LECTURE 5

PRELIMINARY STATEMENT OF A CANDIDATE "LAW"

INTRODUCTION

Coevolutionarily constructible communities of molecular Maxwell Demons, Autonomous Agents, may evolve to three apparently different phase transitions:

A) The dynamical "edge of chaos" within and among members of the community, thereby simultaneously achieving a coarse graining of each agent's world and maximizing the capacity to discriminate and act without trembling hands.

B) A "self organized critical" state as a community of

coevolving agents, by tuning landscape structure and coupling, yielding a power law distribution of speciation

and extinction avalanches.

C) A poised position on a generalized "subcritical-supracritical boundary," exhibiting a generalized self-organized critical sustained expansion into the "Adjacent Possible" of the effective phase space of the community.

Coevolution to the edge of chaos within and between Autonomous Agents, on a general subcritical-supracritical boundary, endogenously setting Agent Coarse Graining, tuning fitness landscape structures and couplings between Agents, maximizing the capacity for discriminate actions, hence maximizing the potential diversity of natural games played and Agents evolved, and maximizing the propagation of Work-cum-Record as well as the tendency to flow into the Adjacent Possible.

5.1) PART A OF THE WORKING HYPOTHESIS.

The dynamical "edge of chaos" within and among members of the community, thereby simultaneously achieving a coarse graining of each agent's world and maximizing the capacity to discriminate and act without trembling hands.

i. Consideration of the ways that a Maxwell Demon may fail to exploit the free energy available to act on his own behalf suggest not only that the Record must be updated and that work cycles must be performed and propagated, but that Molecular Maxwell Demons must live in, and hence must mutually create sufficiently smooth, repeatable worlds that they can accumulate useful variations as they coevolve with one another and with the Non-Agent world.

ii. Molecular Maxwell Demons, as non-equilibrium Agents, presumably are typically parallel processing molecular dynamical systems.

For example, any free living cell is a parallel processing dynamical system coordinating molecular events in time and space. Thus, we may consider cells as canonical molecular Autonomous Agents, and as Coevolutionarily constructable non-equilibrium Maxwell Demons.

Use Random Boolean nets as models of such parallel processing networks of molecular events.

Such networks generically behave in three regimes: Ordered, chaotic, and in the vicinity of a phase transition from order to chaos - the "edge of chaos" regime.

* In the "ordered regime" nearby states lie on trajectories which converge in state space. Due to such convergence, the attractors of such system are stable to perturbations, and flows along transients also tend to be stable to perturbations. This spontaneous homeostasis arises due to "irreversible computation." Once two states on trajectories converge on the same successor state in state space, information is lost concerning from which of the two initial states the system has come. In this ordered regime, such systems, including Maxwell Demon Agents, convergent flow along trajectories in state space induces internal correlations within the system, and tends to induce correlations in their collective "local world." Further, the convergent flow allows such Demons to act without trembling hands.

Furthermore, Ordered systems evolve on smooth fitness landscapes, for most mutations cause minor changes in dynamics.

* There is a chaotic regime. Here, nearby states lie on trajectories that diverge in state space. Such sensitivity to initial conditions is the high dimensional hallmark of chaos. Such chaotic systems show no homeostasis. Agents will have trembling hands.

Further, chaotic agents evolve on very rugged landscapes, for most mutations have drastic effects on dynamics.

* There is a phase transition "edge of chaos" region. Poised between order and chaos, dynamical flow along trajectories tends to be neither convergent nor divergent. Plausible arguments, returned to below, suggest that the most complex coordinated behavior without trembling hands may occur in this phase transition regime.

Furthermore, fitness landscapes at the edge of chaos tend to have a spectrum of smooth and rugged features, since most mutations have minor effects, while some have major effects on the dynamics of the system.

Hence part A) Molecular Maxwell Demons will tune their position on an internal order-chaos axis and tune their couplings to other Molecular Maxwell Demons such that the community is at the dynamical edge of chaos, while each cell is at or somewhat within the ordered regime.

