The book’s ultimate goal is to tie these mechanisms into a single overarching framework that suggests ways to steer complex adaptive systems by modifying signal/boundary hierarchies.
The “where to look” guidance of a formal theory is often overlooked. Formun Üstü
Developing a formal theory is akin to learning the rules of a game. Formun Üstü
As we have already seen, signal/boundary systems evolve continually. So the “rules” must provide for origins of new signals and boundaries and their selective modification.
Four categories that are relevant to all signal/boundary systems: diversity, recirculation, niche, and coevolution.
Resources can even be used over and over again via recirculation, a mechanism that is important in sustaining diversity in impoverished circumstances. A money-based system, if I purchase the services of a carpenter, the money doesn’t “disappear” when I pay the carpenter. Rather, the carpenter uses it in turn to make purchases of lumber, food, and other things, perhaps retaining some in savings. The lumber retailer, in turn, pays a wholesaler, and so on. A dollar of new purchase can thus have the effect of many dollars when one looks at the system as a whole. So it is with the nutrients in the rainforest: they pass from organism to organism.
In the modern world, diversity is closely related to specialization.
“Niche” is one of the most important signal/boundary concepts and, at the same time, one of the least understood. Because there are niches within niches, web-like hierarchies result. Niches and hierarchies are common to all signal/boundary systems.
Inappropriate levels of decomposition can make it difficult to answer the question of interest. Every time we examine a signal/boundary system closely, we see coevolution as a pervasive feature. Global trade depends directly on local specialization and global coevolution.
The mechanisms and interactions falling under the broad categories diversity, recirculation, niche and hierarchy, and coevolution are central to understanding a wide range of large-scale and small-scale signal/boundary systems.
The components of a cas are bounded subsystems (agents) that adapt or learn when they interact. Markets, languages, and biological cells all fit the cas framework, the agents being, respectively, buyers and sellers, speakers, and proteins.
Adaptive agents are defined by an enclosing boundary that accepts some signals and ignores others, a “program” inside the boundary for processing and sending signals, and mechanisms for changing (adapting) this program in response to the agent’s accumulating experience. In a market, the agents are buyers and sellers and the signals are bids.
When a question is approached scientifically, the assumptions (premises) must be made explicit. Moreover, the assumptions must be formalized so that standard rules of deduction can be used to derive answers. These rules constrain the argument to simple obvious manipulations, much like moving pieces according to the rules of a game. Most cas agents turn out to be persistent patterns imposed on flows. You cannot learn the rules of chess by keeping only the statistics of observed moves. The patterns persist because they repair themselves when disturbed.
Newton’s equations have to be modified when objects move near the speed of light. Both thought experiments and computer-based models provide ways of exploring the behaviors of unfamiliar mechanisms or combinations of mechanisms. Computer-based models have become a major tool for investigating complex adaptive systems because they can handle conditional “IF this happens, THEN take this action” interactions. Such interactions pose difficulties for traditional equation-based models because, in mathematical terms, they are nonlinear (non-additive). In this respect, the computer models are akin to experiments. Many runs may be necessary to gain an overview of the outcomes.
Whether the model is equation-based or computer-based, there are three distinct approaches to constructing a model. These approaches are distinguished by their objectives.
1. The epicycle model and similar models are data-driven models, often called parametric.
2. The use of data-driven models is the most familiar of the three modeling tactics. The objective is to construct a model that uses data to make predictions. Theories and models for weather prediction are good examples.
3. An existence-proof model is used to show that something is possible.
Typically, exploratory models start with a designated set of mechanisms, such as the various bonds between amino acids, with the objective of finding out what can happen when these mechanisms interact. Exploratory models have a particularly important role when we first begin to study a complex system, such as a cas. Exploratory models often develop into existence-proof models. Exploratory models show the adequacy or the inadequacy of a set of mechanisms for generating a certain range of signal/boundary observations. An exploratory model can suggest previously unsuspected connections and interactions. In searching for powerful models, this temptation to inclusiveness should be resisted. A model’s clarity and generality depend directly on how much detail has been set aside. Phrasing questions is an art form, not a deductive process.
