Managing the Transition of Ventures as Complex Systems
Part II

Bryan S. Coffman
July 23, 1997

This article summarizes Stuart Kauffman’s book At Home in the Universe. All of the principles that are discussed concerning complex systems are his, or if attributed to others, may be found in his book. The conclusions drawn with respect to venture management and transition management in organizations are a mixture of mine and Dr. Kauffman’s. The models from the Taylor Modeling Language are copyrighted, of course, by MG Taylor Corporation.


Related Articles:
Part I: Selection, Self-Organization, and Autocatalysis
Part III: Coevolution on Coupled Fitness Landscapes and Patch Theory


Requirements for Order in Emergent Systems
We know a little bit now about how systems become autocatalytic. But consider the autocatalytic set of molecules once more. Imagine that there are new molecules entering the pool and also realize that some random, uncatalyzed reactions can create new molecules as well. These new entrants may enter the autocatalytic set or they may inhibit one or several reactions in the set. Either way, the products of the set change, and in this way the set can vary over different generations. However, there must be a balance between stability and change in the autocatalytic set. If stability dominates, then the set becomes frozen and cannot evolve. If change dominates, then chaos sets in.

We’re looking for another phase transition here, one between order and chaos in a system’s behavior. The presence of the autocatalytic set is a manifestation of order. All of the reactions are occurring in a very deterministic fashion that we can map. There is no variation in the behavior of the set unless it is changed by the addition of random molecules in some way. This type of homeostasis is good! Translated to the business world, it means that consumers can trust that when they take a stereo system out of a box and plug it in, it will work. The autocatalytic set that created the stereo is a representation of the ordered regime of behavior. But without some variability in the equation, we’d all still be listening to Victrolas instead of CD players.

To uncover the requirements for order, Kauffman uses a model called an NK network. Here’s how it works.

N = the number of nodes in the network.
K = the number of inputs to each node (coming from other nodes in the network, not from outside of it).
P = the rules of logic governing how each node decides what its next state will be, given the state of the inputs from other nodes to which it is connected.

Imagine further that each node is a light bulb that can be on or off. We can represent this with a 1 and a 0. Whether a node is on or off is a function of the K inputs it receives. An input is the state of the node that sends the input. So imagine a piece of a network consisting of just three nodes, N1, N2 and N3. Let’s say that N2 and N3 are both inputs to N1 (and conversely, N1 is an input to N2 and N3--in these networks, the connections run both ways simultaneously). At a certain time we look at the network and see that N1 is "off", N2 is "on" and N3 is "off". The inputs to N1 at that time are "on" (N2’s output) and "off" (N3’s output). The result is that N1 is "off", so there must be a rule governing N1 that says "when N2='on' and N3='off', the state of N1 will be 'off'."

The functions, or rules that nodes use to determine whether they will be on or off are known as Boolean functions and are logical gates like AND, OR, IF NOT IF, and so on. The particular rule that N1 is using in the preceding paragraph is an AND gate, meaning that both N2 and N3 have to be "on" for the state of N1 to be "on".

There are several key things to remember about this "toy world":

  • There are a bunch of nodes, N in the network
  • The nodes are connected to each other by K connections each
  • A connection means that the two nodes at opposite ends of any given connection send each other information concerning their current state (on or off in the case of light bulbs)
  • Each node uses a function or rule to govern its behavior based on the inputs it receives from the other nodes it’s connected to
  • Therefore, when a node provides input to another node that determines its behavior, it’s acting like a catalyst.

In computer simulations of NK networks, inputs between nodes are assigned randomly. Rules of behavior for each node are assigned randomly. The initial state of every node in the system is assigned randomly. Then the system is started to see what will happen. At first a set of twinkling lights appears. After a while one of several behaviors emerges for the entire network. The number of cycles it takes for the system to settle down into a "solution" or order is called the state cycle. If the state cycle is too long, the network will maintain the appearance and behavior of a chaotic system.

