Life as an autopoietic system — an attempt at structural-realistic enlightenment —
“Evolutionary theories in a structural realist perspective”
Abstract
I would now like to take up this task in this part and attempt to explain the self-organization of life with the help of a structural realist approach. To this end, I would first like to describe the initial problem in Darwin’s theory of evolution, which can be seen as an example of the “underdetermination of empirical theories by the evidence” (Bas van Fraassen).
The evidence for Darwin’s theory of evolution indicates that there is an underdetermination with regard to its empirical adequacy, which can also be demonstrated mathematically. I would then like to present new mathematical approaches from the Stochastic Evolutionary Dynamics research group at the Max Planck Institute for Evolutionary Biology. This will be followed by a transition to structural realism, which explicitly does not refer to the dualistic and reductionist difference of “inside vs. outside”, but attempts to describe the self-referential process of the structural coupling of life with its environment in terms of a multivalent logic according to Gotthard Günther. Methodologically, I would first like to establish 5 axioms on life, from which I then derive postulates on the possible emergence of life. I have been inspired by Giulio Tononi’s “Integrated Information Theory” (IIT) in terms of formalism and terminology.
“Survival of the fittest” — the struggle for survival of evolutionary theories
When the British natural scientist Charles Darwin (1809–1882) finally published his theories on evolution as “Natural Selection” in the summer of 1858 after more than 20 years of work and his groundbreaking magnum opus “On the Origin of Species” a year later in 1859, the following years and decades saw one of the Kuhnian “scientific revolutions” described above in the biology that was just being formed. The sub-discipline of evolutionary biology that later emerged has built on this to this day, and it is by no means the author’s intention to attack the core of the 5 basic principles contained therein:
1. evolution as such, the variability of species;
2. the common descent of all living beings;
3. gradualism, change through the smallest steps;
4. reproduction of species or speciation in populations
5. and natural selection as the most important, if not the only, mechanism of evolution. (Charles Darwin: On the Origin of Species by Means of Natural Selection, or The Preservation of Favoured Races in the Struggle for Life , 1859)
There is also a competing, earlier theory of evolution by the French biologist Jean-Baptiste de Lamarck (1744–1829) with its two basic theories on the interaction of two factors:
- undirected adaptation to external changes
- linear progress on a linear ladder of complexity
was in a “battle for survival” with Darwin’s theory of evolution. However, it has been partly inherited in the form of modern epigenetics, although the directionality of “linear progress” had to be sacrificed in favor of the probabilistic nature of Darwin’s “natural selection”.
The above-mentioned basic principles of the theory of evolution should not be called into question here, as the author expressly wishes to distance himself from unscientific creationism. The question goes much deeper — in the truest sense of the word — into the matter. How something like life could arise from dead matter in the first place and how matter still manages to organize itself today. Because from a mathematical stochastic point of view, there could actually be something to an argument that is unfortunately often put forward by creationists:
“To create a single medium-sized human protein, evolution had to put more than 300 amino acids together in the right order. This could not have been a coincidence. Since each member of a molecule consists of one of 20 possible amino acids, there are more than 20,300 ways to build such a protein. Next to such a number, even the number of atoms in the observable universe seems negligible. Even if redundancies that make some sequences equivalent from a biochemical point of view are not included, it would indeed be highly unlikely that evolution could find the right combinations purely through random mutations, even after billions of years.
But the creationists’ argument has a crucial catch: evolution does not test genetic sequences by chance alone. It works with natural selection and has probably also found ways to limit the immeasurable space of genetic possibilities to smaller, researchable sub-areas.” (Jordana Cepelewicz: Algorithms practice evolution, in: Spektrum.de — IT/Tech — Lässt sich Evolution mit Mathematik und Algorithmen modellieren?, 2019)
In this respect, the old models of evolutionary theory fail and require a stochastic extension in terms of information theory. The “chance” and “selection” arguments alone are no longer sufficient. There must also be the aforementioned “self-organization of life as an autopoietic system” from within; without, however, having to fall into the old dualism of “inside vs. outside”. One way out of this dilemma could be provided by “stochastic evolutionary dynamics”, which uses algorithms to develop mainly population-genetic and epidemiological simulation models, but which can certainly be applied to the big picture.
