At Home In The Universe

1. At Home In The Universe The Search for the Laws of Self-Organization and Complexity (Stuart Kaufmann, 1995)

2. The Problem With Darwinism • Darwinism has effectively destroyed man’s ancient conviction that he is something special. Rather it conceives of man’s evolution as quite accidental, due to random causes. In this view the order of the human body is as improbable as a “Rube Goldberg machine” (see next slide). Moreover, the 2nd Law of Thermodynamics indicates that order is constantly dissolving into disorder. These views are alienating and gloomy. “Science, not sin, has indeed lost us our paradise.” (10) • Darwinists often say that “were the tape played over… the forms of organisms would surely differ dramatically” (7), (cf. SJ Gould), but Kauffman believes only the details would differ - the “patterns” of life would be the same (14).

4. The Problem With Darwinism (cont.) • Darwin’s theory assumed the “very” gradualaccumulation of useful variations, but paleontological evidence of the Cambrian Explosion and the Permian Extinction prove that evolution was anything but uniformly gradual. • For Darwinists, “time is in fact the hero of the plot,” meaning that “with very many trials, the unthinkably improbable becomes the virtually assured.” On the other hand, it has been calculated that “in the history of the earth, there could conceivably have been 2.5 X 1051 attempts to create life by chance, but only a 1 in 1040,000 probability that a single bacterium, such as E. coli, could be created in any one of these chances. This is a vast degree of improbability (44). [quotation].

5. Autocatalytic Sets • Consequently, life did not gradually evolve from the simple to the complex. Instead, it is a “natural property of complex chemical systems, that when the number of different kinds of molecules in a chemical soup passes a certain threshold, a self-sustaining network of reactions – an autocatalytic metabolism – will suddenly appear” (47). • This is a radical view with no experimental basis, but science will succeed in creating these self-reproducing molecular systems in 10-20 years. (Has it happened yet?)

6. Autocatalytic Sets (cont.) • The key concept is catalysis, and “a living organism is a system of chemicals that has the capacity to catalyze its own reproduction” (49). Catalysis allows the molecular reactions to take place “very much faster.” • (Why is increased speed of molecular reaction important? While it is tempting to conclude that it reduces the improbability of Darwinian evolution, Kaufmann doesn’t make that argument. Rather it seems that it makes the reaction timeframe more similar to what we see in living systems, heightening the analogy with those systems)..

8. Autocatalytic Sets (cont.) • A property of “random graphs” is that as more and more connections are made between the dots, and a certain ratio of dots to connecting lines is achieved, all the dots will be connected to the whole. This is a phase transition. If the dots are buttons and the connecting lines threads, picking up one button will result in picking them all up once the phase transition point has been reached.

10. Autocatalytic Sets (cont.) • “The analogue in the origin-of-life theory will be that when a large enough number of reactions are catalyzed in a chemical reaction system, a vast web of catalyzed reactions will suddenly crystallize. Such a web, it turns out, is almost certainly autocatalytic – almost certainly self-sustaining, alive” (58) (emphasis added). • (This is a significant leap in the argument. What, exactly, does he mean here by “self-sustaining, alive?” I presume he means capable of overcoming the dissipating effects of entropy. It’s mainly argument by analogy.) • The spontaneous emergence of such chemical webs is deeper than chemistry. It is rooted in mathematics (60). As the diversity and complexity of molecules in the system increases, so must the ratio of reactions to chemical “dots” also increase (proportion of reactions to dots). In other words, the number of reactions increases exponentially as the kinds and complexity of molecules increases.

12. Autocatalytic Sets (cont.) • If you make a rule that the chance of a given molecule being a catalyst for a reaction between molecules is a million to one, then when the diversity of molecules reaches the point that the ratio of reactions to polymers is a million to one, at that point each polymer will catalyze one reaction. When that point is reached, then it is highly probable that an autocatalytic web of catalytic reactions will form (64). • “The experiment has not been done with real chemicals yet… but on the computer (“in silico”), a living system swarms into existence.” • Not only is such a system self-sustaining, but it is nearly self-reproducing. When the number of copies of each molecule has doubled, the system can, “in principle”, break into two identical systems. This has been verified by experiment (72) (but what kinds of experiments? He gives no details on this).

13. Autocatalytic Sets (cont.) • (The key concept in autocatalytic systems is what happens between the parts, the reactions they have with each other. In this sense, the whole is larger than the sum of the parts. Moreover, any reaction between two molecules enabled by a third molecule implies spontaneous order).

