Scale invariance in biology: Coincidence or footprint of a universal mechanism?

Biological Reviews of the Cambridge Philosophical Society

Volumn 76, Issue 2, 2001, Pages 161-209

  Gisiger, T ^a,b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b INSTITUT PASTEUR   (France)

Author keywords

Chaos; Complex systems; Criticality; Ecology; Epidemics; Evolution; Fractals; Models; Neurobiology; Scale invariance

Indexed keywords

BIOLOGY; CHAOTIC DYNAMICS; ECOLOGY; EVOLUTION; FRACTAL ANALYSIS; MATHEMATICAL ANALYSIS; NERVE CELL NETWORK; PHYSICS; REVIEW; SPECIES DIFFERENCE;

ANIMALS; BRAIN; DISEASE OUTBREAKS; ECOLOGY; EVOLUTION; FRACTALS; HUMANS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS;

EID: 0035039580     PISSN: 14647931     EISSN: None     Source Type: Journal    
DOI: 10.1017/S1464793101005607     Document Type: Review

References (165)

1. AIZAWA, Y., MURAKAMI, C. & KOHYAMA, T. (1984). Statistical mechanics of intermittent chaos. Progress of Theoretical Physics 79, 96-124.
2. ANDERSON, R. M. & MAY, R. M. (1991). Infectious Diseases of Humans, Dynamics and Control. Oxford University Press.
3. ARIELI, A., STERKIN, A., GRINVALD, A. & AERTSEN, A. (1996). Dynamics of ongoing activity: explanation of the large variability in evoked cortical responses. Science 273, 1868-1871.
4. BAI-LIN, H. (1989). Elementary Symbolic Dynamics. World Scientific Publishing.
5. BAK, P. (1990). Self-organized criticality. Physica A163, 403-409.
6. BAK, P. (1996). How Nature Works: the Science of Self-Organized Criticality. Springer-Verlag.
7. BAK, P. & CHEN, K. (1989). The physics of fractals. Physica D38, 5-12.
8. BAK, P. & CHEN, K. (1991). Self-organized criticality. Scientific American 264, 46-53.
9. BAK, P., CHEN, K. & CREUTZ, M. (1989). Self-organized criticality in the 'Game of Life'. Nature 342, 780-782.
10. BAK, P., CHEN, K. & TANG, C. (1990). A forest-fire model and some thoughts on turbulence. Physics Letters A147, 297-300.
11. BAK, P., FLYVBJERG, H. & LAUTRUP, B. (1992). Coevolution in a rugged fitness landscape. Physical Review A46, 6724-6730.
12. BAK, P. & PACZUSKI, M. (1993). Why nature is complex. Physics World 6, 39-43.
13. BAK, P. & PACZUSKI, M. (1995). Complexity, contigency, and criticality. Proceedings of the National Academy of Sciences of the United States of America 92, 6689-6696.
14. BAK, P. & SNEPPEN, K. (1993). Punctuated equilibrium and criticality in a simple model of evolution. Physical Review Letters 71, 4083-4086.
15. BAK, P., TANG, C. & WIESENFELD, K. (1987). Self-organized criticality: an explanation of 1/f noise. Physical Review Letters 59, 381-384.
16. BAK, P., TANG, C. & WIESENFELD, K., (1988). Self-organized criticality. Physical Review A38, 364-374.
17. BARNSLEY, M. (1988). Fractals Everywhere. Academic Press Inc.
18. BARTLETT, M. S. (1957). Measles periodicity and community size. Journal of the Royal Statistical Society A120, 48-70.
19. BARTLETT, M. S. (1960). The critical community size for measles in the United States. Journal of the Royal Statistical Society A123, 37-44.
20. BASCOMPTE, J. & SOLÉ, R. V. (1995). Rethinking complexity: modelling spatiotemporal dynamics in ecology. Trends in Ecology and Evolution 10, 361-366.
21. BELOUSOV, B. P. (1959). Sbornik Referatov po Radiacioni Medicine, 145ff (in Russian).
22. BENTON, M. J. (1993). The Fossil Record 2, London: Chapman and Hall.
23. BENTON, M. J. (1995). Diversification and extinction in the history of life. Science 268, 52-58.
24. BERLEKAMP, E. R., CONWAY, J. H. AND GUY, R. K. (1982). Winning Ways for Your Mathematical Plays, Vol. 2, Academic Press.
