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Mathematical and Computational Challenges in Population Biology and Ecosystems Science

Simon A. Levin, Bryan Grenfell, Alan Hastings, and Alan S. Perelson
Science • 17 Jan 1997 • Vol 275, Issue 5298 • pp. 334-343 • DOI: 10.1126/science.275.5298.334
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Abstract

Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues—understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales—cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.
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REFERENCE AND NOTES

1.
Levin S. A., Ed., Mathematics and Biology: The Interface (Lawrence Berkeley Laboratory, University of California, Berkeley, CA, 1992).
2.
Murray J. D., Mathematical Biology, vol. 19 of Biomathematics (Springer-Verlag, Heidelberg, 1990); P. J. Hilts, “Eric Steven Lander: Love of Numbers Leads to Chromosome 17,” New York Times, 10 September 1996, p. C1.
3.
May R. M., Science 186, 645 (1974).
4.
Roughgarden J., May R. M., Levin S. A., Eds., Perspectives in Ecological Theory (Princeton Univ. Press, Princeton, NJ, 1989).
5.
Kollman P., Ed. Modeling of Biological Systems: A Workshop at the National Science Foundation (University of California, San Francisco, 14 and 15 March 1996)(technical report).
6.
Lubchenco J., et al., Ecology 72, 371 (1991).
7.
Botkin D. B., Janak J. F., Wallis J. R., J. Ecol. 60 849 (1972);
IBM J. Res. Dev. 16, 101 (1972).
8.
Shugart H. H., West D. C., J. Environ. Manage. 5, 161 (1977).
9.
Huston M. A., Tree Physiol. 9 293 (1991);
Shugart H. H. and , Prentice I. C., in A Systems Analysis of the Global Boreal Forest, , Shugart H. H. , Leemans R. , Bonan G. B., Eds. (Cambridge Univ. Press, Cambridge, 1992), pp. 313–333;
Shugart H. H. and , Smith T. M., Annu. Rev. Ecol. Syst. 23, 15 (1992);
Urban D. L. and , Shugart H. H., in Plant Succession: Theory and Prediction;
Glenn-Lewin D. C. , Peet R. K. , Veblen T. T., Eds. (Chapman and Hall, London, 1992), pp. 249–292;
Pacala S. W. , Canham C. D. , Silander J. A., Can. J. Forest Res. 23, 1980 (1993).
10.
Deutschman D. H.thesis, Cornell University (1996); S. W. Pacala and D. H. Deutschman, Oikos74, 357 (1995).
11.
Pacala S. W., Levin S. A., Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions, , Tilman D., Kareiva P., Eds. (Princeton Univ. Press, Princeton, NJ)in press.
12.
Taylor L. R., Nature 189 732 (1961);
Ma S. K., Modern Theory of Critical Phenomena (Benjamin, New York, 1976);
Wilson K., Rev. Mod. Phys. 55, 583 (1983);
Barenblatt G. I., Scaling Phenomena in Fluid Mechanics (Cambridge Univ. Press, Cambridge, 1994).
13.
Levin S. A., Pacala S. W., in (11).
14.
Barton N. H., Turelli M., Genetics 138 913 (1994);
Lander E. S. and , Schork N. J., Science 265, 2037 (1994);
Risch N. and , Merikangas K., ibid. 273, 1516 (1996).
15.
Reynolds C. W., Comput. Graphics 21 25 (1987);
Gueron S. and , Levin S. A., J. Theor. Biol. 165, 541 (1993);
Gueron S. , Levin S. A. , Rubenstein D. I., ibid. 182, 85 (1996);
Grünbaum D., Evol. Ecol., in press.
16.
Flierl G., Grünbaum D., Levin S. A., Olson D. B., unpublished manuscript.
17.
Bolker B. M., Pacala S. W., Bazzaz F. A., Canham C. D., Levin S. A., Global Change Biol. 1, 373 (1995).
18.
Barton N. H., Philos. Trans. R. Soc. London Ser. B 351, 785 (1996).
19.
Lande R., Evolution 48, 1460 (1994).
20.
Gavrilets S., Hastings A., Proc. R. Soc. London Ser. B 261, 233 (1995).
21.
