DeltaS 2.1 (August 2008)

Copyright © 2003-2010 Elizabeth M. Gillet (excepting code of RELAX-IV [1]). Email URL

DeltaS calculates the measure of pairwise distance Δ between populations, which takes into account the frequencies of the trait states (types) and the pairwise differences between the types. For each pair of populations, Δ expresses the minimum degree to which the frequency distribution of the types within one population must be transformed in order to make it match the distribution in the other population ([2]). Δ reduces to the absolute genetic distance d0 ([3], [4]), if differences between types are equal to 1.


Information requested by query:

  • Number of POPULATIONS (integer)
  • Number of TYPES (integer)
  • FORM of input of TRAIT DIFFERENCES d(i,j) between types i and j:
    "U" for UPPER DIAGONAL differences (i>j) or
    "L" for LOWER DIAGONAL differences (i) (default="L")
  • TRAIT DIFFERENCES d(i,j) between types
  • Maximum NUMBER of matrix COLUMNS per line of output at 8 characters per column + 9 leading characters: Larger matrices are printed blockwise (default="8" columns per line)
  • Show OPTIMAL TRANSFORMATIONS in output? "Y"=yes (default="N")
  • FREQUENCIES of the TYPES in the POPULATIONS: All integer and decimal entries are normalized through division by their population sum.

For queries that request more than one number, the numbers can be separated by commas, blanks, tabs, or carriage returns ("Return").

The input can be entered in two ways:

  • Start DeltaS, which opens a console window, and type in the answers to the queries.
  • Prepare an input file with a text editor in advance, for example as a file named "input.txt", in the DeltaS directory. Run DeltaS by opening a console window (e.g. MS-DOS window, xterm in Linux), change the directory to the DeltaS directory, and type in the command

    "DeltaS.exe < input.txt" (for W32) or "./Delta < input.txt" (for Linux)


Besides being printed to the console window, the output is printed to the following files:

"outsummary.txt" and screen: Summary of results, comprising

  • Trait differences between types
  • Frequencies of the types in the populations
  • Optimal transformations, if selected
  • Pairwise distances Δ between populations
  • Pairwise distances d0 between populations

"outdelta.txt": Pairwise distances Δ between populations (input for other programs)

"outd0.txt": Pairwise distances d0 between populations (input for other programs)


  • DeltaS is compiled using the GNU Fortran compiler g77 for Windows (32-bit Win98 and WinXP) and the GNU Fortran compiler gfortran for Linux (SuSE 10.3).
  • The minimum degree of transformation is a solution of the Transportation Problem, for which DeltaS incorporates open source code from the program RELAX-IV ( [1].
  • Send comments, suggestions, and bug reports to

DOWNLOAD DeltaS (Version 2.1, August 2008)

DeltaS for (91,221)
Contents: DeltaS.exe, README, COPYING

DeltaS for Linux:deltas-2.1-linux.tar.gz (158,266)
Contents: DeltaS, README, COPYING


Bugfix of version 2.0 for input of "FREQUENCIES of the TYPES in the POPULATIONS? All integer and decimal entries are normalized through division by their population sum": Decimal entries are now supported.


[1] Bertsekas D.P., Tseng P. 1994. RELAX-IV: A faster version of the RELAX code for solving minimum cost flow problems.

[2] Gillet E.M., Gregorius H.-R., Ziehe M. 2004. May inclusion of trait differences in genetic cluster analysis alter our views? Forest Ecology and Management 197, 149-158.

[3] Gregorius H.-R. 1974. Genetischer Abstand zwischen Populationen. I. Zur Konzeption der genetischen Abstandsmessung. Silvae Genetica 23: 22-27.

[4] Gregorius H.-R. 1984. A unique genetic distance. Biometrical Journal 26:13-18.

[5] Gregorius H.-R., Gillet E.M., Ziehe M. 2003. Measuring differences of trait distributions between populations. Biometrical Journal 45: 959-973.

DeltaS is free software: you can redistribute it under the terms of the GNU General Public License (GPL) v.3, as published by the Free Software Foundation. DeltaS is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of merchantability or fitness for a particular purpose. Reassembling is not permitted. For details see the GNU General Public License, a copy of which is contained in the file COPYING included in the download file, or see

Department of Forest Genetics and Forest Tree Breeding,
Büsgen-Institute, University of Göttingen

Abteilung Forstgenetik und Forstpflanzenzüchtung, Büsgen-Institut, Universität Göttingen

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Last update of this page: November 17, 2008