Recent Advances in Correlation Studies of Spatial Patterns of Genetic Variation

  • Bryan K. Epperson
Part of the Evolutionary Biology book series (EBIO, volume 27)

Abstract

The spatial distribution of genetic variation has long been recognized as an important feature of population genetics. Our understanding of the basic spatial-temporal dynamics of genetic variation in populations continues to improve through theoretical and experimental studies. Dating back to the original work of Wright (1943) and Malécot (1948), theoretical work has indicated that spatial distributions of genetic variation should often differ strongly from random or uniform distributions. Nonrandomness, or spatial structuring, can strongly influence, and be strongly influenced by, many other important aspects of population genetics, including mating system, individual fitness, inbreeding depression, and the action of various other forms of natural selection, including environmental selection (e.g., Sokal, 1979; Epperson, 1990a). A large body of experimental studies of spatial structure of genetic variation confirms the theoretical predictions. Extensive reviews include those by Endler (1977), Bradshaw (1984), Nagylaki (1986), and Slatkin (1985, 1987).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allard, R. W., 1975, The mating system and micro-evolution, Genetics 79:115–126.PubMedGoogle Scholar
  2. Argyres, A. Z., and Schmitt, J., 1991, Microgeographical genetic structure of morphological and life history traits in a natural population of Impatiens capensis, Evolution 45:178–189.Google Scholar
  3. Aroian, L. A., 1985, Time series in m dimensions: Past, present and future, in: Time Series Analysis: Theory and Practice 6 (O. D. Anderson, J. K. Ord, and E. A. Robertson, eds.), pp. 241–261, Elsevier/North-Holland, Amsterdam.Google Scholar
  4. Barbujani, G., 1987, Autocorrelation of gene frequencies under isolation by distance, Genetics 117:777–782.PubMedGoogle Scholar
  5. Bartlett, M. S., 1971, Physical nearest-neighbor models and non-linear time-series, J. Appl. Prob. 8:222–232.CrossRefGoogle Scholar
  6. Bennett, R. J., 1979, Spatial Time Series, Pion, London.Google Scholar
  7. Bennett, R. J., Haining, R. P., and Wilson, A. G., 1985, Spatial structure, spatial interaction, and their integration: A review of alternative models, Environ. Planning A 17:625–645.CrossRefGoogle Scholar
  8. Bodmer, W. F., 1960, Discrete stochastic processes in population genetics, J. R. Stat. Soc. B 22:218–236.Google Scholar
  9. Bodmer, W. F., and Cavalli-Sforza, L. L., 1968, A migration matrix model for the study of random genetic drift, Genetics 59:565–592.PubMedGoogle Scholar
  10. Box, G. E. P., and Jenkins, G. M., 1976, Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco.Google Scholar
  11. Bradshaw, A. D., 1984, Ecological significance of genetic variation between populations, in: Perspectives on Plant Population Ecology (R. Dirzo and J. Sarukhan, eds.), pp. 213–228, Sinauer, Sunderland, Massachusetts.Google Scholar
  12. Brown, A. H. D., and Albrecht, L., 1980, Variable outcrossing and the genetic structure of predominantly self-pollinated species, J. Theor. Biol. 82:591–606.PubMedCrossRefGoogle Scholar
  13. Brown, B. A., and Clegg, M. T., 1984, Influence of flower color polymorphism on genetic transmission in a natural population of the common morning glory, Ipomoea purpurea, Evolution 38:796–803.Google Scholar
