Darwinian selection leads to Gaia

The Gaia hypothesis, in its strongest form, states that the Earth's atmosphere, oceans, and biota form a tightly coupled system that maintains environmental conditions close to optimal for life. According to Gaia theory, optimal conditions are intrinsic, immutable properties of living organisms. It is assumed that the role of Darwinian selection is to favor organisms that act to stabilize environmental conditions at these optimal levels. In this paper, an alternative form of Gaia theory based on more traditional Darwinian principles is proposed. In the new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions. A simple Daisyworld model is used to illustrate this convergence phenomenon. Sensitivity analysis of the Daisyworld model suggests that in stable ecosystems, the convergence of equilibrium and optimal conditions is inevitable, provided there are no externally driven shocks to the system. The end result may appear to be the product of a cooperative venture, but is in fact the outcome of Darwinian selection acting upon "selfish" organisms.     

盖娅假说:在争议中发展

自从1972年Lovelock提出盖娅假说已经过去了40年,但围绕它的争议却从未停止过。盖娅假说在反对者的批评中与支持者的证明中不断发展。当前,最极端形式的盖娅假说基本上已被摒弃,尤其是那种明显带有目的论的说法。弱盖娅提出的"有机体可以影响他们的环境,有机体与环境的反馈耦合可以塑造两者的进化"这两个观点也已经是普遍接受的事实。除此之外,盖娅假说提出的其他3个命题却饱受争议。(1)内在平衡的盖娅:生物调节反馈有助于环境的内在平衡。反对者认为,生物反馈稳定全球环境的说法,与冰芯记录和大量的气候反馈研究结果相矛盾的。支持者认为,地球生物-环境系统的内在平衡可以产生于正负反馈的混合。盖娅假说关心的是地球几十亿年的历史,盖娅假说在较短时间尺度内可证伪,并不意味着其在较长时间尺度内也可证伪。(2)最优的盖娅:生物调节环境,使环境更加适合生物的生存。关于有机体的繁荣主要是由于他们对环境的改变,还是由于他们对环境的适应,目前尚未有结论。但盖娅的支持者认为,当生物-环境系统受到干扰或崩溃时,主导过程将显现。拥有较强环境反馈的系统,将易于快速过渡到新的状态,而由适应主导的过程将改变得较为平缓。反对者同意生物通过生物调节作用影响环境条件以使自身受益,但是生物首先要适应环境条件通过自然选择才能得以繁荣发展的。地球形成这样的环境条件,很可能纯粹是一种运气。(3)自然选择的盖娅:生物调节反馈产生于达尔文式的自然选择。反对者认为,"自然选择支持促进生命效应"的说法并非普遍有效,只有当遗传特征赋予携带者繁殖优势时,自然选择才会支持它。自然选择是机制,而非原则。支持者认为自然选择并不是盖娅系统环境调节的必要条件;基于副产品的自然选择,可以解决许多进化论学者提出的物种合作中的欺骗问题;自然选择并不总是支持促进生命的效应,但在当遗传特征使携带者相对非携带者受益时,自然选择可以使特征携带者产生进化优势。虽然争议依然存在并将持续下去,但作为假说生产者,盖娅假说已经证明了它的价值。但是在人类活动对生物圈影响不断增强的背景下,盖娅假说必须与人类活动相结合,否则必然走向衰落,并被其他理论或假说所替代。在此基础上,未来盖娅假说的研究者们需要继续努力探索可以应用于生物圈的一般性原则,并坚持系统性的思考方法。在具体的方法方面,可以利用系统度量指标;建立新的模型,尤其是建立关于生物地球化学循环过程的机理模型;搞清楚不同尺度过程的成本与收益。     

