Complexity, individuation and function in ecology Part I, sec 1 Complexity and Organization Prof. John Collier (Departamento de Filosofia, Universidade de Kwazulu-Natal, África do Sul. Pesquisador Visitante do Laboratório de Ensino, Filosofia e História das Ciências (LEFHBio), Programa Ciência sem Fronteiras)

Outline I.1: Complexity and organization a.Definitions and reasons for focus on organized complexity i.Collier, John and C.A. Hooker Complexly organised dynamical systems. Open Systems and information Dynamics, 6: Collier, John and C.A. Hooker Complexly organised dynamical systems. Open Systems and information Dynamics, 6: ii.Rosen and von Foerster on simple and complex systems: Last chapter of Rosen, R., Essays on Life Itself. Columbia University Press, New York. Hertz Diagram from H. Pattee. Hertz Diagram b.Problems of representing complex systems, modelling relation i.Two Faces of Maxwell's Demon Reveal the Nature of Irreversibility. Studies in the Hist and Phil of Science,1990: Two Faces of Maxwell's Demon Reveal the Nature of Irreversibility ii.Chemero, Anthony, and Michael T Turvey Autonomy and Hypersets. Bio Systems 91 (2) (February): 320–30. iii.Hertz diagram from Howard Pattee c.Problems with managing complex systems i.Organized complexity: Properties, models and the limits of understanding (Havana 2004)Organized complexity: Properties, models and the limits of understanding

Mathematical complexity The minimal amount of information that it takes to describe something Formalized as algorithmic complexity: the length of the shortest self-delimiting computer program that can produce something’s structure. Amount of information. Note: depends on programming language, but this is negligible for very complex things Corresponds to complicatedness (see next slide).

Why is complexity important? There are two kinds of complexity – The first we call simply complicated. requires much thinking or computing but can be reduced to its parts and then added together traditional science applies – The second is complexly organized cannot be reduced to its parts (emergent) requires a revolutionary new kind of thinking

Definitions of Complexity And Organization Complexity can mean merely complicated, or it can mean complexly organized. Complicatedness can be measured by finding the most compressed form of the information in a system or property. Complexly organized means that the system or property involved is convoluted; it affects itself not merely locally but also over larger scales. Organization is a causal correlation (real pattern) in a system or property at various scales. Organization can be measured by “logical depth”, the amount of steps required to produce the surface form from the most compressed form.

Organization The basic idea of an organized system is that it is interconnected in complex ways, so that there are both local and non-local effects. A system can be strictly hierarchical, with either – the higher levels are the sum of the effects of the parts, or – the behaviour of the parts is strictly controlled from above. – Such systems are decomposable and are not complexly organized. Complex organization – involves neither summation nor top down control, but shows an interaction of bottom-up effects and top-down effects – Complexly organized systems cannot be decomposed

Measuring organization Logical depth (Bennett): the minimal computation time to produce the surface structure from a maximally compressed form Sophistication (Atlan): The number of logically simple steps required to produce a structure from its components Thermodynamic depth: the minimal work required to produce a structure from its components

Some systems that are troublesome for traditional methods Weather (storm paths) Climate change (many interacting factors) Living systems (cells, organisms, ecosystems) The Economy (as in 2008) Family Therapy (interactions depend on each other) Road traffic flow (as in Salvador) Ecosystems

Kinds of systems Type I systems are typical of basic examples of laws: pendulum, crystal Type II systems are typical of engineered systems: computer Type III systems have statistical behaviour: gas, stars in a cluster Type IV systems cover everything else

What makes Type IV systems difficult? Mathematically difficult or impossible to solve – Mutual interaction of parts (nonlinearity) – Parts interact in aspects, often different for different interactions (partial differentials) Cannot be broken up into parts (analyzed) that can then be added together (synthesized) Mutual interaction between the whole and the parts (upward and downward causation)