5.1.1) Let each Agent be a single cell organism.

Let an ecosystem be a WEB of single cell organisms.

Let each cell in the WEB receive molecular input signals from certain other types of cells, its "input" eco-neighbors.

Let each cell internally process its molecular inputs.

Let each cell mount a response to some of its molecular inputs and combinations of inputs.

Let each cell send its outputs to its specific types of "output" eco-neighbors.

Then a community of cells is itself a parallel processing dynamical system. Each cell may itself be within the ordered regime, at the edge of chaos, or the chaotic regime. Simultaneously, the community, considered as a parallel processing dynamical system, may itself be within the ordered regime, the chaotic regime, or at the edge of chaos.

Were each cell itself, in isolation, in the chaotic regime, then after coupling, almost certainly the community as a whole would be in the chaotic regime. In that regime, Agents cannot act without trembling hands. Thus, each cell could cope by:

i. retreating into its internal ordered regime.

ii. decreasing the richness of its couplings to any other agent.

iii. Decreasing the number of other types of agents it is coupled to in the ecosystem community.

5.1.2) The above may be elaborated in more detail:

Consider a "WEB" of input and output signals among a diverse set of cellular Agents. Let each agent have convergent internal flow in its state space. Let each Agent have inputs and outputs from and to specific other (types of) Agents and perhaps to its own type of Agent.

i. If the flow within each Agent is convergent, but each Agent receives and sends signals from several different types of agents, then the different "output" agents receiving output signals from one agent, despite the fact that each induces convergent flow internally, may converge to distinct regions of their "product" state space. That is, even if all agents were to have the same state space, the flow within that state space might be different. The SAME output volume from one agent, sent to three different agents, might lead to convergence within each, but DIVERGENCE between the three.

ii. Thus, think of the total flow along trajectories in the state space of the entire WEB of Agents. That total flow might be Locally Divergent, hence Chaotic; the total flow in the entire state space might be locally convergent, on average, hence Ordered; or the total flow might be neither convergent nor divergent, hence on the Edge of Chaos.

iii. Presumably, as agents tune how deep in the ordered regime each is individually, how many different molecular input and output signals are exchanged, and how many types of other agents and how different those agents are from one another, the total flow in the entire state space tunes from chaotic to ordered.

a. More generally, it is reasonable to suppose that if each Agent were internally Chaotic, and each Agent coupled to very many very different Agents, the total flow in the entire state space would be very chaotic.

b. If each Agent is internally far in the ordered regime, and each agent receives and sends signals to rather few types of reasonably similar clusters of other Agents, then plausibly, the entire flow in total space is in the Ordered Regime.

c. For any given coupling between Agents, movement by each Agent deeper into the Ordered regime presumably tends to make the total flow less chaotic.

d. For Agents internally in the ordered regime, reducing the diversity of other Agents as ecosystem inputs and outputs neighbors and their similarity to the Agent, presumably tends to move the total system toward the ordered regime.

e. For Agents internally in the ordered regime, reducing the diversity of molecular inputs and outputs exchanged with each of their ecosystem neighbors presumably tends to move the total system toward the ordered regime.

Points a-e above suggest strongly that natural selection's tuning Agents internal locations on the Order - Chaos axis, and by tuning the couplings to other Agents, can tune whether the global linked ecosystem lies in the Ordered regime, the chaotic regime or at the edge of Chaos.

More generally, in a parameter space comprised at least of each cell's position on its internal order-chaos axis, the average number of ecosystem neighbors of each cell, the number of exchanged molecular variables, and perhaps the total diversity of types of cells, M, there will be a critical surface for the dynamics of the entire community of agents separating the chaotic regime from the ordered regime. This critical surface exhibits the trade-off possibilities among the above parameters such that the community is at the edge of chaos.

