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Darwinian dynamics of a juvenile-adult model
1. | Department of Mathematics, Interdisciplinary Program in Applied Mathematics, 617 N Santa Rita, University of Arizona, Tucson AZ 85721 |
2. | Department of Ecology and Evolutionary Biology, 1041 E. Lowell St, University of Arizona, Tucson, AZ 85721, United States |
References:
[1] |
T. S. Bellows, Jr., Analytical model for laboratory populations of Callosobruchus Chinensis and C. Maculatus,, (Coleoptera: Bruchidae), 51 (1982), 263.
doi: 10.2307/4324. |
[2] |
J. M. Cushing and Jia Li, On Ebenman's model for the dynamics of a population with competing juveniles and adults,, Bulletin of Mathematical Biology, 51 (1989), 687. Google Scholar |
[3] |
J. M. Cushing and Zhou Yicang, The net reproductive value and stability in structured population models,, Natural Resource Modeling, 8 (1994), 1. Google Scholar |
[4] |
J. M. Cushing, Cycle chains and the LPA model,, Journal of Difference Equations and Applications, 9 (2003), 655.
doi: 10.1080/1023619021000042216. |
[5] |
J. M. Cushing, Nonlinear semelparous Leslie models,, Mathematical Biosciences and Engineering, 3 (2006), 17.
doi: 10.3934/mbe.2006.3.17. |
[6] |
J. M. Cushing, Three stage semelparous Leslie models,, Journal of Mathematical Biology, 59 (2009), 75.
doi: 10.1007/s00285-008-0208-9. |
[7] |
J. M. Cushing, On the relationship between $r$ and $R_{0}$ and its role in the bifurcation of equilibria of Darwinian matrix models,, Journal of Biological Dynamics, 5 (2011), 277.
doi: 10.1080/17513758.2010.491583. |
[8] |
J. M. Cushing, A dynamic dichotomy for a system of hierarchical difference equations,, Journal of Difference Equations and Applications, 18 (2012), 1.
doi: 10.1080/10236198.2011.628319. |
[9] |
J. M. Cushing and S. M. Henson, Stable bifurcations in semelparous Leslie models,, Journal of Biological Dynamics, 6 (2012), 80.
doi: 10.1080/17513758.2012.716085. |
[10] |
N. V. Davydova, O. Diekmann and S. A. van Gils, Year class coexistence or competitive exclusion for strict biennials?,, Journal of Mathematical Biology, 46 (2003), 95.
doi: 10.1007/s00285-002-0167-5. |
[11] |
N. V. Davydova, "Old and Young: Can They Coexist?", Ph.D Dissertation, (2004). Google Scholar |
[12] |
N. V. Davydova, O. Diekmann and S. A. van Gils, On circulant populations. I. The algebra of semelparity,, Linear Algebra and its Applications, 398 (2005), 185.
doi: 10.1016/j.laa.2004.12.020. |
[13] |
O. Diekmann, N. Davydova and S. van Gils, On a boom and bust year class cycle,, Journal of Difference Equations and Applications, 11 (2005), 327.
doi: 10.1080/10236190412331335409. |
[14] |
B. Ebenman, Niche differences between age and classes and intraspecific competition in age-structured populations,, Journal of Theoretical Biology, 124 (1987), 25.
doi: 10.1016/S0022-5193(87)80249-7. |
[15] |
B. Ebenman, Competition between age classes and population dynamics,, Journal of Theoretical Biology, 131 (1988), 389.
doi: 10.1016/S0022-5193(88)80036-5. |
[16] |
J. Guckenheimer, G. Oster and A. Ipaktchi, The dynamics of density-dependent population models,, Journal of Mathematical Biology, 4 (1977), 101.
doi: 10.1007/BF00275980. |
[17] |
M. P. Hassell, J. H. Lawton and R. M. May, Patterns of dynamical behaviour in single-species populations,, Journal of Animal Ecology. 45 (1976), 45 (1976), 471.
doi: 10.2307/3886. |
[18] |
H. Keilhöfer, "Bifurcation Theory: An Introduction with Applications to PDEs,", Applied Mathematical Sciences 156, 156 (2004).
|
[19] |
R. Kon, Nonexistence of synchronous orbits and class coexistence in matrix population models,, SIAM Journal of Applied Mathematics, 66 (2005), 616.
doi: 10.1137/05062353X. |
[20] |
R. Kon and Y. Iwasa, Single-class orbits in nonlinear Leslie matrix models for semelparous populations,, Journal of Mathematical Biology. 55 (2007), 55 (2007), 781.
