메뉴 건너뛰기




Volumn 59, Issue 5, 2009, Pages 659-696

Diffusion approximations for one-locus multi-allele kin selection, mutation and random drift in group-structured populations: A unifying approach to selection models in population genetics

Author keywords

Coalescent process; Covariance formulas; Diffusion approximation; Effective population size; Fundamental theorem of natural selection; Group selection; Island model; Kin selection; Relatedness coefficients; Replicator equation

Indexed keywords

ALGORITHM; ALLELE; ANIMAL; ARTICLE; BIOLOGICAL MODEL; DIPLOIDY; GENE FREQUENCY; GENETIC DRIFT; GENETIC SELECTION; GENETICS; GENOTYPE; INBREEDING; METHODOLOGY; MUTATION; POPULATION DENSITY; POPULATION GENETICS; POPULATION MIGRATION; PROBABILITY;

EID: 70349912265     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0248-1     Document Type: Article
Times cited : (22)

References (84)
  • 1
    • 0001182331 scopus 로고
    • A condition for group selection to prevail over counteracting individual selection
    • Aoki K (1982) A condition for group selection to prevail over counteracting individual selection. Evolution 36: 832-842.
    • (1982) Evolution , vol.36 , pp. 832-842
    • Aoki, K.1
  • 2
    • 0015596050 scopus 로고
    • Group selection on the boundary of a stable population
    • Boorman S, Levitt PR (1973) Group selection on the boundary of a stable population. Theor Popul Biol 4: 85-128.
    • (1973) Theor Popul Biol , vol.4 , pp. 85-128
    • Boorman, S.1    Levitt, P.R.2
  • 4
    • 0037398222 scopus 로고    scopus 로고
    • Selection in a subdivided population with dominance or local frequency dependence
    • Cherry JL (2003a) Selection in a subdivided population with dominance or local frequency dependence. Genetics 163: 1511-1518.
    • (2003) Genetics , vol.163 , pp. 1511-1518
    • Cherry, J.L.1
  • 5
    • 0038463589 scopus 로고    scopus 로고
    • Selection in a subdivided population with local extinction and recolonization
    • Cherry JL (2003b) Selection in a subdivided population with local extinction and recolonization. Genetics 164: 789-795.
    • (2003) Genetics , vol.164 , pp. 789-795
    • Cherry, J.L.1
  • 6
    • 0037279710 scopus 로고    scopus 로고
    • A diffusion approximation for selection and drift in a subdivided population
    • Cherry JL, Wakeley J (2003) A diffusion approximation for selection and drift in a subdivided population. Genetics 163: 421-428.
    • (2003) Genetics , vol.163 , pp. 421-428
    • Cherry, J.L.1    Wakeley, J.2
  • 7
    • 0016670565 scopus 로고
    • Hard and soft selection in a subdivided population
    • Christiansen FB (1975) Hard and soft selection in a subdivided population. Am Nat 109: 11-16.
    • (1975) Am Nat , vol.109 , pp. 11-16
    • Christiansen, F.B.1
  • 8
    • 0017808468 scopus 로고
    • Sex ratio and local resource competition in a prosimian primate
    • Clark AB (1978) Sex ratio and local resource competition in a prosimian primate. Science 201: 163-165.
    • (1978) Science , vol.201 , pp. 163-165
    • Clark, A.B.1
  • 10
    • 0008571628 scopus 로고
    • Sufficient conditions for genetic polymorphism
    • Deakin MAB (1966) Sufficient conditions for genetic polymorphism. Am Nat 100: 690-692.
    • (1966) Am Nat , vol.100 , pp. 690-692
    • Deakin, M.A.B.1
  • 11
    • 0015391762 scopus 로고
    • On the neighbor effect and the evolution of altruistic traits
    • Eshel I (1972) On the neighbor effect and the evolution of altruistic traits. Theor Popul Biol 3: 258-277.
    • (1972) Theor Popul Biol , vol.3 , pp. 258-277
    • Eshel, I.1
  • 12
    • 84980148617 scopus 로고
    • A class of degenerate diffusion processes occurring in population genetics
    • Ethier SN (1976) A class of degenerate diffusion processes occurring in population genetics. Comm Pure Appl Math 29: 483-493.