Mathematical difficulty of solutions Equation:AlgebraicOrdinary DifferentialPartial Differential One ParameterTrivialEasyDifficult Linear EquationsSeveral ParametersEasyDifficultIntractable Many ParametersIntractable Impossible One ParameterVery Difficult Impossible Nonlinear EquationsSeveral ParametersVery DifficultImpossible Many ParametersImpossible

Some consequences of the difficulty Type IV systems Unpredictability in detail Cannot be fully controlled Principle of Unintended Consequences Formed by self-organization, they create the conditions for their own existence. Type IV systems resist attempts to change them. No computable model for processes in many cases (I will go into this more in discussion of emergence)

Biology is characteristically made of type IV systems Non-reducible Mechanistic explanations are limited Function is relevant in explanations and biological explanations are incomplete without them. Complete models of biological systems inevitably leave something out. Information as well as energy is important.

Form (pattern) dominates in biology In most of the physical sciences constraints are secondary, processes being governed by energy flows. In biology, however, energy differences are small, and information flows are primary. Information is a measure of form (or pattern), so changes in pattern are primary in biology. Biological function (anticipation) requires quick shifts from one state to another, ruling out deep energy wells.

Pattern in biology Patterns in biology are found (famously) in systematics, but also in developmental theory, evolutionary theory, and more recently in systems biology. Shape is also important in molecular biology (enzymes, immunology, etc.). Pattern change is a form of dynamics, as it involves a time parameter. However it is not a dynamical theory in the stronger sense of being based in forces and flows, or in causal relations. I will argue that pattern dynamics alone are inadequate for the study of pattern change.

Biological laws are primarily laws about change or constancy of form In the physical sciences most laws involve energy either directly or indirectly. Because form dominates in biology, biological laws (such as they are) involve the preservation of form or change of form in regular ways. This might be why many philosophers have denied the existence of laws in biology. Biological laws are often local to a system type (after K. Waters). This is not unheard of in the physical sciences (e.g., geomorphology), but it is less common, and universal laws are preferred.

Examples of biological laws and principles involving form 1 Hardy-Weinberg equilibrium: the “no force” law of population genetics – governs relative gene frequencies ( a pattern). Modifications govern changes of gene frequencies due to mutation, migration, assortative mating, etc. D’Arcy Thompson’s observation that changes in biological form involve distortions that can be explained in terms of relative growth rates. Dollo’s law (in some/many respects)

Examples of biological laws and principles involving form 2 Immunological distinction between self and non-self. Template model of enzyme action. Evo/devo: preservation of developmental units across functional and genetic variation. More generally, biological systems are self- organizing, showing closure, but remaining open to some degree.

How to approach such systems Information theory will be highly relevant, and we need to consider how information systems can self-organize. We need models that are robust, but not necessarily complete, working both from the bottom up and the top down. In order to have testable models rather than just data collections we need causal models in which we can vary causal factors.

Modelling systems There are many ways to build models of systems, and most are useful to some extent. However causal models are the most useful as they can be tested through interventions in the system to see how it responds. Statistical models can provide evidence from which to derive and eventually test theories. Other kinds of quantitative models (e.g., information flow and correlations) are also useful for the same purposes, but can target specific system relations and qualitative properties. Qualitative models can be useful for understanding systems, especially when the above are not available.

Observer dependent versus intrinsic There is a widespread view that it is only our theories that are complex, not systems themselves. (Prevalent in Systems Theory) However some theories are better than others. – Useful because of simplifying assumptions that make them tractable – Useful because they are accurate But there is some truth to observer dependence

Models and reality There is a sense in which we can only work with models. This has been over-emphasized. The world can surprise us; our models can be shown to be inaccurate when we interact with the world. If our world was completely made of models we construct, this could not happen.