Biocomplexity: adaptive behavior in complex stochastic dynamical systems

Existing methods of complexity research are capable of describing certain specifics of bio systems over a given narrow range of parameters but often they cannot account for the initial emergence of complex biological systems, their evolution, state changes and sometimes-abrupt state transitions. Chaos tools have the potential of reaching to the essential driving mechanisms that organize matter into living substances. Our basic thesis is that while established chaos tools are useful in describing complexity in physical systems, they lack the power of grasping the essence of the complexity of life. This thesis illustrates sensory perception of vertebrates and the operation of the vertebrate brain. The study of complexity, at the level of biological systems, cannot be completed by the analytical tools, which have been developed for non-living systems. We propose a new approach to chaos research that has the potential of characterizing biological complexity. Our study is biologically motivated and solidly based in the biodynamics of higher brain function. Our biocomplexity model has the following features, (1) it is high-dimensional, but the dimensionality is not rigid, rather it changes dynamically; (2) it is not autonomous and continuously interacts and communicates with individual environments that are selected by the model from the infinitely complex world; (3) as a result, it is adaptive and modifies its internal organization in response to environmental factors by changing them to meet its own goals; (4) it is a distributed object that evolves both in space and time towards goals that is continually re-shaping in the light of cumulative experience stored in memory; (5) it is driven and stabilized by noise of internal origin through self-organizing dynamics. The resulting theory of stochastic dynamical systems is a mathematical field at the interface of dynamical system theory and stochastic differential equations. This paper outlines several possible avenues to analyze these systems. Of special interest are input-induced and noise-generated, or spontaneous state-transitions and related stability issues.     

Open systems living in a closed biosphere: a new paradox for the Gaia debate

While energetically open, the biosphere is appreciably closed from the standpoint of matter exchange. Matter cycling and recycling is hence a necessary and emergent property of the global-scale system known as Gaia. But how can an aggregate of open-system life forms have evolved and persisted for billions of years within a planetary system that is largely closed to matter influx and outflow? The puzzling nature of a closed yet persistent biosphere draws our attention to the course of evolution of fundamental metabolic strategies and matter-capture techniques. It suggests a facet of the Gaia hypothesis, framed in terms of persistence. The oceans, atmosphere, soils and biota constitute a complex system which maintains and adjusts matter cycling and recycling within the constraints of planetary closure such that open-system forms of life can persist. This weaker version of the Gaia hypothesis may be useful because it readily lends itself to at least one form of test. What is the solution to the closed biosphere puzzle, and does it indicate that Gaia merits status as a discrete entity? We suggest several disciplines within the field of biology that might provide tools and perspectives toward reaching a solution. These disciplines include artificial closed ecosystems, prokaryote evolution, the nexus of thermodynamics and evolutionary biology, and hierarchy theory in ecosystem modeling and evolution theory.     

Ways to test stochastic dynamic programming models empirically

Stochastic dynamic programming (SDP) models are widely used to predict optimal behavioural and life history strategies. We discuss a diversity of ways to test SDP models empirically, taking as our main illustration a model of the daily singing routine of birds. One approach to verification is to quantify model parameters, but most SDP models are schematic. Because predictions are therefore qualitative, testing several predictions is desirable. How state determines behaviour (the policy) is a central prediction that should be examined directly if both state and behaviour are measurable. Complementary predictions concern how behaviour and state change through time, but information is discarded by considering behaviour rather than state, by looking only at average state rather than its distribution, and by not following individuals. We identify the various circumstances in which an individual's state/behaviour at one time is correlated with its state/behaviour at a later time. When there are several state variables the relationships between them may be informative. Often model parameters represent environmental conditions that can also be viewed as state variables. Experimental manipulation of the environment has several advantages as a test, but a problem is uncertainty over how much the organism's policy will adjust. As an example we allow birds to use different assumptions about how well past weather predicts future weather. We advocate mirroring planned empirical investigations on the computer to investigate which manipulations and predictions will best test a model. Copyright 2000 The Association for the Study of Animal Behaviour.     

Do evolution and ecology need the Gaia hypothesis?

Gaia theory, which describes the life-environment system of the Earth as stable and self-regulating, has remained at the fringes of mainstream biological science owing to its historically inadequate definition and apparent incompatibility with individual-level natural selection. The key issue is whether and why the biosphere might tend towards stability and self-regulation. We review the various ways in which these issues have been addressed by evolutionary and ecological theory, and relate these to 'Gaia theory'. We then ask how this theory extends the perspectives offered by these disciplines, and how it might be tested by novel modelling approaches and laboratory experiments using emergent technologies.     

