A complex adaptive system is a

system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...

that is '' complex'' in that it is a dynamic network of interactions, but the behavior of the ensemble may not be predictable according to the behavior of the components. It is '' adaptive'' in that the individual and

collective behavior The expression collective behavior was first used by Franklin Henry Giddings and employed later by Robert Park and Ernest Burgess, Herbert Blumer, Ralph H. Turner and Lewis Killian, and Neil Smelser to refer to social processes and events ...

mutate and self-organize corresponding to the change-initiating micro-event or collection of events. It is a "complex macroscopic collection" of relatively "similar and partially connected micro-structures" formed in order to adapt to the changing environment and increase their survivability as a macro-structure. The Complex Adaptive Systems approach builds on

replicator dynamics In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory. The replicator equation differs from other equations used to model replication, such as the quasispecie ...

. The study of complex adaptive systems, a subset of

nonlinear dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

s, is an interdisciplinary matter that attempts to blend insights from the natural and social sciences to develop system-level models and insights that allow for

heterogeneous agents In economic theory and econometrics, the term heterogeneity refers to differences across the units being studied. For example, a macroeconomic model in which consumers are assumed to differ from one another is said to have heterogeneous agents. ...

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states ...

, and emergent behavior.

Overview

The term ''complex adaptive systems'', or '' complexity science'', is often used to describe the loosely organized academic field that has grown up around the study of such systems. Complexity science is not a single theory—it encompasses more than one theoretical framework and is interdisciplinary, seeking the answers to some fundamental questions about

living Living or The Living may refer to: Common meanings *Life, a condition that distinguishes organisms from inorganic objects and dead organisms ** Living species, one that is not extinct *Personal life, the course of an individual human's life * H ...

, adaptable, changeable systems. Complex adaptive systems may adopt hard or softer approaches. Hard theories use formal language that is precise, tend to see agents as having tangible properties, and usually see objects in a behavioral system that can be manipulated in some way. Softer theories use natural language and narratives that may be imprecise, and agents are subjects having both tangible and intangible properties. Examples of hard complexity theories include Complex Adaptive Systems (CAS) and Viability Theory, and a class of softer theory is Viable System Theory. Many of the propositional consideration made in hard theory are also of relevance to softer theory. From here on, interest will now center on CAS. The study of CAS focuses on complex, emergent and macroscopic properties of the system.

John H. Holland John Henry Holland (February 2, 1929 – August 9, 2015) was an American scientist and Professor of psychology and Professor of electrical engineering and computer science at the University of Michigan, Ann Arbor. He was a pioneer in what became ...

said that CAS "are systems that have a large numbers of components, often called agents, that interact and adapt or learn". Typical examples of complex adaptive systems include: climate; cities; firms; markets; governments; industries; ecosystems; social networks; power grids; animal swarms; traffic flows; social insect (e.g. ant) colonies; the

brain A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as Visual perception, vision. I ...

and the

immune system The immune system is a network of biological processes that protects an organism from diseases. It detects and responds to a wide variety of pathogens, from viruses to parasitic worms, as well as cancer cells and objects such as wood splinte ...

; and the

cell Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery ...

and the developing

embryo An embryo is an initial stage of development of a multicellular organism. In organisms that reproduce sexually, embryonic development is the part of the life cycle that begins just after fertilization of the female egg cell by the male spe ...

. Human social group-based endeavors, such as

political parties A political party is an organization that coordinates candidates to compete in a particular country's elections. It is common for the members of a party to hold similar ideas about politics, and parties may promote specific political ideology ...

communities A community is a social unit (a group of living things) with commonality such as place, norms, religion, values, customs, or identity. Communities may share a sense of place situated in a given geographical area (e.g. a country, village, to ...

geopolitical Geopolitics (from Greek γῆ ''gê'' "earth, land" and πολιτική ''politikḗ'' "politics") is the study of the effects of Earth's geography (human and physical) on politics and international relations. While geopolitics usually refers to ...

organizations An organization or organisation (Commonwealth English; see spelling differences), is an entity—such as a company, an institution, or an association—comprising one or more people and having a particular purpose. The word is derived from ...

war War is an intense armed conflict between states, governments, societies, or paramilitary groups such as mercenaries, insurgents, and militias. It is generally characterized by extreme violence, destruction, and mortality, using regular o ...