The “Evolutionary Graph Theory” (EGT) — long live mathematics
“Evolutionary graph theory is a field of research that lies at the intersection of graph theory, probability theory and mathematical biology. Evolutionary graph theory is an approach to studying the effects of topology on the evolution of a population. That the underlying topology can have a significant impact on the outcomes of the evolutionary process is most clearly illustrated in a paper by Erez Lieberman, Christoph Hauert and Martin Nowak[1].
In evolutionary graph theory, individuals occupy the nodes of a weighted, directed graph, and the weight wi j of an edge from node i to node j indicates the probability that i takes the place of j. This is a property of graphs. A property studied for graphs with two types of individuals is the fixation probability, which is defined as the probability that a single randomly placed mutant of type A replaces a population of type B.According to the isothermal theorem, a graph only has the same fixation probability as the corresponding Moran process if it is isothermal, i.e. the sum of all weights that lead to a node is the same for all nodes. For example, a complete graph with equal weights describes a Moran process.” (Source: https://en.wikipedia.org/wiki/Evolutionary_graph_theory)
Ouch ha! This sophisticated mathematical construct can perhaps best be compared with the concept of “Kolmogorov complexity” and thus perhaps explained more comprehensibly:
“In very general terms, let us take, for example, a two-dimensional abstract network with n nodes. If this network undergoes a change of state, the nodes shift and form an area with a higher (information) density at a certain point. In biological systems, this density is stored genetically and forms a metastructural control unit.”
This means that structures have a self-referentiality that can be described on the basis of stochastic, linear distributions. In evolutionary graph theory (EGT), structurally coupled graphs with different weights in the nodes are created.If you like, an information-theoretical self-organization of the autopoietic system from within in order to pass on information with the smallest possible number of characters and the greatest possible information density.
This “Kolmogorov complexity”, named after the Russian mathematician Andrei Nikolayevich Kolmogorov, “is a measure of the structuredness of a character string and is given by the length of the shortest program that generates this character string. This shortest program thus gives the best compression of the string without losing information.” (https://de.wikipedia.org/wiki/Kolmogorow-Komplexit%C3%A4t)
However, the Kolmogorov complexity has the crucial catch that it cannot be calculated. This is where the “Bayesian networks” and “Markov chains”, which will be explained later, come into play. But at least we have already gained a new starting point for not leaving the self-organization of life to pure chance alone. The “chance” factor has the unpleasant property of having far too many degrees of freedom, which would lead to far too many possible choices and thus cost far too much time and energy.With 20300 possibilities for one protein alone, you can perhaps imagine that the probabilistic possibilities for the formation of a living organism are of dizzying proportions. So nature must have found a way to break away from pure “trial and error”. In other words, to “reinvent the wheel every time”, but to develop something like “genetic algorithms” that can act like heuristics. These so-called “genetic algorithms” are also used in programming to avoid redundancies, code in a more structured way and thus save time and energy.
“Genetic algorithms always start with a handful of randomly selected solutions. These are usually not yet good. However, the solutions in genetic algorithms are seen as organisms whose characteristics are described in a kind of genetic code. This code is then subjected to a combination of manipulations, as in evolution. These can be random mutations or interventions that mimic the genetic mixing processes in nature. This results in a further generation of organisms, which in turn are tested for their fitness, i.e. their ability to solve the task. Repeating these steps can lead to highly adapted individuals: good solutions to the problem at hand.” (Jordana Cepelewicz: Algorithms practice evolution, in: Spektrum.de — IT/Tech — Lässt sich Evolution mit Mathematik und Algorithmen modellieren?, 2019)
The genetic algorithms of Evolutionary Graph Theory are in turn used in Stochastic Evolutionary Dynamics to run population genetic and epidemiological simulation models in silico. The aim here is to better map the evolutionary dynamics of bacterial strains in vitro, for example, and to draw conclusions about the self-organization of life.