Social plasticity in fish: integrating mechanisms and function

Social plasticity is a ubiquitous feature of animal behaviour. Animals must adjust the expression of their social behaviour to the nuances of daily social life and to the transitions between life‐history stages, and the ability to do so affects their Darwinian fitness. Here, an integrative framework is proposed for understanding the proximate mechanisms and ultimate consequences of social plasticity. According to this framework, social plasticity is achieved by rewiring or by biochemically switching nodes of the neural network underlying social behaviour in response to perceived social information. Therefore, at the molecular level, it depends on the social regulation of gene expression, so that different brain genomic and epigenetic states correspond to different behavioural responses and the switches between states are orchestrated by signalling pathways that interface the social environment and the genotype. At the evolutionary scale, social plasticity can be seen as an adaptive trait that can be under positive selection when changes in the environment outpace the rate of genetic evolutionary change. In cases when social plasticity is too costly or incomplete, behavioural consistency can emerge by directional selection that recruits gene modules corresponding to favoured behavioural states in that environment. As a result of this integrative approach, how knowledge of the proximate mechanisms underlying social plasticity is crucial to understanding its costs, limits and evolutionary consequences is shown, thereby highlighting the fact that proximate mechanisms contribute to the dynamics of selection. The role of teleosts as a premier model to study social plasticity is also highlighted, given the diversity and plasticity that this group exhibits in terms of social behaviour. Finally, the proposed integrative framework to social plasticity also illustrates how reciprocal causation analysis of biological phenomena (i.e. considering the interaction between proximate factors and evolutionary explanations) can be a more useful approach than the traditional proximate–ultimate dichotomy, according to which evolutionary processes can be understood without knowledge on proximate causes, thereby black‐boxing developmental and physiological mechanisms.     

A mechanistic theory of personality‐dependent movement behaviour based on dynamic energy budgets

Consistent between‐individual differences in movement are widely recognised across taxa. In addition, foraging plasticity at the within‐individual level suggests a behavioural dependency on the internal energy demand. Because behaviour co‐varies with fast‐slow life history (LH) strategies in an adaptive context, as theoretically predicted by the pace‐of‐life syndrome hypothesis, mass/energy fluxes should link behaviour and its plasticity with physiology at both between‐ and within‐individual levels. However, a mechanistic framework driving these links in a fluctuating ecological context is lacking. Focusing on home range behaviour, we propose a novel behavioural‐bioenergetics theoretical model to address such complexities at the individual level based on energy balance. We propose explicit mechanistic links between behaviour, physiology/metabolism and LH by merging two well‐founded theories, the movement ecology paradigm and the dynamic energetic budget theory. Overall, our behavioural‐bioenergetics model integrates the mechanisms explaining how (1) behavioural between‐ and within‐individual variabilities connect with internal state variable dynamics, (2) physiology and behaviour are explicitly interconnected by mass/energy fluxes, and (3) different LHs may arise from both behavioural and physiological variabilities in a given ecological context. Our novel theoretical model reveals encouraging opportunities for empiricists and theoreticians to delve into the eco‐evolutionary processes that favour or hinder the development of between‐individual differences in behaviour and the evolution of personality‐dependent movement syndromes.     

A simple mathematical model of adaptation to high osmolarity in yeast

We present a simple ordinary differential equation (ODE) model of the adaptive response to an osmotic shock in the yeast Saccharomyces cerevisiae. The model consists of two main components. First, a biophysical model describing how the cell volume and the turgor pressure are affected by varying extra-cellular osmolarity. The second component describes how the cell controls the biophysical system in order to keep turgor pressure, or equivalently volume, constant. This is done by adjusting the glycerol production and the glycerol outflow from the cell. The complete model consists of 4 ODEs, 3 algebraic equations and 10 parameters. The parameters are constrained from various literature sources and estimated from new and previously published absolute time series data on intra-cellular and total glycerol. The qualitative behaviour of the model has been successfully tested on data from other genetically modified strains as well as data for different input signals. Compared to a previous detailed model of osmoregulation, the main strength of our model is its lower complexity, contributing to a better understanding of osmoregulation by focusing on relationships which are obscured in the more detailed model. Besides, the low complexity makes it possible to obtain more reliable parameter estimates.     

