The Use of Factor Analysis in Modeling 
Natural Communities of Plants and Animals 
Robert W. Poole 
THE ProspLeM oF Mope.inc ComMunitiss of plants or 
animals can be studied either by observing the charac- 
teristics of the community as a whole or by determining 
the interactions among and within individual species. 
At the community level most attention has been focused 
on descriptive community analysis, species diversity, and 
energy flow. At the one- and two-species levels some 
aspects of the problem that have been, and are being, 
intensively studied are population demography, preda- 
tion, competition, parasitism, and spatial distribution. 
These basic interactions have been reasonably well de- 
scribed, and they have been integrated in the modeling 
of spruce budworm populations in Canada (Morris 
1963). However, even this one-species model is very 
complex and requires the determination of a large 
number of parameters. 
It is just as conceivable to go from the community 
level to the individual species as from the species to the 
community. The purpose of. this paper is to explore 
this approach using a statistical technique known as 
factor analysis. Factor analysis is a statistical technique 
for picking out the underlying factors causing the vari- 
ance in a set of variables. 
Factor analysis originated in the psychological sci- 
ences but is now also being used in the biological sci- 
ences. Its first uses in biology were by Goodall (1954) 
and Sokal & Hunter (1955), and it has since been used 
extensively in numerical taxonomy (e.g. Sokal & Sneath 
1963; Schnell 1970) in the delimiting of the natural 
associations of plants (e.g. Dagnelie 1965) and in palaeo- 
ecology by Reyment (1963). 
Factor analysis, primarily the form known as prin- 
‘ipal components analysis, has been used in biology for 
he most part as a classification technique, although there 
lave been some attempts to make associations between 
nvironmental variables and species using correlation co- 
‘ficients in a factor-analysis framework (e.g. Dagnelie 
1965). Factor analysis was originally developed to esti- 
nate and define the factors causing the observed re- 
ponses in a series of variables and is here used in this 
€nse rather than as a classification technique. 
This paper is divided into three parts. The first 
ives a brief review of basic ecological principles nec- 
ssary for the following two sections. The second section 
lescribes the statistical procedures considered and the 
nalysis of a specific example. The third section con- 
ee 
, This paper is published by authority of the State of Illinois, IRS 
h. 127, Par. 58.1 - Dr. Robert W. Poole is Assistant Taxonomist, 
ection of Faunistic Surveys and Insect Identification, Illinois Natural 
listory Survey, Urbana. 
siders the assumptions of the factor analytic model and 
compares them to the initial ecological generalities to 
see if the model really does mirror the workings of the 
community or if it only produces a set of mathematically 
correct but ecologically meaningless numbers. I have 
tried to emphasize the implications of the assumptions 
underlying the factor analysis and deemphasize the 
mathematics. Many university computing centers have 
the programs used in this paper, and interested persons 
can find the mathematics underlying the technique in 
Harman (1967). 
I wish to express my appreciation to those persons 
who have either read the manuscript or helped with 
the analysis of the example used in this paper: Dr. 
George F. Kawash of the Department of Psychology, 
University of Illinois; Dr. K. W. Dickman of the 
SOUPAC office of the Department of Computer Sci- 
ence, University of Illinois; Dr. Robert H. Whittaker 
of the Division of Biological Sciences, Cornell Univer- 
sity; Dr. Richard B. Root of the Department of En- 
tomolgy, Cornell University; Mrs. Kathleen Eickwort 
of the Department of Entomology, Cornell University; 
and my wife Beverly. I also wish to thank Dr. Philip 
W. Smith and O. F. Glissendorf of the Illinois Natural 
History Survey for their editorial contributions to the 
paper. 
FACTORS AND SPECIES POPULATIONS 
A population of an animal rarely stays at a constant 
level; usually it is either increasing or decreasing. 
Whether and how much a population increases or de- 
creases depends on the environmental factors controlling 
the limits of that population. If conditions are favor- 
able, the population increases; if they are not favor- 
able, it decreases. A species population can be affected 
by several factors, and the factors may be interacting 
among themselves. This basic relationship is diagram- 
med in Fig. 1. Not all of the factors are of equal im- 
portance to the species population, one factor usually 
being more important than the others. If the effect of 
a factor on a population depends on the density of the 
population, it is referred to as a density-dependent fac- 
tor, and if it does not depend on density, it is referred 
to as a density-independent factor. 
In a community of two or more species, a factor in- 
fluencing one species may also influence other species 
in the community. The effect of this common factor 
may vary from species to species, being more important 