Nagylaki T., Introduction to Theoretical Population Genetics, vol. 21 of Biomathematics (Springer-Verlag, Berlin, 1992); A. Hastings, in Some Mathematical Questions in Biology: Models in Population Biology, A. Hastings, Ed., vol. 20 of Lectures on Mathematics in the Life Sciences (American Mathematical Society, Providence, RI, 1989), pp. 27–54.
22.
Feldman M. W., Christiansen F. B., Otto S. P., Genetics 129, 297 (1991).
23.
Fox G. A., Hastings A., ibid. 132, 277 (1992).
24.
As an example, the analytical results for a special case [W. P. Robinson, M. A. Asmussen, G. Thomson, Genetics 129, 925 (1991)] were coupled with numerical results (W. P. Robinson, A. Cambonthomsen, N. Borot, W. Klitz, G. Thomson, ibid., p. 931) to understand the evolution of a three-locus system.
25.
Burger R., Wagner G. P., Stettinger F., Evolution 43, 1748 (1989).
26.
Baird S. J. E., ibid. 49, 1038 (1995).
27.
Gavrilets S., Hastings A., Genet. Res. 65, 63 (1995).
28.
Kauffman S. A., Physica D 42, 135 (1990).
29.
Wagner G. P., Altenberg L., Evolution 50, 967 (1996).
30.
Ray T. S., in Artificial Life II, , Langton C. G., Taylor C., Farmer J. D., Rasmussen S., Eds. (Santa Fe Institute, Santa Fe, NM, 1992), pp. 371-408;
Langton C. G., Ed., Artificial Life, vol. 12 of Santa Fe Institute Studies in the Sciences of Complexity (Addison-Wesley, Redwood City, CA, 1989).
31.
Banzhaf W., Eckman F. H., Eds., Evolution As a Computational Process, vol. 899 of Lecture Notes in Computer Science (Springer-Verlag, Heidelberg, 1995); J. H. Holland, Adaptation in Natural and Artificial Systems (MIT Press, Cambridge, MA, 1992); J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge, MA, 1992); I. Rechenberg, Evolutionsstrategie '94 (Frommann, Stuttgart, 1994).
32.
Kauffman S., Levin S. A., J. Theor. Biol. 128 11 (1987);
Muhlenbein H. and , Schlierkamp-Voosen D., in Evolution as a Computational Process, , Banzhaf W. and , Eckman F. H., Eds., vol. 899 of Lecture Notes in Computer Science (Springer-Verlag, Heidelberg, 1995), pp. 142–168.
33.
Maynard Smith J., Evolution and the Theory of Games (Cambridge Univ. Press, Cambridge, 1982).
34.
Hamilton W. D., J. Theor. Biol. 7, 1 (1964).
35.
Axelrod R., Hamilton W. D., Science 211, 1390 (1981).
36.
Boyd R., Lorberbaum J. P., Nature 327, 58 (1987).
37.
Miller J. H., J. Econ. Behav. Organ. 29, 87 (1996).
38.
Nowak M. A., May R. M., Nature 359 826 (1992);
Nowak M. A. , Bonhoeffer S. , May R. M., Proc. Natl. Acad. Sci. U.S.A. 91, 4877 (1994);
Durrett R. and , Levin S. A., J. Theor. Biol., in press.
39.
Dytham C., Shorrock S. B., Evol. Ecol. 9, 508 (1995).
40.
Kinzig A. P., Harte J.in preparation; E. Klopfer, unpublished manuscript.
41.
Bergman A., Feldman M. W., Theor. Popul. Biol. 48, 251 (1995).
42.
Levin S. A., in Coevolution, , Nitecki M., Ed. (Univ. of Chicago Press, Chicago, 1983), pp. 21-65;
in Population Biology , Freedman H. and , Strobeck C., Eds., vol. 52 of Lecture Notes in Biomathematics (Springer-Verlag, Berlin, 1983), pp. 328-334;
May R. M. and , Anderson R. M., in Coevolution, , Futuyma D. J. and , Slatkin M., Eds. (Sinauer, Sunderland, MA, 1983), pp. 186-206.
43.
Anderson R. M., May R. M., Infectious Diseases of Humans: Dynamics and Control (Oxford Univ. Press, Oxford, 1991).
44.
Dietz K., Statist. Methods Med. Res. 2, 23 (1993).
45.