The lights never stop twinkling; in other words, they never settle down into a pattern. This is the chaotic regime of behavior. In the chaotic regime, random changes (mutations) in the state of individual nodes can cause cascades or avalanches of change to sweep across the network in a phenomenon called divergence. This propagation of change hints at the influence of positive feedback loops.

The lights stop twinkling; some remain on and some remain off in set patterns that never change after the system settles down at the end of its state cycle. This is the ordered regime. Once a system has reached the ordered regime, small, random changes (mutations) in the state of nodes in the system are usually damped out in a process called convergence and the network returns quickly to its previous, ordered state. The damping out phenomenon is reminiscent of the negative feedback loops found in cybernetics.

Most of the lights stop twinkling but there are islands where the lights twinkle continuously in a fixed pattern. This is the complex regime—tenuously connected islands of variability in a sea of order. In this regime, random changes made in the ordered portion will be damped out but random changes in the islands will tend to propagate from island to island, allowing the network to adapt.

If stability of the network is most important, the ordered regime must be discovered quickly; searching for types of networks whose state cycle is short. When continued evolution of the network takes priority, we seek the edge of chaos regime where islands of variability are connected to one another across the larger sea of order. What adjustments to N, K or P yield networks that adapt?


First, K, the number of inputs to each node may be tuned. Networks with high K values exhibit more chaotic behavior. This is easy to understand. If the current state of everything depended upon the behavior of everything else, nothing would settle down to a solution. This is one of the problems with consensus, by the way. There are too many conflicting demands on each node, and the rule that each node uses says that you’ve got to placate all of the conflicting demands. And every node is trying to do the same thing! What a mess.

In Kauffman’s toy model, the complex regime emerges when K=2 (the ordered regime exists where K=1). That’s kind of surprising at first glance but intuitively understandable. Consider matrix management style organizations where each worker reports to a functional boss and a project boss at once. Now imagine each employee reporting to a third or fourth boss. Chaos erupts out of the conflicting demands. I’m not claiming that all people in all organizations should only have two catalytic connections to other people or artifacts in the enterprise. Such a proposition is clearly nonsense, but it is interesting to think of bureaucracies, participative management, and DesignShop® events in the light of the K=2 phenomenon. At some point in traditional organizations the number of connections between nodes--the number of other people, things, processes, environmental changes, whose behavior has a direct influence on someone's behavior--crosses some threshold and the individual or business unit at the focal point of this high density of catalytic connections will flip from being deeply ordered (never changing) to being intensely chaotic (never settling down).

But what if K is greater than 2? We each must be connected to dozens of other nodes whose behavior can cause us to reevaluate our current course of action and change our own state. Can such chaotic networks be tuned as well to behave in the complex regime? Yes. To do so the P variable must be adjusted--the rules of logic that each node uses to transform its inputs to outputs. Rules can be selected which allow the control of the ratio of nodes that are "on" or "off" in the network. This adjusts the amount of chaos present in the network. Such Boolean functions are called canalizing functions, meaning that "at least one input has a value that by itself can completely determine the response of the node." In effect, the node can substantially ignore the other inputs. Canalizing functions remove conflict for the nodes in question.

What does this mean to organizations? Assume that the P variable in enterprises is the amount of uniformity demanded based on the rules that nodes use to do their work. (This is a VERY loose analogy, by the way.) A wide range in variability of the rules AND a high number of catalytic connections results in chaos. To keep the number of catalytic connections in the network high, the variability in the rules is attenuated. This has implications on the latitude of freedom that network members have in choosing information that determines how they accomplish their jobs. In densely catalytic networks, too much freedom in the influence of different inputs may inject so much conflict in the system at each node that the network will never settle down out of chaotic behavior.

Too much attenuation of the P variable will cause the network to sink out of the complex regime into the ordered regime. When the company policy manual or the corporate culture restricts nodes in the enterprise from engaging in decision by design, the enterprise loses its ability to adapt.

By tuning the number of connections and removing some conflict in the rules that nodes use to calculate their behavior (based on the behavior of other nodes), the network may steer itself into that zone of complexity to optimize both order and adaptability.