Requirement 1 Signals and boundaries, and all things employing them, should be defined with the help of a formal grammar that specifies allowable combinations of building blocks. A small set of generators (e.g., the axioms of Euclidean geometry) is transformed by a small set of rules (e.g., rules of deduction) into a large array of objects of interest (e.g., theorems about geometry).
Requirement 2 Each generator used by the signal/boundary grammar should have a location in an underlying geometry, and combinations of generators should be mobile within that geometry. Local conditions play an essential role in the adaptation and evolution of complex adaptive systems.
Requirement 3 The grammar should be capable of generating programmable agents—bounded conglomerates that can execute arbitrary signal-processing programs. In more general terms, the agents must be “programmable,” using the generators and rules provided by the grammar. In short, we should define boundaries, and the resulting agents, as signal-processing conglomerates over a fixed set of generators. Identical agent-conglomerates can have distinct individual histories because of conditional reactions to different local environments and agents. Behaviors that enhance the persistence of a particular agent configuration favor the future influence of that configuration, as well as adaptations based on that configuration. As an agent-conglomerate becomes more complicated, its structure may actually develop as the agent matures, as in the case of multi-celled organisms.
Requirement 4 The signal/boundary grammar must provide for reproduction by collecting resources, whereby an agent-conglomerate reproduces by collecting copies of the generators that define its structure. Agents acquire generators from the strings of elements that pass through their outer boundary. The elements so acquired can be recombined to form building blocks for a copy of the agent. To provide for this process, the grammar discussed in the previous three requirements must be extended to emphasize using acquired elements to create new boundaries and conglomerates. When the new conglomerates combine to make a new version of the agent, reproduction is implemented. An agent-conglomerate that does not produce such a copy eventually dissolves (dies).
Requirement 4, in combination with the other three requirements, characterizes a signal/boundary theory in which signals, boundaries, and rules are represented by strings generated from a small alphabet. Agents are defined by specifying a boundary hierarchy that contains signals and rules at various levels. The agents are situated in an underlying geometry, and agents are formed out of a spatially distributed population.
The generating procedure must provide for the generation of agents with any possible programmable behavior, so that an agent’s behavior is not arbitrarily limited by the generating procedure. Then the generating procedure must provide for Darwinian selection in which agents that collect resources more rapidly than others contribute more of their characteristics to future generations. In particular, “subroutines” that appear in rapidly reproducing agents should appear in new combinations in the future.
The agents are diverse rather than standardized, and both their behavior and their structure change as they interact. Formun Altı
There is no universal competitor or global optimum in a cas. Because of these ever-increasing possibilities for interaction, improvements are always possible. For individual agents, the mechanisms of change aim at improvement rather than optimization. Innovation is a regular feature of cas.
In a complex adaptive system, equilibria are rare and temporary. Adaptation by recombination of “building blocks” is a continuing process at all levels, and coevolution clearly has a central role in this continuing adaptation. Because the agents incorporate adaptive mechanisms, the systems continue to innovate. In other words, the mechanisms of change are primarily mechanisms of exploration rather than exploitation. Lack of a universal competitor and innovation also imply that cas agents change their behavior on two different time scales.
Fast The immediate reaction of an agent to the signals from other agents is conditional, taking a condition/action form.
Slow Agent adaptation in the evolutionary sense requires the appearance of new agents in the cas.
In a cas, anticipations change the course of the system. In a cas, the environment includes other agents, so the internal model usually includes models of other agents.
These three characteristics—no universal competitor, innovation, and anticipation—pose different barriers to understanding, but they do help in setting requirements that cas agents must meet.
Classifier systems (Lanzi 2000), provide a class of formally defined, rule-based signal-processing systems useful for defining agents. Individual rules in the system, called classifiers, are of the form IF (a required set of signals is present) THEN (send an outgoing signal based on these signals). Genetic algorithms, when applied to classifier systems, provide a computer-executable model of populations undergoing natural selection. A fitness function assigns to each string the number of offspring it will produce. In this “string of genes” format, each gene on the string is drawn from a fixed set of alternatives, called alleles.
