Four correlates of complex behavioral networks: Differentiation, behavior, connectivity, and compartmentalization: Carving networks at their joints: Survey

Some of the most complex networks are those that (i) have been engineered under selective pressure (either economic or evolutionary), and (ii) are capable of eliciting network-level behaviors. Some examples are nervous systems, ant colonies, electronic circuits and computer software. Here we provide evidence that many such selected, behavioral networks are similar in at least four respects. (1) Differentiation: Nodes of different types are used in a combinatorial fashion to build network structures through local connections, and networks accommodate more structure types via increasing the number of node types in the network (i.e., increasing differentiation), not via increasing the length of structures. (2) Behavior: Structures are themselves combined globally to implement behaviors, and networks accommodate a greater behavioral repertoire via increasing the number of lower-level behavior types (including structures), not via increasing the length of behaviors. (3) Connectivity: In order for structures in behavioral networks to combine with other structures within a fixed behavior length, the network must maintain an invariant network diameter, and this is accomplished via increasing network connectivity in larger networks. (4) Compartmentalization: Finally, for reasons of economical wiring, behavioral networks become increasingly parcellated. Special attention is given to nervous systems and computer software, but data from a variety of other behavioral selected networks are also provided, including ant colonies, electronic circuits, web sites and businesses. A general framework is introduced illuminating why behavioral selected networks share these four correlates. Because the four above features appear to apply to computer software as well as to biological networks, computer software provides a useful framework for comprehending the large-scale function and organization of biological networks. © 2005 Wiley Periodicals, Inc. Complexity 10: 13–40, 2005

[1]  J. Kaas.  Why Does the Brain Have So Many Visual Areas? , 1989, Journal of Cognitive Neuroscience.

[2]  R. S. Rodger,et al.  Computing a grammar for sequences of behavioural acts , 1979, Animal Behaviour.

[3]  Michael I. Jordan,et al.  Computational Consequences of a Bias toward Short Connections , 1992, Journal of Cognitive Neuroscience.

[4]  Leah Krubitzer,et al.  Organization of sensory cortex in a Madagascan insectivore, the tenrec (Echinops telfairi) , 1997, The Journal of comparative neurology.

[5]  W. Schleidt,et al.  A Proposal for a Standard Ethogram, Exemplified by an Ethogram of the Bluebreasted Quail (Coturnix chinensis) , 1984 .

[6]  J. Kaas,et al.  Subdivisions of auditory cortex and processing streams in primates. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[7]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Braitenberg,et al.  Cortical architectonics: General and areal , 1978 .

[9]  T. Powell,et al.  The basic uniformity in structure of the neocortex. , 1980, Brain : a journal of neurology.

[10]  Valentino Braitenberg,et al.  Brain Size and Number of Neurons: An Exercise in Synthetic Neuroanatomy , 2004, Journal of Computational Neuroscience.

[11]  Lesley M. Pickard,et al.  Statistical techniques for modelling software quality in the ESPIRIT REQUEST project , 1987 .

[12]  M. Woldenberg,et al.  Relation of branching angles to optimality for four cost principles. , 1986, Journal of theoretical biology.

[13]  C. D. Murray.  THE PHYSIOLOGICAL PRINCIPLE OF MINIMUM WORK APPLIED TO THE ANGLE OF BRANCHING OF ARTERIES , 1926, The Journal of general physiology.

[14]  P. Blau.  A FORMAL THEORY OF DIFFERENTIATION IN ORGANIZATIONS , 1970 .

[15]  J. Kaas.  The organization of neocortex in mammals: implications for theories of brain function. , 1987, Annual review of psychology.

[16]  Mark A Changizi,et al.  Three Puzzles in Hierarchical Evolution1 , 2003, Integrative and comparative biology.

[17]  R E Marc,et al.  Pattern recognition of amino acid signatures in retinal neurons , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[18]  Moshe Abeles,et al.  Corticonics: Neural Circuits of Cerebral Cortex , 1991 .

[19]  G. Mitchison.  Axonal trees and cortical architecture , 1992, Trends in Neurosciences.