  14. Campbell, D. R., and Dooley, J. L., 1992, The spatial scale of genetic differentiation in a hummingbird-pollinated plant: Comparison with models of isolation by distance, Am. Nat. 139:735–748.CrossRefGoogle Scholar
  15. Cavalli-Sforza, L. L., and Feldman, M. W., 1990, Spatial subdivision of populations and estimates of genetic variation, Theor. Popul. Biol. 37:3–25.PubMedCrossRefGoogle Scholar
  16. Charlesworth, D., and Charlesworth, B., 1990, Inbreeding depression with heterozygote advantage and its effect on selection for modifiers changing the outcrossing rate, Evolution 44:870–888.CrossRefGoogle Scholar
  17. Cliff, A. D., and Ord, J. K., 1981, Spatial Processes, Pion, London.Google Scholar
  18. Dewey, S. E., and Heywood, J. S., 1988, Spatial genetic structure in a population of Psychotria nervosa. I. Distribution of genotypes, Evolution 42:834–838.CrossRefGoogle Scholar
  19. Ellstrand, N. C., Torres, A. M., and Levin, D. A., 1978, Density and the rate of apparent outcrossing in Helianthus annus (Asteraceae), Syst. Bot. 3:403–407.CrossRefGoogle Scholar
  20. Endler, J. A., 1977, Geographic Variation, Speciation, and Clines, Princeton University Press, Princeton, New Jersey.Google Scholar
  21. Ennos, R. A., and Clegg, M. T., 1982, Effect of population substructuring on estimates of outcrossing rate in plant populations, Heredity 48:283–292.CrossRefGoogle Scholar
  22. Epperson, B. K., 1983, Multilocus genetic structure of natural populations of lodgepole pine, Ph.D. dissertation, Department of Genetics, University of California, Davis.Google Scholar
  23. Epperson, B. K., 1990a, Spatial patterns of genetic variation within plant populations, in: Plant Population Genetics, Breeding, and Genetic Resources (A. H. D. Brown, M. T. Clegg, A. L. Kahler, and B. S. Weir, eds.), pp. 229–253, Sinauer, Sunderland, Massachusetts.Google Scholar
  24. Epperson, B. K., 1990b, Spatial autocorrelation of genotypes under directional selection, Genetics 124:757–771.PubMedGoogle Scholar
  25. Epperson, B. K., 1992, Spatial structure of genetic variation within populations of forest trees, New Forests 6:257–278.CrossRefGoogle Scholar
  26. Epperson, B. K., 1993, Spatial and space-time correlations in systems of subpopulations with genetic drift and migration, Genetics 133:711–727.PubMedGoogle Scholar
  27. Epperson, B. K., (submitted), Spatial and space-time correlations in systems of subpopulations with stochastic migration, Theor. Popul. Biol., submitted.Google Scholar
  28. Epperson, B. K., and Allard, R. W., 1984, Allozyme analysis of the mating system in lodgepole pine populations, J. Hered. 75:212–214.Google Scholar
  29. Epperson, B. K., and Allard, R. W., 1987, Linkage disequilibrium between allozymes in natural populations of lodgepole pine, Genetics 115:341–352.PubMedGoogle Scholar
  30. Epperson, B. K., and Allard, R. W., 1989, Spatial autocorrelation analysis of the distribution of genotypes within populations of lodgepole pine, Genetics 121:369–377.PubMedGoogle Scholar
  31. Epperson, B. K., and Clegg, M. T., 1986, Spatial autocorrelation analysis of flower color polymorphisms within substructured populations of morning glory (Ipomoea purpurea), Am. Nat. 128:840–858.CrossRefGoogle Scholar
  32. Epperson, B. K., and Clegg, M. T., 1987, Frequency-dependent variation for outcrossing rate among flower color morphs of Ipomoea purpurea, Evolution 41:1302–1311.Google Scholar