Cliff A. D., Haggett P., Atlas of Disease Distributions: Analytic Approaches to Epidemiologic Data (Blackwell, Oxford, 1988); D. Mollison and S. A. Levin, in (56), pp. 384–398.
46.
Ferguson N. M., Anderson R. M., May R. M., in (11).
47.
Bolker B. M., Grenfell B. T., Proc. R. Soc. London Ser. B 251, 75 (1993).
48.
Cliff A. D., Haggett P., Smallman-Raynor M., Measles: An Historical Geography of a Major Human Viral Disease from Global Expansion to Local Retreat, 1840–1990 (Blackwell, Oxford, 1993).
49.
Grenfell B. T., Chaos from Real Data: The Analysis of Non-Linear Dynamics in Short Ecological Time Series, , Perry J. N., Smith R., Eds. (Academic Press, New York)in press.
50.
Olsen L. F., Schaffer W. M., Science 249, 499 (1990).
51.
Grenfell B. T., J. R. Stat. Soc. Ser. B 54, 383 (1992).
52.
Lloyd A. L., May R. M., J. Theor. Biol. 179, 1 (1996).
53.
Bolker B. M., Grenfell B. T., Proc. Natl. Acad. Sci. U.S.A. 93, 12648 (1996).
54.
Keeling M. J., Grenfell B. T., Science 275, 65 (1997).
55.
Becker N. G., Dietz K., Math. Biosci. 127 207 (1995);
Becker N. G. , Bahrampour A. , Dietz K., ibid. 129, 189 (1995).
56.
Grenfell B. T., Dobson A. P., Ecology of Infectious Diseases in Natural Populations (Cambridge Univ. Press, Cambridge, 1995).
57.
Bobashev G. V., Ellner S., Nychka D. W., Grenfell B. T., Math. Biosci.in press.
58.
Ellner S., in (49).
59.
Blanchard P., Bolz G. F., Kruger T., Mathematical Modelling on Random Graphs of the Spread of Sexually-Transmitted Diseases with Emphasis on HIV Infection (Springer, Berlin, 1990).
60.
Kretzschmar M., Morris M., Math. Biosci. 133 165 (1996);
Morris M. and, Dean L., Am. J. Epidemiol. 140, 217 (1994).
61.
Ghani A. C., Swinton J., Garnett G. P., Sex. Transm. Dis.in press.
62.
Anderson R. M., Garnett G. P., Lancet 348, 1010 (1996).
63.
Anderson R. M., et al., Nature 382, 779 (1996).
64.
Nee S., Holmes E. C., May R. M., Harvey P. H., Philos. Trans. R. Soc. London Ser. B 344 77 (1994);
Harvey P. H., May R. M., Nee S., Evolution 48, 523 (1994).
65.
Austin D. J., Anderson R. M., Parasitology 113, 157 (1996).
66.
Lively C. M., Apanius V.in (56), pp. 421–449; C. A. Gilligan, Phytopathology75, 61 (1985).
67.
Grenfell B. T., Dietz K., Roberts M. G.in (56), pp. 362–383; B. T. Grenfell, K. Wilson, V. S. Isham, H. E. G. Boyd, K. Dietz, Parasitology111, S135 (1996).
68.
Gupta S., et al., Nature Med. 2, 437 (1996).
69.
Pease C., Theor. Popul. Biol. 31 422 (1987);
Andreasen V. , Levin S. A. , Lin J., Z. Angew. Math. Mech. 76 (suppl. 2), 421 (1996);
Andreasen V. , Lin J. , Levin S. A., J. Math. Biol., in press.
70.
Anderson R. M., May R. M., Gupta S., Parasitology 99 (suppl.), S59 (1989).
71.
Perelson A. S., in Mathematical and Statistical Approaches to AIDS Epidemiologyvol. 83 of Lecture Notes in Biomathematics, , Castillo-Chavez C., Ed. (Springer-Verlag, New York, 1989), pp. 350-370R. M. Anderson and R. M. May, in Cell to Cell Signalling: From Experiments to Theoretical Models, A. Goldbeter, Ed. (Academic Press, New York, 1989), pp. 335–349; A. R. McLean and M. A. Nowak, J. Theor. Biol. 155, 69 (1992); A. S. Perelson, D. E. Kirschner, R. J. De Boer, Math. Biosci. 114, 81 (1993); A. R. McLean, Trends Microbiol. 1, 9 (1993); D. Schenzle, Stat. Med. 13, 2067 (1994); P. Essunger and A. S. Perelson, J. Theor. Biol. 170, 367 (1994); S. D. W. Frost and A. R. McLean, J. Acquired Immune Defic. Syndr. 7, 236 (1994); H. J. Bremermann, ibid. 9, 459 (1995); J. E. Mittler, B. R. Levin, R. Antia, ibid. 12, 233 (1996).
