Abstract
A method to compute identity coefficients of two genes in the stepping-stone model with partial selfing is developed. The identity coefficients in partially selfing populations are computed from those in populations without selfing as functions of s (selfing rate), m (migration rate), N (subpopulation size), n (number of subpopulations) and u (mutation rate). For small m, 1/N and u, it is shown that approximate formulae for the identity coefficients of two genes from different individuals are the same as those in random mating populations if we replace N in the latter with N(1−s/2). Thus, the effects of selfing on genetic variability are summarized as reducing variation within subpopulations and increasing differentiation among subpopulations by reducing the subpopulation size. The extent of biparental inbreeding as measured by the genotypic correlation between truly outcrossed mates was computed in the one-dimensional stepping-stone model. The correlation was shown to be independent of the selfing rate and starts to fall off as the migration rate increases when mN is larger than 0.1.
Similar content being viewed by others
Article PDF
References
Brown, A H D. 1990. Genetic characterization of plant mating systems. In: Brown A. H. D., Clegg, M. T., Kahler, A. L. and Weir, B. S. (eds) Plant Population Genetics, Breeding, and Genetic Resources, pp. 145–162. Sinauer Associates, Sunderland, MA.
Caballero, A, and Hill, W G. 1992. Effective size of nonrandom mating populations. Genetics, 130, 909–916.
Clegg, M T. 1990. Molecular diversity in plant populations. In: Brown, A. H. D., Clegg, M. T., Kahler, A. L. and Weir, B. S. (eds) Plant Population Genetics, Breeding, and Genetic Resources, pp. 98–115. Sinauer Associates, Sunderland, MA.
Ennos, R A, and Clegg, M T. 1982. Effect of population substructuring on estimates of outcrossing rate in plant populations. Heredity, 48, 283–292.
Garza, J C, Slatkin, M, and Freimer, N B. 1995. Microsatellite allele frequencies in humans and chimpanzees, with implications for constraints on allele size. Mol Biol Evol, 12, 594–603.
Golding, G B, and Strobeck, C. 1980. Linkage disequilibrium in a finite population that is partially selfing. Genetics, 94, 777–789.
Griffiths, R C. 1981. The number of heterozygous loci between two randomly chosen completely linked sequence of loci in two subdivided population models. Math Biol, 12, 251–261.
Hedrick, P W, and Cockerham, C C. 1986. Partial inbreeding: equilibrium heterozygosity and the heterozygosity paradox. Evolution, 40, 856–861.
Karron, J D, Thumser, N N, Tucker, R, and Hessenauer, A J. 1995. The influence of population density on outcrossing rates in Mimulus ringens. Heredity, 75, 175–180.
Kimura, M. 1953. “Stepping stone” model of population. Ann Rep Nat Inst Genet, 3, 63–65.
Kimura, M. 1968. Evolutionary rate at the molecular level. Nature, 217, 624–626.
Kitamura, K, Rahman, M Y B A, Ochiai, Y, and Yoshimaru, H. 1994. Estimation of the outcrossing rate on Dryobalanops aromatica Gaertn. f. in primary and secondary forests in Brunei, Borneo, Southeast Asia. Pl Sp Biol, 9, 37–41.
Maruyama, K, and Tachida, H. 1992. Genetic variability and geographical structure in partially selfing populations. Jap J Genet, 67, 39–51.
Maruyama, T. 1977. Stochastic Problems in Population Genetics. Springer, Berlin.
Murawski, D A, and Hamrick, J L. 1991. The effect of the density of flowering individuals on the mating systems of nine tropical tree species. Heredity, 67, 167–174.
Murawski, D A, and Hamrick, J L. 1992. The mating system of Cavanillesia platanifolia under extremes of flowering-tree density: a test of predictions. Biotropica, 24, 99–101.
Nei, M, and Li, W-H. 1979. Mathematical model for studying genetic variation in terms of restriction endonucleases. Proc Natl Acad Sci USA, 76, 5269–5273.
Ohta, T, and Kimura, M. 1973. A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genet Res, 22, 201–204.
Pollak, E. 1987. On the theory of partially inbreeding finite populations. I. Partial selfing. Genetics, 117, 353–360.
Röder, M S, Plaschke, J, König, S U, Börner, A, Sorrels, M E, Tankskey, S D, and Ganal, M W. 1994. Abundance, variability and chromosomal location of microsatellites in wheat. Mol Gen Genet, 246, 327–333.
Slatkin, M. 1991. Inbreeding coefficients and coalescence times. Genet Res, 58, 167–175.
Slatkin, M, and Voelm, L. 1991. FST in a hierarchical island model. Genetics, 127, 627–629.
Tachida, H. 1985. Joint frequencies of alleles determined by separate formulations for mating and mutation systems. Genetics, 111, 963–974.
Terauchi, R. 1994. A polymorphic microsatellite marker from the tropical tree Dryobalanops lanceolata (Dipterocarpaceae). Jap J Genet, 69, 567–576.
Waller, D M, and Knight, S E. 1989. Genetic consequences of outcrossing in the cleistogamous annual, Impatiens capensis. II. Outcrossing rates and genotypic correlations. Evolution, 43, 860–869.
Watterson, G A. 1975. On the number of segregating sites in genetical models without recombination. Theor Pop Biol, 7, 256–276.
Yang, G P, Saghai Maroof, M A, Xu, C G, Zhang, Q, and Biyashev, R M. 1994. Comparative analysis of microsatellite DNA polymorphism in landraces and cultivars of rice. Mol Gen Genet, 245, 187–194.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tachida, H., Yoshimaru, H. Genetic diversity in partially selfing populations with the stepping-stone structure. Heredity 77, 469–475 (1996). https://doi.org/10.1038/hdy.1996.173
Received:
Issue Date:
DOI: https://doi.org/10.1038/hdy.1996.173