Evolutionary suicide through a non-catastrophic bifurcation: adaptive dynamics of pathogens with frequency-dependent transmission

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• 作者：Barbara Boldin ; Éva Kisdi
• 关键词：Adaptive dynamics ; Evolutionary suicide ; Non ; catastrophic bifurcation ; Transcritical bifurcation ; Extinction ; Virulence ; Frequency ; dependent incidence ; 92D15 ; 92D30 ; 92D40
• 刊名：Journal of Mathematical Biology
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：72
• 期：4
• 页码：1101-1124
• 全文大小：6,107 KB
• 参考文献：Alizon S, Hurford A, Mideo N, Van Baalen M (2009) Virulence evolution and the trade-off hypothesis: history, current state of affairs and the future. J Evolut Biol 22(2):245–259CrossRef
  Allen LJ (2007) Introduction to mathematical biology. Pearson/Prentice Hall, Upper Saddle River
  Anderson RM, May R (1982) Coevolution of hosts and parasites. Parasitology 85(2):411–426CrossRef
  Antonovics J, Iwasa Y, Hassell MP (1995) A generalized model of parasitoid, venereal, and vector-based transmission processes. Am Nat 145:661–675
  Berec L, Maxin D (2013) Fatal or harmless: extreme bistability induced by sterilizing, sexually transmitted pathogens. Bull Math Biol 75(2):258–273CrossRef MathSciNet MATH
  Bernhauerová V, Berec L (2015) Role of trade-off between sexual and vertical routes for evolution of pathogen transmission. Theor Ecol 8(1):23–36CrossRef
  Boldin B (2006) Introducing a population into a steady community: the critical case, the center manifold, and the direction of bifurcation. SIAM J Appl Math 66(4):1424–1453CrossRef MathSciNet MATH
  Boldin B, Diekmann O (2008) Superinfections can induce evolutionarily stable coexistence of pathogens. J Math Biol 56(5):635–672CrossRef MathSciNet MATH
  Boldin B, Kisdi É (2012) On the evolutionary dynamics of pathogens with direct and environmental transmission. Evolution 66(8):2514–2527CrossRef
  Boots M, Sasaki A (2003) Parasite evolution and extinctions. Ecol Lett 6(3):176–182CrossRef
  de Jong MCM, Diekmann O, Heesterbeek H (1995) How does transmission of infection depend on population size. In: Mollison D (ed) Epidemic models: their structure and relation to data, vol 5. Cambridge University Press, Cambridge, pp 84–94
  Diekmann O, Heesterbeek H, Britton T (2012) Mathematical tools for understanding infectious disease dynamics. Princeton University Press, PrincetonCrossRef
  Ferriere R, Legendre S (2013) Eco-evolutionary feedbacks, adaptive dynamics and evolutionary rescue theory. Philo Trans R Soc B: Biol Sci 368(1610):2012.0081CrossRef
  Gandon S, Day T (2009) Evolutionary epidemiology and the dynamics of adaptation. Evolution 63(4):826–838CrossRef
  Geritz SAH, Kisdi É, Meszéna G, Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evolut Ecol 12(1):35–57CrossRef
  Getz WM, Pickering J (1983) Epidemic models: thresholds and population regulation. Am Nat 162:892–898
  Gyllenberg M (2008) Evolutionary suicide. ERCIM News 73. http://​ercim-news.​ercim.​eu/​en73/​special/​evolutionary-suicide . Accessed 14 Nov 2015
  Gyllenberg M, Parvinen K (2001) Necessary and sufficient conditions for evolutionary suicide. Bull Math Biol 63(5):981–993CrossRef
  Gyllenberg M, Service R (2011) Necessary and sufficient conditions for the existence of an optimisation principle in evolution. J Math Biol 62(3):359–369CrossRef MathSciNet MATH
  Gyllenberg M, Parvinen K, Dieckmann U (2002) Evolutionary suicide and evolution of dispersal in structured metapopulations. J Math Biol 45(2):79–105CrossRef MathSciNet MATH
  Gyllenberg M, Metz JAJ, Service R (2011) When do optimisation arguments make evolutionary sense? In: The mathematics of Darwin’s legacy, mathematics and biosciences in interaction. Birkhäuser/Springer Basel AG, Basel, pp 233–268
  Hardin G (1968) The tragedy of the commons. Science 162(3859):1243–1248CrossRef
  Heesterbeek J, Metz JA (1993) The saturating contact rate in marriage-and epidemic models. J Math Biol 31(5):529–539CrossRef MathSciNet MATH
  Hilker FM, Langlais M, Malchow H (2009) The allee effect and infectious diseases: extinction, multistability, and the (dis-) appearance of oscillations. Am Nat 173(1):72–88CrossRef