  33. Feldman, M. W., and Christiansen, F. B., 1975, The effect of population subdivision on two loci without selection, Genet. Res. 24:151–167.CrossRefGoogle Scholar
  34. Felsenstein, J., 1975, A pain in the torus: Some difficulties with models of isolation by distance, Am. Nat. 109:359–368.CrossRefGoogle Scholar
  35. Fenster, C. B., 1991, Gene flow in Chamaecrista fasciculata. II. Gene establishment, Evolution 45:410–422.CrossRefGoogle Scholar
  36. Fisher, R. A., and Ford, E. B., 1947, The spread of a gene in natural conditions in a colony of the moth Panaxia dominula L., Heredity 1:143–174.CrossRefGoogle Scholar
  37. Fix, A. G., 1975, Fission-fusion and lineal effect: Aspects of the population structure of the Semai Senoi of Malaysia, Am. J. Phys. Anthropol. 43:295–302.PubMedCrossRefGoogle Scholar
  38. Fix, A. G., 1978, The role of kin-structured migration in genetic microdifferentiation, Ann. Hum. Genet. 41:329–339.PubMedCrossRefGoogle Scholar
  39. Fix, A. G., 1993, Kin-structured migration and isolation by distance, Hum. Biol. 65:193–210.PubMedGoogle Scholar
  40. Fleming, W. H., and Su, C.-H., 1974, Some one-dimensional migration models in population genetics theory, Theor. Popul. Biol. 5:431–449.PubMedCrossRefGoogle Scholar
  41. Haining, R. P., 1977, Model specification in stationary random fields, Geogr. Anal. 9:107–109.CrossRefGoogle Scholar
  42. Haining, R. P., 1978, The moving average model for spatial interaction, Trans. Inst. Br. Geogr. 3:202–225.CrossRefGoogle Scholar
  43. Haining, R. P., 1979, Statistical test and process generators for random field models, Geogr. Anal. 11:45–64.CrossRefGoogle Scholar
  44. Hamrick, J. L., and Godt, M. J. W., 1990, Allozyme diversity in plant species, in: Plant Population Genetics, Breeding, and Genetic Resources (A. H. D. Brown, M. T. Clegg, A. L. Kahler, and B. S. Weir, eds.), pp. 43–63, Sinauer, Sunderland, Massachusetts.Google Scholar
  45. Harpending, H. C., 1973, Discussion of relationship of conditional kinship to a priori kinship, following paper by N. E. Morton, in: Genetic Structure of Populations (N. E. Morton, ed.), pp. 78–79, University of Hawaii Press, Honolulu.Google Scholar
  46. Heywood, J. S., 1991, Spatial analysis of genetic variation in plant populations, Annu. Rev. Ecol. Syst. 22:335–355.CrossRefGoogle Scholar
  47. Holsinger, K. E., 1988, Inbreeding depression doesn’t matter: The genetic basis of mating system evolution, Evolution 42:1235–1244.CrossRefGoogle Scholar
  48. Hooper, P. M., and Hewings, G. J. D., 1981, Some properties of space-time processes, Geogr. Anal. 13:203–223.CrossRefGoogle Scholar
  49. Imaizumi, Y., Morton, N. E., and Harris, D. E., 1970, Isolation by distance in artificial populations, Genetics 66:569–582.PubMedGoogle Scholar
  50. Jacquard, A., 1973, A distance between individuals whose genealogies are known, in: Genetic Structure of Populations (N. E. Morton, ed.), pp. 82–86, University of Hawaii Press, Honolulu.Google Scholar
  51. Kimura, M., 1953, “Stepping stone” model of population, Annu. Rep. Nat. Inst. Genet. Jpn. 3:62–63.Google Scholar
  52. Kimura, M., and Weiss, G. H., 1964, The stepping stone model of population structure and the decrease of genetic correlation with distance, Genetics 49:561–576.PubMedGoogle Scholar
  53. Knowles, P., 1990, Spatial genetic structure within two natural stands of black spruce [Picea mariana (Mill) B. S. P.], Silvae Genet. 40:13–19.Google Scholar
