 
annot exceed the number of variables. Each of the 
‘alculated factors is affected in part by the inclusion 
f error variance and variance due to specific rather 
han common factors. Therefore the factors become 
nore and more trivial and unreliable as the factoring 
roceeds, so that the factors calculated after the first 
ew have no real meaning. A commonly used breaking 
oint in factoring is when the eigenvalue of the factor 
alls below 1.00 (listed under variance in Lables 2). 
Jsing this criterion, the first three factors are signifi- 
ant. The factor loadings of each factor on the 10 
pecies are given in Table 3. Factor loadings are a 
ype of correlation between a factor and a variable, or 
tore specifically, the weight of each factor in account- 
1g for the variance of a given variable. In other words 
factor 1 had a loading of .47 on a given variable, 
and the loadings of the factors on the variables are only 
one of an essentially infinite number of possibilities. In 
other words there is an infinite number of factor matrices 
that when multiplied by their transpose will restore the 
original correlation matrix. The factors as they come 
out of the principal axis method are orthogonal to each 
other (uncorrelated). These calculated factors do not 
necessarily correspond in any way with the real attributes 
of the environment controlling the fluctuations of the 
species populations. One of this infinite array of answers 
is the correct one, however, and the problem is to find 
it. The variables can be plotted on each factor as has 
been done in Fig. 3 for factors 1 and 2. Factor 3 could 
be included and the variables would then be in a three- 
dimensional space. The addition of a fourth factor 
would be in hyperspace. Any of the possible solutions 
to the problem can be arrived at by rotating these axes 
(factors) and reading off the new factor loadings on 
each variable. This is an oversimplified explanation of 
rotation and a more complete account can be found 
in Cattell (1965) and Harman (1967). 