, and terrorist networks are also considered CAS. The

internet The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, p ...

and

cyberspace Cyberspace is a concept describing a widespread interconnected digital technology. "The expression dates back from the first decade of the diffusion of the internet. It refers to the online world as a world 'apart', as distinct from everyday re ...

—composed, collaborated, and managed by a complex mix of

human–computer interaction Human–computer interaction (HCI) is research in the design and the use of computer technology, which focuses on the interfaces between people (users) and computers. HCI researchers observe the ways humans interact with computers and design te ...

s, is also regarded as a complex adaptive system. CAS can be hierarchical, but more often exhibit aspects of "self-organization". The term complex adaptive system was coined in 1968 by sociologist

Walter F. Buckley Walter Frederick Buckley (April 17, 1921 – January 27, 2006) was an American sociologist, and professor of sociology at the University of New Hampshire. Buckley was among the first to apply concepts from general systems theory based on the work ...

who proposed a model of

cultural evolution Cultural evolution is an evolutionary theory of social change. It follows from the definition of culture as "information capable of affecting individuals' behavior that they acquire from other members of their species through teaching, imitation ...

which regards psychological and socio-cultural systems as analogous with biological

species In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriat ...

. In the modern context, complex adaptive system is sometimes linked to

memetics Memetics is a study of information and culture. While memetics originated as an analogy with Darwinian evolution, digital communication, media, and sociology scholars have also adopted the term "memetics" to describe an established empirical stud ...

, or proposed as a reformulation of memetics. Michael D. Cohen and

Robert Axelrod Robert Marshall Axelrod (born May 27, 1943) is an American political scientist. He is Professor of Political Science and Public Policy at the University of Michigan where he has been since 1974. He is best known for his interdisciplinary work o ...

however argue the approach is not

social Darwinism Social Darwinism refers to various theories and societal practices that purport to apply biological concepts of natural selection and survival of the fittest to sociology, economics and politics, and which were largely defined by scholars in We ...

sociobiology Sociobiology is a field of biology that aims to examine and explain social behavior in terms of evolution. It draws from disciplines including psychology, ethology, anthropology, evolution, zoology, archaeology, and population genetics. Within ...

because, even though the concepts of variation, interaction and selection can be applied to modelling '

population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction usi ...

s of business strategies', for example, the detailed evolutionary mechanisms are often distinctly unbiological. As such, complex adaptive system is more similar to

Richard Dawkins Richard Dawkins (born 26 March 1941) is a British evolutionary biologist and author. He is an emeritus fellow of New College, Oxford and was Professor for Public Understanding of Science in the University of Oxford from 1995 to 2008. An ...

's idea of replicators.

General properties

What distinguishes a CAS from a pure

multi-agent system A multi-agent system (MAS or "self-organized system") is a computerized system composed of multiple interacting intelligent agents.Hu, J.; Bhowmick, P.; Jang, I.; Arvin, F.; Lanzon, A.,A Decentralized Cluster Formation Containment Framework fo ...

(MAS) is the focus on top-level properties and features like

self-similarity __NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically se ...

complexity Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, leading to nonlinearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to ch ...

emergence In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole. Emergenc ...

and

self-organization Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when suffic ...

. A MAS is defined as a system composed of multiple interacting agents; whereas in CAS, the agents as well as the system are adaptive and the system is

self-similar __NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically se ...

. A CAS is a complex, self-similar collectivity of interacting, adaptive agents. Complex Adaptive Systems are characterized by a high degree of adaptive capacity, giving them resilience in the face of

perturbation Perturbation or perturb may refer to: * Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial deposits over time * Perturbat ...