doi: 10.1007/s00285-007-0111-9. |
[21] |
R. Kon, Competitive exclusion between year-classes in a semelparous biennial population,, in, (2008), 79.
doi: 10.1007/978-0-8176-4556-4. |
[22] |
R. Kon, Permanence induced by life-cycle resonances: The periodical cicada problem,, Journal of Biological Dynamics, 6 (2012), 855.
doi: 10.1080/17513758.2011.594098. |
[23] |
P. H. Leslie and J. C. Gower, The properties of a stochastic model for two competing species,, Biometrika, 45 (1958), 316.
|
[24] |
W. Liu, Global analysis of an Ebenman's model of population with two competing age classes,, Acta Mathematicae Applicatae Sinica, 11 (1995), 160.
doi: 10.1007/BF02013151. |
[25] |
M. Loreau, Competition between age-classes and stability of stage structured populations: A re-examination of Ebenman's model,, Journal of Theoretical Biology, 144 (1990), 567.
doi: 10.1016/S0022-5193(05)80090-6. |
[26] |
R. M. May, G. R. Conway, M. P. Hassell and T. R. E. Southwood, Time delays, density-dependence and single species oscillations,, Journal of Animal Ecology, 43 (1974), 747.
doi: 10.2307/3535. |
[27] |
R. M. May, Biological populations obeying difference equations: Stable points, stable cycles, and chaos,, Journal of Theoretical Biology, 49 (1975), 645.
doi: 10.1016/0022-5193(75)90078-8. |
[28] |
R. M. Nisbet and L. C. Onyiah, Population dynamic consequences of competition within and between age classes,, Journal of Mathematical Biology, 32 (1994), 329.
doi: 10.1007/BF00160164. |
[29] |
D. A. Roff, "The Evolution of Life Histories: Theory and Analysis,", Chapman and Hall, (1992). Google Scholar |
[30] |
W. O. Tschumy, Competition between juveniles and adults in age-structured populations,, Theoretical Population Biology, 21 (1982), 255.
doi: 10.1016/0040-5809(82)90017-X. |
[31] |
T. L. Vincent and J. S. Brown, "Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics,", Cambridge University Press, (2005).
doi: 10.1017/CBO9780511542633. |
[32] |
A. Wikan and E. Mjølhus, Overcompensatory recruitment and generation delay in discrete age-structured population models,, Journal of Mathematical Biology, 35 (1996), 195.
doi: 10.1007/s002850050050. |
[33] |
A. Wikan, Dynamic consequences of reproductive delay in Leslie matrix models with nonlinear survival probabilities,, Mathematical Biosciences, 146 (1997), 37.
doi: 10.1016/S0025-5564(97)00074-6. |
show all references
References:
[1] |
T. S. Bellows, Jr., Analytical model for laboratory populations of Callosobruchus Chinensis and C. Maculatus,, (Coleoptera: Bruchidae), 51 (1982), 263.
doi: 10.2307/4324. |
[2] |
J. M. Cushing and Jia Li, On Ebenman's model for the dynamics of a population with competing juveniles and adults,, Bulletin of Mathematical Biology, 51 (1989), 687. Google Scholar |
[3] |
J. M. Cushing and Zhou Yicang, The net reproductive value and stability in structured population models,, Natural Resource Modeling, 8 (1994), 1. Google Scholar |
[4] |
J. M. Cushing, Cycle chains and the LPA model,, Journal of Difference Equations and Applications, 9 (2003), 655.
doi: 10.1080/1023619021000042216. |
[5] |
J. M. Cushing, Nonlinear semelparous Leslie models,, Mathematical Biosciences and Engineering, 3 (2006), 17.
doi: 10.3934/mbe.2006.3.17. |
[6] |
J. M. Cushing, Three stage semelparous Leslie models,, Journal of Mathematical Biology, 59 (2009), 75.
doi: 10.1007/s00285-008-0208-9. |
[7] |
J. M. Cushing, On the relationship between $r$ and $R_{0}$ and its role in the bifurcation of equilibria of Darwinian matrix models,, Journal of Biological Dynamics, 5 (2011), 277.
doi: 10.1080/17513758.2010.491583. |
[8] |
J. M. Cushing, A dynamic dichotomy for a system of hierarchical difference equations,, Journal of Difference Equations and Applications, 18 (2012), 1.
doi: 10.1080/10236198.2011.628319. |
[9] |
J. M. Cushing and S. M. Henson, Stable bifurcations in semelparous Leslie models,, Journal of Biological Dynamics, 6 (2012), 80.
doi: 10.1080/17513758.2012.716085. |
[10] |
N. V. Davydova, O. Diekmann and S. A. van Gils, Year class coexistence or competitive exclusion for strict biennials?,, Journal of Mathematical Biology, 46 (2003), 95.
