Stochastic game dynamics under demographic fluctuations

Proceedings of the National Academy of Sciences of the United States of America

Volumn 112, Issue 29, 2015, Pages 9064-9069

  Huang, Weini ^a   Hauert, Christoph ^b   Traulsen, Arne ^a  

^a MAX PLANCK INSTITUTE FOR EVOLUTIONARY BIOLOGY   (Germany)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Changing population size; Evolutionary games; Stochastic dynamics

Indexed keywords

ARTICLE; COMPETITION; CONTROLLED STUDY; DEMOGRAPHY; EVOLUTIONARY ADAPTATION; FREQUENCY DEPENDENT SELECTION; GAME; GROWTH RATE; LOTKA VOLTERRA EQUATION; MASS EXTINCTION; MATHEMATICAL MODEL; POPULATION DENSITY; POPULATION DYNAMICS; POPULATION GROWTH; POPULATION SIZE; PRIORITY JOURNAL; STOCHASTIC MODEL; HUMAN; SPECIES EXTINCTION; STATISTICS; THEORETICAL MODEL;

DEMOGRAPHY; EXTINCTION, BIOLOGICAL; GAME THEORY; HUMANS; MODELS, THEORETICAL; POPULATION DENSITY; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

EID: 84937440592     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1418745112     Document Type: Article

References (45)

