# Complexity by Subtraction

- 781 Downloads
- 9 Citations

## Abstract

The eye and brain: standard thinking is that these devices are both complex and functional. They are complex in the sense of having many different types of parts, and functional in the sense of having capacities that promote survival and reproduction. Standard thinking says that the evolution of complex functionality proceeds by the addition of new parts, and that this build-up of complexity is driven by selection, by the functional advantages of complex design. The standard thinking could be right, even in general. But alternatives have not been much discussed or investigated, and the possibility remains open that other routes may not only exist but may be the norm. Our purpose here is to introduce a new route to functional complexity, a route in which complexity starts high, rising perhaps on account of the spontaneous tendency for parts to differentiate. Then, driven by selection for effective and efficient function, complexity *decreases* over time. Eventually, the result is a system that is highly functional and retains considerable residual complexity, enough to impress us. We try to raise this alternative route to the level of plausibility as a general mechanism in evolution by describing two cases, one from a computational model and one from the history of life.

## Keywords

Evolution Complexity Constructive neutral evolution Irreducible complexity ZFEL## Notes

### Acknowledgments

The main ideas described in this paper originated at a catalysis meeting at the National Evolutionary Synthesis Center (NESCent) in Durham, NC, USA. They were developed further and finalized into the current paper during a subsequent short-term research visit of WH at, and supported by, NESCent. We thank Robert Brandon for suggesting the apt and evocative phrase “complexity by subtraction.” Finally, one of us (DM) would like to thank Benedikt Hallgrimsson for discussions decades ago, discussions that turned out to be foundational in the development of the ZFEL.