  54. Krishna-Iyer, P. V., 1949, The first and second moments of some probability distributions arising from points on a lattice and their applications, Biometrika 36:135–141.Google Scholar
  55. Lande, R., 1991, Isolation by distance in a quantitative trait, Genetics 128:443–452.PubMedGoogle Scholar
  56. Latter, B. D. H., and Sved, J. A., 1981, Migration and mutation in stochastic models of gene frequency change. II. Stochastic migration with a finite number of islands, J. Math. Biol. 13:95–104.CrossRefGoogle Scholar
  57. Levin, D. A., 1981, Dispersal versus gene flow in plants, Ann. Missouri Bot. Gard. 68:233–253.CrossRefGoogle Scholar
  58. Levin, D. A., and Fix, A. G., 1989, A model of kin-migration in plants, Theor. Appl. Genet. 77:332–336.CrossRefGoogle Scholar
  59. Lewontin, R. C., and Krakauer, J., 1973, Distribution of gene frequency as a test of the theory of the selective neutrality of polymorphisms. Genetics 74:175–195.PubMedGoogle Scholar
  60. Malécot, G., 1948, Les mathématiques de l’hérédité, Masson, Paris.Google Scholar
  61. Malécot, G., 1967, Identical loci and relationship, Proc. 5th Berkeley Symp. Math. Stat. Prob. 4:317–332.Google Scholar
  62. Malécot, G., 1973, Isolation by distance, in: Genetic Structure of Populations (N. E. Morton, ed.), pp. 72–75, University of Hawaii Press, Honolulu.Google Scholar
  63. Mantel, N., 1967, The detection of disease clustering and a generalized regression approach, Cancer Res. 27:209–220.PubMedGoogle Scholar
  64. Maruyama, T., 1969, Genetic correlations in the stepping stone model with non-symmetrical migration rates, J. Appl. Prob. 6:463–477.CrossRefGoogle Scholar
  65. Maruyama, T., 1971, Analysis of population structure. II. Two dimensional stepping stone models of finite length and other geographically structured populations, Ann. Hum. Genet. 35:411–423.CrossRefGoogle Scholar
  66. Merzeau, D., DiGiusto, F., Comps, B., Thiebaut, B., Letouzey, J., and Cuguen, J., 1989, Genetic control of isozyme systems and heterogeneity of pollen contribution in Beech (Fagus sylvatica L.), Silvae Genet. 38:195–201.Google Scholar
  67. Morton, N. E., 1973a, Kinship and population structure, in: Genetic Structure of Populations (N. E. Morton, ed.), pp. 66–69, University of Hawaii Press, Honolulu.Google Scholar
  68. Morton, N. E., 1973b, Kinship bioassay, in: Genetic Structure of Populations (N. E. Morton, ed.), pp. 158–163, University of Hawaii Press, Honolulu.Google Scholar
  69. Morton, N. E., 1982, Estimation of demographic parameters from isolation by distance, Hum. Hered. 32:37–41.PubMedCrossRefGoogle Scholar
  70. Nagylaki, T., 1974, The decay of genetic variability in geographically structured populations, Proc. Natl. Acad. Sci. USA 71:2932–2936.PubMedCrossRefGoogle Scholar
  71. Nagylaki, T., 1978, A diffusion model for geographically structured populations, J. Math. Biol. 9:101–114.CrossRefGoogle Scholar
  72. Nagylaki, T., 1986, Neutral models of geographical variation, in: Stochastic Spatial Processes (P. Tauta, ed.), pp. 216–237, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  73. Nei, M., 1973, Analysis of gene diversity in subdivided populations, Proc. Natl. Acad. Sci. USA 70:3321–3323.PubMedCrossRefGoogle Scholar
  74. Oden, N. L., 1984, Assessing the significance of a spatial correlogram, Geogr. Anal. 16:1–16.CrossRefGoogle Scholar
