Le Quatrième Coin/The 4thCorner
Pierre LegendreMay 1996
Département de sciences biologiques
Université de Montréal
The 4thcorner method, which was presented at the NT95 meeting, offers a way of analyzing relationships between the supplementary variables associated with the rows and columns of a binary (presenceabsence) data table (Legendre et al., 1997). The problem which motivated the development of the method is the following: How does one relate the biological and behavioral characteristics of animals (matrix B) to habitat characteristics of the locations at which they are found (matrix C), given the distribution of animals across sampling sites (matrix A)? Statistical parameters in matrix D are estimated by the following matrix operation: D = C A' B. They are tested for significance using a permutation procedure. Random permutations of matrix A can be obtained under four different permutational models. Documents available for distribution include:

Macintosh version
 Fortran source code
 Compiled versions of the program for Macintosh computers using 680x0, 680x0 + FPU, or PowerPC processor
 Program documentation, in Word 5 (Macintosh)
 A folder containing three ASCII files, called A1, B1 and C1, corresponding to Example 1 of the documentation
For the researcher with a huge dataset, we have compiled a version (PowerMacintosh only) that can accomodate 550 species, 800 stations and 50 behavioral / habitat characteristics. The usual program limits are 300, 30 and 30 respectively. This bigger version requires about 15 megabytes of RAM to function, it will not work in less. So if you have a smaller problem, please use the regular version above.

DOS/Textonly version
 Fortran source code.
 16 and 32bit compiled versions of the program for DOS computers
 Program documentation, in Word for Windows 2
 A folder containing three ASCII files, called A1, B1 and C1, corresponding to Example 1 of the documentation
 Download the Tiahura transect fish data set Text files of the data used in the journal article below
Legendre, P., R. Galzin & M. L. HarmelinVivien. 1997. Relating behavior to habitat: solutions to the fourthcorner problem. Ecology 78: 547562.