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Modelling the evolutionary dynamics of host resistance-related traits in a susceptible-infected community with density-dependent mortality
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China |
This study explores the evolutionary dynamics of host resistance based on a susceptible-infected population model with density-dependent mortality. We assume that the resistant ability of susceptible host will adaptively evolve, a different type of host differs in its susceptibility to infection, but the resistance to a pathogen involves a cost such that a less susceptible host results in a lower birth rate. By using the methods of adaptive dynamics and critical function analysis, we find that the evolutionary outcome relies mainly on the trade-off relationship between host resistance and its fertility. Firstly, we show that if the trade-off curve is globally concave, then a continuously stable strategy is predicted. In contrast, if the trade-off curve is weakly convex in the vicinity of singular strategy, then evolutionary branching of host resistance is possible. Secondly, after evolutionary branching in the host resistance has occurred, we examine the coevolutionary dynamics of dimorphic susceptible hosts and find that for a type of concave-convex-concave trade-off curve, the finally evolutionary outcome may contain a relatively higher susceptible host and a relatively higher resistant host, which can continuously stably coexist on a long-term evolutionary timescale. If the convex region of trade-off curve is relatively wider, then the finally evolutionary outcome may contain a fully resistant host and a moderately resistant host. Thirdly, through numerical simulation, we find that for a type of sigmoidal trade-off curve, after branching due to the high cost in terms of the birth rate, always the branch with stronger resistance goes extinct, the eventually evolutionary outcome includes a monomorphic host with relatively weaker resistance.
References:
[1] |
T. Ammunét, T. Klemola and K. Parvinen,
Consequences of asymmetric competition between resident and invasive defoliators: A novel empirically based modelling approach, Theor. Popul. Biol., 92 (2014), 107-117.
doi: 10.1016/j.tpb.2013.12.006. |
[2] |
R. M. Anderson and R. M. May,
Coevolution of hosts and parasites, Parasitology, 85 (1982), 411-426.
doi: 10.1017/S0031182000055360. |
[3] |
J. Antonovics and P. H. Thrall,
The cost of resistance and the maintenance of genetic polymorphism in host-pathogen systems, Proc. Roy. Soc. B, 257 (1994), 105-110.
doi: 10.1098/rspb.1994.0101. |
[4] |
A. Best, R. Bowers and A. White,
Evolution, the loss of diversity and the role of trade-offs, Math. Biosci., 264 (2015), 86-93.
doi: 10.1016/j.mbs.2015.03.011. |
[5] |
A. Best, H. Tidbury, A. White and M. Boots, The evolutionary dynamics of within-generation immune priming in invertebrate hosts, J. Royal Society Interface, 10 (2013).
doi: 10.1098/rsif.2012.0887. |
[6] |
A. Best, A. White and M. Boots,
The implications of coevolutionary dynamics to host-parasite interactions, Amer. Naturalist, 173 (2009), 779-791.
doi: 10.1086/598494. |
[7] |
A. Best, A. White and M. Boots,
The evolution of host defence when parasites impact reproduction, Evolutionary Ecology Research, 18 (2017), 393-409.
|
[8] |
B. Boldin, S. A. H. Geritz and É. Kisdi,
Superinfections and adaptive dynamics of pathogen virulence revisited: A critical function analysis, Evolutionary Ecology Research, 11 (2009), 153-175.
|
[9] |
M. H. Bonds,
Host life-history strategy explains parasite-induced sterility, Amer. Naturalist, 168 (2006), 281-293.
doi: 10.1086/506922. |
[10] |
M. Boots, A. Best, M. R. Miller and A. White,
The role of ecological feedbacks in the evolution of host defence: What does theory tell us, Philos. Trans. Roy. Soc. B, 364 (2009), 27-36.
doi: 10.1098/rstb.2008.0160. |
[11] |
M. Boots and M. Begon,
Trade-offs with resistance to a granulosis virus in the Indian meal moth, examined by a laboratory evolution experiment, Functional Ecology, 7 (1993), 528-534.
doi: 10.2307/2390128. |
[12] |
M. Boots and R. G. Bowers,
Three mechanisms of host resistance to microparasites–avoidance, recovery and tolerance–show different evolutionary dynamics, J. Theoretical Biology, 201 (1999), 13-23.
doi: 10.1006/jtbi.1999.1009. |
[13] |
M. Boots and R. G. Bowers,
The evolution of resistance through costly acquired immunity, Proc. Roy. Soc. B, 271 (2004), 715-723.
doi: 10.1098/rspb.2003.2655. |
[14] |
M. Boots and Y. Haraguchi,
The evolution of costly resistance in host-parasite systems, Amer. Naturalist, 153 (1999), 359-370.