Scale dependency 1 We typically focus on a particular scale. This is dependent on our interests. Things can be (apparently) simple at one space or time scale, but not at another. This sort of simplicity is not correlated with scale size. – Macroscopic thermodynamic properties in steady state systems versus molecular motions – Local molecular motions versus intermediate scale molecular motions in Bénard Cells

Scale dependency 2 For particular interests some scales are more appropriate than others. However we can make mistakes about the appropriate scale. This can be due to: – External conditions interact in complex ways with internal conditions – Boundary conditions are not fixed – Or (more often) some combination of the two

Causal models If you have a causal model of a system, then it is possible to make interventions (variations) to see how the system responds. This method can also be used to test causal hypotheses. – For example, we can hold all other variables constant and see how a system responds to variation of one variable to see if it is causally relevant, and in which way. Unfortunately, complex systems do not respond in a linear way, so causal intervention can be misleading. Therefore, we need a prior understanding of the basic dynamical forces and flows in a system to see (and perhaps predict or make hypotheses about) the effects of causal connections within the system.

Hertz’ model system (after Howard Pattee) Pattee makes a clear distinction between observer and system, not just between model and object. He calls this the “epistemic cut”. Note that interaction with the object is omitted on his account, so there is no feedback loop between model and object.

Rosen’s model system Originally due to Hertz (see Pattee approach), but Rosen seems to have come up with it independently The basic idea is that we have – A natural (including man-made) system we wish to model, which has a causal structure – A model, which is a set of logical relations, sometimes called a structure in logic (models in logic are things that have a structure) A model is accurate inasmuch as its logical structure maps the causal structure of the intended system (perhaps incompletely, or only in certain respects). This permits self-modelling, required for strong anticipation, which I will discuss in a later class. Generic models have no specific conditions and apply to most systems of their kind, given initial and boundary conditions. Models of complex systems, however, are not generic, and depend on specific dynamical conditions because system laws and boundary conditions cannot be separated. I will discuss this further in a later class on emergence.

Rosen: Modelling a formal system

Rosen: Modelling a Natural System

Explanations of complexly organized systems (and properties) Emergence and self-organization are closely linked, and I will assume that spontaneous self-organization is the source of emergent structures and processes. I will deal with this more in a later class. Organization can appear from previous organization, or through emergence. Emergence explains new organization as a production of self- organizing processes (e.g., Kauffman, though he does not carefully distinguish between self reorganization and self-organization). Robert Rosen (Life Itself) gave conditions for emergence (nonmechanism) in terms of a) properties of models and b) properties of networks, and claimed these are equivalent. The network property implying emergence is closure to efficient causation. However this is not a readily observable condition, since there may well be missed open network descriptions for a network with closed loops. One other problem is that no complexly organized system can be modeled with a superposition of simple models.

Testing for complex organization However models using must be tested independently. Otherwise we can only invoke the confirmation of the model to the real systems in question. However, since predictability and reducibility fail in emergence explanations, how to test is not straight forward. We must pay attention to the dynamics of the hypothesized model, and see whether or not the dynamics of the actual system support a complex model or not. The best we can do is to test for the right sort of dynamical conditions in the system for the hypothesis to be true. Only dynamical conditions have effects, and can be controlled. Anything that involves no dynamical conditions is not subject to manipulation, and is not accessible to us through experimental method (or observation). Typically we can either determine the dynamical properties of an emergent system by looking at the basic forces involved by the type of objects involved, or by taking the system apart and examining the sorts of forces involved, assuming that the forces do not mysteriously change in the assembled system. In many cases this works.

Testing complexity in physics Solar system harmonics 1.Moon (1:1 orbit to rotation) 2.Jupiter’s moons (in various harmonies with each other) 3.Mercury (2:3 orbit to rotation) Laplace explained the stability of such systems, but even in his own time people questioned how they came to be that way. (The time scale problem.) Chaotic regions in phase space are resolved through dissipation (self- reorganization) to form harmonic orbits. Selection of orbit is nonreducible and nonpredictable. The dynamics are Lagrangian, but nonHamiltonian. Lesson: dissipation is required for self organization; the system must be nonHamiltonian, and not a step function. I will follow this more in the discussion of emergence

