Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A model for genetic relationship among offspring from open-pollinated plant populations

  • 26 Accesses

  • 4 Citations


Based on monoecious, diploid plant species, a model is constructed to determine genetic relationship within the seed production of an open-pollinated population, characterized by its rates of self-fertilization, population density and mode of pollen dispersal. Genetic relationship is measured by the coefficient of inbreeding of a seed produced by a mother plant located at a specified place, or by the coefficient of kinship between two seeds, produced from the same mother plant or produced from two different mother plants separated by a certain distance. The influence of the single parameters on these coefficients is demonstrated by some typical examples, which show that dimensionality of the habitat (one- or two-dimensional), as well as, range and type of pollen dispersal, has little influence on the relationship between seed produced from the same mother plant and, on the other hand, emphasize the important role of the rate of self-fertilization and population density. Some remarks on how to apply Wright's concept of neighbourhood to continuous plant populations close this paper.

This is a preview of subscription content, log in to check access.


  1. Fleming, W.H.; Chau-Hsing Su: Some One-Dimensional Migration Models in Population Genetics Theory. Theor. Popul. Biol. 5, 431–449 (1974)

  2. Gregorius, H.-R.: A model for genetic relationship in areally continuous plant population. (1975, in preparation)

  3. Malécot, G.: Les mathématiques de l'hérédité, Vol.1. Paris: Masson et Cie. 1948

  4. Malécot, G.: Quelques schemas probabilities sur la variabilité des populations naturelles. Ann. Univ. Lyon, Sciences, Section A 13, 37–60 (1950)

  5. Malécot, G.: Identical loci and relationship. Proc. 5th Berkeley Symp. Math. Stat. Prob. 4, 317–332 (1967)

  6. Malécot, G.: The Mathematics of Heredity. San Francisco: Freeman & Co. 1969

  7. Maruyama, T.: Rate of decrease of genetic variability in a two-dimensional continuous population of finite size. Genetics 70, 639–651 (1972)

  8. Squillace, A.E.: Average Genetic Correlations Among Offspring From Open-Pollinated Forest Trees. Silvae Genetica (1975, in press)

  9. Wright, S.: Isolation by distance. Genetics 23, 114–138 (1943)

  10. Wright, S.: Isolation by distance under diverse systems of mating. Genetics 31, 39–59 (1946)

Download references

Author information

Additional information

Communicated by H. Stubbe

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gregorius, H.-. A model for genetic relationship among offspring from open-pollinated plant populations. Theoret. Appl. Genetics 46, 109–115 (1975). https://doi.org/10.1007/BF00281649

Download citation


  • Plant Species
  • Population Density
  • Seed Production
  • Genetic Relationship
  • Single Parameter