    • (1976) Comm Pure Appl Math , vol.29 , pp. 483-493
    • Ethier, S.N.1
  • 13
    • 0002307944 scopus 로고
    • Diffusion approximations of Markov chains with two time scales and applications to population genetics
    • Ethier SN, Nagylaki T (1980) Diffusion approximations of Markov chains with two time scales and applications to population genetics. Adv Appl Prob 12: 14-49.
    • (1980) Adv Appl Prob , vol.12 , pp. 14-49
    • Ethier, S.N.1    Nagylaki, T.2
  • 14
    • 0015310384 scopus 로고
    • The sampling theory of selectively neutral alleles
    • Ewens WJ (1972) The sampling theory of selectively neutral alleles. Theor Popul Biol 3: 87-112.
    • (1972) Theor Popul Biol , vol.3 , pp. 87-112
    • Ewens, W.J.1
  • 15
    • 0024748186 scopus 로고
    • An interpretation and proof of the fundamental theorem of natural selection
    • Ewens WJ (1989) An interpretation and proof of the fundamental theorem of natural selection. Theor Popul Biol 36: 167-180.
    • (1989) Theor Popul Biol , vol.36 , pp. 167-180
    • Ewens, W.J.1
  • 19
    • 0000521299 scopus 로고
    • Relation d'identité en génétique I.-Postulats et axiomes mendéliens
    • Gillois M (1965) Relation d'identité en génétique I.-Postulats et axiomes mendéliens. Ann Inst Henri Poincaré B2: 1-94.
    • (1965) Ann Inst Henri Poincaré , vol.B2 , pp. 1-94
    • Gillois, M.1
  • 20
    • 0002729243 scopus 로고
    • A geometric view of relatedness
    • Grafen A (1985) A geometric view of relatedness. Oxford Surv Evol Biol 2: 28-89.
    • (1985) Oxford Surv Evol Biol , vol.2 , pp. 28-89
    • Grafen, A.1
  • 21
    • 26244441703 scopus 로고    scopus 로고
    • Ewens' sampling formula and related formulae: Combinatorial proofs, extensions to variable population size and applications to ages of alleles
    • Griffiths WJ, Lessard S (2005) Ewens' sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles. Theor Popul Biol 68: 167-177.
    • (2005) Theor Popul Biol , vol.68 , pp. 167-177
    • Griffiths, W.J.1    Lessard, S.2
  • 22
    • 0013770258 scopus 로고
    • The genetical evolution of social behaviour I and II
    • Hamilton WD (1964) The genetical evolution of social behaviour I and II. J Theor Biol 7: 1-52.
    • (1964) J Theor Biol , vol.7 , pp. 1-52
    • Hamilton, W.D.1
  • 23
    • 0014219333 scopus 로고
    • Extraordinary sex ratios
    • Hamilton WD (1967) Extraordinary sex ratios. Science 156: 477-488.
    • (1967) Science , vol.156 , pp. 477-488
    • Hamilton, W.D.1
  • 24
    • 0014955324 scopus 로고
    • Selfish and spiteful behaviour in an evolutionary model
    • Hamilton WD (1970) Selfish and spiteful behaviour in an evolutionary model. Nature 228: 1218-1220.
    • (1970) Nature , vol.228 , pp. 1218-1220
    • Hamilton, W.D.1
  • 30
    • 0000660047 scopus 로고
    • Diffusion models in population genetics
    • Kimura M (1964) Diffusion models in population genetics. J Appl Prob 1: 177-232.
    • (1964) J Appl Prob , vol.1 , pp. 177-232
    • Kimura, M.1
  • 31
    • 77957184334 scopus 로고
    • Evolution of an altruistic trait through group selection as studied by the diffusion equation method
    • Kimura M (1984) Evolution of an altruistic trait through group selection as studied by the diffusion equation method. IMA J Math Appl Med Biol 1: 1-15.
    • (1984) IMA J Math Appl Med Biol , vol.1 , pp. 1-15
    • Kimura, M.1
  • 32
    • 84856715072 scopus 로고
    • A matrix inequality
    • Kingman JFC (1961) A matrix inequality. Quart J Math 12: 78-80.