[20]  M. Changizi.  Relationship between number of muscles, behavioral repertoire size, and encephalization in mammals. , 2003, Journal of theoretical biology.

[21]  P. Greenfield,et al.  Language, tools and brain: The ontogeny and phylogeny of hierarchically organized sequential behavior , 1991, Behavioral and Brain Sciences.

[22]  Jon H. Kaas,et al.  Why is Brain Size so Important:Design Problems and Solutions as Neocortex Gets Biggeror Smaller , 2000 .

[23]  M. Pettersson.  Complexity and evolution , 1996 .

[24]  R. Marc,et al.  Amino Acid Signatures in the Primate Retina , 1996, The Journal of Neuroscience.

[25]  P. Hof,et al.  Cellular distribution of the calcium-binding proteins parvalbumin, calbindin, and calretinin in the neocortex of mammals: phylogenetic and developmental patterns , 1999, Journal of Chemical Neuroanatomy.

[26]  J. Prothero,et al.  Cortical scaling in mammals: a repeating units model. , 1997, Journal fur Hirnforschung.

[27]  Jon H Kaas,et al.  Topographic Maps are Fundamental to Sensory Processing , 1997, Brain Research Bulletin.

[28]  Mark A. Changizi,et al.  Principles underlying mammalian neocortical scaling , 2001, Biological Cybernetics.

[29]  A. Burkhalter,et al.  Hierarchical organization of areas in rat visual cortex , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[30]  James W. Valentine,et al.  Hierarchies in biology and paleontology , 1996, Paleobiology.

[31]  C D Murray,et al.  The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume. , 1926, Proceedings of the National Academy of Sciences of the United States of America.

[32]  L. Krubitzer.  The organization of neocortex in mammals: are species differences really so different? , 1995, Trends in Neurosciences.

[33]  M. Hofman.  On the evolution and geometry of the brain in mammals , 1989, Progress in Neurobiology.

[34]  J. Kaas,et al.  Cortical connections of striate and extrastriate visual areas in tree shrews , 1998, The Journal of comparative neurology.

[35]  C. Gallistel.  The Organization of Action: A New Synthesis , 1982 .

[36]  E. Bizzi,et al.  Neural basis of motor control and its cognitive implications , 1998, Trends in Cognitive Sciences.

[37]  Mark A. Changizi.  The economy of the shape of limbed animals , 2001, Biological Cybernetics.

[38]  M. Young.  The organization of neural systems in the primate cerebral cortex , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[39]  Paul Horowitz,et al.  The Art of Electronics , 1980 .

[40]  Shinsuke Shimojo,et al.  Character complexity and redundancy in writing systems over human history , 2005, Proceedings of the Royal Society B: Biological Sciences.

[41]  J. W. Valentine,et al.  Morphological complexity increase in metazoans , 1994, Paleobiology.

[42]  C. Cherniak,et al.  Large-scale optimization of neuron arbors. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[43]  O. I. Fukson,et al.  Adaptability of innate motor patterns and motor control mechanisms , 1986, Behavioral and Brain Sciences.

[44]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[45]  R. Guillery.  Histology of the Nervous System by Santiago Ramón y Cajal. Translated into English from the French edition by Neely Swanson and Larry W. Swanson, Oxford University Press, 1995. $195.00 (1672 pp) ISBN 0 19 507 4017 , 1996, Trends in Neurosciences.

[46]  Bourke.  Colony size, social complexity and reproductive conflict in social insects , 1999 .

[47]  J. Kaas,et al.  Subdivisions of auditory cortex and ipsilateral cortical connections of the parabelt auditory cortex in macaque monkeys , 1998, The Journal of comparative neurology.

[48]  Johan Bollen,et al.  The evolution of complexity , 1999 .

[49]  Eric W. Weisstein.  New Kind of Science , 2004 .

[50]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[51]  Jon H. Kaas,et al.  The emergence and evolution of mammalian neocortex , 1995, Trends in Neurosciences.

[52]  J. Kaas,et al.  Topography, architecture, and connections of somatosensory cortex in opossums: Evidence for five somatosensory areas , 1996, The Journal of comparative neurology.

