A dynamical systems perspective on vegetation theory

A dynamical systems perspective is employed to develop a simple conceptual model of vegetation and environment as coupled dynamical systems. The conceptual model characterizes the influence of environment on vegetation, the effect of vegetation on the environment, and the subsequent response of vegetation to the modified environment. Vegetation and environmental dynamics are modeled as trajectories in complementary state spaces, with the trajectories jointly determined by the position of a given site in both spaces. The vegetation and environment state spaces are coupled by the physiological requirements of the component species and the modification of environment by vegetation. From a dynamical systems perspective, current vegetation theory and analyses overemphasize environmental determination of vegetation composition and neglect the effects of vegetation on environment. A dynamical systems perspective is capable of synthesizing previous concepts of vegetation; the continuum and community type concepts are possible consequences of site specific differences in vegetation metabolism and environmental plasticity.I would like to acknowledge the helpful comments and criticisms of Drs G. Cottam, J. D. Aber, T. F. H. Allen, R. P. McIntosh, C. G. Lorimer, and anonymous reviewers.I would like to thank the University of Wisconsin, Madison for a fellowship which supported this research. This paper is dedicated with great respect and gratitude to Professor G. Cottam on the occasion of his retirement from the University of Wisconsin.     

Global view of bionetwork dynamics: adaptive landscape

Based on recent work, I will give a nontechnical brief review of a powerful quantitative concept in biology, adaptive landscape, ini- tially proposed by S. Wright over 70 years ago, reintroduced by one of the founders of molecular biology and by others in different bio- logical contexts, but apparently forgotten by modem biologists for many years. Nevertheless, this concept finds an increasingly important role in the development of systems biology and bionetwork dynamics modeling, from phage lambda genetic switch to endogenous net- work for cancer genesis and progression. It is an ideal quantification to describe the robustness and stability of bionetworks. Here, I will first introduce five landmark proposals in biology on this concept, to demonstrate an important common thread in theoretical biology. Then I will discuss a few recent results, focusing on the studies showing theoretical consistency of adaptive landscape. From the perspec- tive of a working scientist and of what is needed logically for a dynamical theory when confronting empirical data, the adaptive landscape is useful both metaphorically and quantitatively, and has captured an essential aspect of biological dynamical processes. Though at the theoretical level the adaptive landscape must exist and it can be used across hierarchical boundaries in biology, many associated issues are indeed vague in their initial formulations and their quantitative realizations are not easy, and are good research topics for quantitative biologists. I will discuss three types of open problems associated with the adaptive landscape in a broader perspective.     

Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep

Under selected conditions, nonlinear dynamical systems, which can be described by deterministic models, are able to generate so-called deterministic chaos. In this case the dynamics show a sensitive dependence on initial conditions, which means that different states of a system, being arbitrarily close initially, will become macroscopically separated for sufficiently long times. In this sense, the unpredictability of the EEG might be a basic phenomenon of its chaotic character. Recent investigations of the dimensionality of EEG attractors in phase space have led to the assumption that the EEG can be regarded as a deterministic process which should not be mistaken for simple noise. The calculation of dimensionality estimates the degrees of freedom of a signal. Nevertheless, it is difficult to decide from this kind of analysis whether a process is quasiperiodic or chaotic. Therefore, we performed a new analysis by calculating the first positive Lyapunov exponent L ₁ from sleep EEG data. Lyapunov exponents measure the mean exponential expansion or contraction of a flow in phase space. L ₁ is zero for periodic as well as quasiperiodic processes, but positive in the case of chaotic processes expressing the sensitive dependence on initial conditions. We calculated L ₁ for sleep EEG segments of 15 healthy men corresponding to the sleep stages I, II, III, IV, and REM (according to Rechtschaffen and Kales). Our investigations support the assumption that EEG signals are neither quasiperiodic waves nor a simple noise. Moreover, we found statistically significant differences between the values of L ₁ for different sleep stages. All together, this kind of analysis yields a useful extension of the characterization of EEG signals in terms of nonlinear dynamical system theory.     

