Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Necessity and Chance: deterministic chaos in ecology and evolution

Author(s): Robert M. May
Journal: Bull. Amer. Math. Soc. 32 (1995), 291-308.
MSC (1991): Primary 92D40, 92-02, 58F13, 58-02
MathSciNet review: 1307905
Retrieve article in: PDF

References | Similar articles | Additional information

References:

[1]
R. M. May, Simple mathematical models with very complicated dynamics, Nature \textbf{261} (1976), 459--467.
[2]
C. W. Clark, Mathematical bioeconomics {\rm (second ed.)}, Wiley, New York, 1990. MR 1044994
[3]
R. M. Anderson and R. M. May, Infectious diseases of humans\,{\rm :} Dynamics and control, Oxford Univ. Press, Oxford, 1991.
[4]
R. M. May and M. A. Nowak, Superinfection, metapopulation dynamics, and the evolution of diversity, J. Theoret. Biol. \textbf{170} (1994), 95--114.
[5]
M. A. Nowak, R. M. May, and K. Sigmund, Immune responses against multiple epitopes, J. Theoret. Biol. (1995) (in preparation).
[6]
D. Tilman, R. M. May, C. L. Lehman, and M. A. Nowak, Habitat destruction and the extinction debt, Nature \textbf{371} (1994), 65--66.
[7]
P. A. B. Moran, Some remarks on animal population dynamics, Biometrics \textbf{6} (1950), 250--258.
[8]
W. E. Ricker, Stock and recruitment, J. Fish. Res. Bd. Canad. \textbf{11} (1954), 559--623.
[9]
A. N. Sharkovsky, Coexistence of cycles of a continuous map of the line into itself, Ukrain. Mat. Zh. \textbf{16} (1964), 61--71. MR 159905
[10]
T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly \textbf{82} (1975), 985--992. MR 385028
[11]
R. M. May and G. F. Oster, Bifurcations and dynamic complexity in simple ecological models, Amer. Natur. \textbf{110} (1976), 573--599.
[12]
E. N. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci. \textbf{20} (1963), 130--141.
[13]
T. Mullin (ed.), The nature of chaos, Oxford Univ. Press, Oxford, 1993.
[14]
L. A. Smith, Local optimal prediction{\rm :} Exploiting strangeness and the variation of sensitivity to initial conditions, Philos. Trans. Roy. Soc. London Ser. A \textbf{348} (1994), 371--381.
[15]
R. C. L. Wolff, Local Lyapunov exponents\,{\rm :} Looking closely at chaos, J. Roy. Statist. Soc. Ser. B \textbf{54} (1992), 353--357. MR 1160475
[16]
I. Hanski, P. Turchin, E. Korpim\"aki, and H. Henttonen, Population oscillations of boreal rodents\,{\rm :} Regulation by mustilid predators leads to chaos, Nature \textbf{364} (1993), 232--235.
[17]
G. Sugihara, B. T. Grenfell, and R. M. May, Distinguishing error from chaos in ecological time series, Philos. Trans. Roy. Soc. London Ser. B \textbf{330} (1991), 235--251.
[18]
L. F. Olsen and W. M. Schaffer, Chaos versus noisy periodicity\,{\rm :} Alternative hypotheses for childhood epidemics, Science \textbf{249} (1990), 499--504.
[19]
G. Sugihara, Nonlinear forecasting for the classification of natural time series, Philos. Trans. Roy. Soc. London Ser. A \textbf{348} (1994), 477--495.
[20]
B. Le Baron, Chaos and nonlinear forecastability in finance and economics, Philos. Trans. Roy. Soc. London Ser. A \textbf{348} (1994), 397--404. MR 1300159
[21]
D. Ruelle, Deterministic chaos\,{\rm :} The science and the fiction, Proc. Roy. Soc. London Ser. A \textbf{42} (1990), 241--248. MR 1039785
[22]
A. S. Weigend and N. A. Gershenfeld, Time series prediction{\rm :} Forecasting the future and understanding the past, Addison-Wesley, Reading, MA, 1993.
[23]
H. Tong, A personal overview of nonlinear time series analysis from a chaos perspective, Scand. J. Statist. (1995). MR 1363222
[24]
A. M. Hastings, C. L. Hom, S. Ellner, P. Turchin, and H. C. J. Godfray, Chaos in ecology\,{\rm :} Is Mother Nature a strange attractor\,{\rm ?}, Ann. Rev. Ecol. Syst. \textbf{24} (1993), 1--33.
[25]
M. Casdagli, Chaos and deterministic versus stochastic nonlinear modelling, J. Roy. Statist. Soc. Ser. B \textbf{54} (1992), 303--328. MR 1160473
[26]
G. Sugihara and R. M. May, Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature \textbf{344} (1990), 734--741.
[27]