When the genetic algorithm is used with classifier systems, the population consists of strings representing the rules of the system. Then the genetic algorithm, generation by generation, searches for improvement within the set of possible rules. When rules of above-average fitness share well-linked clusters of alleles, crossover rapidly uncovers and exploits those possibilities. An agent is situated when it is placed in an environment that consists of other agents and “inanimate” objects such as obstacles and patches of resources. For cas signal-processing agents, we will invoke a set of detectors for determining the changing features of the surrounding environment.
Individual rules in a classifier system, like the individual instructions for a computer program, are generally simple and easy to understand. However, a system with many interacting rules is as difficult to analyze as a computer program with many subroutines. Interestingly, most reactions between proteins are determined by relatively small subsequences, called active sites, within the string defining the protein. Uniform distribution corresponds to a classifier-system signal list making all signals available to all rules.
The state of a game at any time is the placement of game pieces on the board. Just as the play of the game amounts to moving from board configuration to board configuration according to the rules of the game, so the dynamics of a system amounts to moving from state to state according to the laws of the system. In most games, the play from any board configuration B onward doesn’t depend on the moves leading to configuration B. What is “legal” from configuration B onward depends only on B, not on how you got to B. The same is true in physics: knowing the state of a system is sufficient for determining future possibilities.
Network theory, more formally called graph theory, offers a general way of describing arbitrary cas interactions by extracting the pattern from the details. Thus, by operating on tags in signals and conditions used by established signal/boundary interactions, cross-breeding and other adaptive mechanisms can produce new, redirected signals and conditions. In order to understand signal/boundary systems we must consider the formation of boundaries and signals, not just their existence.
In complex adaptive systems in general, and in signal/boundary systems in particular, adaptive mechanisms mediate the formation of new structures, often adding specialized versions of existing components to an agent. As a result, flows of resources and signals in the agent pass through increasing numbers of stages, each of which encompasses some special activity of the original flow.
Nevertheless, Smith’s pin factory illustrates three major characteristics of signal/boundary interactions: that new boundaries distinguish the specialists, that resources flow from specialist to specialist, and that signals synchronize interactions.
Building block is a generator if it is immutable over the span of its existence. It may be copied and it may be combined with other generators, but it has a fixed set of “connectors” subject to a fixed set of connection rules, as in the case of chemical elements. Removal of a generator is often disastrous, as in the removal of a single instruction from a computer program. A building block is a conglomerate if it can grow and “fission” into additional conglomerates related to the “parent” conglomerate. In most cases, a conglomerate can be defined in terms of an interconnected set of generators. However, a conglomerate isn’t of much interest unless it persists long enough to serve as a building block for more complex structures.
Conglomerates can usually be described in terms of changing combinations of building blocks drawn from the next lower level of description—neurons in the case of the brain, reactions in the case of the cell, and so on. In complex adaptive systems, emergent properties often occur when coevolving signals and boundaries generate new levels of organization. Newer signals and boundaries can then emerge from combinations of building blocks at this new level of organization.
In particular, Darwinian selection, acting on a signal/boundary system, can ensure that only building blocks residing in fit structures survive to be tested in other structures. When a building block is tested and survives in a variety of contexts, its usefulness becomes well confirmed in a statistical sense. The procedures examined here, rather than treating individual building blocks independently of one another, place strong emphasis on context provided by other building blocks. Ignoring context would be tantamount to ignoring the conditional interactions that highlight signal/boundary interactions.
Recombination occurs because the chromosomes that control development pair up, and one chromosome within a pair physically crosses over the other, exchanging segments on one side of the crossover point. Recombination is a strong method for introducing plausible new rules, but those rules are hypotheses that must be tested and selected. Darwinian selection has been suggested, but how do we implement it in this rule-based approach? There are three requirements:
1. There must be a population so that the rules can compete.
2. There must be a comparison of rules that results in a rating that indicates the rule’s performance within the population.
3. There must be a selection process, so that rules that are successful in the competition can be favored.
Rules that are stronger (better confirmed as hypotheses) should contribute more to the evolving organization of the signal/boundary system. Recombination and reproduction are then applied to the rules to explore further possibilities (hypotheses). A boundary can be copied only if sufficient elements are collected to make a copy of the corresponding entry and exit tags, and an agent’s rate of reproduction is determined by its ability to collect relevant elements. The agent’s internal compartments will be treated as a collection of tag-based urns. This treatment yields the constrained diffusion typical of coupled reactions mediated by semi-permeable membranes.