doi: 10.1086/303181. |
[15] |
M. Boots, A. White, A. Best and R. Bowers,
How specificity and epidemiology drive the coevolution of static trait diversity in hosts and parasites, Evolution, 68 (2014), 1594-1606.
doi: 10.1111/evo.12393. |
[16] |
R. G. Bowers, A. Hoyle, A. White and M. Boots,
The geometric theory of adaptive evolution: Trade-off and invasion plots, J. Theoret. Biol., 233 (2005), 363-377.
doi: 10.1016/j.jtbi.2004.10.017. |
[17] |
R. G. Bowers,
The basic depression ratio of the host: The evolution of host resistance to microparasites, Proc. Roy. Soc. B, 268 (2001), 243-250.
doi: 10.1098/rspb.2000.1360. |
[18] |
R. G. Bowers,
A baseline model for the apparent competition between many host strains: The evolution of host resistance to microparasites, J. Theoret. Biol., 200 (1999), 65-75.
doi: 10.1006/jtbi.1999.0976. |
[19] |
R. G. Bowers, M. Boots and M. Begon,
Life-history trade-offs and the evolution of pathogen resistance: Competition between host strains, Proc. Roy. Soc. B, 257 (1994), 247-253.
doi: 10.1098/rspb.1994.0122. |
[20] |
R. S. Cantrell, C. Cosner and K. Y. Lam,
Resident-invader dynamics in infinite dimensional systems, J. Differential Equations, 263 (2017), 4565-4616.
doi: 10.1016/j.jde.2017.05.029. |
[21] |
F. B. Christiansen,
On conditions for evolutionary stability for a continuously varying character, Amer. Naturalist, 138 (1991), 37-50.
doi: 10.1086/285203. |
[22] |
R. Cressman,
CSS, NIS and dynamic stability for two-species behavioral models with continuous trait spaces, J. Theoret. Biol., 262 (2010), 80-89.
doi: 10.1016/j.jtbi.2009.09.019. |
[23] |
F. Dercole and S. Rinaldi, Analysis of Evolutionary Processes: The Adaptative Dynamics Approach and its Applications, Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, 2008.
doi: 10.1515/9781400828340.![]() ![]() ![]() |
[24] |
F. Dercole,
Remarks on branching-extinction evolutionary cycles, J. Math. Biol., 47 (2003), 569-580.
doi: 10.1007/s00285-003-0236-4. |
[25] |
U. Dieckmann and M. Doebeli,
On the origin of species by sympatric speciation, Nature, 400 (1999), 354-357.
doi: 10.1038/22521. |
[26] |
O. Diekmann, P. E. Jabin, S. Mischler and B. Perthame,
The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach, Theor. Popul. Biol., 67 (2005), 257-271.
doi: 10.1016/j.tpb.2004.12.003. |
[27] |
U. Dieckmann and R. Law,
The dynamical theory of coevolution: A derivation from stochastic ecological processes, J. Math. Biol., 34 (1996), 579-612.
doi: 10.1007/BF02409751. |
[28] |
U. Dieckmann, J. A. J. Metz and M. W. Sabelis, Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management, Cambridge University Press, Cambridge, 2005.
doi: 10.1017/CBO9780511525728.![]() ![]() |
[29] |
M. Doebeli and U. Dieckmann, Evolutionary branching and sympatric speciation caused by different types of ecological interactions, Amer. Naturalist, 156 (2000), S77–S101.
doi: 10.1086/303417. |
[30] |
I. Eshel,
Evolutionary and continuous stability, J. Theoret. Biol., 103 (1983), 99-111.
doi: 10.1016/0022-5193(83)90201-1. |
[31] |
C. Ferris and A. Best,
The evolution of host defence to parasitism in fluctuating environments, J. Theoret. Biol., 440 (2018), 58-65.
doi: 10.1016/j.jtbi.2017.12.006. |
[32] |
S. Gandon, P. Agnew and Y. Michalakis,
Coevolution between parasite virulence and host life-history traits, Amer. Naturalist, 160 (2002), 374-388.
doi: 10.1086/341525. |
[33] |
F. Gascuel, M. Choisy and J. M. Duplantier, et al., Host resistance, population structure and the long-term persistence of bubonic plague: Contributions of a modelling approach in the Malagasy focus, PLoS Comput. Biol., 9 (2013).
doi: 10.1371/journal.pcbi.1003039. |
[34] |
S. A. H. Geritz, É. Kisdi, G. Meszéna and J. A. J. Metz,
Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evolutionary Ecology, 12 (1998), 35-57.
doi: 10.1023/A:1006554906681. |
[35] |
S. A. H. Geritz, E. van der Meijden and J. A. J. Metz,
Evolutionary dynamics of seed size and seedling competitive ability, Theor. Popul. Biol., 55 (1999), 324-343.
