8 
temperature are available, to include maximum temper- 
ature in the data matrices as another variable. If maxi- 
mum temperature as a variable loads heavily with one 
factor and little with other factors, it is likely that this 
factor is in some way related to maximum tempera- 
ture. Determining the identity of every significant fac- 
tor is not easy and depends on extensive field work. 
However, factor analysis indicates how many significant 
factors to look for, and the weightings of these factors 
on every species in the community. Even if a factor 
is interpreted incorrectly, as maximum temperature, the 
use of maximum temperature measurements for that 
factor may still give correct predictive answers, a pro- 
cedure not very scientific but pragmatically important. 
It must be emphasized that the mathematical factors 
never exactly correspond to the environmental factors, 
but they may be so heavily loaded on the environmental 
factors that measurements of the environmental factors 
can be used as approximations to the mathematical 
factors. 
The other problem in identification is the rotation 
of the factors derived from the principal axis method 
analysis to some position where they correspond to real 
parts of the environment. If the factors are not rotated, 
the hypothesis is that the factors tend to influence all 
of the variables; however, if rotated to simple structure, 
it is assumed that the real factors tend to influence 
significantly only a few of the variables. In a real situa- 
tion neither hypothesis may be the correct one. For 
example, if in a community of insects rainfall was im- 
portant to all of the species, but at the same time each 
species was restricted in its choice of food plants, there 
would be one factor influencing all of the species, and 
several other factors that influenced only a few variables 
each. This situation clearly does not fit the hypothesis 
behind the factors as they come from the principal axis 
analysis or after rotation of the factors to simple struc- 
ture. 
It is also possible to rotate the factors to fit a specific 
hypothesis, but because it is not possible to formulate a 
specific hypothesis for the example used in this paper, 
this rotation has not been done. The most difficult prob- 
lem connected with this type of community analysis 
should now be apparent. To rotate the calculated fac- 
tors to a position where they represent real factors of the 
environment, a correct hypothesis of the type of factors 
involved and the relative numbers of each (such as two 
factors influencing all of the species and three factors in- 
fluencing only two or three species) is needed. The prob- 
lem is what stage in the identification of factors is to be 
carried out first—the identification of factors or the rota- 
tion of the calculated factors to fit actual factors in the 
environment. Each is partially dependent on the other. As 
a working technique it should be possible, by extensive 
field work and experimentation, to formulate a rough hy- 
pothesis as to the percentage of significant factors that will 
influence a limited number of the species. For example, 
it might be known that rainfall influences a certain 
number of species, and there is reason to believe that 
it is important to virtually all the species in the com- 
munity. On the other hand, it might be known that 
most species in the community tend to be limited in 
their selection of food plants. Given four significant 
factors, a rough hypothesis might be that one factor in- 
fluences all of the species, and three others influence 
only a few of them. From the set of calculated factors, 
the first (the one accounting for the most variance) 
is likely to be factor 1 of the hypothesis, with the other 
three factors being fitted to the groups of species that 
they load most heavily with. The factors could then be 
rotated to fit the rough hypothesis, and the hypothesis 
could possibly be reformulated as a result of the rota- 
tion. 
Every possible rotation of the factor vectors is, of 
course, an approximation to the real situation. Some 
of the approximations will be good, others not so good. 
A question of practical importance is whether or not 
the answers derived from each rotation are much dif- 
ferent from each other. The answer to this question 
will only come through use of the factor-analysis tech- 
nique. In the example used in this paper, the differences 
between the factor loadings of the orthogonal factors 
and the factors rotated to simple structure are slight. 
It has usually been found in psychology that the changes 
in factor loadings by rotation to simple structure are 
slight (Kawash, personal communication) . Simple struc- 
ture rotation tends to rotate out small error factors and 
is used more for that reason than for the hypothesis it 
represents (Cattell 1965). Even if the factors are not 
correctly rotated, the appoximation may still be close 
Computational Procedure 
Having carried out a principal components analysi 
of the data and having partially explained the problem: 
of rotation and communalities, the complete facto 
analysis will now be carried out. In the following sec 
tion the predictive equations are formulated and _ th 
possible usefulness of the technique is discussed. 
As discussed in the preceding section, a possible aic 
in the identification of the factors is to place measure 
ments of presumed factors into the correlation matrix a 
variables and then note if any of the calculated factor 
load heavily on them. Hunter (1966) gave data for rain 
fall, mean maximum temperature, and mean minimun 
temperature for each month of her study. She assume¢ 
that rainfall was one of the most important factor: 
pointing out that its effect probably acted upon th 
larvae, or perhaps initiated egg laying in the adult: 
Hunter stated that the average time for developmen 
from egg to adult is about 2 months. Because thes 
three environmental measurements are more likely to b 
important to the larvae that later give rise to the adult 
than to the adults directly, the three measurements hav 
been entered as variables with the species with a 2 
month lead. 
The correlation matrix of the 13 variables was com 