5.1.3) I propose that an evolutionary process brings the entire community to the edge of chaos, and each cell to a position on its internal order-chaos axis to within the ordered regime.

i. Assume that by mutation and selection, each cell population is able to TUNE ITS LOCATION ON THE ORDER-CHAOS AXIS.

a. That is, by virtue of selection for fitter variants, each cell can tune whether the dynamical flow in its state space is, ON AVERAGE, LOCALLY CONVERGENT (THE ORDERED REGIME), LOCALLY DIVERGENT (THE CHAOTIC REGIME), OR NEITHER CONVERGENT NOR DIVERGENT (THE EDGE OF CHAOS).

b. Here, locally convergent flow means that initial states that are nearby in state space in the Hamming sense, (000000) is close to (000001), tend to converge closer to one another along the trajectories each initial state lies on.

ii. Assume that each cell, in its evolution by natural selection, can tune which specific other types of cells it interacts with.

a. In short, we assume selection can act on the connectivity of the ecosystem web.

b. Note strong evidence from FOOD WEB DATA that real species typically tune the number of eco-neighbors to something like four other species. (Pimm and colleagues). In short, it is true that species tune species connectivity in communities.

iii. Assume that each type of cell, in its evolution by natural selection, can tune how many different types of molecules it receives as inputs and sends as outputs to other Agents in the community.

That is, cells not only evolve how many other types of cells they interact with, but how richly coupled each cell is with any specific eco-neighbor.

Thus, an evolutionary process can, in principle tune a community's location on the dynamical order-chaos axis.

5.1.4) The Convergent Flow In State Space Leading To The SAME Output Response Corresponds BOTH to Categorization of the World by the Agent, AND ALSO TO THE COARSE GRAINING OF THAT WORLD by the Coevolving Molecular Maxwell Demon.

i. Based on the theory of parallel processing networks, states lying in one basin of attraction may be thought of as a "content addressable memory," where the attractor is the "memory." More generally, the attractor may be thought of as the "category," while the basin of attraction of states flowing to it are the "stimulus generalization" belonging to the same category.

ii. More generally still, a parallel processing system in an exogenous environment may never reach its attractors due to persistent signals and noise from the outside. Nevertheless, convergent flow of a volume of states to the "same" response by the system constitutes categorization by the system of that set of input states as the SAME.

iii. Given some "response time" to any input signal pattern, the state space of the Agent is partitioned into "conical" volumes, each leading to a specific response.

THIS PARTITIONING INTO DISCRETE RESPONSE VOLUMES CONSTITUTES BOTH THE CATEGORIZATION CARRIED OUT BY THE AGENT, AND THE COARSE GRAINING OF ITS WORLD.

iv. Thus, we have ENDOGENIZED BOTH KNOWLEDGE AND COARSE GRAINING WITHIN OUR COEVOLVING AUTONOMOUS AGENTS as they propagate and diversify Work-cum-Record.

5.1.5) Evidence supporting the hypothesis that Autonomous Agents evolve to the dynamical edge of chaos.

i. Recent evidence strongly suggests that eukaryotic genetic regulatory networks are astonishingly close to the "edge of chaos."

a. The human genome harbors about 100,000 structural genes.

b. Different cell types correspond to different patterns of activities among these 100,000 genes.

c. Thirty years work on random Boolean network models of genomic regulatory systems has shown that networks in the ordered regime, perhaps near the edge of chaos, have many properties that parallel many features of real genomic systems.

Interpret a cell type as an attractor. then:

1. The number of states along a cyclic attractor is about the square root of the number of genes, hence localizes a cell type to a tiny volume of state space.

2. The number of attractors is also about a square root of the number of genes, predicting that the number of cell types in a human should be about 317. The observed number is said to be 265. The "square root law" fits the increase of cell types across phyla and genomic complexity reasonably well.

3. Cell types, as attractors, exhibit homeostasis.

4. Each cell type can be perturbed by altering the activity of one gene at a time to "differentiate" into only a few other cell types, hence pathways of differentiation exist.