doi: 10.1006/tpbi.1998.1409. |
[36] |
S. A. H. Geritz, É. Kisdi and P. Yan,
Evolutionary branching and long-term coexistence of cycling predators: Critical function analysis, Theor. Popul. Biol., 71 (2007), 424-435.
doi: 10.1016/j.tpb.2007.03.006. |
[37] |
S. A. H. Geritz, M. Gyllenberg, F. J. A. Jacobs and K. Parvinen,
Invasion dynamics and attractor inheritance, J. Math. Biol., 44 (2002), 548-560.
doi: 10.1007/s002850100136. |
[38] |
S. A. H. Geritz,
Resident-invader dynamics and the coexistence of similar strategies, J. Math. Biol., 50 (2005), 67-82.
doi: 10.1007/s00285-004-0280-8. |
[39] |
A. Hoyle, R. G. Bowers, A. White and M. Boots,
The influence of trade-off shape on evolutionary behaviour in classical ecological scenarios, J. Theoret. Biol., 250 (2008), 498-511.
doi: 10.1016/j.jtbi.2007.10.009. |
[40] |
J. Johansson, J. Ripa and N. Kuckländer,
The risk of competitive exclusion during evolutionary branching: Effects of resource variability, correlation and autocorrelation, Theor. Popul. Biol., 77 (2010), 95-104.
doi: 10.1016/j.tpb.2009.10.007. |
[41] |
É. Kisdi and S. A. H. Geritz,
Adaptive dynamics of saturated polymorphisms, J. Math. Biol., 72 (2016), 1039-1079.
doi: 10.1007/s00285-015-0948-2. |
[42] |
É. Kisdi,
Evolutionary branching under asymmetric competition, J. Theoret. Biol., 197 (1999), 149-162.
doi: 10.1006/jtbi.1998.0864. |
[43] |
É. Kisdi,
Trade-off geometries and the adaptive dynamics of two co-evolving species, Evolutionary Ecology Research, 8 (2006), 959-973.
|
[44] |
É. Kisdi, F. J. A. Jacobs and S. A. H. Geritz,
Red Queen evolution by cycles of evolutionary branching and extinction, Selection, 2 (2002), 161-176.
doi: 10.1556/Select.2.2001.1-2.12. |
[45] |
A. R. Kraaijeveld and H. C. J. Godfray,
Trade-off between parasitoid resistance and larval competitive ability in Drosophila melanogaster, Nature, 389 (1997), 278-280.
doi: 10.1038/38483. |
[46] |
A. R. Kraaijeveld, S. J. Layen and P. H. Futerman, et al., Lack of phenotypic and evolutionary cross-resistance against parasitoids and pathogens in Drosophila melanogaster, PloS One, 7 (2012).
doi: 10.1371/journal.pone.0053002. |
[47] |
P. Landi, F. Dercole and S. Rinaldi,
Branching scenarios in eco-evolutionary prey-predator models, SIAM J. Appl. Math., 73 (2013), 1634-1658.
doi: 10.1137/12088673X. |
[48] |
R. Law, P. Marrow and U. Dieckmann,
On evolution under asymmetric competition, Evolutionary Ecology, 11 (1997), 485-501.
doi: 10.1023/A:1018441108982. |
[49] |
O. Leimar,
Multidimensional convergence stability, Evolutionary Ecology Research, 11 (2009), 191-208.
|
[50] |
B. Lemaitre and J. Hoffmann,
The host defense of Drosophila melanogaster, Annual Rev. Immunology, 25 (2007), 697-743.
doi: 10.1146/annurev.immunol.25.022106.141615. |
[51] |
S. Lion and J. A. J. Metz,
Beyond $R_{0}$ Maximisation: On pathogen evolution and environmental dimensions, Trends Ecol. Evol., 33 (2018), 458-473.
doi: 10.1016/j.tree.2018.02.004. |
[52] |
J. Maynard Smith, Evolution and the Theory of Games, Cambridge University Press, Cambridge, 1982.
doi: 10.1017/CBO9780511806292.![]() ![]() |
[53] |
C. de Mazancourt and U. Dieckmann,
Trade-off geometries and frequency-dependent selection, Amer. Naturalist, 164 (2004), 765-778.
doi: 10.1086/424762. |
[54] |
M. A. Mealor and M. Boots,
An indirect approach to imply trade-off shapes: Population level patterns in resistance suggest a decreasingly costly resistance mechanism in a model insect system, J. Evolutionary Biol., 19 (2006), 326-330.
doi: 10.1111/j.1420-9101.2005.01031.x. |
[55] |
R. Medzhitov,
Recognition of microorganisms and activation of the immune response, Nature, 449 (2007), 819-826.