Agential autonomy and biological individuality

What is a biological individual? How are biological individuals individuated? How can we tell how many individuals there are in a given assemblage of biological entities? The individuation and differentiation of biological individuals are central to the scientific understanding of living beings. I propose a novel criterion of biological individuality according to which biological individuals are autonomous agents. First, I articulate an ecological–dynamical account of natural agency according to which, agency is the gross dynamical capacity of a goal-directed system to bias its repertoire to respond to its conditions as affordances. Then, I argue that agents or agential dynamical systems can be agentially dependent on, or agentially autonomous from, other agents and that this agential dependence/autonomy can be symmetrical or asymmetrical, strong or weak. Biological individuals, I propose, are all and only those agential dynamical systems that are strongly agentially autonomous. So, to determine how many individuals there are in a given multiagent aggregate, such as multicellular organism, a colony, symbiosis, or a swarm, we first have to identify how many agential dynamical systems there are, and then what their relations of agential dependence/autonomy are. I argue that this criterion is adequate to the extent that it vindicates the paradigmatic cases, and explains why the paradigmatic cases are paradigmatic, and why the problematic cases are problematic. Finally, I argue for the importance of distinguishing between agential and causal dependence and show the relevance of agential autonomy for understanding the explanatory structure of evolutionary developmental biology.     

Approximation for limit cycles and their isochrons

Local analysis of trajectories of dynamical systems near an attractive periodic orbit displays the notion of asymptotic phase and isochrons. These notions are quite useful in applications to biosciences. In this note, we give an expression for the first approximation of equations of isochrons in the setting of perturbations of polynomial Hamiltonian systems. This method can be generalized to perturbations of systems that have a polynomial integral factor (like the Lotka-Volterra equation).     

Evolving experience-dependent robust behaviour in embodied agents

In this work, based on behavioural and dynamical evidence, a study of simulated agents with the capacity to change feedback from their bodies to accomplish a one-legged walking task is proposed to understand the emergence of coupled dynamics for robust behaviour. Agents evolve with evolutionary-defined biases that modify incoming body signals (sensory offsets). Analyses on whether these agents show further dependence to their environmental coupled dynamics than others with no feedback control is described in this article. The ability to sustain behaviours is tested during lifetime experiments with mutational and sensory perturbations after evolution. Using dynamical systems analysis, this work identifies conditions for the emergence of dynamical mechanisms that remain functional despite sensory perturbations. Results indicate that evolved agents with evolvable sensory offset depends not only on where in neural space the state of the neural system operates, but also on the transients to which the inner-system was being driven by sensory signals from its interactions with the environment, controller, and agent body. Experimental evidence here leads discussions on a dynamical systems perspective on behavioural robustness that goes beyond attractors of controller phase space.     

Robustness, evolvability, and neutrality

Biological systems, from macromolecules to whole organisms, are robust if they continue to function, survive, or reproduce when faced with mutations, environmental change, and internal noise. I focus here on biological systems that are robust to mutations and ask whether such systems are more or less evolvable, in the sense that they can acquire novel properties. The more robust a system is, the more mutations in it are neutral, that is, without phenotypic effect. I argue here that such neutral change--and thus robustness--can be a key to future evolutionary innovation, if one accepts that neutrality is not an essential feature of a mutation. That is, a once neutral mutation may cause phenotypic effects in a changed environment or genetic background. I argue that most, if not all, neutral mutations are of this sort, and that the essentialist notion of neutrality should be abandoned. This perspective reconciles two opposing views on the forces dominating organismal evolution, natural selection and random drift: neutral mutations occur and are especially abundant in robust systems, but they do not remain neutral indefinitely, and eventually become visible to natural selection, where some of them lead to evolutionary innovations.     