5. A frozen component of genes in fixed states of activity or inactivity on all cell types should exist - and does.

6. The genome should exhibit a modest number of "unfrozen" islands of "twinkling genes." These islands are functionally isolated from one another by the frozen sea. The islands should be the loci of developmental decisions. The size distribution of the islands should, and does, predict modestly well the typical differences in gene activity patterns of different cell types.

7. Transient alteration in the activity of any single gene trigger a modest avalanche of changes, or "damage" in the activities of other genes. This is as observed. No gene, if perturbed, is able to alter the activity of a large fraction - for example 20,000 of other genes.

5.1.5.1) The new data are the following:

i. With S. Harris and A. Wuensche, we have examined published data on 103 regulated eukaryotic genes. The data derives from the actual driving of transcription from adjacent cis acting DNA sequences.

ii. The data is cast into Boolean form based on 'synergy." If input "a" causes slight transcription, and input "b" causes slight transcription, while "a" AND "b" cause high transcription, we classify this as the Boolean "AND" function of two inputs.

iii. The data covers 17 genes with K = 2 inputs, 53 genes with K = 3 inputs, 27 genes with K = 4 inputs, and 6 genes with K = 5 inputs.

iv. Canalizing Boolean functions, such as "AND" have the defining property that at least one input has one value that suffices to determine the activity of the regulated gene. The "AND" function has two canalizing inputs, since "a" or "b" alone, by being "off" can guarantee that the regulated gene is inactive.

v. As K increases, the number of Boolean functions is 2 to the 2 to the K.

vi. The fraction of Boolean functions of K inputs that are canalizing on one or more inputs decreases rapidly as K increases.

vii. Among the K = 3, K= 4, and K = 5 input genes, the observed distribution of canalizing functions is far greater than would be the case were Boolean functions sampled at random.

viii. Boolean functions can also be classified by a parameter, P, which measures the biased propensity of that function to output predominately a1 or a 0. For "AND" of two inputs, P = .75. For the "OR" function of two inputs P also = .75. In both cases, the predominate value occurs for 3 of the 4 input combinations. P ranges from 0.5 to 1.0.

ix. The observed set of K = 3, K = 4, and K = 5 genes is also biased toward high P values.

x. Analysis of the data shows that, conditioned upon the P value, there is a residual strong bias towards high numbers of canalizing inputs. Conversely, conditioned upon the number of canalizing inputs, there is no residual bias toward high P values. Hence the observed bias can be entirely accounted for as a bias towards canalizing functions.

5.1.5.2) These data strongly support the hypothesis that real genomic regulatory networks are very close to the edge of chaos.

i. Random Boolean networks were constructed with the precise observed bias toward high number of canalizing inputs for K = 3 genetic networks. At that bias, networks are almost precisely poised between order and chaos.

The position on the order-chaos axis was determined by measuring mean "one state transition" convergence or divergence in state space as a function of initial Hamming distance between two states. Thus, two initial states at an initial normalized Hamming distance, Dt, flow to two successor states at a distance Dt+1. If trajectories diverge, Dt+1 is greater than Dt. If trajectories converge, Dt+1 is less than Dt.

At the phase transition, nearby states (Dt small) neither converge nor diverge. I.e. Dt+1 = Dt.

While the observed bias, where the probability that an input is canalizing is 0.75 for K = 3 genes, results in networks at the phase transition, a lowering of the probability that an input is canalizing yields networks in the chaotic regime. An increase in the bias above 0.75 yields networks deeper in the ordered regime.

For K = 4 genes, the observed bias that an input is canalizing is 0.65. This value for K = 4 networks, yields networks exactly on the order-chaos phase transition. Smaller biases yield chaos. Larger biases yield deeper positions in the ordered regime.