doi: 10.1038/nature06246. |
[56] |
J. A. J. Metz, R. M. Nisbet and S. A. H. Geritz,
How should we define 'fitness' for general ecological scenarios?, Trends Ecol. Evol., 7 (1992), 198-202.
doi: 10.1016/0169-5347(92)90073-K. |
[57] |
G. Meszéna, M. Gyllenberg, F. J. Jacobs and J. A. J. Metz, Link between population dynamics and dynamics of Darwinian evolution, Phys. Rev. Lett., 95 (2005).
doi: 10.1103/PhysRevLett.95.078105. |
[58] |
M. R. Miller, A. White and M. Boots,
The evolution of host resistance: Tolerance and control as distinct strategies, J. Theoret. Biol., 236 (2005), 198-207.
doi: 10.1016/j.jtbi.2005.03.005. |
[59] |
M. R. Miller, A. White and M. Boots,
The evolution of parasites in response to tolerance in their hosts: The good, the bad and apparent commensalism, Evolution, 60 (2006), 945-956.
doi: 10.1111/j.0014-3820.2006.tb01173.x. |
[60] |
M. R. Miller, A. White and M. Boots,
Host life span and the evolution of resistance characteristics, Evolution, 61 (2007), 2-14.
doi: 10.1111/j.1558-5646.2007.00001.x. |
[61] |
M. A. Nowak and K. Sigmund,
Evolutionary dynamics of biological games, Science, 303 (2004), 793-799.
doi: 10.1126/science.1093411. |
[62] |
K. Parvinen,
Evolutionary suicide, Acta Biotheoretica, 53 (2005), 241-264.
doi: 10.1007/s10441-005-2531-5. |
[63] |
A. Peschel and H. G. Sahl,
The co-evolution of host cationic antimicrobial peptides and microbial resistance, Nature Rev. Microbiology, 4 (2006), 529-536.
doi: 10.1038/nrmicro1441. |
[64] |
O. Restif and J. C. Koella,
Shared control of epidemiological traits in a coevolutionary model of host-parasite interactions, Amer. Naturalist, 161 (2003), 827-836.
doi: 10.1086/375171. |
[65] |
O. Restif and J. C. Koella, Concurrent evolution of resistance and tolerance to pathogens, Amer. Naturalist, 164 (2004), E90–E102.
doi: 10.1086/423713. |
[66] |
D. A. Roff, Life History Evolution, Sinauer Associates, Sunderland, MA, 2002. |
[67] |
B. A. Roy and J. W. Kirchner,
Evolutionary dynamics of pathogen resistance and tolerance, Evolution, 54 (2000), 51-63.
doi: 10.1111/j.0014-3820.2000.tb00007.x. |
[68] |
J. Sardanyés and R. V. Solé,
Chaotic stability in spatially-resolved host-parasite replicators: The Red Queen on a lattice, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 17 (2007), 589-606.
doi: 10.1142/S0218127407017458. |
[69] |
E. Shim and A. P. Galvani, Evolutionary repercussions of avian culling on host resistance and influenza virulence, PloS One, 4 (2009).
doi: 10.1371/journal.pone.0005503. |
[70] |
M. L. Simoes, E. P. Caragata and G. Dimopoulos,
Diverse host and restriction factors regulate mosquito-pathogen interactions, Trends in Parasitology, 34 (2018), 603-616.
doi: 10.1016/j.pt.2018.04.011. |
[71] |
S. C. Stearns, The Evolution of Life Histories, Oxford University Press, Oxford, 1992.
![]() |
[72] |
T. O. Svennungsen and É. Kisdi,
Evolutionary branching of virulence in a single-infection model, J. Theoret. Biol., 257 (2009), 408-418.
doi: 10.1016/j.jtbi.2008.11.014. |
[73] |
A. N. Theodosopoulos, A. K. Hund and S. A. Taylor,
Parasites and host species barriers in animal hybrid zones, Trends Ecol. Evol., 34 (2019), 19-30.
doi: 10.1016/j.tree.2018.09.011. |
[74] |
W. Wang, Y. Li and H. W. Hethcote,
Bifurcations in a host-parasite model with nonlinear incidence, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), 3291-3307.
doi: 10.1142/S0218127406016793. |
[75] |
J. Zu, K. F. Wang and M. Mimura,
Evolutionary branching and evolutionarily stable coexistence of predator species: Critical function analysis, Math. Biosci., 231 (2011), 210-224.
doi: 10.1016/j.mbs.2011.03.007. |
[76] |
J. Zu, J. L. Wang and J. Q. Du,
Adaptive evolution of defense ability leads to diversification of prey species, Acta Biotheoretica, 62 (2014), 207-234.