1. Taylor PD, Jonker L (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40:145-156.
2. Nowak MA, Sasaki A, Taylor C, Fudenberg D (2004) Emergence of cooperation and evolutionary stability in finite populations. Nature 428(6983):646-650.
3. Cohen JE, Luczak T, Newman CM, Zhou ZM (1990) Stochastic structure and nonlinear dynamics of food webs: Qualitative stability in a Lotka-Volterra cascade model. Proc Biol Sci 240:607-627.
4. Krebs CJ, et al. (1995) Impact of food and predation on the snowshoe hare cycle. Science 269(5227):1112-1115.
5. Gilg O, Hanski I, Sittler B (2003) Cyclic dynamics in a simple vertebrate predator-prey community. Science 302(5646):866-868.
6. Rohani P, Earn DJD, Grenfell BT (1999) Opposite patterns of synchrony in sympatric disease metapopulations. Science 286(5441):968-971.
7. Benincà E, et al. (2008) Chaos in a long-term experiment with a plankton community. Nature 451(7180):822-825.
8. Mao X, Sabanis S, Renshaw E (2003) Asymptotic behaviour of the stochastic Lotka-Volterra model. J Math Anal Appl 287:141-156.
9. McKane AJ, Newman TJ (2004) Stochastic models in population biology and their deterministic analogs. Phys Rev E Stat Nonlin Soft Matter Phys 70(4 Pt 1):041902.
10. Ovaskainen O, Meerson B (2010) Stochastic models of population extinction. Trends Ecol Evol 25(11):643-652.
11. Black AJ, McKane AJ (2012) Stochastic formulation of ecological models and their applications. Trends Ecol Evol 27(6):337-345.
12. Gokhale CS, Papkou A, Traulsen A, Schulenburg H (2013) Lotka-Volterra dynamics kills the Red Queen: Population size fluctuations and associated stochasticity dramatically change host-parasite coevolution. BMC Evol Biol 13:254.
13. Nowak MA (2006) Evolutionary Dynamics (Harvard Univ Press, Cambridge, MA).
14. Ayala FJ, Campbell CA (1974) Frequency-dependent selection. Annu Rev Ecol Syst 5:115-138.
15. Gigord LDB, Macnair MR, Smithson A (2001) Negative frequency-dependent selection maintains a dramatic flower color polymorphism in the rewardless orchid Dactylorhiza sambucina (L.) Soo. Proc Natl Acad Sci USA 98(11):6253-6255.
16. Nowak MA, Sigmund K (2004) Evolutionary dynamics of biological games. Science 303(5659):793-799.
17. Koskella B, Lively CM (2009) Evidence for negative frequency-dependent selection during experimental coevolution of a freshwater snail and a sterilizing trematode. Evolution 63(9):2213-2221.
18. Huang W, Haubold B, Hauert C, Traulsen A (2012) Emergence of stable polymorphisms driven by evolutionary games between mutants. Nat Commun 3:919.
19. Maynard Smith J (1982) Evolution and the Theory of Games (Cambridge Univ Press, Cambridge, UK).
20. Hauert C, Holmes M, Doebeli M (2006) Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc Biol Sci 273(1600):2565-2570.
21. rd Ed.
22. Bianchi TS, Jones CG, Shachak M (1989) Positive feedback of consumer population density on resource supply. Trends Ecol Evol 4(8):234-238.
23. nd Ed.
24. Zeeman ML (1995) Extinction in competitive Lotka-Volterra systems. Proc Am Math Soc 123(1):87-96.
25. Hofbauer J, Sigmund K (1998) Evolutionary Games and Population Dynamics (Cambridge Univ Press, Cambridge, UK).
26. Pianca ER (1970) On r- and K-selection. Am Nat 104(940):592-597.
27. Kuno E (1991) Some strange properties of the logistic equation defined with r and K: Inherent defects or artifacts? Res Popul Ecol (Kyoto) 33(1):33-39.
28. Mallet J (2012) The struggle for existence: How the notion of carrying capacity, K, obscures the links between demography, Darwinian evolution, and speciation. Evol Ecol Res 14(5):627-665.
29. Geritz SAH, Kisdi E (2012) Mathematical ecology: Why mechanistic models? J Math Biol 65(6-7):1411-1415.
30. Novak S, Chatterjee K, Nowak MA (2013) Density games. J Theor Biol 334:26-34.
31. Valle RR, Kuno E, Nakasuji F (1989) Competition between laboratory populations of green leafhoppers, Nephotettix spp. (Homoptera: Cicadellidae). Res Popul Ecol (Kyoto) 31(1):53-72.
32. Bowers R, Whilte A, Boots M, Geritz SAH, Kisdi E (2003) Evolutionary branching/speciation: Contrasting results from systems with explict or emergent carrying capacities. Evol Ecol Res 5(6):1-9.
33. Chinag H-D, Hirsch MW, Wu FF (1988) Stability regions of nonlinear autonomous dynamical systems. IEEE Trans Automat Contr 33(1):16-27.
34. Skyrms B (2003) The Stag-Hunt Game and the Evolution of Social Structure (Cambridge Univ Press, Cambridge, UK).
35. Doebeli M, Hauert C (2005) Models of cooperation based on the prisoner's dilemma and the snowdrift game. Ecol Lett 8(7):748-766.
36. Gillespie D (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22(4):403-434.
37. Parker M, Kamenev A (2009) Extinction in the Lotka-Volterra model. Phys Rev E Stat Nonlin Soft Matter Phys 80(2 Pt 1):021129.
38. Eriksson A, Elías-Wolff F, Mehlig B (2013) Metapopulation dynamics on the brink of extinction. Theor Popul Biol 83:101-122.
39. Ferriere R, Legendre S (2013) Eco-evolutionary feedbacks, adaptive dynamics and evolutionary rescue theory. Philos Trans R Soc Lond B Biol Sci 368(1610):20120081.
40. Kimura M (1962) On the probability of fixation of mutant genes in a population. Genetics 47:713-719.
41. Durrett R, Levin SA (1994) The importance of being discrete (and spatial). Theor Popul Biol 46(3):363-394.
42. Szabó G, Fáth G (2007) Evolutionary games on graphs. Phys Rep 446(4-6):97-216.
43. Mobilia M, Georgiev IT, Täuber UC (2007) Phase transitions and spatio-temporal fluctuations in stochastic lattice Lotka-Volterra models. J Stat Phys 128(1-2):447-483.
44. McKane AJ, Newman TJ (2005) Predator-prey cycles from resonant amplification of demographic stochasticity. Phys Rev Lett 94(21):218102.
45. Reichenbach T, Mobilia M, Frey E (2006) Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model. Phys Rev E Stat Nonlin Soft Matter Phys 74(5 Pt 1):051907.