[53]  P. J. B. Slater,et al.  Describing Sequences of Behavior , 1973 .

[54]  C Cherniak,et al.  Modeling the large-scale geometry of human coronary arteries. , 2000, Canadian journal of physiology and pharmacology.

[55]  W. M. Evangelist.  Software complexity metric sensitivity to program structuring rules , 1983, J. Syst. Softw..

[56]  Carver Mead,et al.  Analog VLSI and neural systems , 1989 .

[57]  Maurice H. Halstead,et al.  Elements of software science (Operating and programming systems series) , 1977 .

[58]  Christopher Cherniak,et al.  Local optimization of neuron arbors , 1992, Biological Cybernetics.

[59]  J L Ringo,et al.  Neuronal interconnection as a function of brain size. , 1991, Brain, behavior and evolution.

[60]  J. Prothero,et al.  Scaling of cortical neuron density and white matter volume in mammals. , 1997, Journal fur Hirnforschung.

[61]  J. Kaas,et al.  Cortical organization in shrews: Evidence from five species , 1999, The Journal of comparative neurology.

[62]  Eytan Ruppin,et al.  Examining the volume efficiency of the cortical architecture in a multi-processor network model , 1993, Biological Cybernetics.

[63]  Stamatis Vassiliadis,et al.  Software metrics for the microcode of computer systems , 1994, J. Syst. Softw..

[64]  A. Roy,et al.  A generalization of the optimal models of arterial branching. , 1982, Bulletin of mathematical biology.

[65]  C. Peterson,et al.  Topological properties of citation and metabolic networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[66]  D. V. Essen,et al.  A tension-based theory of morphogenesis and compact wiring in the central nervous system , 1997, Nature.

[67]  C Cherniak,et al.  Component placement optimization in the brain , 1991, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[68]  Scott N. Woodfield,et al.  A study of several metrics for programming effort , 1981, J. Syst. Softw..

[69]  John Shepherd,et al.  A critical examination of software science , 1981, J. Syst. Softw..

[70]  V. Mountcastle.  The columnar organization of the neocortex. , 1997, Brain : a journal of neurology.

[71]  R. Marc,et al.  Amino acid signatures in the normal cat retina. , 1998, Investigative ophthalmology & visual science.

[72]  B L Whitsel,et al.  Minicolumnar activation patterns in cat and monkey SI cortex. , 1993, Cerebral cortex.

[73]  D. Pugh,et al.  Dimensions of Organization Structure , 1968 .

[74]  Christoph Adami,et al.  Evolution of Differentiated Expression Patterns in Digital Organisms , 1999, ECAL.

[75]  K A C ELLIOTT,et al.  Activity of acetylcholine system in cerebral cortex of various unanesthetized mammals. , 1952, The American journal of physiology.

[76]  R. Carneiro,et al.  On the Relationship between Size of Population and Complexity of Social Organization , 1967, Southwestern Journal of Anthropology.

[77]  Michel A. Hofman,et al.  Size and Shape of the Cerebral Cortex in Mammals (Part 1 of 2) , 1985 .

[78]  S. Wang,et al.  Scaling laws in the mammalian neocortex: Does form provide clues to function? , 2002, Journal of neurocytology.

[79]  C. Adami,et al.  Introduction To Artificial Life , 1997, IEEE Trans. Evol. Comput..

[80]  Louis Lefebvre,et al.  Grooming in crickets: Timing and hierarchical organization , 1981, Animal Behaviour.

[81]  Louis N. Gray,et al.  System Size and Structural Differentiation in Military Organizations: Testing a Baseline Model of the Division of Labor , 1971, American Journal of Sociology.

[82]  Béla Bollobás,et al.  Random Graphs , 1985 .

[83]  M. Changizi.  Universal scaling laws for hierarchical complexity in languages, organisms, behaviors and other combinatorial systems. , 2001, Journal of theoretical biology.

[84]  W Schreiner,et al.  Structural quantification and bifurcation symmetry in arterial tree models generated by constrained constructive optimization. , 1996, Journal of theoretical biology.