72.
Nowak M. A., May R. M., Anderson R. M., AIDS 4 1095 (1990);
Nowak M. A., et al., Science 254, 963 (1991).
73.
Wolinsky S. M., et al., Science 272 537 (1996);
Nowak M. A., et al., ibid. 274, 1008 (1996);
Wolinsky S. M., et al., ibid., p. 1010;
De Boer R. J. and , Boerlijst M. C., Proc. Natl. Acad. Sci. U.S.A. 91, 544 (1994);
Stilianakis N. I. , Schenzle D. , Dietz K., Math. Biosci. 121, 235 (1994).
74.
Nowak M. A., et al., Nature 375 606 (1995);
Nowak M. A. and , Bangham C. R. M., Science 272, 74 (1996);
Klenerman P., et al., Proc. Natl. Acad. Sci. U.S.A., in press.
75.
Nowak M. A., May R. M., Sigmund K., J. Theor. Biol. 175, 325 (1995).
76.
McLean A. R., Nowak M. A., AIDS 6 71 (1992);
Frost S. D. W. and , McLean A. R., ibid. 8, 323 (1994);
McLean A. R. and , Frost S. D. W., Rev. Med. Virol. 5, 141 (1995);
Kirschner D., Notices Am. Math. Soc. 43, 191 (1996);
Kirschner D. and , Webb G. F., Bull. Math. Biol. 58, 367 (1996);
de Jong M. D., et al., Proc. Natl. Acad. Sci. U.S.A. 93, 5501 (1996);
De Boer R. J. and , Boucher C. A. B., Proc. R. Soc. London Ser. B 263, 899 (1996);
Nowak M. A., et al., J. Theor. Biol., in press;
Stilianakis N. I., et al., J. Virol., in press.
77.
Wei X., et al., Nature 373 117 (1995);
Ho D. D., et al., ibid., p. 123..
78.
Perelson A. S., et al., Science 271, 1582 (1996).
79.
Perelson A. S., et al., in preparation.
80.
Feng Y., Broder C. C., Kennedy P. E., Berger E. A., Science 272 872 (1996);
Deng H. K., et al., Nature 381, 661 (1996);
Dragic T., et al., ibid., p. 667..
81.
Liu R., et al., Cell 86 367 (1996);
Samson M., et al., Nature 382, 722 (1996);
Huang Y., et al., Nature Med. 2, 1240 (1996).
82.
Wu L., et al., Nature 384 179 (1996);
Trkola A., et al., ibid., p. 184..
83.
Kirschner D. E., Perelson A. S., in Mathematical Population Dynamics: Analysis of Heterogeneity and the Theory of Epidemics, , Arino O., Axelrod D. E., Kimmel M., Langlais M., Eds. (Wuerz, Winnipeg, Canada, 1995), pp. 295-310.
84.
Nowak M. A., et al., Proc. Natl. Acad. Sci. U.S.A. 93 4398 (1996);
Lam N. P., et al., Hepatology, in press.
85.
Bloom B. R., Nature 358 538 (1992);
Richman D. D.,Adv. Exp. Med. Biol. 394, 383 (1996);
van Es H. H., Skamene E., Schurr E. ,Clin. Invest. Med. 16, 285 (1993);
Cohen M. L. ,Trends Microbiol. 2.
86.
Haase A. T., et al., Science 274, 985 (1996).
87.
Walker W. L., Cook J., Bull. Math. Biol. 58, 1047 (1996).
88.
Saga T., et al., Proc. Natl. Acad. Sci. U.S.A. 92, 8999 (1995).
89.
Kepler T. B., Perelson A. S., ibid. 8219;
Jacob J., Przylepa J., Miller C., Kelsoe K. J., J. Exp. Med. 178, 1293 (1993);
Seiden P. E. and, Celada F., Eur. J. Immunol. 26, 1350 (1996);
Agur Z., Mazor G., Meilijson I., Proc. R. Soc. London Ser. B 245, 147 (1991).