    • (1961) Quart J Math , vol.12 , pp. 78-80
    • Kingman, J.F.C.1
  • 34
    • 0009321799 scopus 로고
    • Semigroups of conditioned shifts and approximation of Markov processes
    • Kurtz TG (1975) Semigroups of conditioned shifts and approximation of Markov processes. Ann Prob 3: 618-642.
    • (1975) Ann Prob , vol.3 , pp. 618-642
    • Kurtz, T.G.1
  • 35
    • 0027008225 scopus 로고
    • Relatedness and inclusive fitness with inbreeding
    • Lessard S (1992) Relatedness and inclusive fitness with inbreeding. Theor Popul Biol 42: 284-307.
    • (1992) Theor Popul Biol , vol.42 , pp. 284-307
    • Lessard, S.1
  • 36
    • 0027511040 scopus 로고
    • Adaptive topography in fertility-viability selection models: An alternative to inclusive fitness in kin selection models
    • Lessard S (1993) Adaptive topography in fertility-viability selection models: an alternative to inclusive fitness in kin selection models. Theor Popul Biol 43: 281-309.
    • (1993) Theor Popul Biol , vol.43 , pp. 281-309
    • Lessard, S.1
  • 37
    • 0031260119 scopus 로고    scopus 로고
    • Fisher's fundamental theorem of natural selection revisited
    • Lessard S (1997) Fisher's fundamental theorem of natural selection revisited. Theor Popul Biol 52: 119-136.
    • (1997) Theor Popul Biol , vol.52 , pp. 119-136
    • Lessard, S.1
  • 38
    • 22144485943 scopus 로고    scopus 로고
    • Long-term stability from fixation probabilities in finite populations: New perspectives for ESS theory
    • Lessard S (2005a) Long-term stability from fixation probabilities in finite populations: New perspectives for ESS theory. Theor Popul Biol 68: 19-27.
    • (2005) Theor Popul Biol , vol.68 , pp. 19-27
    • Lessard, S.1
  • 39
    • 26444517327 scopus 로고    scopus 로고
    • Kin selection is implicated in partial sib-mating populations with constant viability differences before mating
    • Lessard S (2005b) Kin selection is implicated in partial sib-mating populations with constant viability differences before mating. Genetics 171: 407-413.
    • (2005) Genetics , vol.171 , pp. 407-413
    • Lessard, S.1
  • 40
    • 35549003524 scopus 로고    scopus 로고
    • An exact sampling formula for the Wright-Fisher model and a conjecture about the finite-island model
    • Lessard S (2007) An exact sampling formula for the Wright-Fisher model and a conjecture about the finite-island model. Genetics 177: 1249-1254.
    • (2007) Genetics , vol.177 , pp. 1249-1254
    • Lessard, S.1
  • 41
    • 9244245259 scopus 로고    scopus 로고
    • Kin selection and coefficients of relatedness in family-structured populations with inbreeding
    • Lessard S, Rocheleau G (2004) Kin selection and coefficients of relatedness in family-structured populations with inbreeding. Theor Popul Biol 66: 287-306.
    • (2004) Theor Popul Biol , vol.66 , pp. 287-306
    • Lessard, S.1    Rocheleau, G.2
  • 42
    • 0001493328 scopus 로고
    • Genetic equilibrium when more than one ecological niche is available
    • Levene H (1953) Genetic equilibrium when more than one ecological niche is available. Am Nat 87: 311-313.
    • (1953) Am Nat , vol.87 , pp. 311-313
    • Levene, H.1
  • 44
    • 72449123025 scopus 로고
    • Selection in and of populations
    • J. A. Moore (Ed.), New York: Natural History Press
    • Lewontin RC (1965) Selection in and of populations. In: Moore JA(eds) Ideas in modern biology. Natural History Press, New York, pp 292-311.
    • (1965) Ideas in Modern Biology , pp. 292-311
    • Lewontin, R.C.1
  • 45
    • 0001742504 scopus 로고
    • La consanguinité dans une population limitée
    • Malécot G (1946) La consanguinité dans une population limitée. C R Acad Sci Paris 222: 841-843.
    • (1946) C R Acad Sci Paris , vol.222 , pp. 841-843
    • Malécot, G.1
  • 46
    • 3142699705 scopus 로고
    • Stochastic theory of population genetics
    • Maruyama T (1983) Stochastic theory of population genetics. Bull Math Biol 45: 521-554.