25. BERRYMAN, A. A. & MILLSTEIN, J. A. (1989). Are ecological systems chaotic - And if not, why not? Trends in Ecology and Evolution 4, 26-29.
26. BINEY, J. J., DOWRICK, N. J., FISHER, A. J. & NEWMAN, M. E. J. (1992). The Theory of Critical Phenomena. Clarendon Press.
27. BLARER, A. & DOEBELI, M. (1996). In the red zone. Nature 380, 589-590.
28. BROADBENT, S. R. & HAMMERSLEY, J. M. (1957). Percolation processes. I. Crystals and mazes. Proceedings of the Cambridge Philosophical Society 53, 629-641.
29. BURLANDO, B. (1990). The fractal dimension of taxonomic systems. Journal of Theoretical Biology 146, 99-114.
30. BURLANDO, B. (1993). The fractal geometry of evolution. Journal of Theoretical Biology 163, 161-172.
31. CAMPBELL, M.J. & JONES, B.W. (1972). Cyclic changes in insulin needs of an unstable diabetic. Science 177, 889-891.
32. CHANGEUX, J.-P. (1985). Neuronal man: the biology of mind. Pantheon Books.
33. CHANGEUX, J.-P. (1993). A critical view of neuronal models of learning and memory. Memory concepts - 1993: basic and clinical aspects (Elsevier Science Publishers), 413-433.
34. CHIALVO, D. R. & BEK, P. (1999). Learning from mistakes. Neuroscience 90, 1137-1148.
35. CHRISTENSEN, K., CORRAL, A., FRETTE, V., FEDER, J. & JOSSANG, T. (1996). Tracer dispersion in a self-organized critical system. Physical Review Letters 77, 107-110.
36. CHRISTENSEN, K., FOGEDBY, H. C. & JENSEN, H. J. (1991). Dynamical and spatial aspects of sandpile cellular automata. Journal of Statistical Physics 63, 653-684.
37. CHRISTENSEN, K., OLAMI, Z. & BAK, P. (1992). Deterministic 1/f noise in nonconservative models of self-organized criticality. Physical Review Letters 68, 2417-2420.
38. CLAR, S., DROSSEL, B. & SCHWABL, F. (1994). Scaling laws and simulation results for the self-organized critical forest-fire model. Physical Review E50, 1009-1018.
39. COGGIN, S. J. & PAZUN, J. L. (1996). Dynamic complexity in Physarum polycephalum shuttle streaming. Protoplasma 194, 243-249.
40. COHEN, J. L. (1995). Unexpected dominance of high frequencies in chaotic nonlinear population models. Nature 378, 610-612.
41. COSTA, U. M. S., LYRA, M. L., PLASTINO, A. R. & TSALLIS, C. (1997) Power-law sensitivity to initial conditions within a logisticlike family of maps: fractality and nonextensivity. Physical Review E56, 245-250.
42. DA SILVA, L., PAPA, A. R. R. & DE SOUZA, A. M. C. (1998). Criticality in a simple model for brain functioning. Physical Review A242, 343-348.
43. DEHAENE, S. (1997). Number Sense: How the Brain Creates Mathematics. Oxford University Press.
44. DE LOS RIOS, P. & ZHANG, Y.-C. (1999). Universal 1/f noise from dissipative self-organized criticality models. Physical Review Letters 82, 472-475.
45. DROSSEL B. & SCHWABL, F. (1992). Self-organized critical forest-fire model. Physical Review Letters 69, 1629-1632.
46. EINSTEIN, A. & INFELD, L. (1938). The Evolution of Physics: the Growth of Ideas from Early Concept to Relativity and Quanta. Simon and Schuster, New York.
47. ELDEREDGE, N. & GOULD, S.J. (1972). Models in Paleobiology. San Francisco: Freeman, Cooper.
48. FALCONER, K. J. (1985). The Geometry of Fractal Sets. Cambridge University Press.
49. FEDER, J. (1988). Fractals. Plenum Press.
50. FEIGENBAUM, M. J. (1978). Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics 19, 25-52.
51. FEIGENBAUM, M. J. (1979). The universal metric properties of nonlinear transformations. Journal of Statistical Physics 21, 669-706.
52. FERSTER, D. (1996). Is neural noise just a nuisance? Science 273, 1812.