Other Comments on Transition Management and Requirements for Order

  1. The more inputs required for decision making, the more conflict in the system, and the more chaos
    Traditional hierarchy gets around this by enforcing strict rules on who can talk to whom. Matrix management attempts to relieve the constriction through a controlled system of expanding the number of connections per node. Ad-hoc arrangements, such as the modular system of delivering a DesignShop reconfigure the network and its connections based upon the work at hand, thus offering a more flexible response.
  2. A warning for participative management and consensus management styles: trying to resolve too many conflicting inputs creates chaos.
  3. A warning for strict hierarchical and bureaucratic organizations: eliminating too many inputs or restricting the decision-making process stops adaptation and innovation.
  4. Steering complex systems:
    1. To increase order, decrease dependent connectivity (where one node relies upon information concerning the state of a number of other nodes in its decision making process)
    2. To increase adaptability, increase connectivity
    3. To reduce conflict, many individuals automatically tune out the effect of most of the input they receive from other nodes so that they can make faster decisions: they take charge of tuning their own P variable.
    4. To reduce conflict, many organizations add layers of rules, policies and procedures which serve to override input from multiple sources. If too many policies are instituted, the organization may enter the deep ordered regime from which attempts to adapt will prove fruitless.
    5. To increase order, add more rules to reduce options at the node level.
    6. To increase adaptability, allow more decisions to emerge from interaction between nodes.


The Evolution of Living Systems on Correlated Fitness Landscapes

"Evolution is a process of attempting to optimize systems riddled with conflicting constraints."

How does selection work? Imagine two types of bacteria, red and blue. Imagine further that they are present in equal numbers in some vat with adequate food available.
Assume that the red bacteria expresses a gene that allows it to undergo cell division every 10 minutes, while the blue bacteria does not express that gene, and it divides in 20 minutes, or double the time. Over a short period of time, the red bacteria population will grow to vastly eclipse that of the blue bacteria. The red bacteria is not "selected" in any ordinary sense of the word. No one is doing the selection. The genetic makeup of the red bacteria, and the capabilities this makeup bestows on the organism allow it to eclipse, in some manner, the presence of other bacteria who lack a competitive genetic makeup.

But by what process does an organism become more successful or more fit in its niche? Certainly not all changes in the genetic code allow for an increase in fitness. Genes work with one another in a sort of network like that described in the previous section. They have the ability to turn one another on and off. In such networks circumstances like the density of connections and the rules for decision making may lead to chaos or to order or to the complex regime at the edge of chaos. If the genetic code is a sort of program, then what effect are mutations likely to have on it? Think about the applications programs like the HTML editor this article was composed upon. Imagine that Microsoft Front Page were suddenly subject to random mutations in the lines of its code. The application rapidly turns to garbage. There’s no redundancy in the system to offer continued stability.

Redundancy is one of the first lessons of evolving systems that should be applied to organizations. This has applications in theories concerning continuous improvement and reengineering. If you try to make the enterprise too efficient, then its response to evolutionary pressures will be collapse.

Biologists have long used the metaphor of a landscape to describe the march of a species toward fitness. Imagine a terrain like the Appalachians or the Alps. The peaks represent high points of fitness, where an organism is highly compatible with the demands of its niche. Evolution is a process of moving from the valleys to the peaks.

But fitness is rarely dependent on the state of one isolated gene. It depends instead on the coupling between genes, known as epistatic coupling. This coupling, when diagrammed, looks like a network where each node is a gene and the connections between them are inputs to the gene’s behavior. This sounds familiar. Indeed, the familiar NK network may be employed to expose some of the parameters that influence fitness. Remember that N is the number of nodes and K is the number of inputs that determine each node’s behavior.

Now tune the K value to see what happens. If K=0, and none of the nodes are connected, there is a single peak on the fitness landscape and it takes N/2 steps to attain the peak. So if there are 100,000 genes, it will take 50,000 generations on average to reach the peak. Once there, there’s nowhere else to go. This is the ideal of gradualism in evolutionary thinking. Small changes in the genome over time lead species inexorably upward in a gradual way to well-defined peaks. This doesn’t sound unreasonable until the landscape has a tendency to deform due to the interaction of other species in the ecosystem.