  75. Oden, N. L., and Sokal, R. R., 1986, Directional autocorrelation: An extension of spatial correlograms to two dimensions, Syst. Zool. 35:608–617.CrossRefGoogle Scholar
  76. Perry, D. J., and Knowles, P., 1991, Spatial genetic structure within three sugar maple (Acer saccharum Marsh.) stands, Heredity 66:137–142.CrossRefGoogle Scholar
  77. Pfeifer, P. E., and Deutsch, S. J., 1980, A three-stage iterative procedure of space-time modelling, Technometrics 22:35–47.CrossRefGoogle Scholar
  78. Price, M. V., and Waser, N. M., 1979, Pollen dispersal and optimal outcrossing in Delphinium nelsoni, Nature 277:294–297.CrossRefGoogle Scholar
  79. Prout, T., 1973, Appendix to Mitton, J. B., and Koehn, R. K., Population genetics of marine pelecypods. III. Epistasis between functionally related isozymes in Mytilas edulis, Genetics 73:487–496.Google Scholar
  80. Ritland, K., 1985, The genetic mating structure of subdivided populations. I. Open-mating model, Theor. Popul. Biol. 27:51–74.CrossRefGoogle Scholar
  81. Rogers, A. R., 1987, A model of kin-structured migration, Evolution 41:417–426.CrossRefGoogle Scholar
  82. Rogers, A. R., 1988, Three components of genetic drift in subdivided populations, Am. J. Phys. Anthropol. 77:435–449.PubMedCrossRefGoogle Scholar
  83. Rogers, A. R., and Eriksson, A. W., 1988, Statistical analysis of the migration component of genetic drift, Am. J. Phys. Anthropol. 77:451–457.PubMedCrossRefGoogle Scholar
  84. Rogers, A. R., and Harpending, H. C., 1986, Migration and genetic drift in human populations, Evolution 40:1312–1327.CrossRefGoogle Scholar
  85. Rohlf, F. J., and Schnell, G. D., 1971, An investigation of the isolation-by-distance model, Am. Nat. 105:295–324.CrossRefGoogle Scholar
  86. Sakai, K., 1985, Studies on breeding structure in two tropical tree species, in: Population Genetics in Forestry (H. R. Gregorius, ed.), pp. 212–225, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  87. Sawyer, S., 1976, Results for the stepping stone models for migration in population genetics, Ann. Prob. 4:699–728.CrossRefGoogle Scholar
  88. Schaal, B. A., 1975, Population structure and local differentiation in Liatris cylindracea, Am. Nat. 109:511–528.CrossRefGoogle Scholar
  89. Schmitt, J., and Gamble, S. E., 1990, The effect of distance from the parental site on offspring performance and inbreeding depression in Impatiens capensis: A test of the local adaptation hypothesis, Evolution 44:2022–2030.CrossRefGoogle Scholar
  90. Schnabel, A., and Hamrick, J. L., 1990, Organization of genetic diversity within and among populations of Gleditsia triacanthos (Leguminosae), Am. J. Bot. 77:1060–1069.CrossRefGoogle Scholar
  91. Schnabel, A., Lauschman, R. H., and Hamrick, J. L., 1991, Comparative genetic structure of two co-occurring tree species, Madura pomifera (Moraceae) and Gleditsia triacanthos (Leguminosae), Heredity 67:357–364.CrossRefGoogle Scholar
  92. Schoen, D. J., and Clegg, M. T., 1985, The influence of flower color on outcrossing rate and male reproductive success in Ipomoea purpurea, Evolution 39:1242–1249.CrossRefGoogle Scholar
  93. Schoen, D. J., and Latta, R. G., 1989, Spatial autocorrelation of genotypes in populations of Impatiens pallid and Impatiens capensis, Heredity 63:181–189.CrossRefGoogle Scholar
  94. Shaw, D. V., Kahler, A. L., and Allard, R. W., 1981, A multilocus estimator of mating system parameters in plant populations, Proc. Natl. Acad. Sci. USA 78:1298–1302.PubMedCrossRefGoogle Scholar