Modeling of dynamical systems through deep learning

This review presents a modern perspective on dynamical systems in the context of current goals and open challenges. In particular, our review focuses on the key challenges of discovering dynamics from data and finding data-driven representations that make nonlinear systems amenable to linear analysis. We explore various challenges in modern dynamical systems, along with emerging techniques in data science and machine learning to tackle them. The two chief challenges are (1) nonlinear dynamics and (2) unknown or partially known dynamics. Machine learning is providing new and powerful techniques for both challenges. Dimensionality reduction methods are used for projecting dynamical methods in reduced form, and these methods perform computational efficiency on real-world data. Data-driven models drive to discover the governing equations and give laws of physics. The identification of dynamical systems through deep learning techniques succeeds in inferring physical systems. Machine learning provides advanced new and powerful algorithms for nonlinear dynamics. Advanced deep learning methods like autoencoders, recurrent neural networks, convolutional neural networks, and reinforcement learning are used in modeling of dynamical systems.     

From the science of learning (and development) to learning engineering

ABSTRACT

In this issue, Cantor and colleagues synthesize a broad representation of the literature on the science of learning, and how learning changes over the course of development. Their perspective highlights three important factors about the emerging field of science of learning and development: (1) that it draws insights from increasingly diverse fields of research inquiry, from neuroscience and social science to computer science and adversity science; (2) that it provides a means to understand principles that generalize across learners, and yet also allow individual differences in learning to emerge and inform; and (3) that it recognizes that learning occurs in context, and is thus a shared responsibility between the learner, the instructor, and the environment. Here I discuss how this complex systems dynamical perspective can be integrated with the emerging framework of ‘learning engineering’ to provide a blueprint for significant innovations in education.     

Learning shapes spontaneous activity itinerating over memorized states

Learning is a process that helps create neural dynamical systems so that an appropriate output pattern is generated for a given input. Often, such a memory is considered to be included in one of the attractors in neural dynamical systems, depending on the initial neural state specified by an input. Neither neural activities observed in the absence of inputs nor changes caused in the neural activity when an input is provided were studied extensively in the past. However, recent experimental studies have reported existence of structured spontaneous neural activity and its changes when an input is provided. With this background, we propose that memory recall occurs when the spontaneous neural activity changes to an appropriate output activity upon the application of an input, and this phenomenon is known as bifurcation in the dynamical systems theory. We introduce a reinforcement-learning-based layered neural network model with two synaptic time scales; in this network, I/O relations are successively memorized when the difference between the time scales is appropriate. After the learning process is complete, the neural dynamics are shaped so that it changes appropriately with each input. As the number of memorized patterns is increased, the generated spontaneous neural activity after learning shows itineration over the previously learned output patterns. This theoretical finding also shows remarkable agreement with recent experimental reports, where spontaneous neural activity in the visual cortex without stimuli itinerate over evoked patterns by previously applied signals. Our results suggest that itinerant spontaneous activity can be a natural outcome of successive learning of several patterns, and it facilitates bifurcation of the network when an input is provided.     

Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.     

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.     

Identifying and evaluating layers of vulnerability – a way forward

“Vulnerability” is a key concept for research ethics and public health ethics. This term can be discussed from either a conceptual or a practical perspective. I previously proposed the metaphor of layers to understand how this concept functions from the conceptual perspective in human research. In this paper I will clarify how my analysis includes other definitions of vulnerability. Then, I will take the practical‐ethical perspective, rejecting the usefulness of taxonomies to analyze vulnerabilities. My proposal specifies two steps and provides a procedural guide to help rank layers. I introduce the notion of cascade vulnerability and outline the dispositional nature of layers of vulnerability to underscore the importance of identifying their stimulus condition. In addition, I identify three kinds of obligations and some strategies to implement them. This strategy outlines the normative force of harmful layers of vulnerability. It offers concrete guidance. It contributes substantial content to the practical sphere but it does not simplify or idealize research subjects, research context or public health challenges.     

Menstruation, perimenopause, and chaos theory

This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided.     