The uniqueness of biological self-organization: challenging the Darwinian paradigm

Here we discuss the challenge posed by self-organization to the Darwinian conception of evolution. As we point out, natural selection can only be the major creative agency in evolution if all or most of the adaptive complexity manifest in living organisms is built up over many generations by the cumulative selection of naturally occurring small, random mutations or variants, i.e., additive, incremental steps over an extended period of time. Biological self-organization—witnessed classically in the folding of a protein, or in the formation of the cell membrane—is a fundamentally different means of generating complexity. We agree that self-organizing systems may be fine-tuned by selection and that self-organization may be therefore considered a complementary mechanism to natural selection as a causal agency in the evolution of life. But we argue that if self-organization proves to be a common mechanism for the generation of adaptive order from the molecular to the organismic level, then this will greatly undermine the Darwinian claim that natural selection is the major creative agency in evolution. We also point out that although complex self-organizing systems are easy to create in the electronic realm of cellular automata, to date translating in silico simulations into real material structures that self-organize into complex forms from local interactions between their constituents has not proved easy. This suggests that self-organizing systems analogous to those utilized by biological systems are at least rare and may indeed represent, as pre-Darwinists believed, a unique ascending hierarchy of natural forms. Such a unique adaptive hierarchy would pose another major challenge to the current Darwinian view of evolution, as it would mean the basic forms of life are necessary features of the order of nature and that the major pathways of evolution are determined by physical law, or more specifically by the self-organizing properties of biomatter, rather than natural selection.     

A fitness based analysis of Daisyworld

The Gaia hypothesis [Lovelock, J., Margulis, L., 1974. Atmospheric homeostasis: the Gaia hypothesis. Tellus 26, 1], that the earth functions as a self-regulating system, has never sat particularly comfortably with ideas in mainstream biology [Anon, 2002. In pursuit of arrogant simplicities. Nature 416, 247]. A lack of any clear role for evolution in the model has led to claims of teleology-that self-regulation emerges because it is pre-ordained to do so [Doolittle, W.F., 1981. Is nature really motherly? CoEvol. Q. 58-63; Dawkins, R., 1979. The Extended Phenotype. Oxford University Press, Oxford]. The Daisyworld parable [Watson, A.J., Lovelock, J.E., 1983. Biological homeostasis of the global environment--the parable of Daisyworld. Tellus B 35, 284], a simple mathematical illustration of Gaia, went some way to addressing these critiques but, despite recent success in incorporating natural selection [Stocker, S.,1995. Regarding mutations in Daisyworld models. J. Theor. Biol. 175, 495; Lenton, T.M., 1998. Gaia and natural selection. Nature 394, 439; Lenton, T.M., Lovelock, J.E., 2001. Daisyworld revisited: quantifying biological effects on planetary self-regulation. Tellus B 53, 288; Wood, A.J., Ackland, G.J., Lenton, T.M., 2006. Mutation of albedo and growth response leads to oscillations in a spatial Daisyworld. J. Theor. Biol. 242, 188], it remains a widely held view that the ideas are inconsistent with biological principles. We show that standard methodology from quantitative genetics can be used to predict the stationary states and dynamic behaviour of Daisyworlds. The system regulates its temperature due to the low-level evolutionary dynamics of competition between the thermally coupled daisies, no higher level principle is invoked. A reconciliation of Gaia with evolutionary theory may allow further development of evolutionary arguments for the existence of global self-regulatory systems.     

Retrograde adaptive resonance theory based on the role of nitric oxide in long-term potentiation

Adaptive resonance theory (ART) demonstrates how the brain learns to recognize and categorize vast amounts of information by using top–down expectations and attentional focusing. ART 3, one member of the ART family, embeds the computational properties of the chemical synapse in its search process, but it converges slowly and is lack of stability when being applied in pattern recognition and analysis. To overcome these problems, Nitric Oxide (NO), which serves as a newly discovered retrograde messenger in Long-Term Potentiation (LTP), is introduced in retrograde adaptive resonance theory (ReART) model presented in this paper. In the presented model a novel search hypothesis is proposed to incorporate angle and amplitude information of an external input vector to decide whether the input matches the long-term memory (LTM) weights of an active node or not, and the embedded NO retrograde mechanism makes the search procedure a closed loop, which improves the stability and convergence speed of the transmitter releasing mechanism in a synapse. To make the model more adaptive and practical, a forgetting mechanism is built to improve the weights updating process. Experimental results indicate that the proposed ReART model achieves low error rate, fast convergence and self-organizing weights regulation. Action Editor: Christiane Linster     