doi: 10.1007/s10441-014-9218-8. |
[77] |
J. Zu, B. Yuan and J. Q. Du,
Top predators induce the evolutionary diversification of intermediate predator species, J. Theoret. Biol., 387 (2015), 1-12.
doi: 10.1016/j.jtbi.2015.09.024. |
show all references
References:
[1] |
T. Ammunét, T. Klemola and K. Parvinen,
Consequences of asymmetric competition between resident and invasive defoliators: A novel empirically based modelling approach, Theor. Popul. Biol., 92 (2014), 107-117.
doi: 10.1016/j.tpb.2013.12.006. |
[2] |
R. M. Anderson and R. M. May,
Coevolution of hosts and parasites, Parasitology, 85 (1982), 411-426.
doi: 10.1017/S0031182000055360. |
[3] |
J. Antonovics and P. H. Thrall,
The cost of resistance and the maintenance of genetic polymorphism in host-pathogen systems, Proc. Roy. Soc. B, 257 (1994), 105-110.
doi: 10.1098/rspb.1994.0101. |
[4] |
A. Best, R. Bowers and A. White,
Evolution, the loss of diversity and the role of trade-offs, Math. Biosci., 264 (2015), 86-93.
doi: 10.1016/j.mbs.2015.03.011. |
[5] |
A. Best, H. Tidbury, A. White and M. Boots, The evolutionary dynamics of within-generation immune priming in invertebrate hosts, J. Royal Society Interface, 10 (2013).
doi: 10.1098/rsif.2012.0887. |
[6] |
A. Best, A. White and M. Boots,
The implications of coevolutionary dynamics to host-parasite interactions, Amer. Naturalist, 173 (2009), 779-791.
doi: 10.1086/598494. |
[7] |
A. Best, A. White and M. Boots,
The evolution of host defence when parasites impact reproduction, Evolutionary Ecology Research, 18 (2017), 393-409.
|
[8] |
B. Boldin, S. A. H. Geritz and É. Kisdi,
Superinfections and adaptive dynamics of pathogen virulence revisited: A critical function analysis, Evolutionary Ecology Research, 11 (2009), 153-175.
|
[9] |
M. H. Bonds,
Host life-history strategy explains parasite-induced sterility, Amer. Naturalist, 168 (2006), 281-293.
doi: 10.1086/506922. |
[10] |
M. Boots, A. Best, M. R. Miller and A. White,
The role of ecological feedbacks in the evolution of host defence: What does theory tell us, Philos. Trans. Roy. Soc. B, 364 (2009), 27-36.
doi: 10.1098/rstb.2008.0160. |
[11] |
M. Boots and M. Begon,
Trade-offs with resistance to a granulosis virus in the Indian meal moth, examined by a laboratory evolution experiment, Functional Ecology, 7 (1993), 528-534.
doi: 10.2307/2390128. |
[12] |
M. Boots and R. G. Bowers,
Three mechanisms of host resistance to microparasites–avoidance, recovery and tolerance–show different evolutionary dynamics, J. Theoretical Biology, 201 (1999), 13-23.
doi: 10.1006/jtbi.1999.1009. |
[13] |
M. Boots and R. G. Bowers,
The evolution of resistance through costly acquired immunity, Proc. Roy. Soc. B, 271 (2004), 715-723.
doi: 10.1098/rspb.2003.2655. |
[14] |
M. Boots and Y. Haraguchi,
The evolution of costly resistance in host-parasite systems, Amer. Naturalist, 153 (1999), 359-370.
doi: 10.1086/303181. |
[15] |
M. Boots, A. White, A. Best and R. Bowers,
How specificity and epidemiology drive the coevolution of static trait diversity in hosts and parasites, Evolution, 68 (2014), 1594-1606.
doi: 10.1111/evo.12393. |
[16] |
R. G. Bowers, A. Hoyle, A. White and M. Boots,
The geometric theory of adaptive evolution: Trade-off and invasion plots, J. Theoret. Biol., 233 (2005), 363-377.
doi: 10.1016/j.jtbi.2004.10.017. |
[17] |
R. G. Bowers,
The basic depression ratio of the host: The evolution of host resistance to microparasites, Proc. Roy. Soc. B, 268 (2001), 243-250.
doi: 10.1098/rspb.2000.1360. |
[18] |
R. G. Bowers,
A baseline model for the apparent competition between many host strains: The evolution of host resistance to microparasites, J. Theoret. Biol., 200 (1999), 65-75.
doi: 10.1006/jtbi.1999.0976. |
[19] |
R. G. Bowers, M. Boots and M. Begon,
Life-history trade-offs and the evolution of pathogen resistance: Competition between host strains, Proc. Roy. Soc. B, 257 (1994), 247-253.