Testing organization in development in sea urchins Network emergence in the Sea Urchin A Genomic Regulatory Network for Development Abstract Development of the body plan is controlled by large networks of regulatory genes. A gene regulatory network that controls the specification of endoderm and mesoderm in the sea urchin embryo is summarized here. The network was derived from large-scale perturbation analyses, in combination with computational methodologies, genomic data, cis-regulatory analysis, and molecular embryology. The network contains over 40 genes at present, and each node can be directly verified at the DNA sequence level by cis-regulatory analysis. Its architecture reveals specifc and general aspects of development, such as how given cells generate their ordained fates in the embryo and why the process moves inexorably forward in developmental time. “But even from the first-stage model, But even from the first-stage model,which just states the interactions that occur at each node, there emerge system properties that can only be perceived at the network level. which just states the interactions that occur at each node, there emerge system properties that can only be perceived at the network level.” Eric H. Davidson, et al, 1 MARCH 2002 VOL 295 SCIENCE pp www.sciencemag.org

The test: look for closed loops This suggests that there are emergent properties in the network, and would be a confirming instance. Is there a test of this hypothesis? Assembly of parts from earlier subnetworks, assembled themselves from smaller genetically translated parts. This seems not to be the case, given the stages mapped and their dynamical relationships. Self reorganization. This is possible on the evidence in the paper, with constructing parts being dissipated as development progresses. Spontaneous self organization. This is also possible on the evidence in the paper. As above producing processes dissipate some of the order. In order to distinguish between reorganization and spontaneous self organization, further studies are required. But the case is a candidate, and the test could be on the mapped processes with further analysis for whether there is the production of new information, or all information is in the original protoplasm and genetic information. Similar considerations apply to the evolutionary origin of the network properties, but testing will require comparison across other families (all sea urchins have the same first 16 stages).

Rotating flagellae Claimed by creationists (e.g., Behe) to be impossible to evolve. But actually involve only two genetic changes. The resulting diagram of protein interactions shows the characteristic closed loops of a self- organized system. Is it a good test of self-organization?

Copyright ©2007 by the National Academy of Sciences Liu, Renyi and Ochman, Howard (2007) Proc. Natl. Acad. Sci. USA 104, Fig. 1. Distribution of flagellar proteins (excluding chemotaxis proteins) among flagellated bacterial species

Copyright ©2007 by the National Academy of Sciences Liu, Renyi and Ochman, Howard (2007) Proc. Natl. Acad. Sci. USA 104, Fig. 2. Congruence between species tree and flagellar protein tree

Copyright ©2007 by the National Academy of Sciences Liu, Renyi and Ochman, Howard (2007) Proc. Natl. Acad. Sci. USA 104, Fig. 3. Network of relationships among flagellar core proteins

Copyright ©2007 by the National Academy of Sciences Liu, Renyi and Ochman, Howard (2007) Proc. Natl. Acad. Sci. USA 104, Fig. 4. Protein sequence similarity among the proximal rod protein FlgF, the distal rod protein FlgG, and the hook protein FlgE in E. coli

Testing complexity: accomplished? Does the explanation require some form of self organization? The closed loops strongly suggests this, but a better explanation of the processes would strengthen the hypothesis of self-organization. The evidence is not sufficient for emergence. It is compatible, as it stands now. The hypothesis that it is due to gradualist selection on large changes in the genome due to duplication is possible, and is the current best explanation. Further testing is required for this hypothesis as well.

Conclusions Organized complexity comes from prior organized complexity or from self organization. Self organization models have been used, and are in various degrees of confirmation and testing. They are intrinsically difficult to test. Organized complexity coming from pre-existing should be traceable to pre- existing organized complexity. This is required for testing the hypothesis of pre-existing organized complexity as the source of later organized complexity (both in development and evolution). Darwinian selection supposes complexity arises though the accumulation of environmental influences on greater complexity produced by organisms. However, sufficient pre-existing complexity must exist to account for the accumulation of functional complexity. Self-organization does not require either pre-existing complexity or organization, but does require self-organization conditions. All of the required conditions can be determined by observations, so potentially it is possible to test among good version of the relevant hypotheses.