Let’s look at the other extreme. Suppose K=N-1. In other words, suppose each node is connected to every other node except itself. The resulting landscape is a surrealistic nightmare of many impossibly steep peaks, cliffs, and valleys. An adaptive walk on this landscape to a local peak can be accomplished in only a few steps. It also turns out that the fittest peak on this landscape is only half the height of the single peak on the K=0 landscape. More connections don't lead to better solutions. And there’s no telling whether any particular peak is the most fit or not.

As K is tuned from a value of 2 through a value of 8 the zone for the higher peaks is revealed (not as high as the K=0 option, though). Selection seeks good landscapes to evolve on. An interesting feature of the K=2 through K=8 landscapes is that there are far fewer peaks than in the K=N-1 landscape and the peaks tend to be clustered together. Once on a peak, chances are other good choices for greater fitness lie close at hand. This means that the highest peaks can be scaled from the greatest number of initial positions, particularly in the K=2 landscape.

How quickly these different peaks can be scaled depends upon the mutation rate and the number of nodes in the network. If either the mutation rate or the number of nodes becomes too large, the population tends to disperse rather than converge on local peaks. Its behavior becomes more frenetic. This is called error catastrophe.

At the beginning of this section I used Kauffman’s blue and red bacteria example. Bacteria multiply by dividing; there is no sex involved (in general). So bacteria depend mostly upon random mutation as a mechanism for moving uphill to local fitness peaks. Once on a peak, there is no mechanism to move down (well there is, but let’s assume there is not, because the mechanism in question will not help our organizational theory much). All things being equal, organisms cannot devolve in order to climb successive peaks. The devolved individuals would no longer be as fit as other members in the population and would die out. Why would it be important to move down? Because the peak an organism or an enterprise or a species or an industry finds itself on may not be the highest peak on the landscape. It may be the lowest peak on the fitness landscape instead. So how can a population on one peak move downhill in order to climb an adjacent higher peak? Or, more accurately, how can a population of organisms get a higher view of the whole terrain?

This is where sex, or more specifically, the recombination of DNA, plays a role. Imagine a herd of turtles on a fitness landscape (yes, a herd of turtles--just checking to see if you made it this far. . .). The father is on one peak and the mother is on another, distant peak. They wish to explore the terrain between them. By mating and sharing their DNA, their offspring will inhabit a spot on the terrain in-between them. This spot may be more or less fit than either of the parents, but it’s the only way to find out what the terrain is like there. If the terrain is not so good, chances are that offspring will not be selected for further experiments. But even if the offspring is selected as a future mate, then there will be an opportunity to explore yet more terrain.

It might seem that long jump strategy is the best one to use in a search procedure on fitness landscapes. Find two parents who are far apart from each other on the landscape so that the space equidistant between them may be explored. This is a good strategy, but only under certain conditions. The reason has to do with the correlation of the landscape. If I’m hiking in the Appalachians I know that the next step I take will be roughly correlated with the elevation I am currently on. Of course there are occasional cliffs, but for much of my walk on the mountains, a step in either direction takes me down some small amount or up some small amount. This is what is meant by a correlated landscape. K=2 to K=8 landscapes are correlated landscapes. Even if I hop out four or five steps, most of the time, I’m a little higher or a little lower than I was before. But what is the elevation a mile from where I am? There is little correlation. I could end up a good deal higher or a good deal lower in elevation.

Right after a catastrophe or at the birth of a new innovation, that’s the time to use the long jump strategy. Chances are that the organization is not too high on the landscape to begin with, and a long jump has a better chance to increase its elevation than plodding up the hill out of the marshes. This is a period of rapid, dramatic, successive innovations in a variety of directions--borrowing each other's ideas, people and methods. But after all of the players have moved up some degree in fitness, they may not think it’s wise to risk losing what they’ve gained. So in the middle game, smaller steps are more reasonable. It’s also a feature of fitness landscapes that as an organization climbs up each step, finding the next step up after that becomes exponentially harder. In the end game, once a high peak is attained, it’s best stay there. Why? Well, all small steps lead inevitably back down. And long jumps have an overwhelming probability of taking you far down in fitness level because there are only a minuscule number of peaks in all of state space. Your chances of landing on one higher than the one you’re on are infinitesimal.

