Autonomy and hypersets

This paper has two primary aims. The first is to provide an introductory discussion of hyperset theory and its usefulness for modeling complex systems. The second aim is to provide a hyperset analysis of several perspectives on autonomy: Robert Rosen's metabolism-repair systems and his claim that living things are closed to efficient cause, Maturana and Varela's autopoietic systems, and Kauffman's cataytically closed systems. Consequences of the hyperset models for Rosen's claim that autonomous systems have non-computable models are discussed.     

Modelling Primate Behavioral Ecology

Models play an important role in any mature science because they force us to make explicit our assumptions about how a phenomenon works and allow us to explore the way in which different variables influence a complex biological system. I review the principal kinds of models that could be used to study primate behavior and ecology: linear programming models, systems models, optimality models, stochastic dynamic programming models and agent-based simulation models. Although less use has been made of modelling in primatology than in some other areas of behavioral ecology, there is considerable scope for exploiting the predictive and explanatory power of models in the field.     

A Rosen etymology

This essay contains a few of my interpretations of Robert Rosen's conception of Nature. I shall study the four notions that form the core of his whole-lifetime's scientific work: simple system, mechanism, complex system, and organism. Their set-theoretic interconnections culminate in Rosen's new taxonomy of natural systems.     

Organizational invariance and metabolic closure: analysis in terms of (M,R) systems

This article analyses the work of Robert Rosen on an interpretation of metabolic networks that he called (M,R) systems. His main contribution was an attempt to prove that metabolic closure (or metabolic circularity) could be explained in purely formal terms, but his work remains very obscure and we try to clarify his line of thought. In particular, we clarify the algebraic formulation of (M,R) systems in terms of mappings and sets of mappings, which is grounded in the metaphor of metabolism as a mathematical mapping. We define Rosen's central result as the mathematical expression in which metabolism appears as a mapping f that is the solution to a fixed-point functional equation. Crucially, our analysis reveals the nature of the mapping, and shows that to have a solution the set of admissible functions representing a metabolism must be drastically smaller than Rosen's own analysis suggested that it needed to be. For the first time, we provide a mathematical example of an (M,R) system with organizational invariance, and we analyse a minimal (three-step) autocatalytic set in the context of (M,R) systems. In addition, by extending Rosen's construction, we show how one might generate self-referential objects f with the remarkable property f(f)=f, where f acts in turn as function, argument and result. We conclude that Rosen's insight, although not yet in an easily workable form, represents a valuable tool for understanding metabolic networks.     

An abstract cell model that describes the self-organization of cell function in living systems

The principal aim of systems biology is to search for general principles that govern living systems. We develop an abstract dynamic model of a cell, rooted in Mesarovi? and Takahara's general systems theory. In this conceptual framework the function of the cell is delineated by the dynamic processes it can realize. We abstract basic cellular processes, i.e., metabolism, signalling, gene expression, into a mapping and consider cell functions, i.e., cell differentiation, proliferation, etc. as processes that determine the basic cellular processes that realize a particular cell function. We then postulate the existence of a 'coordination principle' that determines cell function. These ideas are condensed into a theorem: If basic cellular processes for the control and regulation of cell functions are present, then the coordination of cell functions is realized autonomously from within the system. Inspired by Robert Rosen's notion of closure to efficient causation, introduced as a necessary condition for a natural system to be an organism, we show that for a mathematical model of a self-organizing cell the associated category must be cartesian closed. Although the semantics of our cell model differ from Rosen's (M,R)-systems, the proof of our theorem supports (in parts) Rosen's argument that living cells have non-simulable properties. Whereas models that form cartesian closed categories can capture self-organization (which is a, if not the, fundamental property of living systems), conventional computer simulations of these models (such as virtual cells) cannot. Simulations can mimic living systems, but they are not like living systems.     

Re-mapping Robert Rosen's (M,R)-systems

The central concern of this paper is to re-evaluate Rosen's replicating (M,R)-systems, presented in his book 'Life Itself ', where M and R signify metabolism and repair, respectively. We look anew at Rosen's model of an organism in the light of extensive research into natural hierarchical systems, and the paper presents conclusions drawn from a comparison between Rosen's relational model and that of a birational complementary natural hierarchy. We accept that Rosen's relational model provides a useful stepping stone to understanding the nature of life, but also suggest that it induces potentially digressive conclusions. We conclude that a binary segregation of relational assemblies into mechanisms and organisms is insufficient, and indicate how a threefold segregation throws new light on Rosen's model. An organism is not 'the complement of a mechanism': the complement of a mechanism is its ecosystem. An organism is the 'complex interface' between mechanism and ecosystem.     