[85]  J. M. Douglas,et al.  Analysing the patterning of a sequence of discrete behavioural events , 1979, Animal Behaviour.

[86]  Richard Durbin,et al.  A dimension reduction framework for understanding cortical maps , 1990, Nature.

[87]  V. Mountcastle.  Modality and topographic properties of single neurons of cat's somatic sensory cortex. , 1957, Journal of neurophysiology.

[88]  David N. Card,et al.  Resolving the software science anomaly , 1987, J. Syst. Softw..

[89]  S. Shimojo,et al.  Parcellation and Area-Area Connectivity as a Function of Neocortex Size , 2005, Brain, Behavior and Evolution.

[90]  R. Passingham,et al.  Anatomical differences between the neocortex of man and other primates. , 1973, Brain, behavior and evolution.

[91]  Mark A. Changizi,et al.  Universal laws for hierarchical systems , 2002 .

[92]  W Schreiner,et al.  The branching angles in computer-generated optimized models of arterial trees , 1994, The Journal of general physiology.

[93]  J. Kaas,et al.  The evolution of isocortex. , 1995, Brain, behavior and evolution.

[94]  J. Allman,et al.  A neuronal morphologic type unique to humans and great apes. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[95]  Leah Krubitzer,et al.  Arealization of the Neocortex in Mammals: Genetic and Epigenetic Contributions to the Phenotype , 2000, Brain, Behavior and Evolution.

[96]  Patrice Y. Simard,et al.  Time is of the essence: a conjecture that hemispheric specialization arises from interhemispheric conduction delay. , 1994, Cerebral cortex.

[97]  Jack W Scannell,et al.  The connectional organization of neural systems in the cat cerebral cortex , 1993, Current Biology.

[98]  Giorgio M Innocenti,et al.  The representation of the visual field in three extrastriate areas of the ferret (Mustela putorius) and the relationship of retinotopy and field boundaries to callosal connectivity. , 2002, Cerebral cortex.

[99]  Arne Ø. Mooers,et al.  Size and complexity among multicellular organisms , 1997 .

[100]  J. Sundsten,et al.  Folding of the Cerebral Cortex in Mammals , 1984 .

[101]  M Zamir,et al.  Optimality principles in arterial branching. , 1976, Journal of theoretical biology.

[102]  J. C. Fentress.  Ethological Models of Hierarchy and Patterning of Species-Specific Behavior , 1983 .

[103]  Hofman Ma.  The fractal geometry of convoluted brains. , 1991 .

[104]  G. Simmel.  The Number of Members as Determining the Sociological Form of the Group. I , 1902, American Journal of Sociology.

[105]  Review of A new kind of science by Stephen Wolfram. Wolfram Media Inc., 2002 , 2002 .

[106]  M. Dawkins,et al.  Hierachical organization and postural facilitation: Rules for grooming in flies , 1976, Animal Behaviour.

[107]  D. Chklovskii,et al.  A wire length minimization approach to ocular dominance patterns in mammalian visual cortex , 2000 .

[108]  Naveed A. Sherwani,et al.  Algorithms for VLSI Physical Design Automation , 1999, Springer US.

[109]  John Tyler Bonner.  Dividing the labour in cells and societies , 1993 .

[110]  Robin Allott,et al.  The Motor Theory of Language: Origin and Function , 1992 .

[111]  E. G. Jones,et al.  Microcolumns in the cerebral cortex. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[112]  H. Frahm,et al.  Comparison of brain structure volumes in Insectivora and Primates. I. Neocortex. , 1982, Journal fur Hirnforschung.

[113]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

[114]  M A Changizi,et al.  Scaling of differentiation in networks: nervous systems, organisms, ant colonies, ecosystems, businesses, universities, cities, electronic circuits, and Legos. , 2002, Journal of theoretical biology.

[115]  Alan Peters,et al.  The Organization of the Primary Visual Cortex in the Macaque , 1994 .

[116]  C. Ofria,et al.  Genome complexity, robustness and genetic interactions in digital organisms , 1999, Nature.