Increased throughput, then, lets the agent collect the resources needed to copy its structures more rapidly. Accordingly, increased throughput is linked to the agent’s Darwinian fitness—the agent’s contribution to future generations. Cash plays a similar role in an economic niche, and its passage through a chain of buyers and sellers gives rise to the multiplier effect.
More generally, in a network, a niche is a community having a great number of internal connections but relatively fewer external connections, making it possible for the community to exhibit partially autonomous behavior. In each case, recirculation of resources means that activity in the niche cannot be determined by simply adding up the activities of the different agents occupying the niche.
Language acquisition, looked at in this way, is a system that adds generative rules as the learning agent’s experience refines its levels of consciousness. The result is an acquired set of generators (vocabulary) and a progressively refined set of generating rules (a grammar).
The objective of a dgs (dynamic generated system) framework for studying signal/boundary systems is similar. Find dgs generators and generating rules that open the way to modeling arbitrary signal/boundary systems, with particular emphasis on the coevolution of signals and boundaries.
It is helpful to re-examine the four interlocking models of signal/boundary interactions keeping the points just made in mind. The italicized words in the following four descriptions refer to the five requirements—building blocks, spatial distribution, programmability, implicit fitness, and internal models:
• Classifier-system models specify the performance/ credit assignment/ rule discovery activities of an adaptive agent in a complex adaptive system. Because a classifier system (cfs) uses a population of rules (strings), rule discovery can be implemented with a genetic algorithm, using recombination to generate new tags. Because the rules can be sequenced, cfs models can implement any computer-executable model, supplying programmability. In particular, sets of rules can act as internal models—subroutines that allow an agent to look ahead and anticipate consequences of current actions.
• Reaction nets model the interactions of adaptive agents in collecting and processing resources. The flows of resources in a population of agents are handily modeled with reaction nets. When tags are used to define the net, progressive changes in the net can also be generated.
• Tagged urns specify the effect of boundaries on the throughput of coupled reactions. Boundaries can be modified by changing the entry and exit tags, thus making it possible to study the coevolution of signals and boundaries.
• Echo models situate agents in a geometry and specify an agent’s structure in terms of elements that can be obtained by collecting resources available at sites in the geometry. By requiring an agent to collect the resources necessary for replication, an implicit fitness is introduced—a fitness that can change according to the context provided by other agents (e.g., resource exchanges).
With this provision, the concept of niche is explicitly defined in terms of communities of agents. Formun Altı
This model of ontogeny uses the dgs format to reformulate five biological mechanisms discussed in earlier chapters: gene (de-)repression, semi-permeable membranes, cell adhesion, catalyzed reactions, and replication through reassembly.
All complex adaptive systems exhibit obvious internal boundaries that divide the cas into a diverse array of semi-autonomous subsystems called agents. Each agent has a “program” that guides its interactions with other agents and other parts of its environment. To provide a common framework for the programs used by different kinds of cas agents, the book concentrates on classifier systems for the following reasons:
• Classifier systems use conditional (If/Then) signal-processing rules, thus capturing the conditional interactions characteristic of signal/boundary systems.
• A classifier system executes many signal-processing rules simultaneously without incurring problems of consistency, thus capturing the simultaneous interactions typical of complex adaptive systems.
• Classifier systems are computationally complete, so any computational procedure (e.g., any agent strategy) can be presented by a set of classifier-system signal-processing rules
• Tags in a classifier system play the role of active sites, motifs, and the like in different complex adaptive systems, allowing direct comparisons of tag-mediated signal/boundary networks in different complex adaptive systems.
• Classifier systems are specifically designed for use with genetic algorithms, so that the coevolution of signals and boundaries can be generated and studied.
• Compartmented populations Using probabilities to designate the concentrations of different colors of balls in an urn allows calculations relevant to the multiplicity of signals in a typical cas compartment; urns arrayed hierarchically mimic a hierarchical arrangement of cas compartments.
• Diffusion through semi-permeable membranes Moving balls from urn to urn, subject to entry and exit conditions, models the effect of diffusion through semi-permeable membranes and the counterparts of constrained diffusion in other signal/boundary systems.