The observed bias for the 6 genes with K = 5 inputs is 0.55, again corresponding to a position very near the phase transition. However, data on 6 genes is far too little to trust.

ii. Additional properties so far investigated for such poised networks show:

a. The formation of a frozen sea of genes in fixed activity patterns.

b. The simultaneous formation of unfrozen twinkling islands.

c. A power law distribution of many small and few large avalanches of damage cascading from transient alterations of the activity of single genes. The largest avalanches propagate to several hundred genes in model networks with 10,000 genes.

This maximum size avalanche corresponds to the rough maximum number of genes whose activity is altered in Drosophila by perturbing the activity of a single gene. Ecdysone induces alterations in 155 genes in the salivary glands during pupariation. Drosophila has about 16,000 genes.

d. The patterns of differences in gene activity patterns on different attractors falls into families that probably mimic real cells.

5.1.5.3) Tentative conclusions:

i. Caveats. Data available may be biased in important ways. In particular, canalizing genes may be easier to study than non-canalizing genes. Ultimately, examination of randomly chosen transcription units can answer this.

ii. Eukaryotic cells from multicelled organisms appear to be poised very close to the phase transition between order and chaos.

iii. If so, the multitude of properties that are simultaneous signatures of this poised position should all be confirmed in real eukaryotic cells. This has not been done.

iv. If confirmed, and extended to free living eukaryotic cells, and to prokaryotes as well, this data will demonstrate that cells, after 1.6 or 3.8 billion years of evolution, have evolved to the phase transition between order and chaos.

If confirmed, this would powerfully support Part A of this working hypothesis. In the meantime, the strong suggestive evidence stands as modestly strong support for the hypothesis.

Further tests also concern examining the dynamical behavior of communities, preferably microbial communities, to see if they are collectively at the near the phase transition between dynamical order and chaos. In principle, this can be carried out by examining such features as avalanches of gene activity changes propagating across members of a community after transient alteration in the activity of a gene in one member or one member species.

5.2) PART B OF THE WORKING HYPOTHESIS.

A "self organized critical" state as a community of coevolving agents, by tuning landscape structure and coupling, yielding a power law distribution of speciation and extinction avalanches.

5.2.1) Part of the ways that coevolving communities of agents will tune the structure and coupling of their fitness landscapes is precisely by tuning the position of each agent on its internal order-chaos axis, and by tuning how richly coupled each agent is to other ecosystem neighbors.

--This aspect of the coevolutionary process affects the control or "coordination" of activities of agents, and hence the very capacity to assemble complex coordinated behaviors within and among community members. However, tuning of positions on dynamical order-chaos axes within and among agents does not address the character of the components of the coordinated actions and the evolution of the "fitness" of those components. Thus, coordinated patterns of gene expression is one thing, but whether the resulting proteins are able to fold and fit one another is a separate issue. --

In tuning how deep in the ordered regime an Agent is, that Agent is thereby also tuning its COARSE GRAINING, and also tuning THE RUGGEDNESS OF ITS FITNESS LANDSCAPE.

i. Deep in the ordered regime, all initial states lead to the SAME final output response. The entire world of the Agent is classified as "FROG." There is but one basin of attraction. The Coarse Graining has but one category.

But also, the fitness landscape will tend to be very smooth. Parallel processing networks with a single basin of attraction tend to be stable to many minor mutations "synaptic weights" or their molecular analogies.

--Consider the analogy to the behavior of the NKCS model of coevolution described in Lecture 1, and in At Home in Universe and Origins of Order. In the NK landscape world, K = 0 landscapes are Fujiyama landscapes with a single peak. When S species are coupled via C couplings among the genes, yet each evolves on an NK landscape with K = 0 then the entire ecosystem is in the coevolutionary chaotic regime. Because there is but a single peak for each species, adaptive moves by one species deform the landscapes of its partners so much that their single Fujiyama peaks move away from their current position on the landscape faster than each species can "chase" the receding peak. The system as a whole is in the red queen chaotic regime.

In the version in At Home in the Universe where species can tune landscape ruggedness and invaders can drive a species with a poor landscape ruggedness extinct, one finds that, deep in the coevolutionary chaotic regime average fitness is low, and it is easy for invaders to succeed. Vast avalanches of extinction events propagate through the system.