Bayesian networks and Markov chains — or how random is chance?
In order to better describe the self-organization of autopoietic systems in Evolutionary Graph Theory in structural terms, a mathematical formulation of stochastics in the form of Bayesian networks and Markov chains is required so that the propagated “metastructures” can be calculated. The dynamic process with its stochastic elements must be mapped and the “special conditional independence” must be taken into account. In other words, it is being investigated whether the probabilistic structure of evolution can be reproduced as an algorithm in a simulation model.
(Source: https://de.wikipedia.org/wiki/Graph_(graph theory)
“A Bayesian network or Bayesian network (named after Thomas Bayes) is a directed acyclic graph (DAG) in which the nodes describe random variables and the edges describe conditional dependencies between the variables. Each node of the network is assigned a conditional probability distribution of the random variable it represents, given the random variables at the parent nodes. They are described by probability tables. This distribution can be arbitrary, but discrete or normal distributions are often used. The parents of a node v are those nodes from which an edge leads to v.
A Bayesian network is used to represent the joint probability distribution of all variables involved as compactly as possible using known conditional independence. The conditional (in)dependence of subsets of the variables is combined with the a priori knowledge.
If X1, …, Xn are some of the random variables occurring in the graph (which are closed by adding parent variables), their joint distribution is calculated as:
P ( X 1 , … , X n ) is a symbolic notation for the joint probability distribution of the random variables X 1 , … , X n . If a node has no parents, the associated probability distribution is an unconditional distribution.
As in the example below, one is often interested in a marginal probability, which is obtained by marginalizing over all possible realizations x j in the state space E j of the random variable X j :
“ (https://de.wikipedia.org/wiki/Bayessches_Netz)
And without wanting or needing to go into the mathematics used here, the previously formulated “inheritance theory of information” in Evolutionary Graph Theory reappears here. The joint probability distribution P of the random variables X 1 , … , X n is only dependent on the conditional nodes of the “parent” random variables. If there are no “parent” random variables for a particular node, this is not so bad, as you can then simply determine the “marginal probabilities” using the “associated probability distribution”.
The whole mathematical process therefore has the great advantage of making the “random variables” calculable as a “conditional probability distribution”. This also makes randomness a little more structured and more tangible for the development of algorithms. This advantage of structuring randomness is not only used for learning in AI development, but can also be used productively to describe mutations in the self-organization of life.
Example of an evolutionary algorithm:
The Rastrigin function is a multimodal function as it has many local extrema. This is a disadvantage for the recombination operator. (Source: https://de.wikipedia.org/wiki/Evolution%C3%A4rer_Algorithmus)
“Probability of a mutation pattern
The probability (likelihood L) of a mutation pattern x under the condition of a mutagenetic tree T is given as the product of two products given in the formula:
Here, the index e runs over all edges of the mutation tree — each e corresponds to a transition between two mutants. The first product runs over all probabilities p(e) of mutations that lead to pattern x, the second product contributes a factor of 1 — p(e) for each mutation that does not lead to x.” (Daniel Hoffmann: Evolution: From biology to mathematics and back again, 2008)
This is not only reminiscent of the mathematical description of Bayesian networks, but also has a direct connection. The evolutionary character of mutations can now be depicted with the help of the probability of mutation patterns. The “theory of inheritance” is again found here in the conditional dependence of the probabilities p(e) of mutations that lead to pattern x. The second product of 1 — p(e) also includes the unconditional probabilities for each mutation that does not lead to x.