doi: 10.1007/s00285-002-0167-5. |
[11] |
N. V. Davydova, "Old and Young: Can They Coexist?", Ph.D Dissertation, (2004). Google Scholar |
[12] |
N. V. Davydova, O. Diekmann and S. A. van Gils, On circulant populations. I. The algebra of semelparity,, Linear Algebra and its Applications, 398 (2005), 185.
doi: 10.1016/j.laa.2004.12.020. |
[13] |
O. Diekmann, N. Davydova and S. van Gils, On a boom and bust year class cycle,, Journal of Difference Equations and Applications, 11 (2005), 327.
doi: 10.1080/10236190412331335409. |
[14] |
B. Ebenman, Niche differences between age and classes and intraspecific competition in age-structured populations,, Journal of Theoretical Biology, 124 (1987), 25.
doi: 10.1016/S0022-5193(87)80249-7. |
[15] |
B. Ebenman, Competition between age classes and population dynamics,, Journal of Theoretical Biology, 131 (1988), 389.
doi: 10.1016/S0022-5193(88)80036-5. |
[16] |
J. Guckenheimer, G. Oster and A. Ipaktchi, The dynamics of density-dependent population models,, Journal of Mathematical Biology, 4 (1977), 101.
doi: 10.1007/BF00275980. |
[17] |
M. P. Hassell, J. H. Lawton and R. M. May, Patterns of dynamical behaviour in single-species populations,, Journal of Animal Ecology. 45 (1976), 45 (1976), 471.
doi: 10.2307/3886. |
[18] |
H. Keilhöfer, "Bifurcation Theory: An Introduction with Applications to PDEs,", Applied Mathematical Sciences 156, 156 (2004).
|
[19] |
R. Kon, Nonexistence of synchronous orbits and class coexistence in matrix population models,, SIAM Journal of Applied Mathematics, 66 (2005), 616.
doi: 10.1137/05062353X. |
[20] |
R. Kon and Y. Iwasa, Single-class orbits in nonlinear Leslie matrix models for semelparous populations,, Journal of Mathematical Biology. 55 (2007), 55 (2007), 781.
doi: 10.1007/s00285-007-0111-9. |
[21] |
R. Kon, Competitive exclusion between year-classes in a semelparous biennial population,, in, (2008), 79.
doi: 10.1007/978-0-8176-4556-4. |
[22] |
R. Kon, Permanence induced by life-cycle resonances: The periodical cicada problem,, Journal of Biological Dynamics, 6 (2012), 855.
doi: 10.1080/17513758.2011.594098. |
[23] |
P. H. Leslie and J. C. Gower, The properties of a stochastic model for two competing species,, Biometrika, 45 (1958), 316.
|
[24] |
W. Liu, Global analysis of an Ebenman's model of population with two competing age classes,, Acta Mathematicae Applicatae Sinica, 11 (1995), 160.
doi: 10.1007/BF02013151. |
[25] |
M. Loreau, Competition between age-classes and stability of stage structured populations: A re-examination of Ebenman's model,, Journal of Theoretical Biology, 144 (1990), 567.
doi: 10.1016/S0022-5193(05)80090-6. |
[26] |
R. M. May, G. R. Conway, M. P. Hassell and T. R. E. Southwood, Time delays, density-dependence and single species oscillations,, Journal of Animal Ecology, 43 (1974), 747.
doi: 10.2307/3535. |
[27] |
R. M. May, Biological populations obeying difference equations: Stable points, stable cycles, and chaos,, Journal of Theoretical Biology, 49 (1975), 645.
doi: 10.1016/0022-5193(75)90078-8. |
[28] |
R. M. Nisbet and L. C. Onyiah, Population dynamic consequences of competition within and between age classes,, Journal of Mathematical Biology, 32 (1994), 329.
doi: 10.1007/BF00160164. |
[29] |
D. A. Roff, "The Evolution of Life Histories: Theory and Analysis,", Chapman and Hall, (1992). Google Scholar |
[30] |
W. O. Tschumy, Competition between juveniles and adults in age-structured populations,, Theoretical Population Biology, 21 (1982), 255.
doi: 10.1016/0040-5809(82)90017-X. |
[31] |
T. L. Vincent and J. S. Brown, "Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics,", Cambridge University Press, (2005).
doi: 10.1017/CBO9780511542633. |
[32] |
A. Wikan and E. Mjølhus, Overcompensatory recruitment and generation delay in discrete age-structured population models,, Journal of Mathematical Biology, 35 (1996), 195.
doi: 10.1007/s002850050050. |
[33] |
A. Wikan, Dynamic consequences of reproductive delay in Leslie matrix models with nonlinear survival probabilities,, Mathematical Biosciences, 146 (1997), 37.
doi: 10.1016/S0025-5564(97)00074-6. |
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