53. FRETTE, V., CHRISTENSEN, K., MALTHE-SORENSSEN, A., FEDER, J., JOSSANG, T. & MEAKIN, P. (1996). Avalanche dynamics in a pile of rice. Nature 379, 49-52.
54. GARDNER, M. (1970). The fantastic combinations of John Conway's new solitaire game 'life'. Scientific American 223, (4) 120-124.
55. GATTASS, R. & DESIMONE, R. (1996). Responses of cells in the superior colliculus during performance of a spatial attention task in the macaque. Revista Brasileira de Biologia 56, 257-279.
56. GILDEN, D. L. (1997). Fluctuations in the time required for elementary decisions, Psychological Science 8, 296-301.
57. GILDEN, D. L., THORNTON, T. & MALLON, M. W. (1995). 1/f noise in human cognition. Science 267, 1837-1839.
58. GOLDBERGER, A. L., RIGNEY, D. R. & WEST, B. J. (1990). Chaos and fractals in human physiology. Scientific American 262, 42-49.
59. GOLDBERGER, A. L. & WEST, B. J. (1987). Fractals in physiology and medicine. Yale Journal of Biology and Medicine 60, 421-435.
60. GOULD, S. J. & ELDEREDGE, N. (1993). Punctuated equilibrium comes of age. Nature 366, 223-227.
61. GOULD, H. & TOBOCHNIK, J. (1988). An Introduction to Computer Simulation Methods: applications to Physical Systems, Part II. Addison-Wesley.
62. GRIEGER, B. (1992). Quaternary climatic fluctuations as a consequence of self-organized criticality. Physica A191, 51-56.
63. GUEVARA, M. R., GLASS, L. & SHRIER, A. (1981). Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science 214, 1350-1353.
64. GUTENBERG, B. (1949). Seismicity of the Earth and Associated Phenomena. Princeton University Press.
65. GUTENBERG, B. & RICHTER, C. F. (1956). Magnitude and energy of earthquakes. Annali di Geofisica 9, 115ff.
66. HALLEY, J. M. (1996). Ecology, evolution and 1/f noise. Trends in Ecology and Evolution 11, 33-37.
67. HAMMERSLEY, J. M. (1983). Origins of percolation theory. Annals of the Israel Physical Society 5, 47-57.
68. HARRISON, R. G. AND BISWAS, D. J. (1986). Chaos in light. Nature 321, 394-401.
69. HASSEL, M. P., COMINS, H. N. & MAY, R. M. (1991). Spatial structure and chaos in insect population dynamics. Nature 353, 255-258.
70. HASTINGS, A., HOM, C. L., ELLNER, S., TURCHIN, P. & GODFRAY, H. C. J. (1993). Chaos in ecology: Is mother nature a strange attractor? Annual Review of Ecological Systems 24, 1-33.
71. HOFFMAN, A. (1989). What, if anything, are mass extinctions? Philosophical Transactions of the Royal Society of London B325, 253-261.
72. HOUSE, M. R. (1989). Ammonoid extinction events. Philosophical Transactions of the Royal Society of London B325, 307-326.
73. HURST, H. E. (1951) Transactions of the American Society of Civil Engineers 116, 770-808.
74. HURST, H. E., BLACK, R. P. & SAMAYKA, Y. M. (1965). Long-Term Storage: an Experimental Study. Constable.
75. JABLONSKI, D. (1991). Extinctions: a paleontological perspective. Science 253, 754-757.
76. JEFFREY, H. J. (1990). Chaos game representation of gene structure. Nucleic Acids Research 18, 2163-2170.
77. JENSEN, H. J. (1990). Lattice gas as a model of 1/f noise. Physical Review Letters 64, 3103-3106.
78. JENSEN, H. J., CHRISTENSEN, K. & FOGEDBY, H. C. (1989). 1/f noise, distribution of lifetimes, and a pile of sand. Physical Review B40, 7425-7427.
79. KAFETZOPOULOS, E., GOUSKOS, S. & EVANGELOU, S. N. (1997). 1/f noise and multifractal fluctuations in rat behavior. Nonlinear Analysis, Theory, Methods and Applications 30, 2007-2013.
80. KAITALA, V. & RANTA, E. (1996). Scientific correspondence. Nature 381, 199.
81. KANEKO, K. (1989). Pattern dynamics in spatiotemporal chaos. Physica D34, 1-41.