Now we just have to get a mathematical grip on the dynamic process character in evolutionary dynamics. A special conditional independence of the factor “time”, in which the present, past and future should be independent of each other, is a necessary condition for the factor “chance”. In other words, the Bayesian network is a probabilistic graphical model (PGM) that uses its graph formalism to compactly model joint probability distributions and (in)dependence relations over a set of random variables. Okay. But in order to achieve a special conditional independence, you have to open up the directionality a little. And this is where the “Markov Random Field” comes into play:
“A Markov Random Field (MRF for short) or Markov network is a statistical model named after the mathematician A. Markov, which describes undirected relationships (e.g. the alignment of elementary magnets) in a field. The field consists of cells that contain random variables and interact with each other in a spatially limited manner (cf. temporal limitation in a Markov chain). […] One of the formal properties of an MRF is the Global Markov Property: Each node (as a representative of the random variable) is independent of all other nodes if all its neighbors are given.” (https://de.wikipedia.org/wiki/Markov_Random_Field)
Markov chain with three states and incomplete connections (source: https://de.wikipedia.org/wiki/Markow-Kette)
Markov blanket: In a Bayesian network, the Markov boundary of node A includes its parents, children and the other parents of all its children. (Source: https://en.wikipedia.org/wiki/Markov_blanket)
With the help of “Markov models”, here specifically “Markov chains” or “Markov ceilings”, the “chance” factor in the Bayesian networks is made more calculable through spatial or temporal limitation. In other words, each node in the Bayesian network can be calculated with a certain probability if all its relations are known.
Now we only need to run the probabilistic algorithms as simulation models on a computer and check to what extent the algorithms are able to depict population-genetic and epidemiological evolutionary dynamics. This is the first time that the model has been compared with the environment. This is important because the algorithms of the simulation model must also be constantly adapted to the actual evidence as a self-referential, recursive feedback loop.
In this respect, the testing of evolutionary theories not only takes place as genetic algorithms in a simulation model, but evolutionary graph theory, for example, is itself subject to a kind of evolution. In order to bring a few more mutation possibilities into play here, a structure-realistic view of evolutionary theories is permitted at the end.
Evolutionary theories in a structure-realistic view — life needs structures
In my view, the “node” for a structure-realistic view of evolutionary theory is given by the structural description of stochastic evolutionary dynamics in Evolutionary Graph Theory.
Assuming that the aforementioned mathematical description models, such as those from evolutionary graph theory, can adequately simulate evolutionary dynamics in nature, this would open up a completely new approach to understanding evolution. The current paradigm in evolutionary biology is based on a dualism of “inside vs. outside”, “organism vs. environment”, “adaptation vs. speciation”, etc., which is always pursued in the sense of a demarcation from the “tertium non datur” of classical systems theory (George Spencer-Brown, Niklas Luhmann) as “difference”.
In my view, the focus of the new paradigm for evolutionary biology should lie more on the concept of polycontexturality according to Gotthard Günther in order to be able to better describe the structural-dynamic process for the emergence of life. Methodologically, I would like to use the formalism and terminology of Giulio Tononi’s “Integrated Information Theory” IIT (2004–2014), which is actually a mathematical theory of the constitution of consciousness, but which, in my view, is also suitable for describing the constitution of life due to its information-theoretical formalism.
The possibilities that arise from a structural description of evolutionary dynamics in Evolutionary Graph Theory open up completely new structural-realistic considerations, such as how life can have arisen as an autopoietic system. To make this a little more precise, I would like to set out below “5 axioms of life” in analogy to IIT, from which I then derive the corresponding “postulates for the possible emergence of life”.
The 5 axioms of life
1. intrinsic existence: a living organism must possess a structural-dynamic difference between “inside” and “outside”,
2. composition: a living organism must be composed of several parts that are more than their sum,
3. information: through its structure, a living organism must also have a content that can be transmitted,
4. integration: a living organism must be able to interact with its environment and adapt,
5. exclusion: a living organism must have a behavior that separates it from its environment
Postulates on the axioms
Regarding 1. intrinsic existence: a living organism first of all requires a structural-dynamic difference between “inside” and “outside”. In other words, without a corresponding structural-dynamic demarcation to the outside, the living organism cannot be defined at all, since in this case it cannot form its own identity/entity. However, this difference is explicitly not intended here as dualism, as the living organism remains part of the environment from a processual point of view and interacts with it (see 4.).