  Lenski RE, May RM (1994) The evolution of virulence in parasites and pathogens: reconciliation between two competing hypotheses. J Theor Biol 169(3):253–265CrossRef
  Matsuda H, Abrams PA (1994a) Runaway evolution to self-extinction under asymmetrical competition. Evolution 48(6):1764–1772
  Matsuda H, Abrams PA (1994b) Timid consumers: self-extinction due to adaptive change in foraging and anti-predator effort. Theor Popul Biol 45(1):76–91
  Metz JAJ, Geritz SAH. Frequency dependence 3.0: picking up on Heino, Metz & Kaitala (1989) (in preparation)
  Metz JAJ, Nisbet RM, Geritz SAH (1992) How should we define fitness for general ecological scenarios? Trends Ecol Evol 7(6):198–202CrossRef
  Metz JAJ, Mylius SD, Diekmann O (2008) When does evolution optimize. Evol Ecol Res 10(5):629–654
  Nunney L, Campbell KA (1993) Assessing minimum viable population size: demography meets population genetics. Trends Ecol Evol 8(7):234–239CrossRef
  Parvinen K (2007) Evolutionary suicide in a discrete-time metapopulation model. Evolut Ecol Res 9(4):619
  Parvinen K (2010) Adaptive dynamics of cooperation may prevent the coexistence of defectors and cooperators and even cause extinction. Proc R Soc B: Biol Sci 277(1693):2493–2501CrossRef
  Parvinen K, Dieckmann U (2013) Self-extinction through optimizing selection. J Theor Biol 333:1–9CrossRef MathSciNet
  Rankin DJ, López-Sepulcre A (2005) Can adaptation lead to extinction? Oikos 111(3):616–619CrossRef
  Rankin DJ, Bargum K, Kokko H (2007) The tragedy of the commons in evolutionary biology. Trends Ecol Evol 22(12):643–651CrossRef
  Ryder JJ, Miller MR, White A, Knell RJ, Boots M (2007) Host-parasite population dynamics under combined frequency-and density-dependent transmission. Oikos 116(12):2017–2026CrossRef
  Sigmund K (2010) The calculus of selfishness. Princeton University Press, PrincetonCrossRef MATH
  Thrall PH, Antonovics J (1997) Polymorphism in sexual versus non-sexual disease transmission. Proc R Soc Lond B: Biol Sci 264(1381):581–587CrossRef
  Thrall PH, Antonovics J, Hall DW (1993) Host and pathogen coexistence in sexually transmitted and vector-borne diseases characterized by frequency-dependent disease transmission. Am Nat 142:543–552
  Thrall PH, Biere A, Uyenoyama MK (1995) Frequency-dependent disease transmission and the dynamics of the silene-ustilago host-pathogen system. Am Nat 145:43–62
  Webb C (2003) A complete classification of Darwinian extinction in ecological interactions. Am Nat 161(2):181–205CrossRef
  
• 作者单位：Barbara Boldin (1)
  Éva Kisdi (2)
  
  1. Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Glagoljaška 8, 6000, Koper, Slovenia
  2. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  Applications of Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1416

文摘

Evolutionary suicide is a riveting phenomenon in which adaptive evolution drives a viable population to extinction. Gyllenberg and Parvinen (Bull Math Biol 63(5):981–993, 2001) showed that, in a wide class of deterministic population models, a discontinuous transition to extinction is a necessary condition for evolutionary suicide. An implicit assumption of their proof is that the invasion fitness of a rare strategy is well-defined also in the extinction state of the population. Epidemic models with frequency-dependent incidence, which are often used to model the spread of sexually transmitted infections or the dynamics of infectious diseases within herds, violate this assumption. In these models, evolutionary suicide can occur through a non-catastrophic bifurcation whereby pathogen adaptation leads to a continuous decline of host (and consequently pathogen) population size to zero. Evolutionary suicide of pathogens with frequency-dependent transmission can occur in two ways, with pathogen strains evolving either higher or lower virulence. Keywords Adaptive dynamics Evolutionary suicide Non-catastrophic bifurcation Transcritical bifurcation Extinction Virulence Frequency-dependent incidence