90.
Kepler T. B., Perelson A. S., Immunol. Today 14, 412 (1993).
91.
Han S., et al., J. Exp. Med. 182, 1635 (1995).
92.
Fishman M. A., Perelson A. S., J. Theor. Biol. 170 25 (1994);
Morel B. F., et al., Bull. Math. Biol. 58, 569 (1996);
Caneiro J., Stewart J., Coutinho A., Int. Immunol. 7, 1265 (1995);
Brass A., Grencis R. K., Else K. J., J. Theor. Biol. 166, 189 (1994).
93.
Fishman M., Perelson A. S., J. Theor. Biol. 160 311 (1993);
De Boer R. J. and , Perelson A. S., ibid. 169, 375 (1994);
Merrill S. J. , De Boer R. J. , Perelson A. S., Rocky Mountain J. Math. 24, 213 (1994).
94.
De Boer R. J., Perelson A. S., J. Theor. Biol. 149 381 (1991);
Seiden P. E. and , Celada F., ibid. 158, 329 (1992).
95.
Gleick J., Chaos: Making of a New Science (Penguin, New York, 1987).
96.
Figure 1 is a frame from the video, D. Deutschman and S. A. Levin, SORTIE Simulations, by Cornell and Princeton Universities; computation by L. Buttel; visualization by C. Devine, Cornell Theory Center, Cornell University.
97.
Dugatkin L. A., Wilson D. S., Am. Nat. 138, 687 (1991).
98.
Schenzle D., IMA J. Math. Appl. Med. Biol. 1, 169 (1984).
99.
Bolker B., ibid. 10, 83 (1993).
100.
Grenfell B. T., Kleczkowski A., Ellner S. P., Bolker B. M., Philos. Trans. R. Soc. London Ser. A 348, 515 (1994).
101.
Bolker B. M., Grenfell B. T., Philos. Trans. R. Soc. London Ser. B 348 309 (1995);
Grenfell B. T. , Bolker B. M. , Kleczkowski A., Proc. R. Soc. London Ser. B 259, 97 (1995).
102.
Ferguson N. M., Nokes D. J., Anderson R. M., Math. Biosci.in press.
103.
Bartlett M. S., J. R. Stat. Soc. Ser. A 120 48 (1957);
ibid. 123, 37 (1960).
104.
Keeling M. J., Rand D. A., unpublished data.
105.
Rhodes C. J., Anderson R. M., Nature 381, 600 (1996).
106.
Fine P. E. M., Clarkson J. A., Int. J. Epidemiol. 12, 332 (1983).
107.
Cliff A. D., Haggett P., Stroup D. F., Cheney E., Stat. Med. 11 1409 (1992);
Grenfell B. T., Kleczkowski A., Gilligan C. A., Bolker B. M., Statistical Methods Med. Res. 4, 160 (1995).
108.
Grenfell B. T., Kleczkowski A., Ellner S. P., in Forecasting and Chaos, , Tong H., Ed. (World Scientific, Singapore, 1994), pp. 321-345.
109.
We thank P. Kollman and the participants in the meeting, “Modeling of Biological Systems,” which inspired this article, and NSF, which funded the workshop. Supported by NASA grant NAGW 4688 and the Andrew Mellon Foundation (S.L.), NSF grant DEB 9629236 (A.H.), the Wellcome Trust (B.G.), NIH grants RR06555 and AI28433 (A.S.P.), and the Jeanne M. Sullivan and Joseph P. Sullivan Foundation. D. Deutschman provided useful comments. Most of all, we thank A. Bordvik, who brought order to a chaotic sequence of drafts of this manuscript.

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Volume 275 | Issue 5298
17 January 1997

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Simon A. Levin
S. A. Levin is in the Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA.
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Bryan Grenfell
B. Grenfell is in the Zoology Department, Cambridge University, Downing Street, Cambridge CB2 3EJ, UK.
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Alan Hastings
A. Hastings is in the Division of Environmental Studies, Institute for Theoretical Dynamics, and Center for Population Biology, University of California, Davis, CA 95616, USA.
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Alan S. Perelson
A. S. Perelson is at Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
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