Under these conditions, species with increasingly rugged landscapes succeed in invading niches and founding daughter species, so good landscapes themselves proliferate. (Note the parallel to Good Jobs Proliferate and to the concept that Niches whose landscapes are readily explored by the current search procedure will be those that are explored.)

As if by an Invisible Hand, the members of the community increase the ruggedness of fitness landscapes to an intermediate ruggedness where fitness is roughly maximized, the probability of extinction is roughly minimized, and a power - law distribution of small and large extinction and speciation events propagate through the community.

5.2.2) The analogy with the NKCS model suggests that if coevolving Maxwell Demons are each deep in the dynamical ordered regime with a single dynamical basin of attraction, a single categorization of their world - FRED - then like the K = 0 NK landscape case, a move by one agent will deform the landscape of its neighbors so that the new optimal category, GEORGE, is too many mutations away to be chased by the first species. The coevolving system should be in the coevolutionary chaotic regime with large avalanches of extinction and speciation events. This should produce a pressure to increase landscape ruggedness by increasing the number of alternative categories and actions that the Agents can undertake. But just this occurs as Agents move on the order-chaos axis away from extreme order:

i. As Agents move from deep in the ordered regime towards the parallel dynamical flow of the edge of chaos,

* the numbers of basins of attractions increase,

* the diversity of discriminated responses to finer grained classes of inputs increase,

* hence the Coarse graining becomes Finer Grained,

* fitness landscape becomes more rugged. Small mutational changes are more likely to change categorization and action patterns of the Agent.

ii. At the edge of chaos internally, the Agent is making the maximum number of "reliable" discriminations it can get away with. In the absence of convergence in its state space, there is no analogue of error correction.

At the edge of chaos, each agent has a fitness landscape with a wide spectrum of "ruggedness" features. Most mutations cause only minor change in categories and actions, some mutations cause quite large changes in categories and actions. The spectrum of small and large adaptive responses allows such agents to cope with small and large changes in their fitness landscapes with small and large alterations in their behaviors.

Thus, by tuning its own position on its internal order-chaos axis, how many other (types of) agents and how different they are, that each Agent interacts with, each Agent is locally tuning the tendency for the dynamics of the community system to lie in the ordered or the chaotic regime.

But tuning the number and differences among eco-neighbors and the number of variables that couple to each of those Agents, IS tuning the couplings among fitness landscapes and how dramatically each deforms by the adaptive moves of its dancing partners.

These observations suggests that communities will coevolve to a position on the critical surface described above such that the community simultaneously is at the dynamical edge of chaos, and that the same position will constitute a self-organized critical state with respect to the coevolutionary dynamics that maximizes mean agent fitness, minimizes mean probability of extinction, and yields a power law distribution of speciation and extinction events.

5.2.3) Uniting all the results above leads to the Working Hypothesis that coevolutionarily assemblable Molecular Maxwell Demon Autonomous Agents will:

* Coevolve internally to the Ordered Regime near the Edge of Chaos,

* Coevolve Collectively to the Ordered Regime near the Edge of Chaos.

* The community will be self-organized critical in the above coevolutionary sense.

-- This form of the hypothesis does not yet address the actual functionalities required of components, such as folding of proteins and affinities of receptors and ligands. --

5.2.4) Evidence that can be accumulated with respect to the above, part B):

i. The observed distribution of extinction events in the Record is, on Raup's latest tally, close to a power law.

ii. The observed life time distribution of genera is close to that predicted by the NKCS model in At Home in the Universe.

iii. If microbial communities are self-organized critical, then genotypically, and in the absence of in migration of new species, the community should be at a genetic Nash equilibrium. That is, it should be difficult for any species to increase its fitness by accepting a mutation. Thus, in the absence of in migration, the community should tend to be genetically stable.

Conversely, if a subcommunity is formed, it should not be at a Nash equilibrium and mutations should tend to accumulate.

