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The work of Glenn F. Webb
The evolutionary dynamics of a population model with a strong Allee effect
1. | Department of Mathematics, Interdisciplinary Program in Applied Mathematics, 617 N Santa Rita, Tucson, Arizona, 85721, United States |
References:
[1] |
P. A. Abrams, Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: An assessment of three methods, Ecology Letters, 4 (2001), 166-175.
doi: 10.1046/j.1461-0248.2001.00199.x. |
[2] |
W. C. Allee, Animal Aggregations, a Study in General Sociology, University of Chicago Press, Chicago, 1931. |
[3] |
W. C. Allee, The Social Life of Animals, 3rd edition, William Heineman Ltd, London and Toronto, 1941. |
[4] |
W. C. Allee, O. Park, T. Park and K. Schmidt, Principles of Animal Ecology, W. B. Saunders Company, Philadelphia, 1949. |
[5] |
D. S. Boukal and L. Berec, Single-species Models of the Allee effect: Extinction boundaries, sex Ratios and mate Encounters, Journal of Theoretical Biology, 218 (2002), 375-394.
doi: 10.1006/jtbi.2002.3084. |
[6] |
F. Courchamp, T. Clutton-Brock and B. Grenfell, Inverse density dependence and the Allee effect, TREE, 14 (1999), 405-410.
doi: 10.1016/S0169-5347(99)01683-3. |
[7] |
F. Courchamp, L. Berec and J. Gascoigne, Allee Effects in Ecology and Conservation, Oxford University Press, Oxford, Great Britain, 2008.
doi: 10.1093/acprof:oso/9780198570301.001.0001. |
[8] |
J. M. Cushing, Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations, Journal of Biological Dynamics, 8 (2014), 57-73.
doi: 10.1080/17513758.2014.899638. |
[9] |
J. M. Cushing and J. Hudson, Evolutionary dynamics and strong Allee effects, Journal of Biological Dynamics, 6 (2012), 941-958.
doi: 10.1080/17513758.2012.697196. |
[10] |
B. Dennis, Allee effects: Population growth, critical density, and the chance of extinction, Natural Resource Modeling, 3 (1989), 481-538. |
[11] |
F. Dercole and S. Rinaldi, Analysis of Evolutionary Processes: The Adaptive Dynamics Approach and Its Applications, Princeton University Press, Princeton, New Jersey, 2008. |
[12] |
L. Edelstein-Keshet, Mathematical Models in Biology, Classics in Applied Mathematics 46, SIAM, Philadelphia, USA, 2005.
doi: 10.1137/1.9780898719147. |
[13] |
S. N. Elaydi and R. J. Sacker, Population models with Allee effect: A new model, Journal of Biological Dynamics , 4 (2010), 397-408.
doi: 10.1080/17513750903377434. |
[14] |
D. S. Falconer and T. F. C. Mackay, Introduction to Quantitative Genetics, Pearson Education Limited, Prentice Hall, Essex, England, 1996. |
[15] |
F. A. Hopf and F. W. Hopf, The role of the Allee effect in species packing, Theoretical Population Biology, 27 (1985), 27-50.
doi: 10.1016/0040-5809(85)90014-0. |
[16] |
M. R. S. Kulenovic and A.-A. Yakubu, Compensatory versus overcompensatory dynamics in density-dependent leslie models, Journal of Difference Equations and Applications, 10 (2004), 1251-1265.
doi: 10.1080/10236190410001652711. |
[17] |
R. Lande, Natural selection and random genetic drift in phenotypic evolution, Evolution, 30 (1976), 314-334. |
[18] |
R. Lande, A quantitative genetic theory of life history evolution, Ecology, 63 (1982), 607-615. |
[19] |
M. A. Lewis and P. Kareiva, Allee dynamics and the spread of invading organisms, Theoretical Population Biology, 43 (1993), 141-158.
doi: 10.1006/tpbi.1993.1007. |
[20] |
J. Lush, Animal Breeding Plans, Iowa State College Press, Ames, Iowa, USA, 1937. |
[21] |
S. P. Otto and T. Day, A Biologist's Guide to Mathematical Modeling in Ecology and Evolution, Princeton University Press, Princeton, New Jersey, USA, 2007. |
[22] |
I. Scheuring, Allee effect increases dynamical stability in populations, Journal of Theoretical Biology, 199 (1999), 407-414.
doi: 10.1006/jtbi.1999.0966. |
[23] |
S. J. Schreiber, Allee effects, extinctions, and chaotic transients in simple population models, Theoretical Population Biology, 64 (2003), 201-209.
doi: 10.1016/S0040-5809(03)00072-8. |
[24] |
T. L. Vincent and J. S. Brown, Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics, Cambridge University Press, New York, 2005.
doi: 10.1017/CBO9780511542633. |
[25] |
G. Wang, X.-G. Liang and F.-Z. Wang, The competitive dynamics of populations subject to an Allee effect, Ecological Modelling, 124 (1999), 183-192.
