Spatial waves of advance with bistable dynamics: Cytoplasmic and genetic analogues of Allee effects

American Naturalist

Volumn 178, Issue 3, 2011, Pages

  Barton, N H ^a   Turelli, Michael ^b  

^a INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA   (Austria)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Critical propagule size; Population replacement; Species invasions; Underdominance; Wave stopping; Wolbachia

Indexed keywords

ALLEE EFFECT; BACTERIUM; BIOLOGICAL INVASION; CHROMOSOME; CYTOPLASM; DISEASE VECTOR; DISPERSAL; INHOMOGENEITY; INSECT; PROPAGULE;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; EVOLUTION; GENE FLOW; GENETICS; INSECT; MICROBIOLOGY; POPULATION DYNAMICS; WOLBACHIA;

ANIMALS; BIOLOGICAL EVOLUTION; GENE FLOW; INSECTS; MODELS, GENETIC; POPULATION DYNAMICS; WOLBACHIA;

HEXAPODA; WOLBACHIA;

EID: 80051522287     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/661246     Document Type: Article

References (111)

1. Aronson, D. G., and H. F. Weinberger. 1975. Nonlinear diffusion in population genetics, combustion, and nerve impulse propagation. Pages 5-49 in J. A. Goldstein, ed. Partial differential equations and related topics. Lecture Notes in Mathematics 446. Springer, New York.
2. Barton, N. H. 1979a. The dynamics of hybrid zones. Heredity 43: 341-359.
3. Barton, N. H. 1979b. Gene flow past a cline. Heredity 43:333-339.
4. Barton, N. H. 1986. The effects of linkage and density-dependent regulation on gene flow. Heredity 57:415-426.
5. Barton, N. H. 1987. The probability of establishment of an advantageous mutation in a subdivided population. Genetical Research 50:35-40.
6. Barton, N. H. 2008. The effect of a barrier to gene flow on patterns of geographic variation. Genetics Research 90:139-149.
7. Barton, N. H., and B. O. Bengtsson. 1986. The barrier to genetic exchange between hybridizing populations. Heredity 56:357-376.
8. Barton, N. H., and K. S. Gale. 1993. Genetic analysis of hybrid zones. Pages 13-45 in R. G. Harrison, ed. Hybrid zones and the evolutionary process. Oxford University Press, Oxford.
9. Barton, N. H., and G. M. Hewitt. 1985. Analysis of hybrid zones. Annual Review of Ecology and Systematics 16:113-148.
10. Barton, N. H. 1989. Adaptation, speciation and hybrid zones. Nature 341: 497-503.
11. Barton, N. H., and S. Rouhani. 1991. The probability of fixation of a new karyotype in a continuous population. Evolution 4:499-517.
12. Bazykin, A. D. 1969. Hypothetical mechanism of speciation. Evolution 23:685-687.
13. Barton, N. H. 1973. Population genetic analysis of disrupting and stabilising selection. 2. Adjacent populations and populations with continuous area. Genetika 9:156-166.
14. Bramson, M. 1983. Convergence of solutions of the Kolmogorov equation to traveling waves. Memoirs of the American Mathematical Society 44:1-190.
15. Brownstein, J. S., E. Hett, and S. L. O'Neill. 2003. The potential of virulent Wolbachia to modulate disease transmission by insects. Journal of Invertebrate Pathology 84:24-29.
16. Carrington, L. B., J. R. Lipkowitz, A. A. Hoffmann, and M. Turelli. 2011. A re-examination of Wolbachia-induced cytoplasmic incompatibility in California Drosophila simulans. PLoS ONE 6:e22565.
17. Caspari, E., and G. S. Watson. 1959. On the evolutionary importance of cytoplasmic sterility in mosquitoes. Evolution 13:568-570.
18. Chow, S. N., and J. Mallet-Paret. 1995. Pattern formation and spatial chaos in lattice dynamical systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 42:746-751.
19. Coleman, S. 1977. Fate of the false vacuum: semiclassical theory. Physical Review D 15:2929-2936.
20. Corless, R. M., G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth. 1996. On the Lambert W function. Advances in Computational Mathematics 5:329-359.
21. Coyne, J. A., N. H. Barton, and M. Turelli. 1997. A critique ofWright's shifting balance theory of evolution. Evolution 51:643-671.
22. Curtis, C. F. 1968. Possible use of translocations to fix desirable genes in insect pest populations. Nature 218:368-369.
23. Duerr, H.-P., K. Kietz, and M. Eichner. 2005. Determinants of the eradicability of filarial infections: a conceptual approach. Trends in Parasitology 21:88-96.