## References

- Adamowicz, S. J., Purvis, A., & Wills, M. A. (2008). Increasing morphological complexity in multiple parallel lineages of the Crustacea.
*Proceedings of the National Academy of Sciences, 105*, 4786–4791.CrossRefGoogle Scholar - Alroy, J. (2001). Understanding the dynamics of trends within evolving lineages.
*Paleobiology, 26*, 319–329.CrossRefGoogle Scholar - Boerlijst, M., & Hogeweg, P. (1991). Self-structuring and selection: Spiral waves as a substrate for prebiotic evolution. In C. G. Langton, C. Taylor, J. D. Farmer & S. Rasmussen (Eds.),
*Artifial life II*(pp. 55–276). Reading: Addison-Wesley.Google Scholar - Bonner, J. T. (1988).
*The evolution of complexity by means of natural selection*. Princeton: Princeton University Press.Google Scholar - Brown, T. A., & McBurnett, M. D. (1996). The emergence of political elites. In M. Coombs & M. Sulcoski (Eds.),
*Proceedings of the International Workshop on Control Mechanisms for Complex Systems*(pp. 143–161).Google Scholar - Buchholtz, E. A., & Wolkovich, E. H. (2005). Vertebral osteology and complexity in Lagenorhynchus acutus.
*Marine Mammal Science, 21*, 411–428.CrossRefGoogle Scholar - Burks, A. W. (Ed) (1970).
*Essays on cellular automata*. Urbana: University of Illinois Press.Google Scholar - Cisne, J. L. (1974). Evolution of the world fauna of aquatic free-living arthropods.
*Evolution, 28*, 337–366.CrossRefGoogle Scholar - Crutchfield, J. P., & Hanson, J. E. (1993). Turbulent pattern bases for cellular automata.
*Physica D, 69*, 279–301.CrossRefGoogle Scholar - Crutchfield, J. P., & Mitchell, M. (1995). The evolution of emergent computation.
*Proceedings of the National Academy of Sciences, 92*(23), 10742–10746.CrossRefGoogle Scholar - Darwin, C. (1859).
*On the origin of species*. London: J. Murray.Google Scholar - Darwin, C. (1862).
*On the various contrivances by which British and foreign orchids are fertilised by insects, and on the food effects of intercrossing*. London: J. Murray.Google Scholar - Das, R., Mitchell, M., Crutchfield, J. P. (1994). A genetic algorithm discovers particle-based computation in cellular automata. In Y. Davidor, H. P. Schwefel & R. Manner (Eds.),
*Parallel problem solving from nature—PPSN III*(pp. 344–353). Berlin: Springer.CrossRefGoogle Scholar - Das, R., Crutchfield, J. P., Mitchell, M., & Hanson, J. E. (1995). Evolving globally synchronized cellular automata. In L. J. Eshelman (Ed.),
*Proceedings of the Sixth International Conference on Genetic Algorithms*(pp. 336–343). Los Altos: Morgan Kaufmann.Google Scholar - Dembski, W. A., & Ruse, M. (Eds.) (2004).
*Debating design*. Cambridge: Cambridge University Press.Google Scholar - Doolittle, W. F. (2012). A ratchet for protein complexity.
*Nature, 481*, 270–271.PubMedGoogle Scholar - Ermentrout, G. B., & Edelstein-Keshet, L. (1993). Cellular automata approaches to biological modeling.
*Journal of Theoretical Biology, 160*, 97–133.CrossRefPubMedGoogle Scholar - Esteve-Altava, B., Marugán-Lobón, J., Botella, H., & Rasskin-Gutman, D. (2012). Structural constraints in the evolution of the tetrapod skull complexity: Willistons Law revisited using network models.
*Evolutionary Biology*. doi: 10.1007/s11692-012-9200-9. - Finnigan, G. C., Hanson-Smith, V., Stevens, T. H., & Thornton, J. W. (2012). Evolution of increased complexity in a molecular machine.
*Nature, 481*, 360–364.PubMedGoogle Scholar - Gardner, M. (1970). The fantastic combinations of John Conway’s new solitaire game “life”.
*Scientific American, 223*(120), 123.Google Scholar - Garey, M. R., & Johnson, D. S. (1979).
*Computers and intractability: A guide to the theory of NP-completeness*. New York: W. H. Freeman.Google Scholar - Goldberg, D. E. (1989) Genetic algorithms in search, optimization, and machine learning. Reading: Addison-Wesley.Google Scholar
- Gray, M. W., Lukeš, J., Archibald, J. M., Keeling, P. J., & Doolittle, W. F. (2010). Irremediable complexity?
*Science, 330*, 920–921.Google Scholar - Gregory, W. K. (1934). Polyisomerism and anisomerism in cranial and dental evolution among vertebrates.
*Proceedings of the National Academy of Sciences, 20*, 1–9.CrossRefGoogle Scholar - Gregory, W. K. (1935). Reduplication in evolution.
*Quarterly Review of Biology, 10*, 272–290.CrossRefGoogle Scholar - Hanson, J. E., & Crutchfield, J. P. (1992). The attractor-basin portrait of a cellular automaton.
*Journal of Statistical Physics, 66*(5/6), 1415–1462.CrossRefGoogle Scholar - Holland, J. H. (1975).
*Adaptation in natural and artificial systems*. Ann Arbor: University of Michigan Press (2nd edn., MIT Press, 1992).Google Scholar - Hordijk, W. (1999).
*Dynamics, emergent computation, and evolution in cellular automata*. PhD thesis, Albuquerque, NM, USA: University of New Mexico.Google Scholar - Hordijk, W. (2013).
*The EvCA project: A brief history*. Complexity (To appear).Google Scholar - Hordijk, W., Crutchfield, J. P., & Mitchell, M. (1996). Embedded particle computation in evolved cellular automata. In T. Toffoli, M. Biafore & J. Leão (Eds.),
*Proceedings of the Conference on Physics and Computation*(pp. 153–158). Cambridge: New England Complex Systems Institute.Google Scholar - Hordijk, W., Crutchfield, J. P., & Mitchell, M. (1998). Mechanisms of emergent computation in cellular automata. In A. E. Eiben, T. Bäck, M. Schoenauer & H. P. Schwefel (Eds.),