    • (1983) Bull Math Biol , vol.45 , pp. 521-554
    • Maruyama, T.1
  • 47
    • 0000841452 scopus 로고
    • Group selection and kin selection
    • Maynard Smith J (1964) Group selection and kin selection. Nature 201: 1145-1147.
    • (1964) Nature , vol.201 , pp. 1145-1147
    • Smith, M.J.1
  • 48
    • 34548719708 scopus 로고
    • The logic of animal conflicts
    • Maynard Smith J, Price G (1973) The logic of animal conflicts. Nature 246: 15-18.
    • (1973) Nature , vol.246 , pp. 15-18
    • Smith, M.J.1    Price, G.2
  • 49
    • 0000804540 scopus 로고
    • Coefficients of relatedness in sociobiology
    • Michod RE, Hamilton WD (1980) Coefficients of relatedness in sociobiology. Nature 288: 694-697.
    • (1980) Nature , vol.288 , pp. 694-697
    • Michod, R.E.1    Hamilton, W.D.2
  • 50
    • 84949558457 scopus 로고
    • Random processes in genetics
    • Moran PAP (1958) Random processes in genetics. Proc Camb Phil Soc 54: 60-71.
    • (1958) Proc Camb Phil Soc , vol.54 , pp. 60-71
    • Moran, P.A.P.1
  • 51
    • 0013287931 scopus 로고
    • The theory of some genetical effects of population subdivision
    • Moran PAP (1959) The theory of some genetical effects of population subdivision. Austr J Biol Sci 12: 109-116.
    • (1959) Austr J Biol Sci , vol.12 , pp. 109-116
    • Moran, P.A.P.1
  • 52
    • 0018822347 scopus 로고
    • The strong-migration limit in geographically structured populations
    • Nagylaki T (1980) The strong-migration limit in geographically structured populations. J Math Biol 9: 101-114.
    • (1980) J Math Biol , vol.9 , pp. 101-114
    • Nagylaki, T.1
  • 53
    • 0023093256 scopus 로고
    • Evolution under fertility and viability selection
    • Nagylaki T (1987) Evolution under fertility and viability selection. Genetics 115: 367-375.
    • (1987) Genetics , vol.115 , pp. 367-375
    • Nagylaki, T.1
  • 55
    • 0029680217 scopus 로고    scopus 로고
    • The diffusion model for migration and selection in a dioecious population
    • Nagylaki T (1996) The diffusion model for migration and selection in a dioecious population. J Math Biol 34: 334-360.
    • (1996) J Math Biol , vol.34 , pp. 334-360
    • Nagylaki, T.1
  • 56
    • 0001069078 scopus 로고    scopus 로고
    • The diffusion model for migration and selection in a plant population
    • Nagylaki T (1997) The diffusion model for migration and selection in a plant population. J Math Biol 35: 409-431.
    • (1997) J Math Biol , vol.35 , pp. 409-431
    • Nagylaki, T.1
  • 57
    • 0033233681 scopus 로고    scopus 로고
    • Coalescents with multiple collisions
    • Pitman J (1999) Coalescents with multiple collisions. Ann Probab 27: 1870-1902.
    • (1999) Ann Probab , vol.27 , pp. 1870-1902
    • Pitman, J.1
  • 58
    • 0014830535 scopus 로고
    • Selection and covariance
    • Price GR (1970) Selection and covariance. Nature (London) 227: 520-521.
    • (1970) Nature (London) , vol.227 , pp. 520-521
    • Price, G.R.1
  • 59
    • 0015330403 scopus 로고
    • Extension of covariance selection mathematics
    • Price GR (1972) Extension of covariance selection mathematics. Am Hum Genet Lond 35: 485-490.
    • (1972) Am Hum Genet Lond , vol.35 , pp. 485-490
    • Price, G.R.1
  • 60
    • 0041731996 scopus 로고    scopus 로고
    • Effective size in simple metapopulation models
    • Rousset F (2003) Effective size in simple metapopulation models. Heredity 91: 107-111.
    • (2003) Heredity , vol.91 , pp. 107-111
    • Rousset, F.1
  • 61
    • 85052429970 scopus 로고    scopus 로고
    • Separation of time scales, fixation probabilities and convergence to evolutionarily stable states under isolation by distance
    • Rousset F (2006) Separation of time scales, fixation probabilities and convergence to evolutionarily stable states under isolation by distance. Theor Popul Biol 69: 165-179.