14. The NK Model • If you assume that each bodily enzyme has only two states, “on” and “off,” and the reactions between them as governed by Boolean rules (i.e. “AND,” “OR,” etc.), a metabolic system may be modeled as a network of lightbulbs connected by wires, an electrical circuit. A molecule catalyzing the formation of another molecule can be thought of as one lightbulb turning on another. • If you had a network of 1,000 bulbs, the total number of states of the network would be 21,000, and even if it took a trillioneth of a second to transition from one state to another, “we could never in the lifetime of the universe see the system complete its orbit.” To be stable, our autocatalytic networks “must avoid veering off on seemingly endless tangents and must settle down into small state cycles – a repertoire of stable behaviors” (78).

16. The NK Model (cont.) • In a series of computer simulations over many years, where N = the number of lightbulbs in the network and K = the number of other lightbulbs connected to each lightbulb in a Boolean relation, it was found that when K = 4 or more, the system blinks chaotically. When K = 1, the system goes to the opposite extreme and freezes up into a single state. It is when K = 2 that order emerges. When N = 100,000 and K = 2, the system cycles through a sequence of only 317 states out of 2100,000 possible states (or attractors). • “I hope this blows your socks off, mine have never recovered since I discovered this almost three decades ago. Here is, forgive me, stunning order” (83) (emphasis added)

17. The NK Model and Human Ontogeny • What accounts for the orderly cell differentiation in ontogeny? • Science has discovered that genes can form genetic circuits and turn one another on and off. Furthermore, these circuits can be of arbitrary logic and complexity (97). • Therefore, the lightbulb model applies equally well to genetic regulatory networks, where each lightbulb corresponds to a gene, the connections between the bulbs to the regulatory relationships among genes, and each “state-cycle attractor in the vast state space of a genomic network is a different cell type” (99, 102). (Since each cell type is made up of the same genes, but each has a distinct on-off pattern, a cell-type is like as a state-cycle attractor).

18. The NK Model and Human Ontogeny (cont.) • If N = 100,000, equal to the number of genes in the human genome, and K = 2, meaning that the activation of each gene is controlled by the states of no more than 2 other genes, we have seen that the number of state-cycles, or cell-types, in this system will be 317, close to the actual number of cell-types in the human body, 256. (Implied conclusion: the order of the human body is not entirely accidental; to some extent it is determined by the properties of its structure). • Caveats: The analogy between genetic networks and Boolean networks is based on “idealizations.” These are the assumptions that genes act like Boolean variables, their interactions like Boolean operators, and that the number of genes which control the state of any other gene does not exceed 2 [K = 2]. For example, it is “literally false” that enzymes “have only two states of activity – on or off, and can switch between them… In reality, enzymes show graded catalytic activities” (74). • (So, given these caveats, how meaningful is the analogy? Is it persuasive,or just interesting?).

19. The NK Model and Genetic Fitness • The NK model may also be used to model genetic “fitness,” where N = the total number of genes in the system (e.g. the human body), and K = the number of genes affecting the fitness of any one gene in the system. It is a network of epistatic interactions (170). • “So we may be able to understand the kind of epistasis that occurs in organisms and its effect on landscapes and evolution without needing to carry out all the experiments to establish all the details of epistatic couplings in any one organism. In short, we can seek general laws in biology concerning the structure and even the evolution of fitness landscapes by building models” (171) (emphasis added). • As K increases, the number of genes affecting the fitness of any one gene increases. This necessarily increases the number of conflicting constraints on the evolution of any one gene, making evolution slower and more difficult (173).

20. The NK Model and Genetic Fitness (cont.) • Conflicting constraints have an increasing effect as an organism evolves toward greater fitness. Its evolution slows exponentially the fitter it becomes. This slowing is as characteristic of technological evolution as it is of biological evolution (179 - 180). • At the other exteme, (in the absence of conflicting constraints) a high rate of mutation naturally effects an “error catastrophe” (184). And, “…for a constant mutation rate per gene, the error catastrophe will arise when the number of genes in the genotype increases beyond a critical number. Thus there appears to be a limit on the complexity of a genome that can be assembled by mutation and selection” (184).

21. The NK Model and Genetic Fitness (cont.) • (Error catastrophe happens when the rate of mutation is so high that harmful effects accumulate faster than natural selection can weed them out (184)) • The NK model is one of the first mathematical models of tunably rugged fitness landscapes. Increasing the K value increases the conflicting constraints on each gene by other genes in an organism, making the landscape more rugged and multi-peaked. As K approaches the value of N, the landscape becomes fully random (and no evolution toward greater fitness is possible) (192). • “The NK model is merely a toy world to tune our intuitions” (205).