82. KAPLAN, D. T. & GLASS, L. (1992). Direct test for determinism in a time series. Physical Review Letters 68, 427-430.
83. KAUFFMAN, S. A. (1989a). Adaptation on rugged fitness landscapes. Lectures in the Sciences of Complexity. The Santa Fe Institute Series (Addison Wesley), 527-618 and 619-712.
84. KAUFFMAN, S. A. (1989b). Principles of adaptation in complex systems. Lectures in the Sciences of Complexity. The Santa Fe Institute Series (Addison Wesley), 619-712.
85. KAUFFMAN, S. A. & JOHNSEN, S., (1991). Coevolution to the edge of chaos: coupled fitness landscapes, poised states and coevolutionary avalanches. Journal of Theoretical Biology 149, 467-505.
86. KAUFFMAN, S. A. & LEVIN, S. (1987). Towards a general theory of adaptive walks on rugged fitness landscapes. Journal of Theoretical Biology 128, 11-45.
87. KEITT, T. H. & MARQUET, P. A. (1996). The introduced Hawaiian avifauna reconsidered: Evidence for self-organized criticality? Journal of Theoretical Biology 182, 161-167.
88. KELLOGG, D. E. (1975). The role of phyletic changes in the evolution of Pseudocubus vema (Radiolaria). Paleobiology 1, 359-370.
89. KERTÉSZ, J. & KISS, L. B. (1990). The noise spectrum in the model of self-organized criticality. Journal of Physics: Mathematical and General A23, L433-L440.
90. KOCH, C. (1997). Computation and the single neuron. Nature 385, 207-210.
91. LANGTON, C. (1990). Computation at the edge of chaos: phase transitions and emergent computation. Physica D42, 12-37.
92. LE BELLAC, M. (1988). Des phénomènes critiques aux champs de jauge. InterEditions/Editions du CNRS.
93. LIBCHABER, A., LAROCHE, C. & FAUVE, S. (1982). Period doubling cascade in mercury, a quantitative measurement. Journal de Physique Lettres 43, L211-L216.
94. LORENZ, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20, 130ff.
95. MANDELBROT, B. B. (1977). Fractals: Form, Chance and Dimension, W. H. Freeman.
96. MANDELBROT, B. B. (1983). The Fractal Geometry of Nature, W. H. Freeman.
97. MANNEVILLE, P. (1980). Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems. Journal of Physics (Paris) 41, 1235-1243.
98. MANRUBIA, S. C. & SOLÉ, R. Y. (1997). On forest spatial dynamics with gap formation. Journal of Theoretical Biology 187, 159-164.
99. MARIS, H. J. & KADANOFF, L. P. (1978). Teaching the renormalization group. American Journal of Physics 46, 652-657.
100. MATA-TOLEDO, R. A. & WILLIS, M. A. (1997). Visualisation of random sequences using the chaos game algorithm. Journal of Systems and Software 39, 3-6.
101. MAY, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459-467.
102. MAYNARD SMITH, J. (1989). The causes of extinction. Philosophical Transactions of the Royal Society of London B325, 241-252.
103. MCNAMEE, J. E. (1991). Fractal perspectives in pulmonary physiology. Journal of Applied Physiology 71, 1-8.
104. MIRAMONTES, O. & ROHANI, P. (1998). Intrinsically generated coloured noise in laboratory insect populations. Proceedings of the Royal Society of London B265, 785-792.
105. NEWMAN, M. E. J. (1996). Self-organized criticality, evolution and the fossil extinction record. Proceedings of the Royal Society of London B263, 1605-1610.
106. NEWMAN, M. E. J. (1997a). A model of mass extinction. Journal of Theoretical Biology 189, 235-252.
107. NEWMAN, M. E. J. (1997b). Evidence for self-organized criticality in evolution. Physica D107, 293-296.
108. NICHOLSON, A. J. (1957). The self-adjustment of populations to change. Cold Spring Harbour Symposia on Quantitative Biology 22, 153-173.
109. NICOLIS, G. & PRIGOGINE, I. (1989). Exploring Complexity: an Introduction. Freeman.