24. Endler, J. A. 1977. Genetic variation, speciation, and clines. Princeton University Press, Princeton, NJ.
25. Engelstädter, J., and A. Telschow. 2009. Cytoplasmic incompatibility and host population structure. Heredity 103:196-207.
26. Faires, J. D., and R. L. Burden. 2002. Numerical methods. 3rd ed. Brooks/Cole, Belmont, CA.
27. Fife, P. C. 1979a. Long time behavior of systems of bistable nonlinear diffusion equations. Archive for Rational Mechanics and Analysis 70:31-46.
28. Fife, P. C. 1979b. Mathematical aspects of reacting and diffusing systems. Springer, Berlin.
29. Fife, P. C., and J. B. McLeod. 1977. Approach of solutions of nonlinear diffusion equations to traveling front solutions. Archive for Rational Mechanics and Analysis 65:335-361.
30. Fisher, R. A. 1937. The wave of advance of advantageous genes. Annals of Eugenics 7:355-369.
31. Flor, M., P. Hammerstein, and A. Telschow. 2007.Wolbachia-induced unidirectional cytoplasmic incompatibility and the stability of infection polymorphism in parapatric host populations. Journal of Evolutionary Biology 20:696-706.
32. Haldane, J. B. S. 1930. A mathematical theory of natural and artificial selection. VI. Isolation. Proceedings of the Cambridge Philosophical Society 26:220-230.
33. Haldane, J. B. S. 1948. The theory of a cline. Journal of Genetics 48:277-284.
34. Hancock, P. A., S. P. Sinkins, and H. C. J. Godfray. 2011. Population dynamic models of the spread of Wolbachia. American Naturalist 177:323-333.
35. Hedges, L. M., J. C. Brownlie, S. L. O'Neill, and K. N. Johnson. 2008. Wolbachia and virus protection in insects. Science 322:702.
36. Himler, A. G., T. Adachi-Hagimori, J. E. Bergen, A. Kozuch, S. E. Kelly, B. E. Tabashnik, E. Chiel, et al. 2011. Rapid spread of a bacterial symbiont in an invasive whitefly is driven by fitness benefits and female bias. Science 332:254-256.
37. Hodgkin, A. L., and A. F. Huxley. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117:500-544.
38. Hofbauer, J. 1999. The spatially dominant equilibrium of a game. Annals of Operations Research 89:233-251.
39. Hoffmann, A. A., and M. Turelli. 1997. Cytoplasmic incompatibility in insects. Pages 42-80 in S. L. O'Neill, J. H. Werren, and A. A. Hoffmann, eds. Influential passengers: inherited microorganisms and arthropod reproduction. Oxford University Press, Oxford.
40. Hoffmann, A. A., B. L. Montgomery, J. Popovici, I. Iturbe-Ormaetxe, P. H. Johnson, F. Muzzi, M. Greenfield, et al. 2011. Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission. Nature, doi:10.1038/nature10356.
41. Jaenike, J., K. A. Dyer, C. Cornish, and M. S. Minhas. 2006. Asymmetrical reinforcement and Wolbachia infection in Drosophila. PLoS Biology 4:e325.
42. Jaenike, J., R. Unckless, S. N. Cockburn, L. M. Boelio, and S. J. Perlman. 2010. Adaptation via symbiosis: recent spread of a Drosophila defensive symbiont. Science 329:212-215.
43. Jansen, V. A. A., M. Turelli, and H. C. J. Godfray. 2008. Stochastic spread of Wolbachia. Proceedings of the Royal Society B: Biological Sciences 275:2769-2776.
44. Kambris, Z., P. E. Cook, H. K. Phuc, and S. P. Sinkins. 2009. Immune activation by life-shortening Wolbachia and reduced filarial competence in mosquitoes. Science 326:134-136.
45. Karlin, S., and J. MacGregor. 1972. Application of method of small parameters to multi-niche population genetic models. Theoretical Population Biology 3:186-209.
46. Keener, J., and J. Sneyd. 2004. Mathematical physiology. Springer, New York.
47. Keitt, T. H., M. A. Lewis, and R. D. Holt. 2001. Allee dynamics and the spread of invading organisms. American Naturalist 157:203-316.
48. Key, K. H. L. 1968. The concept of stasipatric speciation. Systematic Zoology 17:14-22.
49. Kierstead, H., and L. B. Slobodkin. 1953. The size of water masses containing plankton blooms. Journal of Marine Research 12:141-147.
50. Kolmogorov, A. N., I. Petrovsky, and N. Piscounoff. 1937. Etude de l'equation de la diffusion avec croissance de la quantile de matiere et son application a un probleme biologique. Bulletin of the State University of Moscow A: Mathematics and Mechanics 1:1-25.