doi: 10.1098/rspb.1994.0122. |
[20] |
R. S. Cantrell, C. Cosner and K. Y. Lam,
Resident-invader dynamics in infinite dimensional systems, J. Differential Equations, 263 (2017), 4565-4616.
doi: 10.1016/j.jde.2017.05.029. |
[21] |
F. B. Christiansen,
On conditions for evolutionary stability for a continuously varying character, Amer. Naturalist, 138 (1991), 37-50.
doi: 10.1086/285203. |
[22] |
R. Cressman,
CSS, NIS and dynamic stability for two-species behavioral models with continuous trait spaces, J. Theoret. Biol., 262 (2010), 80-89.
doi: 10.1016/j.jtbi.2009.09.019. |
[23] |
F. Dercole and S. Rinaldi, Analysis of Evolutionary Processes: The Adaptative Dynamics Approach and its Applications, Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, 2008.
doi: 10.1515/9781400828340.![]() ![]() ![]() |
[24] |
F. Dercole,
Remarks on branching-extinction evolutionary cycles, J. Math. Biol., 47 (2003), 569-580.
doi: 10.1007/s00285-003-0236-4. |
[25] |
U. Dieckmann and M. Doebeli,
On the origin of species by sympatric speciation, Nature, 400 (1999), 354-357.
doi: 10.1038/22521. |
[26] |
O. Diekmann, P. E. Jabin, S. Mischler and B. Perthame,
The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach, Theor. Popul. Biol., 67 (2005), 257-271.
doi: 10.1016/j.tpb.2004.12.003. |
[27] |
U. Dieckmann and R. Law,
The dynamical theory of coevolution: A derivation from stochastic ecological processes, J. Math. Biol., 34 (1996), 579-612.
doi: 10.1007/BF02409751. |
[28] |
U. Dieckmann, J. A. J. Metz and M. W. Sabelis, Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management, Cambridge University Press, Cambridge, 2005.
doi: 10.1017/CBO9780511525728.![]() ![]() |
[29] |
M. Doebeli and U. Dieckmann, Evolutionary branching and sympatric speciation caused by different types of ecological interactions, Amer. Naturalist, 156 (2000), S77–S101.
doi: 10.1086/303417. |
[30] |
I. Eshel,
Evolutionary and continuous stability, J. Theoret. Biol., 103 (1983), 99-111.
doi: 10.1016/0022-5193(83)90201-1. |
[31] |
C. Ferris and A. Best,
The evolution of host defence to parasitism in fluctuating environments, J. Theoret. Biol., 440 (2018), 58-65.
doi: 10.1016/j.jtbi.2017.12.006. |
[32] |
S. Gandon, P. Agnew and Y. Michalakis,
Coevolution between parasite virulence and host life-history traits, Amer. Naturalist, 160 (2002), 374-388.
doi: 10.1086/341525. |
[33] |
F. Gascuel, M. Choisy and J. M. Duplantier, et al., Host resistance, population structure and the long-term persistence of bubonic plague: Contributions of a modelling approach in the Malagasy focus, PLoS Comput. Biol., 9 (2013).
doi: 10.1371/journal.pcbi.1003039. |
[34] |
S. A. H. Geritz, É. Kisdi, G. Meszéna and J. A. J. Metz,
Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evolutionary Ecology, 12 (1998), 35-57.
doi: 10.1023/A:1006554906681. |
[35] |
S. A. H. Geritz, E. van der Meijden and J. A. J. Metz,
Evolutionary dynamics of seed size and seedling competitive ability, Theor. Popul. Biol., 55 (1999), 324-343.
doi: 10.1006/tpbi.1998.1409. |
[36] |
S. A. H. Geritz, É. Kisdi and P. Yan,
Evolutionary branching and long-term coexistence of cycling predators: Critical function analysis, Theor. Popul. Biol., 71 (2007), 424-435.
doi: 10.1016/j.tpb.2007.03.006. |
[37] |
S. A. H. Geritz, M. Gyllenberg, F. J. A. Jacobs and K. Parvinen,
Invasion dynamics and attractor inheritance, J. Math. Biol., 44 (2002), 548-560.
doi: 10.1007/s002850100136. |
[38] |
S. A. H. Geritz,
Resident-invader dynamics and the coexistence of similar strategies, J. Math. Biol., 50 (2005), 67-82.
doi: 10.1007/s00285-004-0280-8. |
[39] |
A. Hoyle, R. G. Bowers, A. White and M. Boots,
The influence of trade-off shape on evolutionary behaviour in classical ecological scenarios, J. Theoret. Biol., 250 (2008), 498-511.