Fitness Landscape search strategies are mapped onto the Stages of an Enterprise model in the above diagram. During the conception and looping stages the organization makes long jumps across the fitness landscape to search for the highest peaks. As the peaks of performance, product and pricing are attained, the organization settles down to moderate jumps or short steps and reaches success. In the maturity and maintenance phases the organization remains on its peak until its fitness landscape is deformed by the actions of others in its ecosystem. This can cause a dip in performance, leading to a turnaround situation. During turnaround the organization must switch its culture and strategies to embrace long and moderate jumps once again to discover the new peaks on the landscape. During the management of the death process, the organization does not waste resources on making jumps at all. This is much different than the turnaround situation where the organization makes great struggles to remain requisite with its environment.

Note that conditions surrounding the entrepreneurial button lead to the organization employing different strategies simultaneously. While the main portion of the venture takes small steps or remains stationary on its peak, a smaller portion--developing a new idea or product--engages in long jumps to find the most fit peaks. The organization finds itself with the need to manage two radically different cultures at the same time.



Living systems must have redundancy in them to dampen out the effect of miscellaneous, random mutations. Removing redundancy makes the system more efficient, but less able to adapt to changing demands or evolve with its larger ecosystem.

Choosing a Good Landscape by Tuning the K Variable
Selection seeks good landscapes to evolve on. Think of the K inputs per node as conflicting constraints. Then, to create the best advantages for finding good peaks, manage these conflicting options.

  • A minimum of dependencies between nodes minimizes conflict, but yields overall mediocre performance.
  • Too many dependencies between nodes maximizes conflict, leading to multiple, suboptimized standards of performance.
  • A medium number of dependencies between nodes "structures the landscape" so that it's easier to find and migrate to relatively high levels of performance.

Watching the Rate of Mutation
It is possible to try to change an organization too quickly in too many ways. This can happen by adding too many nodes or increasing the rate of mutation—that is, adding new ideas to the pot too quickly. The resulting error catastrophe will cause the organization to wander all over its fitness landscape instead of moving toward local peaks. Change and acquisition must be balanced over time.

Exploring Large Areas of Terrain on the Fitness Landscape Requires Finding a Mate
The way to explore broad areas of the terrain is to find a mate and combine the "DNA" from the two organizations. This can mean partnerships and alliances. But it also means that the alliance should have a specific product, perhaps an organization all to its own, something that can be called an offspring, otherwise the partnership will simply involve one organization ingesting another.

Different Strategies For Different Parts of the Game
Immediately after a major innovation, it pays to make wild jumps across the landscape in search of higher terrain. This can be done with spin-offs, partners, skunk works, broad-based hiring, or acquisitions. Once an organization has established itself on the slope of a high peak, the strategy should begin to shift to shorter hops and finally to single steps in improvement in order to attain the peak. Once the organization has reached the peak, it should stay there unless the mutation rate increases (in which case it will drift along ridges) or the landscape deforms (see the next section). Fortunately, all landscapes deform due to couplings with other organisms and species in the ecosystem, so no one will be "king of the hill" for long.

Increasing Complexity Attenuates Finding Radical Improvements
The more complex the organization, the harder it is to find radical improvements in fitness through drastic changes in its genes. Complexity here is a function of the number of nodes and the number of connections per node. Large, highly integrated organizations simply cannot make radical, innovative leaps. Not because they wouldn’t like to, but because it’s a function of their properties. This is why such organizations resort to skunk works, divestitures, and acquisitions to feed their demand for innovation. It’s also why if the acquisitions are done too thoroughly, the innovation rapidly dies out. There’s too much complexity to sustain it.

concepts concerning complex adaptive systems come from Stuart Kauffman's book At Home in the Universe, 1995, Oxford University Press
application to organizational theory copyright 1997, MG Taylor Corporation. All rights reserved
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