A conceptual framework for the evolution of ecological specialisation

Ecology Letters (2011) 14: 841-851 ABSTRACT: Ecological specialisation concerns all species and underlies many major ecological and evolutionary patterns. Yet its status as a unifying concept is not always appreciated because of its similarity to concepts of the niche, the many levels of biological phenomena to which it applies, and the complexity of the mechanisms influencing it. The evolution of specialisation requires the coupling of constraints on adaptive evolution with covariation of genotype and environmental performance. This covariation itself depends upon organismal properties such as dispersal behaviour and life history and complexity in the environment stemming from factors such as species interactions and spatio-temporal heterogeneity in resources. Here, we develop a view on specialisation that integrates across the range of biological phenomena with the goal of developing a more predictive conceptual framework that specifically accounts for the importance of biotic complexity and coevolutionary events.     

Complex life cycles drive community assembly through immigration and adaptive diversification

Most animals undergo ontogenetic niche shifts during their life. Yet, standard ecological theory builds on models that ignore this complexity. Here, we study how complex life cycles, where juvenile and adult individuals each feed on different sets of resources, affect community richness. Two different modes of community assembly are considered: gradual adaptive evolution and immigration of new species with randomly selected phenotypes. We find that under gradual evolution complex life cycles can lead to both higher and lower species richness when compared to a model of species with simple life cycles that lack an ontogenetic niche shift. Thus, complex life cycles do not per se increase the scope for gradual adaptive diversification. However, complex life cycles can lead to significantly higher species richness when communities are assembled trough immigration, as immigrants can occupy isolated peaks of the dynamic fitness landscape that are not accessible via gradual evolution.     

Where’s the Noise? Key Features of Spontaneous Activity and Neural Variability Arise through Learning in a Deterministic Network

Even in the absence of sensory stimulation the brain is spontaneously active. This background “noise” seems to be the dominant cause of the notoriously high trial-to-trial variability of neural recordings. Recent experimental observations have extended our knowledge of trial-to-trial variability and spontaneous activity in several directions: 1. Trial-to-trial variability systematically decreases following the onset of a sensory stimulus or the start of a motor act. 2. Spontaneous activity states in sensory cortex outline the region of evoked sensory responses. 3. Across development, spontaneous activity aligns itself with typical evoked activity patterns. 4. The spontaneous brain activity prior to the presentation of an ambiguous stimulus predicts how the stimulus will be interpreted. At present it is unclear how these observations relate to each other and how they arise in cortical circuits. Here we demonstrate that all of these phenomena can be accounted for by a deterministic self-organizing recurrent neural network model (SORN), which learns a predictive model of its sensory environment. The SORN comprises recurrently coupled populations of excitatory and inhibitory threshold units and learns via a combination of spike-timing dependent plasticity (STDP) and homeostatic plasticity mechanisms. Similar to balanced network architectures, units in the network show irregular activity and variable responses to inputs. Additionally, however, the SORN exhibits sequence learning abilities matching recent findings from visual cortex and the network’s spontaneous activity reproduces the experimental findings mentioned above. Intriguingly, the network’s behaviour is reminiscent of sampling-based probabilistic inference, suggesting that correlates of sampling-based inference can develop from the interaction of STDP and homeostasis in deterministic networks. We conclude that key observations on spontaneous brain activity and the variability of neural responses can be accounted for by a simple deterministic recurrent neural network which learns a predictive model of its sensory environment via a combination of generic neural plasticity mechanisms.     

Ecosphere,biosphere, or Gaia? What to call the global ecosystem

The terms biosphere, ecosphere, and Gaia are used as names for the global ecosystem. However, each has more than one meaning. Biosphere can mean the totality of living things residing on the Earth, the space occupied by living things, or life and life-support systems (atmosphere, hydrosphere, lithosphere, and pedosphere). Ecosphere is used as a synonym of biosphere and as a term for zones in the universe where life as we know it should be sustainable. Gaia is similar to biosphere (in the sense of life and life-support systems) and ecosphere (in the sense of biosphere as life and life-support systems), but, in its most extreme form, refers to the entire planet as a living entity. A case is made for avoiding the term Gaia (at least as a name for the planetary ecosystem), restricting biosphere to the totality of living things, and adopting the ecosphere as the most apt name for the global ecosystem.     