Described in a structure-realistic concept, the relations that form between the living organism and its environment in a phase space would be of greater significance than the relations (organism, environment) themselves. Described from a structural realist perspective in terms of evolutionary graph theory (EGT), this means that the emerging Bayesian networks or Markov chains have their own information content, which has an intrinsic existence as self-organization from within, independent of the description of the living organism as a whole.
Re 2. composition: a living organism always consists of several parts, but from a mereological point of view it is always more than the sum of its parts. Even the smallest living organisms, such as bacteria or viruses (although in the case of viruses, the limits to life are already reached) consist of several simple components, such as protein shell or RNA/DNA material. The complexity of the composition of living organisms is open-ended and can certainly be explained with the help of adaptation and evolution.
The “adaptive random walk” of evolution can be mapped probabilistically with the help of the Markov Random Field (MRF) or Markov logic networks. The seemingly undirected relationships of Darwin’s theory of evolution, which is often referred to as the “trial and error” method, can now be described with the help of MRFs in a field. “The field consists of cells that contain random variables and interact with each other in a spatially limited way (cf. temporal limitation in a Markov chain).” (https://de.wikipedia.org/wiki/Markov_Random_Field).
From a structural realist perspective, this means that it is no longer necessary to consider the composition of the individual living organism in terms of the emergence of species with new specific characteristics adapted to the environment. Instead, adaptation and evolution can also be described, for example, as a Markov network or, from a temporal perspective, as a Markov chain. This gives us a clear structure of the “chance” factor and allows us to develop better heuristics.
3. information: a living organism is a self-referential, autopoietic system that possesses an information content due to its structure. The information can be stored in the genomes of the cells in the form of DNA. The specific structuring of cell groups into organs or the specific composition of the living organism from its components can also be described as information content. Information can be transferred within the living organism via self-recursive processes, but also outside via inheritance. The structural-dynamic process of information transfer can be illustrated well with the help of Bayesian networks, as the “inheritance theory of information” can be depicted here in evolutionary graph theory. The joint probability distribution of all random variables of a living system can be determined as a function of the conditional nodes of the “parent” random variables. The information content of the overall system is retained despite permutation of the structures of individual areas. Even if there are no “parent” random variables for a particular node, e.g. in the case of mutations, the “marginal probabilities” can be determined on the basis of the “associated probability distribution”.
From the point of view of structural realism, this means that if the relations of the overall system (nodes, edges) are known, structural-dynamic transformations of individual areas can also take place without significantly changing the information content of the overall system. This enables adaptation to the environment and, in the longer term, evolution of the living organism.
Re 4. integration: a living organism must be able to interact with its environment. This means that, despite the closed nature of its intrinsic existence, it requires a material, energetic and informational exchange with its environment. For this purpose, the living organism needs to be integrated into its environment. Metabolism, for example, is an important criterion for defining living organisms. An isolated consideration of the living organism without taking integration into its environment into account therefore does not make much sense.
If we want to describe the constitution of life with the help of evolutionary graph theory, we must therefore take into account that the simulation of population-genetic or epidemiological evolution in the form of Bayesian networks or Markov chains is not a closed system in the sense of systems theory. The integration of several systems is potentially possible, whereby the mathematical and information technology realization for a single system alone is already reaching its limits.
With regard to the structural realist concept, this naturally also leads to an increase in complexity in the form of the “relationalization of relations”, which could also be described as “2nd order cybernetics”.
Re 5. exclusion: here the possibilities of description within the framework of Evolutionary Graph Theory EGT and Structural Realism SR have finally been reached, since the behavior of a living organism is an essential criterion for its vitality, but the representation in EGT and SR is no longer possible. Here, the “flippant final remark” is permitted: “The most important thing about life is that you are alive!”
