GSED 3.0 (January 2015)

Copyright © 1985-2015 Elizabeth M. Gillet. Email URL

GSED ("Genetic Structures from Electrophoresis Data") calculates measures of genetic variation within and among populations for the purpose of characterizing genetic structures in population genetic investigations. Calculations are based on the single- or multilocus frequency distributions of the states of one or more genetic traits in the populations. GSED implements a conceptually and mathematically unified system of data analysis developed at the Department of Forest Genetics and Forest Tree Breeding of the University of Göttingen.

New features:

  • menu-driven choice of options
  • extended tabular output file importable into spreadsheets
  • graphical representations of subpopulation differentiation "snails" in Windows Metafile and Postscript formats

GSED characterizes genetic structures in population genetic investigations for genetic traits of the following types:


  • Codominant DNA markers, such as microsatellites (SSR)
  • Isoenzyme markers, including null alleles
  • Any codominantly expressed gene marker in diploid individuals or tissue
  • Any gene marker in haploid individuals, tissue, or organelles, such as chloroplast or mitochondrial cytotypes


Single-locus distributions:

  • Allele frequencies among haploid maternal gametic contributions
  • Allele frequencies among haploid paternal gametic contributions
  • Allele frequencies at diploid loci
  • Diploid genotype frequencies

Multilocus distributions for arbitrary multilocus combinations:

  • Haplotype frequencies among maternal contributions
  • Haplotype frequencies among paternal contributions
  • Haplotype frequencies
  • Genotype frequencies.


Threshold frequency α for samples of the given size, such that the probability of detecting all types of frequency ≥α is at least 95% [4].
Measures of variation within populations:

  • Diversity v2 [3,8]
  • Total population differentiation δT [8,9]
  • Evenness e [10]

Measures of variation among populations:

  • Genetic distance d0 [1,2,3,5]
  • Subpopulation differentiation Dj and δ [6,7,9,11]
  • χ2 and G-tests of homogeneity

Analysis of genotypic structure:

  • Heterozygosity (observed proportion of heterozygosity Ho [12]
  • Conditional heterozygosity Hc of single-locus genotypes [3,12]
  • Degree of heterozygosity of multilocus genotypes) [3]
  • Test of Hardy-Weinberg structure at single loci
  • Test of product structure at single loci (ordered genotypes only)

Analysis of the gene pool across loci:

  • Within populations: Gene pool diversity v [8]; Hypothetical gametic diversity vgam [3]; Total population differentiation δT of the gene pool [8])
  • Among populations: Genetic distance d0 between gene pools [7]; Differentiation δ of subdivided gene pools [7])


GSED is compiled using the GNU Fortran95 compiler for Win32 and Linux (SuSE 11.0).

Plots and widgets are constructed using routines of the scientific data plotting software DISLIN Copyright © 2009 Helmut Michels

Send comments, suggestions, and bug reports to Email


Download GSED 3.0 program package, including executable, example input, and GSED 3.0 User's Manual

Current version:


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

[2] Gregorius H.-R. 1974. On the concept of genetic distance between populations based on gene frequencies. Proc. Joint IUFRO Meeting, S02.04.1-3, Stockholm, Session I, 17-26.

[3] Gregorius H.-R. 1978. The concept of genetic diversity and its formal relationship to heterozygosity and genetic distance. Mathematical Biosciences 41, 253-271.

[4] Gregorius H.-R. 1980. The probability of losing an allele when diploid genotypes are sampled. Biometrics 36, 643-652.

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

[6] Gregorius H.-R. 1984. Measurement of genetic differentiation in plant populations. Pp. 276-285 in: Gregorius, H.-R. (ed.). Population Genetics in Forestry. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo.

[7] Gregorius H.-R., Roberds J.H. 1986. Measurement of genetical differentiation among subpopulations. Theoretical and Applied Genetics 71, 826-834.

[8] Gregorius H.-R. 1987. The relationship between the concepts of genetic diversity and differentiation. Theoretical and Applied Genetics 74, 397-401.

[9] Gregorius H.-R. 1988. The meaning of genetic variation within and between subpopulations. Theoretical and Applied Genetics 76, 947-951.

[10] Gregorius H.-R. 1990. A diversity-independent measure of evenness. American Naturalist 136, 701-711.

[11] Gregorius H-R. 1996. Differentiation between populations and its measurement. Acta Biotheoretica 44, 23-36.

[12] Gregorius H.-R., Krauhausen J., and Müller-Starck G. 1986. Spatial and temporal genetic differentiation among the seed in a stand of Fagus sylvatica L. Heredity 57, 255-262.

GSED 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. GSED 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. See the GNU General Public License, a copy of which is contained in the file COPYING included in the download file, or see

GSED implements the scientific data plotting software DISLIN Copyright ©2009 Helmut Michels