    • (2006) Theor Popul Biol , vol.69 , pp. 165-179
    • Rousset, F.1
  • 62
    • 0033795207 scopus 로고    scopus 로고
    • A theoretical basis for measures of kin selection in subdivided populations: Finite populations and localized dispersal
    • Rousset F, Billiard S (2000) A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal. J Evol Biol 13: 814-825.
    • (2000) J Evol Biol , vol.13 , pp. 814-825
    • Rousset, F.1    Billiard, S.2
  • 63
    • 0346100692 scopus 로고    scopus 로고
    • Selection and drift in subdivided populations: A straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions
    • Roze D, Rousset F (2003) Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions. Genetics 165: 2153-2166.
    • (2003) Genetics , vol.165 , pp. 2153-2166
    • Roze, D.1    Rousset, F.2
  • 64
    • 4143088093 scopus 로고    scopus 로고
    • The robustness of Hamilton's rule with inbreeding and dominance: Kin selection and fixation probabilities under partial sib-mating
    • Roze D, Rousset F (2004) The robustness of Hamilton's rule with inbreeding and dominance: Kin selection and fixation probabilities under partial sib-mating. Am Nat 164: 214-231.
    • (2004) Am Nat , vol.164 , pp. 214-231
    • Roze, D.1    Rousset, F.2
  • 65
    • 0033233843 scopus 로고    scopus 로고
    • The general coalescent with asynchronous mergers of ancestral lines
    • Sagitov S (1999) The general coalescent with asynchronous mergers of ancestral lines. J Appl Probab 36: 1116-1125.
    • (1999) J Appl Probab , vol.36 , pp. 1116-1125
    • Sagitov, S.1
  • 66
    • 0017731844 scopus 로고
    • Gene flow and genetic drift in a species subject to frequent local extinctions
    • Slatkin M (1977) Gene flow and genetic drift in a species subject to frequent local extinctions. Theor Popul Biol 12: 253-262.
    • (1977) Theor Popul Biol , vol.12 , pp. 253-262
    • Slatkin, M.1
  • 67
    • 0000872113 scopus 로고
    • Evolutionary stability in one-parameter models under weak selection
    • Taylor PD (1989) Evolutionary stability in one-parameter models under weak selection. Theor Popul Biol 36: 125-143.
    • (1989) Theor Popul Biol , vol.36 , pp. 125-143
    • Taylor, P.D.1
  • 68
    • 0029948439 scopus 로고    scopus 로고
    • How to make a kin selection model
    • Taylor PD, Frank SA (1996) How to make a kin selection model. J Theor Biol 180: 27-37.
    • (1996) J Theor Biol , vol.180 , pp. 27-37
    • Taylor, P.D.1    Frank, S.A.2
  • 69
    • 0003280294 scopus 로고    scopus 로고
    • Inclusive fitness in finite deme-structured and stepping-stone populations
    • Taylor PD, Irwin AJ, Day T (2000) Inclusive fitness in finite deme-structured and stepping-stone populations. Selection 1: 153-163.
    • (2000) Selection , vol.1 , pp. 153-163
    • Taylor, P.D.1    Irwin, A.J.2    Day, T.3
  • 70
    • 0017819644 scopus 로고
    • Evolutionarily stable strategies and game dynamics
    • Taylor PD, Jonker L (1978) Evolutionarily stable strategies and game dynamics. Math Biosc 40: 145-156.
    • (1978) Math Biosc , vol.40 , pp. 145-156
    • Taylor, P.D.1    Jonker, L.2
  • 71
    • 0019029068 scopus 로고
    • Theories of kin and group selection: A population genetics perspective
    • Uyenoyama MK, Feldman MW (1980) Theories of kin and group selection: a population genetics perspective. Theor Popul Biol 17: 380-414.
    • (1980) Theor Popul Biol , vol.17 , pp. 380-414
    • Uyenoyama, M.K.1    Feldman, M.W.2
  • 72
    • 0008117367 scopus 로고
    • On relatedness and adaptive topography in kin selection
    • Uyenoyama MK, Feldman MW (1981) On relatedness and adaptive topography in kin selection. Theor Popul Biol 19: 87-123.