110. NYCHKA, D., ELLNER, S., MCCAFFREY, D. & GALLANT, A. R. (1992). Finding chaos in noisy systems. Journal of the Royal Statistical Society B54, 399-426.
111. PAPA, A. R. R. & DA SILVA, L. (1997). Earthquakes in the brain. Theory in Biosciences 116, 321-327.
112. PARISI, G. (1993). Statistical physics and biology. Physics World 6, 42-47.
113. PAUMOGARTNER, D., LOSA, G. & WEIBEL, E. R. (1981). Resolution effect on the stereological estimation of surface and volume and its interpretation in terms of fractal dimension. Journal of Microscopy 121, 51-63.
114. PILGRAM, B. & KAPLAN, D. T. (1999). Nonstationarity and 1/f noise characteristics in heart rate. American Journal of Physiology: Regulatory Integrative and Comparative Physiology 45, R1-R9.
115. PIMM, S. L. & REDFEARN, A. (1988). The variability of population densities. Nature 334, 613-614.
116. POSNER, M. I. & PAVESE, A. (1998). Anatomy of word and sentence meaning. Proceedings of the National Academy of Sciences of the United States of America 95, 899-905.
117. PRESS, W. H. (1978). Flicker noises in astronomy and elsewhere. Comments on Astrophysics 7, 103-119.
118. PRESS, W. H., TEUKOLSKY, S. A., VETTERLING, W. T., FLANNERY, B. P. (1988). Numerical Recipes in C: the Art of Scientific Computing, Second Edition, Cambridge University Press.
119. PROCACCIA, I. & SCHUSTER, H. (1983). Functional renormalization-group theory of universal 1/f noise in dynamical systems. Physical Review A28, 1210-1212.
120. RAUP, D. M. (1986). Biological extinction in earth history. Science 231, 1528-1533.
121. RAUP, D. M. (1989). The case for extraterrestrial causes of extinction. Philosophical Transactions of the Royal Society of London B325, 421-435.
122. RAUP, D. M. & BOYAJIAN, G. E. (1988). Patterns of generic extinction in the fossil record. Paleobiology 14, 109-125.
123. RAUP, D. M. & SEPKOSKI, J. J., JR. (1982). Mass extinctions in the marine fossil records. Science 215, 1501-1502.
124. RAUP, D. M. & SEPKOSKI, J. J., JR. (1984). Periodicity of extinctions in the geological past. Proceedings of the National Academy of Sciences of the United States of America 81, 801-805.
125. RHODES, C. J. & ANDERSON, R. M. (1996a). A scaling analysis of measles epidemics in a small population. Philosophical Transactions of the Royal Society of London B351, 1679-1688.
126. RHODES, C. J. & ANDERSON, R. M. (1996b). Power laws governing epidemics in isolated populations. Nature 381, 600-602.
127. RHODES, C. J. JENSEN, H. J. & ANDERSON, R. M. (1997). On the critical behaviour of simple epidemics. Proceedings of the Royal Society of London B264, 1639-1646.
128. RUTHEN, R. (1993) Adapting to complexity. Scientific American 268, 130-140.
129. SALES, T. R. (1993). Life in one dimension: statistics and self-organized criticality. Journal of Physics A: Mathematical and General 26, 6187-6193.
130. SCHICK, K. L. & VERVEEN, A. A. (1974) 1/f noise with a low frequency white noise limit. Nature 251, 599-601.
131. SEPKOSKI, J. J., JR. (1982). A compendium of fossil marine families Milwaukee. Public Museum Contributions in Biology and Geology 51.
132. SEPKOSKI, J. J., JR. (1993). Ten years in the library: new data confirm paleontological patterns. Paleobiology 19, 43-51.
133. SNEPPEN, K. (1995). Extremal dynamics and punctuated coevolution. Phrsica A221, 168-179.
134. SNEPPEN, K., BAK, P., FLYVBJERG, H. & JENSEN, M. H. (1995). Evolution as a self-organized critical phenomenon. Proceedings of the National Academy of Sciences of the United States of America 92, 5209-5213.
135. SOLÉ, R. V. (1996). On macroevolution, extinctions and critical phenomena. Complexity 1, 40-44.