Laws, constraints, and the modeling relation--history and interpretations

The modeling relation and models of complex systems expressed by non-integrable constraints were developed during ca. 1970-1987, when I worked most closely with Robert Rosen. I contrast the modeling relation within the organism itself as a necessary condition for life and evolution, as Rosen developed it in his fundamental work 'Anticipatory Systems', with the modeling relation within our brain as a necessary condition for understanding life, as Rosen developed it in 'Life Itself'. Our approaches to the modeling relation were complementary. Rosen focused on the formal relational conditions necessary for life, and on the limitations that formal mathematical-symbol systems impose on our models. I focused on the physical conditions necessary for these abstract relations to be realized, and on the symbolic control in organisms that allows open-ended evolution. I contrast Rosen's views on physics and evolution in 'Anticipatory Systems' and later papers with his views in 'Life Itself', and I speculate on why they differ so greatly.     

A complete categorization of multiscale models of infectious disease systems

Modelling of infectious disease systems has entered a new era in which disease modellers are increasingly turning to multiscale modelling to extend traditional modelling frameworks into new application areas and to achieve higher levels of detail and accuracy in characterizing infectious disease systems. In this paper we present a categorization framework for categorizing multiscale models of infectious disease systems. The categorization framework consists of five integration frameworks and five criteria. We use the categorization framework to give a complete categorization of host-level immuno-epidemiological models (HL-IEMs). This categorization framework is also shown to be applicable in categorizing other types of multiscale models of infectious diseases beyond HL-IEMs through modifying the initial categorization framework presented in this study. Categorization of multiscale models of infectious disease systems in this way is useful in bringing some order to the discussion on the structure of these multiscale models.     

New computer architectures as tools for ecological thought

Recent achievements of computer science provide unrivaled power for the advancement of ecology. This power is not merely computational: parallel computers, having hierarchical organization as their architectural principle, also provide metaphors for understanding complex systems. In this sense they might play for a science of ecological complexity a role like equilibrium-based metaphors had in the development of dynamic systems ecology. Parallel computers provide this opportunity through an informational view of ecological reality and multilevel modelling paradigms. Spatial and individual-oriented models allow application and full understanding of the new metaphors in the ecological context.     

Hybrid semi-parametric mathematical systems: bridging the gap between systems biology and process engineering

Systems biology is an integrative science that aims at the global characterization of biological systems. Huge amounts of data regarding gene expression, proteins activity and metabolite concentrations are collected by designing systematic genetic or environmental perturbations. Then the challenge is to integrate such data in a global model in order to provide a global picture of the cell. The analysis of these data is largely dominated by nonparametric modelling tools. In contrast, classical bioprocess engineering has been primarily founded on first principles models, but it has systematically overlooked the details of the embedded biological system. The full complexity of biological systems is currently assumed by systems biology and this knowledge can now be taken by engineers to decide how to optimally design and operate their processes. This paper discusses possible methodologies for the integration of systems biology and bioprocess engineering with emphasis on applications involving animal cell cultures. At the mathematical systems level, the discussion is focused on hybrid semi-parametric systems as a way to bridge systems biology and bioprocess engineering.     

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.     

Causality and complexity: the myth of objectivity in science

Two distinctly different worldviews dominate today's thinking in science and in the world of ideas outside of science. Using the approach advocated by Robert M. Hutchins, it is possible to see a pattern of interaction between ideas in science and in other spheres such as philosophy, religion, and politics. Instead of compartmentalizing these intellectual activities, it is worthwhile to look for common threads of mutual influence. Robert Rosen has created an approach to scientific epistemology that might seem radical to some. However, it has characteristics that resemble ideas in other fields, in particular in the writings of George Lakoff, Leo Strauss, and George Soros. Historically, the atmosphere at the University of Chicago during Hutchins' presidency gave rise to Rashevsky's relational biology, which Rosen carried forward. Strauss was writing his political philosophy there at the same time. One idea is paramount in all this, and it is Lakoff who gives us the most insight into how the worldviews differ using this idea. The central difference has to do with causality, the fundamental concept that we use to build a worldview. Causal entailment has two distinct forms in Lakoff 's analysis: direct causality and complex causality. Rosen's writings on complexity create a picture of complex causality that is extremely useful in its detail, grounding in the ideas of Aristotle. Strauss asks for a return to the ancients to put philosophy back on track. Lakoff sees the weaknesses in Western philosophy in a similar way, and Rosen provides tools for dealing with the problem. This introduction to the relationships between the thinking of these authors is meant to stimulate further discourse on the role of complex causal entailment in all areas of thought, and how it brings them together in a holistic worldview. The worldview built on complex causality is clearly distinct from that built around simple, direct causality. One important difference is that the impoverished causal entailment that accompanies the machine metaphor in science is unable to give us a clear way to distinguish living organisms from machines. Complex causality finds a dichotomy between organisms, which are closed to efficient cause, and machines, which require entailment from outside. An argument can be made that confusing living organisms with machines, as is done in the worldview using direct cause, makes religion a necessity to supply the missing causal entailment.     