J. D. Farmer and J. J. Sidorowich, Exploiting chaos to predict the future and reduce noise, Evolution, Learning and Cognition (Y. C. Lee, ed.), World Scientific Press, New York, 1989, pp. 277--304. MR 1036562
[28]
F. Takens, Detecting strange attractors in turbulence, Lecture Notes in Math. \textbf{898} (1981), 366--381. MR 654900
[29]
P. Grassberger and I. Procaccia, Measuring the strangeness of strange attactors, Phys. D \textbf{9} (1983), 189--208. MR 732572
[30]
B. T. Grenfell, A. Kleczkowski, S. P. Ellner, and B. M. Bolker, Measles as a case study in nonlinear forecasting and chaos, Philos. Trans. Roy. Soc. London Ser. A \textbf{348} (1994), 515--530.
[31]
J. D. Murray, Mathematical biology, Springer-Verlag, Berlin and New York, 1989. MR 1007836
[32]
M. P. Hassell, The dynamics of arthropod predator-prey associations, Princeton Univ. Press, Princeton, NJ, 1978. MR 508052
[33]
A. J. Nicholson and V. A. Bailey, The balance of animal populations. Part {\rm I}, Proc. Zoolog. Soc. London \textbf{1} (1935), 551--598.
[34]
M. P. Hassell and R. M. May, Stability in insect host-parasite models, J. Animal Ecol. \textbf{42} (1973), 693--726.
[35]
S. W. Pacala, M. P. Hassell, and R. M. May, Host-parasitoid associations in patchy environments, Nature \textbf{344} (1990), 150--153.
[36]
M. P. Hassell, R. M. May, S. W. Pacala, and P. L. Chesson, The persistence of host-parasitoid associations in patchy environments, Amer. Natur. \textbf{138} (1991), 568--583.
[37]
M. P. Hassell, H. N. Comins, and R. M. May, Spatial structure and chaos in insect population dynamics, Nature \textbf{353} (1991), 255--258.
[38]
H. N. Comins, M. P. Hassell, and R. M. May, The spatial dynamics of host-parasitoid systems, J. Animal Ecol. \textbf{61} (1992), 735--748.
[39]
R. V. Sol\`e and J. Valls, Spiral waves, chaos and multiple attractors in lattice models of interacting populations, Phys. Lett. A \textbf{166} (1992), 123--128.
[40]
M. P. Hassell, H. N. Comins, and R. M. May, Species coexistence and self-organizing spatial dynamics, Nature \textbf{370} (1994), 290--292.
[41]
D. A. Rand, Measuring and characterizing spatial patterns, dynamics and chaos in spatially extended dynamical systems and ecologies, Philos. Trans. Roy. Soc. London Ser. A \textbf{348} (1994), 497--514.
[42]
R. Axelrod, The evolution of cooperation, Basic Books, New York, 1984.
[43]
R. Axelrod and W. D. Hamilton, The evolution of cooperation, Science \textbf{211} (1981), 1390--1396. MR 686747
[44]
M. A. Nowak and K. Sigmund, Tit for tat in heterogeneous populations, Nature \textbf{355} (1992), 250--253.
[45]
M. A. Nowak and K. Sigmund, Chaos and the evolution of cooperation, Proc. Nat. Acad. Sci. U.S.A. \textbf{90} (1993), 5091--5094.
[46]
R. M. May, More evolution of cooperation, Nature \textbf{327} (1987), 15--17.
[47]
M. A. Nowak and R. M. May, Evolutionary games and spatial chaos, Nature \textbf{359} (1992), 826--829.
[48]
M. A. Nowak and R. M. May, The spatial dilemmas of evolution, Internat. J. Bifur. Chaos \textbf{3} (1993), 35--78. MR 1218718
[49]
M. A. Nowak, S. Bonhoeffer, and R. M. May, More spatial games, Internat. J. Bifur. Chaos \textbf{4} (1994), 33--56. MR 1276803
[50]
M. A. Nowak, S. Bonhoeffer, and R. M. May, Spatial games and the maintenance of cooperation, Proc. Nat. Acad. Sci. U.S.A. \textbf{91} (1994), 4877--4881.
[51]
A. V. M. Herz, Collective phenomena in spatially extended evolutionary games, J. Theoret. Biol. \textbf{169} (1994), 65--87.
[52]
B. A. Huberman and N. S. Glance, Evolutionary games and computer simulations, Proc. Nat. Acad. Sci. U.S.A. \textbf{90} (1993), 7712--7715.
[53]
J. Maynard Smith, Evolution and the theory of games, Cambridge Univ. Press, Cambridge, 1982.
[54]
T. Stoppard, Arcadia, Faber and Faber, London, 1993.

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1991): 92D40, 92-02, 58F13, 58-02

Retrieve articles in all Journals with MSC (1991): 92D40, 92-02, 58F13, 58-02


Additional Information:

DOI: 10.1090/S0273-0979-1995-00598-7
PII: S 0273-0979(1995)00598-7