-- Tentative positive evidence with respect to murine solid tumors with 10 cell types which do not accumulate chromosomal mutations upon transplantation, but do if subsets of the 10 cell types are transplanted. Think of the solid tumor as an ecosystem at a Nash equilibrium that is perturbed if a subset of cell types is transplanted. --

Microbial community subject to invasion and extinction should show power-law distribution of invasion successes and extinction events. Tentative evidence for power-law avalanches in models of community assembly -- Pimm.

Examination for such stable poised microbial communities as to whether, simultaneously, they are dynamically and the edge of chaos in terms of convergence and divergence along trajectories in their collective state space.

5.3) PART C OF THE WORKING HYPOTHESIS.

A poised position on a generalized "subcritical-supracritical boundary," exhibiting a generalized self-organized critical sustained expansion into the "Adjacent Possible" of the effective phase space of the community.

Here I give an incomplete description limited largely to the metabolic level of interacting molecular autonomous agents. In Lecture 6 I discuss the "Adjacent Possible" in more detail, and attempt to expand Part 3 of the Working Hypothesis.

5.3.1) I discussed above, and in Origins of Order and At Home in the Universe, grounds to think that a microbial community will evolve to the subcritical-supracritical boundary. If the community were supracritical, the rate of molecular innovation would be faster than could be coped with by selection. The persistent novelty would kill member species very rapidly, driving the community toward the subcritical regime. Were the community metabolically subcritical, it could accommodate a higher rate of entry of molecular novelty, hence will tend to evolve toward the boundary.

According to this hypothesis, at a metabolic level, the coevolving system will lie on the subcritical-supracritical boundary.

* Generation of novel small molecules will occur in power-law bursts.

* The coevolving system of Autonomous Agents will tend to invade the molecular adjacent possible as fast as is sustainably possible.

5.3.2) Possible evidence related to part C:

If "local" microbial communities are poised on the subcritical-supracritical boundary, then it should be possible to test this by assessing the probability distribution for the number of further novel molecules that will be induced by exposure of the community to an exogenous novel organic molecule, Q. More generally, one could hope to test for well established microbial communities of different species diversity, how the diversity of "input" small molecules is related to the generation of still further small molecules by the community. A supracritical community will act as an amplifier of this input diversity.

Tuning the species diversity on the X axis and input molecular diversity on the Y axis should yield a roughly hyperbolic curve below which a natural community does not amplify input molecular diversity, and above which the community behaves supracritically.

Experimentally, the results should be testable by mass spectroscopy and perhaps by high field NMR. Among the experimental issues is that an explosion of diversity would also, presumably, be associated by a fall in the concentration of most of the family of novel molecules. As concentrations fall, rate of production will fall since occupancy of enzymatic sites will be slight. In addition, detection of very low numbers of novel molecules - an attamole for example, is probably not yet feasible. However, good mass spectroscopy can detect in the femtomole range.

But next, in preparation for further discussion in Lecture 6:

i. By achieving internally the ordered regime near the edge of chaos, while also achieving the collective edge of chaos:

* each Agent internally maximizes the number of discriminations it can get away with,

* thereby also maximizing the complexity of the Natural Games it can play.

ii. Simultaneously, by maximizing the number and diversity of discriminate activities each agent can make:

* The community of Agents maximizes the number of useful novel functions they can jointly discover, hence graft into the ongoing coevolving community of Agents.

iii. By maximizing the discovery of novel functions the coevolving system tends to maximize its flow from the Actual to the Adjacent Possible.

* The boundary position optimizes the average rate of transgression into the Adjacent Possible by grafting novel functions into the agents.

iv. At higher organizational levels, multicelled organisms and economic agents such as firms the rush to the adjacent possible is driven by opportunity for "growth." (New Niches, New Markets). We will find a generalization of the subcritical-supracritical boundary in the next lecture, and grounds to expect that invasion of the Adjacent Possible is self-organized critical.