    • (1981) Theor Popul Biol , vol.19 , pp. 87-123
    • Uyenoyama, M.K.1    Feldman, M.W.2
  • 73
    • 17644449030 scopus 로고
    • Population genetic theory of kin selection: Multiple alleles at one locus
    • Uyenoyama MK, Feldman MW, Mueller LD (1981) Population genetic theory of kin selection: multiple alleles at one locus. Proc Natl Acad Sci USA 78: 5036-5040.
    • (1981) Proc Natl Acad Sci USA , vol.78 , pp. 5036-5040
    • Uyenoyama, M.K.1    Feldman, M.W.2    Mueller, L.D.3
  • 74
    • 0019200386 scopus 로고
    • Kin selection: Its components
    • Wade MJ (1980) Kin selection: its components. Science 210: 665-667.
    • (1980) Science , vol.210 , pp. 665-667
    • Wade, M.J.1
  • 75
    • 0024256618 scopus 로고
    • Extinction and recolonization: Their effects on the genetic differentiation of local populations
    • Wade M, McCauley D (1988) Extinction and recolonization: their effects on the genetic differentiation of local populations. Evolution 42: 995-1005.
    • (1988) Evolution , vol.42 , pp. 995-1005
    • Wade, M.1    McCauley, D.2
  • 76
    • 0037277985 scopus 로고    scopus 로고
    • Polymorphism and divergence for island-model species
    • Wakeley J (2003) Polymorphism and divergence for island-model species. Genetics 163: 411-420.
    • (2003) Genetics , vol.163 , pp. 411-420
    • Wakeley, J.1
  • 77
    • 0034758281 scopus 로고    scopus 로고
    • Gene genealogies in a metapopulation
    • Wakeley J, Aliacar N (2001) Gene genealogies in a metapopulation. Genetics 159: 893-905.
    • (2001) Genetics , vol.159 , pp. 893-905
    • Wakeley, J.1    Aliacar, N.2
  • 78
    • 4143095090 scopus 로고    scopus 로고
    • The many-demes limit for selection and drift in a subdivided population
    • Wakeley J, Takahashi T (2004) The many-demes limit for selection and drift in a subdivided population. Theor Popul Biol 66: 83-91.
    • (2004) Theor Popul Biol , vol.66 , pp. 83-91
    • Wakeley, J.1    Takahashi, T.2
  • 79
    • 0038124402 scopus 로고    scopus 로고
    • Fixation probability and time in subdivided populations
    • Whitlock MC (2003) Fixation probability and time in subdivided populations. Genetics 164: 767-779.
    • (2003) Genetics , vol.164 , pp. 767-779
    • Whitlock, M.C.1
  • 80
    • 0001507896 scopus 로고
    • Coefficients of inbreeding and relationship
    • Wright S (1922) Coefficients of inbreeding and relationship. Am Nat 56: 330-338.
    • (1922) Am Nat , vol.56 , pp. 330-338
    • Wright, S.1
  • 81
    • 0001771498 scopus 로고
    • Evolution in Mendelian populations
    • Wright S (1931) Evolution in Mendelian populations. Genetics 16: 97-159.
    • (1931) Genetics , vol.16 , pp. 97-159
    • Wright, S.1
  • 82
    • 0001530804 scopus 로고
    • Statistical genetics and evolution
    • Wright S (1942) Statistical genetics and evolution. Bull Am Math Soc 48: 223-246.
    • (1942) Bull Am Math Soc , vol.48 , pp. 223-246
    • Wright, S.1
  • 83
    • 0001024012 scopus 로고
    • Isolation by distance
    • Wright S (1943) Isolation by distance. Genetics 28: 114-138.
    • (1943) Genetics , vol.28 , pp. 114-138
    • Wright, S.1
  • 84
    • 0001876571 scopus 로고
    • Random drift and the shifting balance theory of evolution
    • K. Kojima (Ed.), Berlin: Springer
    • Wright S (1970) Random drift and the shifting balance theory of evolution. In: Kojima K(eds) Mathematical topics in population genetics. Springer, Berlin, pp 1-31.
    • (1970) Mathematical Topics in Population Genetics , pp. 1-31
    • Wright, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.