*Parallel Problem Solving from Nature–V*(pp. 613–622). New York: Springer.CrossRefGoogle Scholar - Kauffman, S. A. (1996).
*At home in the universe*. Oxford: Oxford University Press.Google Scholar - Lynch, M. (2007). The fraily of adaptive hypotheses for the origins of organismal complexity.
*Proceedings of the National Academy of Sciences, 104*, 8597–8604.CrossRefGoogle Scholar - Manneville, P., Boccara, N., Vichniac, G. Y., & Bidaux, R. (1990).
*Cellular automata and modeling of complex physical systems*, volume 46 of Springer Proceedings in Physics. New York: Springer.Google Scholar - Marcus, J. M. (2005). A partial solution to the C-value paradox. Lecture Notes in Computer Science, p 3678.Google Scholar
- Margolus, N., Toffoli, T., & Vichniac, G. (1986). Cellular-automata supercomputers for fluid-dynamics modeling.
*Physical Review Letters, 56*(16), 1694–1696.CrossRefPubMedGoogle Scholar - McShea, D. W. (1992). A metric for the study of evolutionary trends in the complexity of serial structures.
*Biological Journal of the Linnean Society, 45*, 39–55.CrossRefGoogle Scholar - McShea, D. W. (1993). Evolutionary changes in the morphological complexity of the mammalian vertebral column.
*Evolution, 47*, 730–740.CrossRefGoogle Scholar - McShea, D. W. (1994). Mechanisms of large-scale evolutionary trends.
*Evolution, 48*, 1747–1763.CrossRefGoogle Scholar - McShea, D. W. (1996). Metazoan complexity and evolution: Is there a trend?
*Evolution, 50*, 477–492.CrossRefGoogle Scholar - McShea, D. W. (2000). Functional complexity in organisms: Parts as proxies.
*Biology and Philosophy, 15*, 641–668.CrossRefGoogle Scholar - McShea, D. W. (2001). The hierarchical structure of organisms: A scale and documentation of a trend in the maximum.
*Paleobiology, 27*, 405–423.CrossRefGoogle Scholar - McShea, D. W. (2002). A complexity drain on cells in the evolution of multicellularity.
*Evolution, 56*, 441–452.PubMedGoogle Scholar - McShea, D. W., & Brandon, R. N. (2010).
*Biologys first law*. Chicago: University of Chicago Press.Google Scholar - McShea, D. W., & Venit, E. P. (2001). What is a part? In G. P. Wagner (Ed.),
*The character concept in evolutionary biology*(pp. 259–284). New York: Academic Press.CrossRefGoogle Scholar - Mitchell, M. (1996).
*An introduction to genetic algorithms*. Cambridge: MIT Press.Google Scholar - Mitchell, M. (1998). Computation in cellular automata: A selected review. In T. Gramss, S. Bornholdt, M. Gross, M. Mitchell & T. Pellizzari (Eds.),
*Nonstandard computation*. Weinheim: VCH Verlagsgesellschaft.Google Scholar - Mitchell, M., Hraber, P. T., & Crutchfield, J. P. (1993). Revisiting the edge of chaos: Evolving cellular automata to perform computations.
*Complex Systems, 7*, 89–130.Google Scholar - Mitchell, M., Crutchfield, J. P., & Hraber, P. T. (1994a). Dynamics, computation, and the “edge of chaos”: A re-examination. In G. A. Cowan, D. Pines & D. Melzner (Eds.),
*Complexity: Metaphors, Models, and Reality*(pp. 497–513). Reading: Addison-Wesley. Santa Fe Institute Studies in the Sciences of Complexity, Proceedings Volume 19.Google Scholar - Mitchell, M., Crutchfield, J. P., & Hraber, P. T. (1994b). Evolving cellular automata to perform computations: Mechanisms and impediments.
*Physica D, 75*, 361–391.CrossRefGoogle Scholar - Packard, N. H. (1988). Adaptation toward the edge of chaos. In J. A. S. Kelso, A. J. Mandell & M. F. Shlesinger (Eds.),
*Dynamic patterns in complex systems*(pp. 293–301). Singapore: World Scientic.Google Scholar - Sidor, C. A. (2001). Simplification as a trend in synapsid cranial evolution.
*Evolution, 55*, 1142–1419.Google Scholar - Simon, P. M., & Nagel, K. (1998). Simplified cellular automaton model for city traffic.
*Physical Review E, 58*(2), 1286–1295.CrossRefGoogle Scholar - Stoltzfus, A. (1999). On the possibility of constructive neutral evolution.
*Journal of Molecular Evolution, 49*, 169–181.CrossRefPubMedGoogle Scholar - Tamayo, P., & Hartman, H. (1988). Cellular automata, reaction-diffusion systems and the origin of life. In C. G. Langon (Ed.),
*Artifial life*(pp. 105–124). Reading: Addison-Wesley.Google Scholar - Taylor, J. S., & Raes, J. (2004). Duplication and divergence: The evolution of new genes and old ideas.
*Annual Review of Genetics, 38*, 615–643.CrossRefPubMedGoogle Scholar - Valentine, J. W., Collins, A. G., & Meyer, C. P. (1994). Morphological complexity increase in metazoans.
*Paleobiology, 20*, 131–142.Google Scholar - Van Valen, L. (1962). A study of fluctuating asymmetry.
*Evolution, 16*, 125–142.CrossRefGoogle Scholar - von Neumann, J. (1966).
*Theory of self-reproducing automata*. In A. W. Burks (Ed.), Urbana: University of Illinois Press.Google Scholar - Vichniac, G. Y. (1984). Simulating physics with cellular automata.
*Physica D, 10*, 96–116.CrossRefGoogle Scholar - Wagner, P. J. (1996). Testing the underlying patterns of active trends.
*Evolution, 50*, 990–1017.CrossRefGoogle Scholar - Weber, B. H., & Depew, D. J. (2004). Darwinism, design, and complex systems dynamics. In W. A. Dembski & M. Ruse (Eds.),
*Debating design*(pp. 173–190). Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Williston, S. W. (1914).
*Water reptiles of the past and present*. Chicago: University of Chicago Press.Google Scholar