  95. Slatkin, M., 1985, Gene flow in natural populations, Annu. Rev. Ecol. Syst. 16:393–430.CrossRefGoogle Scholar
  96. Slatkin, M., 1987, Gene flow and the geographic structure of natural populations, Science 236:787–792.PubMedCrossRefGoogle Scholar
  97. Slatkin, M., and Arter, H. E., 1991a, Spatial autocorrelation methods in population genetics, Am. Nat. 138:499–517.CrossRefGoogle Scholar
  98. Slatkin, M., and Arter, H. E., 1991b, Reply to Sokal and Oden, Am. Nat. 138:522–523.CrossRefGoogle Scholar
  99. Slatkin, M., and Barton, N. H., 1989, A comparison of three indirect methods for estimating average levels of gene flow, Evolution 43:1349–1368.CrossRefGoogle Scholar
  100. Smouse, P. E., and Long, J. C., 1992, Matrix correlation analysis in anthropology and genetics, Yearb. Phys. Anthropol. 35:187–213.CrossRefGoogle Scholar
  101. Smouse, P. E., Long, J. C., and Sokal, R. R., 1986, Multiple regression and correlation extensions of the Mantel test of matrix correspondence, Syst. Zool. 35:627–632.CrossRefGoogle Scholar
  102. Sokal, R. R., 1979, Ecological parameters inferred from spatial correlograms, in: Contemporary Quantitative Ecology and Related Econometrics (G. P. Patil and M. L. Rosenzweig, eds.), pp. 167–196, International Cooperative, Fairland, Maryland.Google Scholar
  103. Sokal, R. R., 1988, Genetic, geographic, and linguistic distances in Europe, Proc. Natl. Acad. Sci. USA 85:1722–1726.PubMedCrossRefGoogle Scholar
  104. Sokal, R. R., and Jacquez, G. M., 1991, Testing inferences about microevolutionary processes by means of spatial autocorrelation analysis, Evolution 45:152–168.CrossRefGoogle Scholar
  105. Sokal, R. R., and Menozzi, P., 1982, Spatial autocorrelations of HLA frequencies in Europe support demic diffusion of early farmers, Am. Nat. 119:1–17.CrossRefGoogle Scholar
  106. Sokal, R. R., and Oden, N. L., 1978a, Spatial autocorrelation in biology. 1. Methodology, Biol. J. Linn. Soc. 10:199–228.CrossRefGoogle Scholar
  107. Sokal, R. R., and Oden, N. L., 1978b, Spatial autocorrelation in biology. 2. Some biological implications and four applications of evolutionary and ecological interest, Biol. J. Linn. Soc. 10:229–249.CrossRefGoogle Scholar
  108. Sokal, R. R., and Oden, N. L., 1991, Spatial autocorrelation analysis as an inferential tool in population genetics, Am. Nat. 138:518–521.CrossRefGoogle Scholar
  109. Sokal, R. R., and Wartenberg, D. E., 1983, A test of spatial autocorrelation analysis using an isolation-by-distance model, Genetics 105:219–237.PubMedGoogle Scholar
  110. Sokal, R. R., Smouse, P. E., and Neel, J. V., 1986, The genetic structure of a tribal population, the Yanomama Indians. XV. Patterns inferred by autocorrelation analysis, Genetics 114:259–287.PubMedGoogle Scholar
  111. Sokal, R. R., Oden, N. L., and Barker, J. S. F., 1987, Spatial structure in Drosophila buzzatii populations: Simple and directional spatial autocorrelation, Am. Nat. 129:122–142.CrossRefGoogle Scholar
  112. Sokal, R. R., Harding, R. M., and Oden, N. L., 1989a, Spatial patterns of human gene frequencies in Europe, Am. J. Phys. Anthropol. 80:267–294.PubMedCrossRefGoogle Scholar
  113. Sokal, R. R., Jacquez, G. M., and Wooten, M. C., 1989b, Spatial autocorrelation analysis of migration and selection, Genetics 121:845–855.PubMedGoogle Scholar
  114. Sorensen, F. C., and Miles, R. S., 1982, Inbreeding depression in height, height growth, and survival of Douglas-fir, ponderosa pine and noble fir to 10 years of age, For. Sci. 28:283–292.Google Scholar