[117]  A. Cowey.  Cortical Maps and Visual Perception the Grindley Memorial Lecture* , 1979, The Quarterly journal of experimental psychology.

[118]  T F Sherman,et al.  On connecting large vessels to small. The meaning of Murray's law , 1981, The Journal of general physiology.

[119]  D. Chklovskii,et al.  Power-law for axon diameters at branch point , 2003, BMC Neuroscience.

[120]  M. Conrad.  Evolving hierarchical systems: Stanley N. Salthe, Columbia University Press, New York, 1985, 343pp. (US$32.50) , 1987 .

[121]  J. C. Fentress,et al.  Grammar of a Movement Sequence in Inbred Mice , 1973, Nature.

[122]  S Traverso,et al.  Neuronal growth and the Steiner problem. , 1992, Rivista di biologia.

[123]  J. Kimberly.  Organizational size and the structuralist perspective: a review, critique, and proposal , 1976 .

[124]  M. Hofman.  Size and shape of the cerebral cortex in mammals. I. The cortical surface. , 1985, Brain, behavior and evolution.

[125]  R. F. Cancho,et al.  Topology of technology graphs: small world patterns in electronic circuits. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[126]  D. McShea.  A COMPLEXITY DRAIN ON CELLS IN THE EVOLUTION OF MULTICELLULARITY , 2002, Evolution; international journal of organic evolution.

[127]  C. D. Murray.  A RELATIONSHIP BETWEEN CIRCUMFERENCE AND WEIGHT IN TREES AND ITS BEARING ON BRANCHING ANGLES , 1927, The Journal of general physiology.

[128]  Daniel W. McShea,et al.  Functional Complexity in Organisms: Parts as Proxies , 2000 .

[129]  D. McShea.  The hierarchical structure of organisms: a scale and documentation of a trend in the maximum , 2001, Paleobiology.

[130]  C. Cherniak.  Neural component placement , 1995, Trends in Neurosciences.

[131]  Mark A. Changizi,et al.  Vagueness, Rationality And Undecidability: A Theory Of Why There Is Vagueness , 1999, Synthese.

[132]  L. Krubitzer,et al.  Modular Subdivisions of Dolphin Insular Cortex: Does Evolutionary History Repeat Itself? , 1998, Journal of Cognitive Neuroscience.

[133]  R. Hall,et al.  Organizational Size, Complexity, and Formalization , 1967 .

[134]  D. McShea.  PERSPECTIVE METAZOAN COMPLEXITY AND EVOLUTION: IS THERE A TREND? , 1996, Evolution; international journal of organic evolution.

[135]  R. Graham,et al.  The Shortest-Network Problem , 1989 .

[136]  H. J. Jerison.  Allometry, Brain Size, Cortical Surface, and Convolutedness , 1982 .

[137]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[138]  D. McShea,et al.  Individual versus social complexity, with particular reference to ant colonies , 2001, Biological reviews of the Cambridge Philosophical Society.

[139]  H. Barlow.  Why have multiple cortical areas? , 1986, Vision Research.

[140]  J. Pettigrew,et al.  Organization of somatosensory cortex in monotremes: In search of the prototypical plan , 1995, The Journal of comparative neurology.

[141]  I. Karsai,et al.  Productivity, individual-level and colony-level flexibility, and organization of work as consequences of colony size. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[142]  G. Mitchison.  Neuronal branching patterns and the economy of cortical wiring , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[143]  M. Woldenberg,et al.  Finding the optimal lengths for three branches at a junction. , 1983, Journal of theoretical biology.

[144]  D. Silverman,et al.  The Structure of Organizations. , 1971 .

[145]  HERBERT A. SIMON,et al.  The Architecture of Complexity , 1991 .

[146]  D. B. Tower,et al.  Structural and functional organization of mammalian cerebral cortex: The correlation of neurone density with brain size. Cortical neurone density in the fin whale (Balaenoptera Physalus L.) with a note on the cortical neurone density in the Indian elephant , 1954, The Journal of comparative neurology.

[147]  T Togawa,et al.  Optimal branching structure of the vascular tree. , 1972, The Bulletin of mathematical biophysics.