The evolution of life cycle complexity in aphids: Ecological optimization or historical constraint?

For decades, biologists have debated why many parasites have obligate multihost life cycles. Here, we use comparative phylogenetic analyses of aphids to evaluate the roles of ecological optimization and historical constraint in the evolution of life cycle complexity. If life cycle complexity is adaptive, it should be evolutionarily labile, that is, change in response to selection. We provide evidence that this is true in some aphids (aphidines), but not others (nonaphidines)—groups that differ in the intensity of their relationships with primary hosts. Next, we test specific mechanisms by which life cycle complexity could be adaptive or a constraint. We find that among aphidines there is a strong association between complex life cycles and polyphagy but only a weak correlation between life cycle complexity and reproductive mode. In contrast, among nonaphidines the relationship between life cycle complexity and host breadth is weak but the association between complex life cycles and sexual reproduction is strong. Thus, although the adaptiveness of life cycle complexity appears to be lineage specific, across aphids, life cycle evolution appears to be tightly linked with the evolution of other important natural history traits.     

Adaptive dynamics of Lotka-Volterra systems with trade-offs: the role of interspecific parameter dependence in branching

We determine the adaptive dynamics of a general Lotka-Volterra system containing an intraspecific parameter dependency--in the form of an explicit functional trade-off between evolving parameters--and interspecific parameter dependencies--arising from modelling species interactions. We develop expressions for the fitness of a mutant strategy in a multi-species resident environment, the position of the singular strategy in such systems and the non-mixed second-order partial derivatives of the mutant fitness. These expressions can be used to determine the evolutionary behaviour of the system. The type of behaviour expected depends on the curvature of the trade-off function and can be interpreted in a biologically intuitive manner using the rate of acceleration/deceleration of the costs implicit in the trade-off function. We show that for evolutionary branching to occur we require that one (or both) of the traded-off parameters includes an interspecific parameter dependency and that the trade-off function has weakly accelerating costs. This could have important implications for understanding the type of mechanisms that cause speciation. The general theory is motivated by using adaptive dynamics to examine evolution in a predator-prey system. The applicability of the general theory as a tool for examining specific systems is highlighted by calculating the evolutionary behaviour in a three species (prey-predator-predator) system.     

Recent models for adaptive personality differences: a review

In this paper we review recent models that provide adaptive explanations for animal personalities: individual differences in behaviour (or suites of correlated behaviours) that are consistent over time or contexts. We start by briefly discussing patterns of variation in behaviour that have been documented in natural populations. In the main part of the paper we discuss models for personality differences that (i) explain animal personalities as adaptive behavioural responses to differences in state, (ii) investigate how feedbacks between state and behaviour can stabilize initial differences among individuals and (iii) provide adaptive explanations for animal personalities that are not based on state differences. Throughout, we focus on two basic questions. First, what is the basic conceptual idea underlying the model? Second, what are the key assumptions and predictions of the model? We conclude by discussing empirical features of personalities that have not yet been addressed by formal modelling. While this paper is primarily intended to guide empiricists through current adaptive theory, thereby stimulating empirical tests of these models, we hope it also inspires theoreticians to address aspects of personalities that have received little attention up to now.     

Gaia again

The ideas of the Gaia hypothesis from the 1960s are today largely included in global ecology and Earth system sciences. The interdependence between biosphere, oceans, atmosphere and geosphere is well-established by data from global monitoring. Nevertheless the theory underlying the holistic view of the homeostatic Earth has remained obscure. Here the foundations of Gaia theory are examined from the recent formulation of the 2nd law of thermodynamics as an equation of motion. According to the principle of increasing entropy, all natural processes, inanimate just as animate, consume free energy, the thermodynamic driving force. All species, abiotic just as biotic are viewed as mechanisms of energy transduction for the global system to evolve toward a stationary state in its surroundings. The maximum entropy state displays homeostasis by being stable against internal fluctuations. When surrounding conditions change or when new mechanisms emerge, the global system readjusts its flows of energy to level newly appeared gradients. Thus, the propositions of Gaia theory and holistic understanding of the global system are recognized as consequences of thermodynamic imperatives.