  115. Strauss, S. H., 1986, Heterosis at allozyme loci under inbreeding and crossbreeding in Pinus attenuata, Genetics 113:115–134.Google Scholar
  116. Strauss, S. H., and Libby, W. J., 1987, Allozyme heterosis in radiata pine is poorly explained by overdominance, Am. Nat. 130:879–890.CrossRefGoogle Scholar
  117. Turner, M. E., Stephens, J. C., and Anderson, W. W., 1982, Homozygosity and patch structure in plant populations as a result of nearest-neighbor pollination, Proc. Natl. Acad. Sci. USA 79:203–207.PubMedCrossRefGoogle Scholar
  118. Upton, G. J. G., and Fingleton, B., 1985, Spatial Data Analysis by Example, Vol. 1, Point Pattern and Quantitative Data, Wiley, New York.Google Scholar
  119. Uyenoyama, M. K., 1986, Inbreeding and the cost of meiosis: The evolution of selfing in populations practicing partial biparental inbreeding, Evolution 40:388–404.CrossRefGoogle Scholar
  120. Uyenoyama, M. K., and Waller, D. M., 1991, Coevolution of self-fertilization and inbreeding depression. I. Mutation-selection balance at one and two loci, Theor. Popul. Biol. 40:14–46.PubMedCrossRefGoogle Scholar
  121. Wagner, D. B., Sun, Z.-X., Govindaraju, D. R., and Dancik, B. P., 1991, Spatial patterns of chloroplast DNA and cone morphology variation within populations of a Pinus banksiana-Pinus contorta sympatric region, Am. Nat. 138:156–170.CrossRefGoogle Scholar
  122. Waser, N. M., 1987, Spatial genetic heterogeneity in a population of the montane perennial plant Delphinium nelsonii, Heredity 58:249–256.CrossRefGoogle Scholar
  123. Waser, P. M., and Elliott, L. F., 1991, Dispersal and genetic structure in kangaroo rats, Evolution 45:935–943.CrossRefGoogle Scholar
  124. Waser, N. M., and Price, M. V., 1989, Optimal outcrossing in Ipomopsis aggregata: Seed set and offspring fitness, Evolution 43:1097–1109.CrossRefGoogle Scholar
  125. Weir, B. S., 1990, Genetic Data Analysis, Sinauer, Sunderland, Massachusetts.Google Scholar
  126. Weir, B. S., and Cockerham, C. C., 1984, Estimating F-statistics for the analysis of population structure, Evolution 38:1358–1370.CrossRefGoogle Scholar
  127. Weiss, G. H., and Kimura, M., 1965, A mathematical analysis of the stepping stone model of genetic correlation, J. Appl. Prob. 2:129–149.CrossRefGoogle Scholar
  128. Whittle, P., 1954, On stationary processes in the plane, Biometrika 41:434–449.Google Scholar
  129. Wright, S., 1943, Isolation by distance, Genetics 28:114–138.PubMedGoogle Scholar
  130. Wright, S., 1946, Isolation by distance under diverse systems of mating, Genetics 31:39–59.Google Scholar
  131. Wright, S., 1951, The genetical structure of populations, Ann. Eugen. 15:323–354.Google Scholar
  132. Wright, S., 1965, The interpretation of population structure by F-statistics with special regard to systems of mating, Evolution 19:395–420.CrossRefGoogle Scholar
  133. Wright, S., 1978, Evolution and the Genetics of Populations, Vol. 4, Variability Within and Among Populations, University of Chicago Press, Chicago.Google Scholar
  134. Yasuda, N., 1968, An extension of Wahlund’s principle to evaluate mating type frequency, Am. J. Hum. Genet. 29:1–23.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Bryan K. Epperson
    • 1
  1. 1.Department of Botany and Plant SciencesUniversity of CaliforniaRiversideUSA

Personalised recommendations