An optimization framework of biological dynamical systems

Different biological dynamics are often described by different mathematical equations. On the other hand, some mathematical models describe many biological dynamics universally. Here, we focus on three biological dynamics: the Lotka-Volterra equation, the Hopfield neural networks, and the replicator equation. We describe these three dynamical models using a single optimization framework, which is constructed with employing the Riemannian geometry. Then, we show that the optimization structures of these dynamics are identical, and the differences among the three dynamics are only in the constraints of the optimization. From this perspective, we discuss the unified view for biological dynamics. We also discuss the plausible categorizations, the fundamental nature, and the efficient modeling of the biological dynamics, which arise from the optimization perspective of the dynamical systems.     

Causality in Complex Systems

Systems involving many interacting variables are at the heart of the natural and social sciences. Causal language is pervasive in the analysis of such systems, especially when insight into their behavior is translated into policy decisions. This is exemplified by economics, but to an increasing extent also by biology, due to the advent of sophisticated tools to identify the genetic basis of many diseases. It is argued here that a regularity notion of causality can only be meaningfully defined for systems with linear interactions among their variables. For the vastly more important class of nonlinear systems, no such notion is likely to exist. This thesis is developed with examples of dynamical systems taken mostly from mathematical biology. It is discussed with particular reference to the problem of causal inference in complex genetic systems, systems for which often only statistical characterizations exist.     

In Defense of Some `Cartesian' Assumptions Concerning the Brain and Its Operation

I argue against a growing radical trend in current theoretical cognitive science that moves from the premises of embedded cognition, embodied cognition, dynamical systems theory and/or situated robotics to conclusions either to the effect that the mind is not in the brain or that cognition does not require representation, or both. I unearth the considerations at the foundation of this view: Haugeland's bandwidth-component argument to the effect that the brain is not a component in cognitive activity, and arguments inspired by dynamical systems theory and situated robotics to the effect that cognitive activity does not involve representations. Both of these strands depend not only on a shift of emphasis from higher cognitive functions to things like sensorimotor processes, but also depend on a certain understanding of how sensorimotor processes are implemented - as closed-loop control systems. I describe a much more sophisticated model of sensorimotor processing that is not only more powerful and robust than simple closed-loop control, but for which there is great evidence that it is implemented in the nervous system. The is the emulation theory of representation, according to which the brain constructs inner dynamical models, or emulators, of the body and environment which are used in parallel with the body and environment to enhance motor control and perception and to provide faster feedback during motor processes, and can be run off-line to produce imagery and evaluate sensorimotor counterfactuals. I then show that the emulation framework is immune to the radical arguments, and makes apparent why the brain is a component in the cognitive activity, and exactly what the representations are in sensorimotor control.     

Simulation modelling of ecological hierarchies in constructive dynamical systems

Organized complexity is a characteristic feature of ecological systems with heterogeneous components interacting at several spatio-temporal scales. The hierarchy theory is a powerful epistemological framework to describe such systems by decomposing them vertically into levels and horizontally into holons. It was at first developed in a temporal and functional perspective and then, in the context of landscape ecology, extended to a spatial and structural approach. So far, most ecological applications of this theory were restricted to observational purposes, using multi-scale analysis to describe hierarchies. In spite of an increasing attention to dynamics of hierarchically structured ecological systems, current simulation models are still very limited in their representation of self-organization in complex adaptive systems. An ontological conceptualization of the hierarchy theory is outlined, focusing on key concepts, such as levels of organization and the compound and component faces of the holons. Various existing formalisms are currently used in simulation modelling, such as system dynamics, discrete event and agent based paradigms. Their ability to express the hierarchical organization of dynamical ecological systems is discussed. It turns out that a multi-modelling approach linking all these formalisms and oriented toward the specification of a constructive dynamical system would be able to express the dynamical structure of the hierarchy (creation, destruction and change of holons) and the functional and structural links between levels of organization.