136. SOLÉ, R. Y. & BASCOMPTE, J. (1996). Are critical phenomena relevant to large-scale phenomena. Proceedings of the Royal Society of London 263, 161-168.
137. SOLÉ, R. V., BASCOMPTE, J. & MANRUBIA, S. C. (1996). Extinction: bad genes or weak chaos. Proceedings of the Royal Society of London B263, 1407-1413.
138. SOLÉ, R. V. & MANRUBIA, S. C. (1995a). Are rain forests self-organized in a critical state? Journal of Theoretical Biology 173, 31-40.
139. SOLÉ, R. V. & MANRUBIA, S. C. (1995b). Self-similarity in rain forests: Evidence for a critical state. Physical Review E51, 6250-6253.
140. SOLÉ, R. V. & MANRUBIA, S. C. (1996). Extinction and self-organized criticality in a model of large-scale evolution. Physical Review E54, R42-R45.
141. SOLÉ, R. V. & MANRUBIA, S. C. (1997). Criticality and unpredictability in macroevolution. Physical Review E55, 4500-4507.
142. SOLÉ, R. Y., MANRUBIA, S. C., BENTON, M. & BAK, P. (1997). Self-similarity of extinction statistics in the fossil record. Nature 388, 764-767.
143. SORNETTE, A. & SORNETTE, D. (1989). Self-organized criticality and earthquakes. Europhysics Letters 9, 197-202.
144. STASSINOPOULOS, D. & BAK, P. (1995). Democratic reinforcement: a principle for brain function. Physical Review E51, 5033-5039.
145. STAUFFER, D. (1979). Scaling theory of percolation clusters. Physics Reports 54, 1-74.
146. STEELE, J. H. (1985). A comparison of terrestrial and marine ecological systems. Nature 313, 355-358.
147. STOKES, T. K., GURNEY, W. S. C., NISBET, R. M. & BLYTHE, S. P. (1988). Parameter evolution in a laboratory insect population. Theoretical Population Theory 34, 248-265.
148. STROGATZ, S. H. (1994). Nonlinear Dynamics and Chaos. Addison-Wesley Publishing.
149. SUGIHARA, G. (1996). Scientific correspondence. Nature 381, 199.
150. SUGIHARA, G. & MAY, R. M. (1990). Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734-741.
151. TANG, C. & BAK, P. (1988). Critical exponents and scaling relations for self-organized critical phenomena. Physical Review Letters 60, 2347-2350.
152. TURCOTTE, D. L. (1992). Fractals and Chaos in Geology and Geophysics. Cambridge University Press.
153. UTIDA, S. (1957). Cyclic fluctuations of population density intrinsic to the host-parasite system. Ecology 38, 442-449.
154. VOSS, R. F. & CLARKE, J. (1975). 1/f noise in music and speech. Nature 258, 317-318.
155. WEST, G. B., BROWN, J. H. & ENQUIST, B. J. (1997). A general model for the origin of allosteric scaling laws in biology. Nature 276, 122-126.
156. WHITE, A., BEGON, M. & BOWERS, R. G. (1996a). Explaining the colour of power spectra in chaotic ecological models. Proceedings of the Royal Society of London B263, 1731-1737.
157. WHITE, A., BOWERS, R. G. & BEGON, M. (1996b). Red/Blue chaotic power spectra. Nature 381, 198.
158. WILSON, K. G. (1979). Problems in physics with many scales of length. Scientific American 241, 158-179.
159. WING, A. M. & KRISTOFFERSON, A. B. (1973). The timing of interresponse intervals. Perception and Psychophysics 14, 455-460.
160. WOLFRAM, S. (1983). Statistical mechanics of cellular automata. Review of Modern Physics 55, 601-644.
161. WOLFRAM, S. (1984). Universality and complexity in cellular automata. Physica D10, 1-35.
162. WOLFRAM, S. (1986). Theory and Applications of Cellular Automata. World Scientific.
163. WRIGHT, S. (1982). Character change, speciation, and the higher taxa. Evolution 36, 427-443.
164. ZHABOTINSKI, A. (1964). Biofizika 9, 306ff (in Russian).
165. ZIPF, G. K. (1949). Human Behaviour and the Principle of Least Effort. Haffner Publishing.