51. Kot, M., M. A. Lewis, and P. van den Driessche. 1996. Dispersal data and the spread of invading organisms. Ecology 77:2027-2042.
52. Lande, R. 1985. The fixation of chromosomal rearrangements in a subdivided population with local extinction and recolonisation. Heredity 54:323-332.
53. Lande, R. 1987. Extinction thresholds in demographic models of territorial populations. American Naturalist 130:624-635.
54. Laven, H. 1951. Crossing experiments with Culex strains. Evolution 5:370-375.
55. Lande, R. 1959. Speciation by cytoplasmic isolation in the Culex pipiens complex. Cold Spring Harbor Symposia on Quantitative Biology 24:166-173.
56. Leung, B., J. M. Drake, and D. M. Lodge. 2004. Predicting invasions: propagule pressure and the gravity of Allee effects. Ecology 85: 1651-1660.
57. Lewis, M. A., and P. Kareiva. 1993. Allee dynamics and the spread of invading organisms. Theoretical Population Biology 43:141-158.
58. Lutscher, F., E. McCauley, and M. Lewis. 2007. Spatial patterns and coexistence mechanisms in systems with unidirectional flow. Theoretical Population Biology 71:267-277.
59. Magori, K., and F. Gould. 2006. Genetically engineered underdominance for manipulations of pest populations: a deterministic model. Genetics 172:2613-2620.
60. Mallet, J. L. B., and M. Joron. 1999. Evolution of diversity in warning color and mimicry: polymorphisms, shifting balance, and speciation. Annual Review of Ecology and Systematics 30:201-233.
61. McMeniman, C. J., R. V. Lane, B. N. Cass, A. W. C. Fong, M. Sidhu, Y. Wang, and S. L. O'Neill. 2009. Stable introduction of a lifeshortening Wolbachia infection into the mosquito Aedes aegypti. Science 323:141-144.
62. Min, K. T., and S. Benzer. 1997. Wolbachia, normally a symbiont of Drosophila, can be virulent, causing degeneration and early death. Proceedings of the National Academy of Sciences of the USA 94: 10792-10796.
63. Mollison, D. 1977. Spatial contact models for ecological and epidemic spread. Journal of the Royal Statistical Society B 39:283-326.
64. Moreira, L. A., I. Iturbe-Ormaetxe, J. A. Jeffery, G. Lu, A. T. Pyke, L. M. Hedges, B. C. Rocha, et al. 2009. A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and Plasmodium.
65. Cell 139:1268-1278.
66. Nagumo, J., S. Arimoto, and S. Yoshizawa. 1962. An active pulse transmission line simulating nerve axon. Proceedings of the Institute of Radio Engineers 150:2061-2070.
67. Nagumo, J., S. Yoshizawa, and S. Arimoto. 1965. Bistable transmission lines. IEEE Transactions on Circuit Theory 12:400-412.
68. Nagylaki, T. 1975. Conditions for the existence of clines. Genetics 80:595-615.
69. Nagylaki, 1976. Clines with variable migration. Genetics 83:867-886.
70. Nagylaki, 1977. Selection in one-and two-locus systems. Springer, Berlin.
71. Nagylaki, 1978a. Clines with asymmetric migration. Genetics 88:813-827.
72. Nagylaki, 1978b. A diffusion model for geographically structured populations. Journal of Mathematical Biology 6:375-382.
73. Neubert, M. G., and H. Caswell. 2000. Demography and dispersal: calculations and sensitivity analysis of invasion speed for structured populations. Ecology 81:1613-1628.
74. Nichols, R. A., and G. M. Hewitt. 1986. Population structure and the shape of a chromosomal cline between two races of Podisma pedestris (Orthoptera: Acrididae). Biological Journal of the Linnean Society 29:301-316.
75. Noor, M. A. F. 1999. Reinforcement and other consequences of sympatry. Heredity 83:503-508.
76. Pialek, J., and N. H. Barton. 1997. The spread of an advantageous allele across a barrier: the effects of random drift and selection against heterozygotes. Genetics 145:493-504.
77. Rasgon, J. L., L. M. Styer, and T. W. Scott. 2003. Wolbachia-induced mortality as a mechanism to modulate pathogen transmission by vector arthropods. Journal of Medical Entomology 40:125-132.
78. Rothe, F. 1981. Convergence to pushed fronts. Rocky Mountain Journal of Mathematics 11:617-633.
79. Rouhani, S., and N. Barton. 1987. Speciation and the "shifting balance" in a continuous population. Theoretical Population Biology 31:465-492.
80. Sanderson, N. 1989. Can gene flow prevent reinforcement? Evolution 43:1123-1235.