doi: 10.1016/S0304-3800(99)00160-X. |
show all references
References:
[1] |
P. A. Abrams, Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: An assessment of three methods, Ecology Letters, 4 (2001), 166-175.
doi: 10.1046/j.1461-0248.2001.00199.x. |
[2] |
W. C. Allee, Animal Aggregations, a Study in General Sociology, University of Chicago Press, Chicago, 1931. |
[3] |
W. C. Allee, The Social Life of Animals, 3rd edition, William Heineman Ltd, London and Toronto, 1941. |
[4] |
W. C. Allee, O. Park, T. Park and K. Schmidt, Principles of Animal Ecology, W. B. Saunders Company, Philadelphia, 1949. |
[5] |
D. S. Boukal and L. Berec, Single-species Models of the Allee effect: Extinction boundaries, sex Ratios and mate Encounters, Journal of Theoretical Biology, 218 (2002), 375-394.
doi: 10.1006/jtbi.2002.3084. |
[6] |
F. Courchamp, T. Clutton-Brock and B. Grenfell, Inverse density dependence and the Allee effect, TREE, 14 (1999), 405-410.
doi: 10.1016/S0169-5347(99)01683-3. |
[7] |
F. Courchamp, L. Berec and J. Gascoigne, Allee Effects in Ecology and Conservation, Oxford University Press, Oxford, Great Britain, 2008.
doi: 10.1093/acprof:oso/9780198570301.001.0001. |
[8] |
J. M. Cushing, Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations, Journal of Biological Dynamics, 8 (2014), 57-73.
doi: 10.1080/17513758.2014.899638. |
[9] |
J. M. Cushing and J. Hudson, Evolutionary dynamics and strong Allee effects, Journal of Biological Dynamics, 6 (2012), 941-958.
doi: 10.1080/17513758.2012.697196. |
[10] |
B. Dennis, Allee effects: Population growth, critical density, and the chance of extinction, Natural Resource Modeling, 3 (1989), 481-538. |
[11] |
F. Dercole and S. Rinaldi, Analysis of Evolutionary Processes: The Adaptive Dynamics Approach and Its Applications, Princeton University Press, Princeton, New Jersey, 2008. |
[12] |
L. Edelstein-Keshet, Mathematical Models in Biology, Classics in Applied Mathematics 46, SIAM, Philadelphia, USA, 2005.
doi: 10.1137/1.9780898719147. |
[13] |
S. N. Elaydi and R. J. Sacker, Population models with Allee effect: A new model, Journal of Biological Dynamics , 4 (2010), 397-408.
doi: 10.1080/17513750903377434. |
[14] |
D. S. Falconer and T. F. C. Mackay, Introduction to Quantitative Genetics, Pearson Education Limited, Prentice Hall, Essex, England, 1996. |
[15] |
F. A. Hopf and F. W. Hopf, The role of the Allee effect in species packing, Theoretical Population Biology, 27 (1985), 27-50.
doi: 10.1016/0040-5809(85)90014-0. |
[16] |
M. R. S. Kulenovic and A.-A. Yakubu, Compensatory versus overcompensatory dynamics in density-dependent leslie models, Journal of Difference Equations and Applications, 10 (2004), 1251-1265.
doi: 10.1080/10236190410001652711. |
[17] |
R. Lande, Natural selection and random genetic drift in phenotypic evolution, Evolution, 30 (1976), 314-334. |
[18] |
R. Lande, A quantitative genetic theory of life history evolution, Ecology, 63 (1982), 607-615. |
[19] |
M. A. Lewis and P. Kareiva, Allee dynamics and the spread of invading organisms, Theoretical Population Biology, 43 (1993), 141-158.
doi: 10.1006/tpbi.1993.1007. |
[20] |
J. Lush, Animal Breeding Plans, Iowa State College Press, Ames, Iowa, USA, 1937. |
[21] |
S. P. Otto and T. Day, A Biologist's Guide to Mathematical Modeling in Ecology and Evolution, Princeton University Press, Princeton, New Jersey, USA, 2007. |
[22] |
I. Scheuring, Allee effect increases dynamical stability in populations, Journal of Theoretical Biology, 199 (1999), 407-414.
doi: 10.1006/jtbi.1999.0966. |
[23] |
S. J. Schreiber, Allee effects, extinctions, and chaotic transients in simple population models, Theoretical Population Biology, 64 (2003), 201-209.
doi: 10.1016/S0040-5809(03)00072-8. |
[24] |
T. L. Vincent and J. S. Brown, Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics, Cambridge University Press, New York, 2005.
doi: 10.1017/CBO9780511542633. |
[25] |
G. Wang, X.-G. Liang and F.-Z. Wang, The competitive dynamics of populations subject to an Allee effect, Ecological Modelling, 124 (1999), 183-192.
doi: 10.1016/S0304-3800(99)00160-X. |
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