Neural hierarchical models of ecological populations

Neural networks are increasingly being used in science to infer hidden dynamics of natural systems from noisy observations, a task typically handled by hierarchical models in ecology. This article describes a class of hierarchical models parameterised by neural networks – neural hierarchical models. The derivation of such models analogises the relationship between regression and neural networks. A case study is developed for a neural dynamic occupancy model of North American bird populations, trained on millions of detection/non‐detection time series for hundreds of species, providing insights into colonisation and extinction at a continental scale. Flexible models are increasingly needed that scale to large data and represent ecological processes. Neural hierarchical models satisfy this need, providing a bridge between deep learning and ecological modelling that combines the function representation power of neural networks with the inferential capacity of hierarchical models.     

Some Aspects of the Biology of Pilaira anomala—An Extremely Versatile Fungus

Abstract

This article describes the rationale for mathematical modelling and computer simulation of ecological systems, and suggests reasons why this is still a relatively unexplored field of biological education. Recently, inexpensive yet extremely versatile modular analogue computing systems have become available from UK suppliers of science teaching equipment. These are suggested as possible alternatives to digital machines for those wishing to introduce modelling and simulation into their teaching. The behaviour of an analogue computer and the operations it performs are described. The application of these ideas to the teaching of population ecology is then illustrated through analogue simulations of exponential growth, logistic growth, and predator-prey interactions. Typical results for each of these three models are presented.     

Tuning the cochlea: wave-mediated positive feedback between cells

Frequency analysis by the mammalian cochlea is traditionally thought to occur via a hydrodynamically coupled ‘travelling wave’ along the basilar membrane. A persistent difficulty with this picture is how sharp tuning can emerge. This paper proposes, and models, a supplementary or alternative mechanism: it supposes that the cochlea analyses sound by setting up standing waves between parallel rows of outer hair cells. In this scheme, multiple cells mutually interact through positive feedback of wave-borne energy. Analytical modelling and numerical evaluation presented here demonstrate that this can provide narrow-band frequency analysis. Graded cochlear tuning will then rely on the distance between rows becoming greater as distance from the base increases (as exhibited by the actual cochlea) and on the wave’s phase velocity becoming slower. In effect, tuning is now a case of varying the feedback delay between the rows, and a prime candidate for a wave exhibiting suitably graded phase velocity—a short-wavelength ‘squirting wave’—is identified and used in the modelling. In this way, resonance between rows could supply both amplification and high Q, characteristics underlying the ‘cochlear amplifier’—the device whose action has long been evident to auditory science but whose anatomical basis and mode of operation are still obscure.     

Robert Rosen in the age of systems biology

The widespread use of the term Systems Biology (SB) signals a welcome recognition that organisms must be understood as integrated systems. Although just what this is taken to mean varies from one group to another, it generally implies a focus on biological functions and processes rather than on biological parts and a reliance on mathematical modeling to arrive at an understanding of these biological processes based on biological observations or measurements. SB, thus, falls directly in the line of reflection carried out by Robert Rosen throughout his work. In the present article, we briefly introduce the various currents of SB and then point out several ways Rosen's work can be used to avoid certain pitfalls associated with the use of dynamical systems models for the study of complex systems, as well as to inspire a productive path forward based on loosely organized cooperation among dispersed laboratories.     

On the neural enrichment of economic models: recasting the challenge

In a recent article in this Journal, Fumagalli (Biol Philos 26:617–635, 2011) argues that economists are provisionally justified in resisting prominent calls to integrate neural variables into economic models of choice. In other articles, various authors engage with Fumagalli’s argument and try to substantiate three often-made claims concerning neuroeconomic modelling. First, the benefits derivable from neurally informing some economic models of choice do not involve significant tractability costs. Second, neuroeconomic modelling is best understood within Marr’s three-level of analysis framework for information-processing systems. And third, neural findings enable choice modellers to confirm the causal relevance of variables posited by competing economic models, identify causally relevant variables overlooked by existing models, and explain observed behavioural variability better than standard economic models. In this paper, I critically examine these three claims and respond to the related criticisms of Fumagalli’s argument. Moreover, I qualify and extend Fumagalli’s account of how trade-offs between distinct modelling desiderata hamper neuroeconomists’ attempts to improve economic models of choice. I then draw on influential neuroeconomic studies to argue that even the putatively best available neural findings fail to substantiate current calls for a neural enrichment of economic models.