Abstract
On the basis of paleological evidence, it has been suggested that biological evolution need not necessarily be characterized by gradual change. Rather, evolutionary history may display saltatory periods of rapid speciation alternating with periods of relative quiescence, the whole dynamic being called punctuated equilibria. The empirical evidence that has been presented in support of this hypothesis has been the object of a vigorous dispute. Mathematical investigations of complex models of biological evolution that contain random elements have demonstrated that these systems can display saltatory behavior. In this paper we address a more abstract question: can saltations occur in the evolution of very simple, deterministic mathematical systems that function in a constant environment? The answer appears to be yes. Saltations appear as a natural dynamical behavior in the evolution of simplistic information processing networks. We stress that these networks do not constitute a model of biological evolution. However, the appearance of saltations in such simple systems suggests that their appearance in a process as complex as biological evolution is not surprising.
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References
Brillouin L (1962) Science and information theory. 2nd edn. Academic Press, New York
Clark RW (1984) The survival of Charles Darwin. A biography of a man and an idea. Random House, New York
Cronin JE, Boaz NT, Stringer CB, Ray K (1981) Tempo and mode in hominid evolution. Nature (London) 292:113–122
Darwin CR (1859) On the origin of species by means of natural selection. 1st edn 1859; 2nd edn 1860; 3rd edn 1861; 4th edn 1866; 5th edn 1869; 6th edn 1872. Murray, London
Dawkins R (1985) What was all the fuss about? Nature (London) 316:683–684
Dawkins R (1986) The blind watchmaker. Longman Scientific and Technical Publications, Essex
Eldredge N (1985) Time frames. The rethinking of Darwinian evolution and the theory of punctuated equilibria. Simon and Schuster, New York
Eldredge N (1986) Unfinished synthesis: biological hierarchies and modern evolutionary thought. Oxford University Press, Oxford
Eldredge N, Gould SJ (1972) Punctuated equilibria: an alternative to phyletic gradualism. In: Schopf TJM (ed) Models in Palaeobiology. Freeman, Cooper and Company, San Francisco, pp 82–115
Eldredge N, Tattersall I (1975) Evolutionary models, phylogenetic reconstruction and another look at hominid phylogeny. Contrib Primat 5:218–242
Futuyma DJ, Lewontin RC, Mayer GC, Seger J, Stubblefield JW (1981) Letter to the editor. Science (Wash) 211:770
Goldschmidt RB (1940) The material basis of evolution. Yale University Press, New Haven, Coun
Gould SJ (1982) Darwinism and the expansion of evolutionary theory. Science (Wash) 216:380–387
Gould SJ (1986) Punctuated equilibrium: empirical response. Science (Wash) 231:439
Gould SJ, Eldredge N (1977) Punctuated equilibria: the tempo and mode of evolution reconsidered. Paleobiology 3:115–151
Halstead LB (1980) Museum of errors. Nature (London) 288:208
Huxley L (ed) (1900) Life and letters of Thomas Henry Huxley, vols 1 and 2. Macmillan, London
Johanson DC, Masao FT, Eck GG, White TD, Walter RC, Kimbel WH, Asfaw B, Manega P, Ndessokia P, Suwa G (1987) New partial skeleton of Homo habilis from Olduvai Gorge, Tanzania. Nature (London) 327:205–209
Jones JS (1981) An uncensored page of fossil history. Nature (London) 293:427–428
Lande R (1985) Expected time for random genetic drift of a population between stable phenotypic states. Proc Natl Acad Sci (USA) 82:7641–7645
Levinton J (1985) Punctuated equilibrium. Science (Wash) 231:1490
Lewin R (1986) Punctuated equilibrium is now old hat. Science (Wash) 231:672–673
Mayr E (1942) Systematics and the origin of species. Reprinted 1982 in the Columbia Classics in Evolution Series. Columbia University Press, New York
Mayr E (1954) Change of genetic environment and evolution. In: Huxley JS, Hardy AC, Ford EB (eds) Evolution as a process. Alien and Unwin, London, pp 157–180
Mayr E, Boucot AJ, Charlesworth B, Lande R, Ginzburg LR, Rost JD, Lindsay DW, Williamson PG (1982) Punctuationism and Darwinism reconciled? The Lake Turkana mollusc sequence. Nature (London) 296:608–612
Mivrat SGJ (1871) On the genesis of species. Macmillan, London
Newman CM, Cohen JE, Kipnis C (1985) Neo-darwinian evolution implies punctuated equilibria. Science (Wash) 315:400–401
Rhodes FHT (1983) Gradualism, punctuated equilibria and the origin of the species. Nature (London) 305:269–272
Saunders RT, Ho MW (1976) On the increase in complexity in evolution. J Theor Biol 63:375–384
Saunders PT, Ho MW (1981) On the increase in complexity in evolution. II. The relativity of complexity and the principle of minimum increase. J Theor Biol 90:515–530
Simpson GG (1944) Tempo and mode in evolution. Columbia University Press, New York
Stanley SM (1979) Macroevolution. Freeman, San Francisco
Stanley SM (1981) The new evolutionary timetable: fossils, genes and the origin of the species. Basic Books, New York
Valentine JW, Walker TD (1986) Diversity trends within a model taxonomic hierarchy. Physica 22D:31–42
Vrba ES (1980) Evolution, species and fossils. How does life evolve? S Afr J Sci 76:61–84
Wade N (1980) Dinosaur battle erupts in British Museum. Science (Wash) 211:35–36
Williamson PG (1981a) Palaeontological documentation of speciation in cenozoic molluscs from Turkana basin. Nature (London) 293:437–443
Williamson PG (1981b) Morphological stasis and developmental constraint: real problems for neo-Darwinism. Nature (London) 294:214–215
Zenger DH (1987) Darwin, Lyell and gradualism. Nature (London) 322:10
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Zimmerman, I.D., Rapp, P.E. Saltatory transitions are a naturally occurring property of evolving systems. Biol. Cybern. 62, 167–175 (1989). https://doi.org/10.1007/BF00203005
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DOI: https://doi.org/10.1007/BF00203005