81. Schofield, P. 2002. Spatially explicit models of Turelli-Hoffmann Wolbachia invasive wave fronts. Journal of Theoretical Biology 215: 121-131.
82. Schreiber, S. J., and J. O. Lloyd-Smith. 2009. Invasion dynamics in spatially heterogeneous environments. American Naturalist 174: 490-505.
83. Servedio, M. R., and M. A. F. Noor. 2007. The role of reinforcement in speciation: theory and data. Annual Review of Ecology, Evolution, and Systematics 34:339-364.
84. Shigesada, N., and K. Kawasaki. 1997. Biological invasions: theory and practice. Oxford University Press, Oxford.
85. Sinkins, S. P., and F. Gould. 2006. Gene drive systems for insect disease vectors. Nature Reviews Genetics 7:427-435.
86. Skellam, J. G. 1951. Random dispersal in theoretical populations. Biometrika 38:196-218.
87. Slatkin, M. 1973. Gene flow and selection in a cline. Genetics 75: 733-756.
88. Soboleva, T. K., P. R. Shorten, A. B. Pleasants, and A. L. Rae. 2003. Qualitative theory of the spread of a new gene into a resident population. Ecological Modelling 163:33-44.
89. Stokes, A. N. 1976. On two types of moving front in quasilinear diffusion. Mathematical Biosciences 31:307-315.
90. Taylor, C. M., and A. Hastings. 2005. Allee effects in biological invasions. Ecology Letters 8:895-908.
91. Teixeira, L., A. Ferreira, and M. Ashburner. 2008. The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster. PLoS Biology 6:e2.
92. Telschow, A., P. Hammerstein, and J. H. Werren. 2005. The effect of Wolbachia versus genetic incompatibilities on reinforcement and speciation. Evolution 59:1607-1619.
93. Telschow, A., M. Flor, Y. Kobayashi, P. Hammerstein, and J. H. Werren. 2007. Wolbachia-induced unidirectional cytoplasmic incompatibility and speciation: mainland-island model. PLoS ONE 8: e701.
94. Tobin, P. C., S. L. Whitmire, D. M. Johnson, O. N. Bjornstad, and M. Liebhold. 2007. Invasion speed is affected by geographical variation in the strength of Allee effects. Ecology Letters 10:36-43.
95. Turelli, M. 2010. Cytoplasmic incompatibility in populations with overlapping generations. Evolution 64:232-241.
96. Turelli, M., and A. A. Hoffmann. 1991. Rapid spread of an inherited incompatibility factor in California Drosophila. Nature 353:440-442.
97. Turelli, M. 1995. Cytoplasmic incompatibility in Drosophila simulans: dynamics and parameter estimates from natural populations. Genetics 140:1319-1338.
98. Turelli, M., N. H. Barton, and J. A. Coyne. 2001. Theory and speciation. Trends in Ecology & Evolution 16:330-343.
99. Viet, R. R., and M. A. Lewis. 1996. Dispersal, population growth, and the Allee effect: dynamics of the house finch invasion of eastern North America. American Naturalist 148:255-274.
100. Walker, T., P. H. Johnson, L. A. Moreira, I. Iturbe-Ormaetxe, F. D. Frentiu, C. J. McMeniman, Y. S. Leong, et al. 2011. The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations. Nature, doi:10.1038/nature10355.
101. Wang, M.-H., and M. Kot. 2001. Speeds of invasion in a model with strong or weak Allee effects. Mathematical Biosciences 171:83-97.
102. Wang, M.-H., M. Kot, and M. G. Neubert. 2002. Integrodifference equations, Allee effects, and invasions. Journal of Mathematical Biology 44:150-168.
103. Weeks, A. R., M. Turelli, W. R. Harcombe, K. T. Reynolds, and A. A. Hoffmann. 2007. From parasite to mutualist: rapid evolution of Wolbachia in natural populations of Drosophila. PLoS Biology 5:e114.
104. Werren, J. H. 1998. Wolbachia and speciation. Pages 245-260 in D. J. Howard and S. H. Berlocher, eds. Endless forms: species and speciation. Oxford University Press, New York.
105. White, M. J. D. 1968. Models of speciation. Science 158:1065-1070.
106. White, M. J. D. 1973. Animal cytology and evolution. Cambridge University Press, Cambridge.
107. Whitten, M. J. 1971. Insect control by genetic manipulation of natural populations. Science 171:682-684.
108. Wright, S. 1931. Evolution in Mendelian populations. Genetics 16: 97-159.
109. Wright, S. 1943. Isolation by distance. Genetics 28:307-320.
110. Wright, S. 1946. Isolation by distance under diverse systems of mating. Genetics 31:39-59.
111. Zeldovich, Y. B., and G. I. Barenblatt. 1959. Theory of flame propagation. Combustion and Flame 3:61-74.