. Other important properties are adaptation (or

homeostasis In biology, homeostasis ( British also homoeostasis) (/hɒmɪə(ʊ)ˈsteɪsɪs/) is the state of steady internal, physical, and chemical conditions maintained by living systems. This is the condition of optimal functioning for the organism and ...

), communication, cooperation, specialization, spatial and temporal organization, and reproduction. They can be found on all levels: cells specialize, adapt and reproduce themselves just like larger organisms do. Communication and cooperation take place on all levels, from the agent to the system level. The forces driving

co-operation Cooperation (written as co-operation in British English) is the process of groups of organisms working or acting together for common, mutual, or some underlying benefit, as opposed to working in competition for selfish benefit. Many animal ...

between agents in such a system, in some cases, can be analyzed with

game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

Characteristics

Some of the most important characteristics of complex systems are: * The number of elements is sufficiently large that conventional descriptions (e.g. a system of

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...

s) are not only impractical, but cease to assist in understanding the system. Moreover, the elements interact dynamically, and the interactions can be physical or involve the exchange of information * Such interactions are rich, i.e. any element or sub-system in the system is affected by and affects several other elements or sub-systems * The interactions are

non-linear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...

: small changes in inputs, physical interactions or stimuli can cause large effects or very significant changes in outputs * Interactions are primarily but not exclusively with immediate neighbours and the nature of the influence is modulated * Any interaction can feed back onto itself directly or after a number of intervening stages. Such feedback can vary in quality. This is known as ''recurrency'' * The overall behavior of the system of elements is not predicted by the behavior of the individual elements * Such systems may be open and it may be difficult or impossible to define system boundaries * Complex systems operate under far from equilibrium conditions. There has to be a constant flow of energy to maintain the organization of the system * Complex systems have a history. They evolve and their past is co-responsible for their present behaviour * Elements in the system may be ignorant of the behaviour of the system as a whole, responding only to the information or physical stimuli available to them locally

& Michael D. Cohen identify a series of key terms from a modeling perspective: * Strategy, a conditional action pattern that indicates what to do in which circumstances * Artifact, a material resource that has definite location and can respond to the action of agents * Agent, a collection of properties, strategies & capabilities for interacting with artifacts & other agents * Population, a collection of agents, or, in some situations, collections of strategies * System, a larger collection, including one or more populations of agents and possibly also artifacts * Type, all the agents (or strategies) in a population that have some characteristic in common * Variety, the diversity of types within a population or system * Interaction pattern, the recurring regularities of contact among types within a system * Space (physical), location in geographical space & time of agents and artifacts * Space (conceptual), "location" in a set of categories structured so that "nearby" agents will tend to interact * Selection, processes that lead to an increase or decrease in the frequency of various types of agent or strategies * Success criteria or performance measures, a "score" used by an agent or designer in attributing credit in the selection of relatively successful (or unsuccessful) strategies or agents Turner and Baker synthesized the characteristics of complex adaptive systems from the literature and tested these characteristics in the context of creativity and innovation. Each of these eight characteristics had been shown to be present in the creativity and innovative processes: * Path dependent: Systems tend to be sensitive to their initial conditions. The same force might affect systems differently. * Systems have a history: The future behavior of a system depends on its initial starting point and subsequent history. * Non-linearity: React disproportionately to environmental perturbations. Outcomes differ from those of simple systems. * Emergence: Each system's internal dynamics affect its ability to change in a manner that might be quite different from other systems. * Irreducible: Irreversible process transformations cannot be reduced back to its original state. * Adaptive/Adaptability: Systems that are simultaneously ordered and disordered are more adaptable and resilient. * Operates between order and chaos: Adaptive tension emerges from the energy differential between the system and its environment. * Self-organizing: Systems are composed of interdependency, interactions of its parts, and diversity in the system.