• Conditional action Using conditional probabilities to represent reaction rules paves the road for using Markov processes to study signal processing in hierarchical arrays of semi-permeable membranes.
• Simultaneous processing Repeated random draws of pairs of colored balls model the effects of simultaneous pairwise reactions occurring in production lines, recycling, niches, and the like.
• Coevolution Using a genetic algorithm to modify signal tags and entry and exit conditions offers a direct approach to adaptive, coevolutionary changes that modify boundary permeability
Because complex adaptive systems are organized around populations, both offspring options can be explored without abandoning advantages already attained by the parents. As a result, succeeding generations make greater use of tags that offer additional advantages. In other words, progressive cross-breeding explores the levels between “craftsman” generalists and “production-line” specialists in the milieu of signals and resources available to the agents. A well-defined, widely applicable concept of niche should encompass common features of the different versions:
Multiplier effects Resources don’t disappear on consumption; they are transformed in passing from agent to agent. As a result, an injection of an additional resource (say, from outside the niche) propagates from agent to agent, multiplying the effects of the injection. (The economic version of this effect was proved by Samuelson.)
Recycling Agents are distributed spatially, and they interact in tangled loops of conditional responses and resource-passing (e.g., phenotypic plasticity in ecosystems (Levin 1999)).
Persistence Often patterns of interaction, imposed on a “flow” of ever-changing agents, persist well beyond the lifetimes of individual agents. These persistent patterns act as niches within which diverse agents can co-exist. The introduction of a new kind of agent to a niche—say, from some other niche (e.g., an invasive species) or by recombination of tags (e.g., a new flu virus)—can cause a torrent of further innovations exploiting the new possibilities.
A niche is a diverse array of agents that regularly exchange resources and depend on that exchange for continued existence. The conditional actions of the agents lead to non-additive effects that cannot be usefully averaged, so a purely statistical approach isn’t likely to provide answers to this question. Statistical approaches wind up in the same cul-de-sac as statistical approaches to understanding computer programming.
The “trends” suggested by a series of “snapshots” based on an average over agents’ activities rarely give reliable predictions or opportunities for control—instead of “clearing” of a market, we get “bubbles” and “crashes.” A more fruitful approach to questions of this kind requires an examination of the coevolution of situated agents—agents that have locations in both a geographic sense and a network sense. The “bandits” offer a boundary-oriented setting for examining situated agents.
With this provision, a “generalist” agent accesses a broad array of urns but often winds up in queues with low payoff per agent because of crowding, whereas a “specialist” agent accesses a queue that is less crowded but more difficult to locate. As we have seen, widely different agent-based signal/boundary systems, ranging from biological cells to governments, exhibit the same general features, notably the following:
· semi-autonomous subsystems (agents)
· hierarchical organization (agents composed of agents)
· sustained diversity (agents exploiting different strategies)
· extensive recycling of resources (agents converting resources and passing them on
However, most complex adaptive systems don’t settle down. In considering mathematical approaches to signal/boundary systems, it is important to recognize that agents situated in a physical environment do encounter regularities. That is, the environments encountered are a highly constrained subset of the set of all conceivable environments. It is a bad mistake to assume that nearly all conceivable environments occur with non-zero probability. In realistic environments, regularities offer exploitable opportunities for the formation of niches involving persistent, interdependent interactions of diverse agents.
Complex adaptive systems—cells, rainforests, markets, language, and the Internet, to name a few—are characterized by complex, ever-changing interactions of signals and boundaries.
This book provides exploratory models for examining the adaptations generated by signal/boundary coevolution. The exploration centers on two kinds of models: adaptive agents and tagged urns.
Adaptive agents (defined by signal-processing rules that provide for parallel processing and adaptation under a genetic algorithm) model the evolution of hierarchical systems that employ many signals (resources) interacting simultaneously
Tagged urns (modifications of the urns used in probability theory) use entry and exit conditions to control the flow of balls (signals) between urns, thus providing explicit formal models of semi-permeable boundaries.
In these models, both signals and boundaries are constructed from building blocks provided by tags and parts of tags—the counterparts of active sites, motifs, and message headers. The framework of dynamic generated systems combines adaptive-agent models and tagged-urn models to provide a precise formalism for exploring the evolution of signal/boundary systems.