doi: 10.1016/j.jtbi.2007.10.009. |
[40] |
J. Johansson, J. Ripa and N. Kuckländer,
The risk of competitive exclusion during evolutionary branching: Effects of resource variability, correlation and autocorrelation, Theor. Popul. Biol., 77 (2010), 95-104.
doi: 10.1016/j.tpb.2009.10.007. |
[41] |
É. Kisdi and S. A. H. Geritz,
Adaptive dynamics of saturated polymorphisms, J. Math. Biol., 72 (2016), 1039-1079.
doi: 10.1007/s00285-015-0948-2. |
[42] |
É. Kisdi,
Evolutionary branching under asymmetric competition, J. Theoret. Biol., 197 (1999), 149-162.
doi: 10.1006/jtbi.1998.0864. |
[43] |
É. Kisdi,
Trade-off geometries and the adaptive dynamics of two co-evolving species, Evolutionary Ecology Research, 8 (2006), 959-973.
|
[44] |
É. Kisdi, F. J. A. Jacobs and S. A. H. Geritz,
Red Queen evolution by cycles of evolutionary branching and extinction, Selection, 2 (2002), 161-176.
doi: 10.1556/Select.2.2001.1-2.12. |
[45] |
A. R. Kraaijeveld and H. C. J. Godfray,
Trade-off between parasitoid resistance and larval competitive ability in Drosophila melanogaster, Nature, 389 (1997), 278-280.
doi: 10.1038/38483. |
[46] |
A. R. Kraaijeveld, S. J. Layen and P. H. Futerman, et al., Lack of phenotypic and evolutionary cross-resistance against parasitoids and pathogens in Drosophila melanogaster, PloS One, 7 (2012).
doi: 10.1371/journal.pone.0053002. |
[47] |
P. Landi, F. Dercole and S. Rinaldi,
Branching scenarios in eco-evolutionary prey-predator models, SIAM J. Appl. Math., 73 (2013), 1634-1658.
doi: 10.1137/12088673X. |
[48] |
R. Law, P. Marrow and U. Dieckmann,
On evolution under asymmetric competition, Evolutionary Ecology, 11 (1997), 485-501.
doi: 10.1023/A:1018441108982. |
[49] |
O. Leimar,
Multidimensional convergence stability, Evolutionary Ecology Research, 11 (2009), 191-208.
|
[50] |
B. Lemaitre and J. Hoffmann,
The host defense of Drosophila melanogaster, Annual Rev. Immunology, 25 (2007), 697-743.
doi: 10.1146/annurev.immunol.25.022106.141615. |
[51] |
S. Lion and J. A. J. Metz,
Beyond $R_{0}$ Maximisation: On pathogen evolution and environmental dimensions, Trends Ecol. Evol., 33 (2018), 458-473.
doi: 10.1016/j.tree.2018.02.004. |
[52] |
J. Maynard Smith, Evolution and the Theory of Games, Cambridge University Press, Cambridge, 1982.
doi: 10.1017/CBO9780511806292.![]() ![]() |
[53] |
C. de Mazancourt and U. Dieckmann,
Trade-off geometries and frequency-dependent selection, Amer. Naturalist, 164 (2004), 765-778.
doi: 10.1086/424762. |
[54] |
M. A. Mealor and M. Boots,
An indirect approach to imply trade-off shapes: Population level patterns in resistance suggest a decreasingly costly resistance mechanism in a model insect system, J. Evolutionary Biol., 19 (2006), 326-330.
doi: 10.1111/j.1420-9101.2005.01031.x. |
[55] |
R. Medzhitov,
Recognition of microorganisms and activation of the immune response, Nature, 449 (2007), 819-826.
doi: 10.1038/nature06246. |
[56] |
J. A. J. Metz, R. M. Nisbet and S. A. H. Geritz,
How should we define 'fitness' for general ecological scenarios?, Trends Ecol. Evol., 7 (1992), 198-202.
doi: 10.1016/0169-5347(92)90073-K. |
[57] |
G. Meszéna, M. Gyllenberg, F. J. Jacobs and J. A. J. Metz, Link between population dynamics and dynamics of Darwinian evolution, Phys. Rev. Lett., 95 (2005).
doi: 10.1103/PhysRevLett.95.078105. |
[58] |
M. R. Miller, A. White and M. Boots,
The evolution of host resistance: Tolerance and control as distinct strategies, J. Theoret. Biol., 236 (2005), 198-207.
doi: 10.1016/j.jtbi.2005.03.005. |
[59] |
M. R. Miller, A. White and M. Boots,
The evolution of parasites in response to tolerance in their hosts: The good, the bad and apparent commensalism, Evolution, 60 (2006), 945-956.