22. The NK Model and Coevolution • Just as the NK model can be used to show how genes interact with genes in a single organism, it can be used to show how traits interact with traits between organisms within an ecosystem (225). Two additional variables introduced to the model, C and S. As K measures the number of other genes connected to any one gene within a single organism, so C measures the number of traits of another organism connected to any one trait of an organism. As N measures the number of genes in a single organism, S measures the number of species in an ecosystem. Then a random fitness number between 0.0 and 1.0 is assigned to each trait (gene). • If then you treat the members of each species as identical in genetic makeup, and postulate that each species mutates a single, randomly-chosen gene in each generation, you can see the model oscillate between order and chaos depending on the variables, K, C, and S. Order is here defined as an Evolutionary Stable Strategy, meaning no further evolution (225).

25. The NK Model and Coevolution (cont.) • A further result is that changing the values of K, C, and S along the axis, from the ordered regime to the chaotic regime, makes average fitness first increase and then decrease. This indicates that highest average fitness of an ecosystem occurs precisely at the point where ordered behavior becomes chaotic, the edge of chaos.

27. The NK Model and Coevolution (cont.) • Yet another result of running this model in computer simulations is that it appears to be self-tuning (232 & 235). [quotation]

29. The NK Model and Coevolution (cont.) • In conclusion, “we do not yet know that ecosystems over evolutionary time coevolve to a self-tuned edge-of-chaos regime, but the parallels between the size of extinction events and the life-span distribution are supportive clues” (239). • “Big and little events can be triggered by the same kind of tiny cause. Poised systems need no massive mover to move massively” (236). (This is implied by the fact that ecosystems tune themselves to operate on the edge of chaos. It’s self-organized criticality, where the smallest cause can send the system into chaos). • “Be careful. Your own best footstep may unleash the very cascade that carries you away” (243)

30. Patches • In the NK model, change is retarded by a high number (K) of dependencies between the parts. Such a state is called “conflict-laden.” To break the gridlock, so that progress can be made, it is useful to divide the network into parts, and let each part operate to its own best advantage, ignoring the constraints put on it by the rest of the network. If the “patch” size is properly chosen, “the coevolving system lies at a phase transition between order and chaos and rapidly finds very good solutions” (253). • (The key here is “properly chosen” patches, and the only rule Kaufmann gives for choosing the proper size is that larger patches lead from chaos to ordered convergence. It’s a trial and error process to find the proper size).

33. Patches (cont.) • One example is the flocking behavior of birds, whereby successful flocking may be achieved by each bird only responding to the birds closest to it, not all the birds in the flock (in contrast to the average position and average direction rules of the “boids’ simulation). • Another example may be in the customer service context of large companies. When serving multiple customers burdens the company with conflicting constraints, it may be best to focus on a subset of the customers, ignoring the rest for the time being (the old 80-20 rule). • Yet another example is that federal network of states, each working for its own advantage, works better than centralized government. (The US system! - how about that?) (271) [quotation]

34. Patches (cont.) • This is nothing less than the reprising of economist Adam Smith’s Invisible Hand, which produces the common good from a multitude of selfish and short-sighted actors and actions (246-247, 262).

35. Grammar Models • A Turing machine (i.e. computer) is analogous to an autocatalytic system in that it employs one string of symbols to act on another string of symbols (276). A computer model may be made in which symbol strings act on other symbol strings which may in turn qualify themselves act on symbol strings, ad infinitum. Such a model is called a “grammar model” (286). It might possibly produce a collectively autocatalytic set of symbol strings (287).

38. Grammar Models (cont.) • “Grammar models…help make evident patterns we know about intuitively but cannot talk about very precisely” (287). • What can be learned from computer models lies in similar patterns they generate, not in the details (283) [quotation] • “…once one sees one of these models, the idea that the web itself drives the ways the web transforms becomes obvious. We know this intuitively, I think. We just have never had a toy world that exhibited to us what we have always known.” This has implications for all kinds of webs, including the economic (292). • Grammar models also suggest that “diversity begets diversity; hence diversity may help beget [economic] growth” (292). Such ideas might eventually have policy implications (297) [quotation]

39. Concluding Comment • “I do not know if the spontaneous order in mathematical models of genomic regulatory systems really is one of the ultimate sources of order in ontogeny. Yet I am heartened by a view of evolution as a marriage of spontaneous order and natural selection” (304)