Modeling and simulation

CAS are occasionally modeled by means of

agent-based model An agent-based model (ABM) is a computational model for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) in order to understand the behavior of a system and wh ...

s and

complex network In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real ...

-based models. Agent-based models are developed by means of various methods and tools primarily by means of first identifying the different agents inside the model. Another method of developing models for CAS involves developing complex network models by means of using interaction data of various CAS components. In 2013 SpringerOpen/BioMed Central launched an online open-access journal on the topic of ''complex adaptive systems modeling'' (CASM). Publication of the journal ceased in 2020.

Evolution of complexity

Living organisms are complex adaptive systems. Although complexity is hard to quantify in biology,

evolution Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...

has produced some remarkably complex organisms. This observation has led to the common misconception of evolution being progressive and leading towards what are viewed as "higher organisms". If this were generally true, evolution would possess an active trend towards complexity. As shown below, in this type of process the value of the most common amount of complexity would increase over time. Indeed, some artificial life simulations have suggested that the generation of CAS is an inescapable feature of evolution. However, the idea of a general trend towards complexity in evolution can also be explained through a passive process. This involves an increase in

variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbe ...

but the most common value, the

mode Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...

, does not change. Thus, the maximum level of complexity increases over time, but only as an indirect product of there being more organisms in total. This type of random process is also called a bounded

random walk In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...

. In this hypothesis, the apparent trend towards more complex organisms is an illusion resulting from concentrating on the small number of large, very complex organisms that inhabit the right-hand tail of the complexity distribution and ignoring simpler and much more common organisms. This passive model emphasizes that the overwhelming majority of species are

microscopic The microscopic scale () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded as the scale be ...

prokaryote A prokaryote () is a single-celled organism that lacks a nucleus and other membrane-bound organelles. The word ''prokaryote'' comes from the Greek πρό (, 'before') and κάρυον (, 'nut' or 'kernel').Campbell, N. "Biology:Concepts & Con ...

s, which comprise about half the world's

biomass Biomass is plant-based material used as a fuel for heat or electricity production. It can be in the form of wood, wood residues, energy crops, agricultural residues, and waste from industry, farms, and households. Some people use the terms bio ...

and constitute the vast majority of Earth's biodiversity. Therefore, simple life remains dominant on Earth, and complex life appears more diverse only because of

sampling bias In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human f ...

. If there is a lack of an overall trend towards complexity in biology, this would not preclude the existence of forces driving systems towards complexity in a subset of cases. These minor trends would be balanced by other evolutionary pressures that drive systems towards less complex states.

References

Literature

* *; commissioned as
report
by the UK government'
Foresight Programme
* Dooley, K., ''Complexity in Social Science'' glossary a research training project of the European Commission. * * * * * * * , M.C. (online)
Looking to systems theory for a reductive explanation of phenomenal experience and evolutionary foundations for higher order thought
Retrieved 15 January 2008. * Hobbs, George & Scheepers, Rens (2010),"Agility in Information Systems: Enabling Capabilities for the IT Function," ''Pacific Asia Journal of the Association for Information Systems'': Vol. 2: Iss. 4, Article 2
Link
*

External links

Complex Adaptive Systems Group
loosely coupled group of scientists and software engineers interested in complex adaptive systems
DNA Wales Research Group
Current Research in Organisational change CAS/CES related news and free research data. Also linked to the Business Doctor & BBC documentary series

of complex adaptive systems on the Principia Cybernetica Web.

single-page description of the 'world' of complexity and related ideas hosted by the Center for the Study of Complex Systems at the University of Michigan.
Complex systems research network

The Open Agent-Based Modeling ConsortiumTEDxRotterdam - Igor Nikolic - Complex adaptive systems
an
The emergence of universal consciousness: Brendan Hughes at TEDxPretoria
Talks discussing various practical examples of complex adaptive systems, including Wikipedia, star galaxies, genetic mutation, and other examples {{DEFAULTSORT:Complex Adaptive System Complex systems theory Systems science *