doi: 10.1111/j.0014-3820.2006.tb01173.x. |
[60] |
M. R. Miller, A. White and M. Boots,
Host life span and the evolution of resistance characteristics, Evolution, 61 (2007), 2-14.
doi: 10.1111/j.1558-5646.2007.00001.x. |
[61] |
M. A. Nowak and K. Sigmund,
Evolutionary dynamics of biological games, Science, 303 (2004), 793-799.
doi: 10.1126/science.1093411. |
[62] |
K. Parvinen,
Evolutionary suicide, Acta Biotheoretica, 53 (2005), 241-264.
doi: 10.1007/s10441-005-2531-5. |
[63] |
A. Peschel and H. G. Sahl,
The co-evolution of host cationic antimicrobial peptides and microbial resistance, Nature Rev. Microbiology, 4 (2006), 529-536.
doi: 10.1038/nrmicro1441. |
[64] |
O. Restif and J. C. Koella,
Shared control of epidemiological traits in a coevolutionary model of host-parasite interactions, Amer. Naturalist, 161 (2003), 827-836.
doi: 10.1086/375171. |
[65] |
O. Restif and J. C. Koella, Concurrent evolution of resistance and tolerance to pathogens, Amer. Naturalist, 164 (2004), E90–E102.
doi: 10.1086/423713. |
[66] |
D. A. Roff, Life History Evolution, Sinauer Associates, Sunderland, MA, 2002. |
[67] |
B. A. Roy and J. W. Kirchner,
Evolutionary dynamics of pathogen resistance and tolerance, Evolution, 54 (2000), 51-63.
doi: 10.1111/j.0014-3820.2000.tb00007.x. |
[68] |
J. Sardanyés and R. V. Solé,
Chaotic stability in spatially-resolved host-parasite replicators: The Red Queen on a lattice, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 17 (2007), 589-606.
doi: 10.1142/S0218127407017458. |
[69] |
E. Shim and A. P. Galvani, Evolutionary repercussions of avian culling on host resistance and influenza virulence, PloS One, 4 (2009).
doi: 10.1371/journal.pone.0005503. |
[70] |
M. L. Simoes, E. P. Caragata and G. Dimopoulos,
Diverse host and restriction factors regulate mosquito-pathogen interactions, Trends in Parasitology, 34 (2018), 603-616.
doi: 10.1016/j.pt.2018.04.011. |
[71] |
S. C. Stearns, The Evolution of Life Histories, Oxford University Press, Oxford, 1992.
![]() |
[72] |
T. O. Svennungsen and É. Kisdi,
Evolutionary branching of virulence in a single-infection model, J. Theoret. Biol., 257 (2009), 408-418.
doi: 10.1016/j.jtbi.2008.11.014. |
[73] |
A. N. Theodosopoulos, A. K. Hund and S. A. Taylor,
Parasites and host species barriers in animal hybrid zones, Trends Ecol. Evol., 34 (2019), 19-30.
doi: 10.1016/j.tree.2018.09.011. |
[74] |
W. Wang, Y. Li and H. W. Hethcote,
Bifurcations in a host-parasite model with nonlinear incidence, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), 3291-3307.
doi: 10.1142/S0218127406016793. |
[75] |
J. Zu, K. F. Wang and M. Mimura,
Evolutionary branching and evolutionarily stable coexistence of predator species: Critical function analysis, Math. Biosci., 231 (2011), 210-224.
doi: 10.1016/j.mbs.2011.03.007. |
[76] |
J. Zu, J. L. Wang and J. Q. Du,
Adaptive evolution of defense ability leads to diversification of prey species, Acta Biotheoretica, 62 (2014), 207-234.
doi: 10.1007/s10441-014-9218-8. |
[77] |
J. Zu, B. Yuan and J. Q. Du,
Top predators induce the evolutionary diversification of intermediate predator species, J. Theoret. Biol., 387 (2015), 1-12.
doi: 10.1016/j.jtbi.2015.09.024. |












Evolutionary outcomes | Evolutionary conditions | Shape of trade-off function |
CSS |
Globally concave | |
EBP |
Concave-convex-concave or sigmoidal | |
CSS |
Concave-convex-concave | |
Extinction of one branch | No attracting singular strategies | Sigmoidal |
Note: CSS means continuously stable strategy; EBP means evolutionary branching point. |
Evolutionary outcomes | Evolutionary conditions | Shape of trade-off function |
CSS |
Globally concave | |
EBP |
Concave-convex-concave or sigmoidal | |
CSS |
Concave-convex-concave | |
Extinction of one branch | No attracting singular strategies | Sigmoidal |
Note: CSS means continuously stable strategy; EBP means evolutionary branching point. |
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