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Lecture notes on hybrid systems
, 2004
"... The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be hi ..."
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The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be highlighted. We will introduce general methods for investigating properties such as existence of solutions, reachability and decidability of hybrid systems. The methods will be demonstrated on the motivating applications. Students who successfully complete the course should be able to appreciate the diversity of phenomena that arise in hybrid systems and how discrete “discrete ” entities and concepts such as automata, decidability and bisimulation can coexist with continuous entities and
Lattice effects observed in chaotic dynamics of experimental populations
 Science
, 2001
"... Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often d ..."
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Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuousstate models have stimulated much ecological research; yet discretestate models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discretestate and continuousstate population models. Neither the discrete nor continuousstate models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuousstate model and the cyclic dynamics predicted by the discretestate models. We suggest that such lattice effects could be an important component of natural population fluctuations. The discovery that simple deterministic population models can display complex aperiodic
Empirical and mechanistic models for the particle export ratio
"... [1] We present new empirical and mechanistic models for predicting the export of organic carbon out of the surface ocean by sinking particles. To calibrate these models, we have compiled a synthesis of field observations related to ecosystem size structure, primary production and particle export fro ..."
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[1] We present new empirical and mechanistic models for predicting the export of organic carbon out of the surface ocean by sinking particles. To calibrate these models, we have compiled a synthesis of field observations related to ecosystem size structure, primary production and particle export from around the globe. The empirical model captures 61 % of the observed variance in the ratio of particle export to primary production (the pe ratio) using seasurface temperature and chlorophyll concentrations (or primary productivity) as predictor variables. To describe the mechanisms responsible for peratio variability, we present sizebased formulations of phytoplankton grazing and sinking particle export, combining them into an alternative, mechanistic model. The formulation of grazing dynamics, using simple power laws as closure terms for small and large phytoplankton, reproduces 74 % of the observed variability in phytoplankton community composition wherein large phytoplankton augment small ones as production increases. The formulation for sinking particle export partitions a temperaturedependent fraction of small and large phytoplankton grazing into sinking detritus. The mechanistic model also captures 61 % of the observed variance in pe ratio, with large phytoplankton in high biomass and relatively cold regions leading to more efficient export. In this model, variability in primary productivity results in a biomassmodulated switch between small and large phytoplankton pathways.
Modelling food webs
 Handbook of Graphs and Networks
, 2002
"... We review theoretical approaches to the understanding of food webs. After an overview of the available food web data, we discuss three different classes of models. The first class comprise static models, which assign links between species according to some simple rule. The second class are dynamical ..."
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We review theoretical approaches to the understanding of food webs. After an overview of the available food web data, we discuss three different classes of models. The first class comprise static models, which assign links between species according to some simple rule. The second class are dynamical models, which include the population dynamics of several interacting species. We focus on the question of the stability of such webs. The third class are species assembly models and evolutionary models, which build webs starting from a few species by adding new species through a process of “invasion ” (assembly models) or “speciation” (evolutionary models). Evolutionary models are found to be capable of building large stable webs. 1
Mutualism Promotes Diversity and Stability in a Simple Artificial Ecosystem
, 2002
"... This work investigates the effect of ecological interactions between organisms on the evolutionary dynamics of a community. A spatially explicit, individual based model is presented, in which organisms compete for space and for resources. We investigated how introducing the potential for mutualistic ..."
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This work investigates the effect of ecological interactions between organisms on the evolutionary dynamics of a community. A spatially explicit, individual based model is presented, in which organisms compete for space and for resources. We investigated how introducing the potential for mutualistic relationships (where the presence of one type of organism stimulates the growth of another type, and vice versa) affected the evolutionary dynamics of the system. Without this potential, one or a small number of individual types of organisms dominated the simulated community from the onset. When mutualistic relationships were allowed, many persisting types arose, with new types appearing continually. Furthermore, we investigated how the stability of the community differed when mutualistic relationships were allowed and disallowed. Our results suggest that the existence of mutualistic relationships improved community stability. KEYWORDS: Ecosystem; evolution; ecological interaction; mutualism; ecosystem diversity; ecosystem stability 1.
Relevance of dynamic clustering to biological networks
 Physica D
, 1994
"... Network of nonlinear dynamical elements often show clustering of synchronization by chaotic instability. Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis of partially ordered states with chaotic itinerancy. First, clustering with bit st ..."
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Network of nonlinear dynamical elements often show clustering of synchronization by chaotic instability. Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis of partially ordered states with chaotic itinerancy. First, clustering with bit structures in a hypercubic lattice is studied. Spontaneous formation and destruction of relevant bits are found, which give selforganizing, and chaotic genetic algorithms. When spontaneous changes of effective couplings are introduced, chaotic itinerancy of clusterings is widely seen through a feedback mechanism, which supports dynamic stability allowing for complexity and diversity, known as homeochaos. Second, synaptic dynamics of couplings is studied in relation with neural dynamics. The clustering structure is formed with a balance between external inputs and internal dynamics. Last, an extension allowing for the growth of the number of elements is
A dynamical model of general intelligence: the positive manifold of intelligence by mutualism. Psychological Review
, 2006
"... Scores on cognitive tasks used in intelligence tests correlate positively with each other, that is, they display a positive manifold of correlations. The positive manifold is often explained by positing a dominant latent variable, the g factor, associated with a single quantitative cognitive or biol ..."
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Scores on cognitive tasks used in intelligence tests correlate positively with each other, that is, they display a positive manifold of correlations. The positive manifold is often explained by positing a dominant latent variable, the g factor, associated with a single quantitative cognitive or biological process or capacity. In this article, a new explanation of the positive manifold based on a dynamical model is proposed, in which reciprocal causation or mutualism plays a central role. It is shown that the positive manifold emerges purely by positive beneficial interactions between cognitive processes during development. A single underlying g factor plays no role in the model. The model offers explanations of important findings in intelligence research, such as the hierarchical factor structure of intelligence, the low predictability of intelligence from early childhood performance, the integration/differentiation effect, the increase in heritability of g, and the Jensen effect, and is consistent with current explanations of the Flynn effect.
Biodiversity, productivity and stability in real food webs
"... The global biodiversity crisis has motivated new theory and experiments that explore relationships between biodiversity (species richness and composition in particular), productivity and stability. Here we emphasize that these relationships are often bidirectional, such that changes in biodiversity ..."
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The global biodiversity crisis has motivated new theory and experiments that explore relationships between biodiversity (species richness and composition in particular), productivity and stability. Here we emphasize that these relationships are often bidirectional, such that changes in biodiversity can be both a cause and a consequence of changes in productivity and stability. We hypothesize that this bidirectionality creates feedback loops, as well as indirect effects, that influence the complex responses of communities to biodiversity losses. Important, but often neglected, mediators of this complexity are trophic interactions. Recent work shows that consumers can modify, dampen or even reverse the directionality of biodiversityproductivitystability linkages inferred from the plant level alone.
Evolutionary Game Theory: Theoretical Concepts and Applications to Microbial Communities
, 2010
"... Ecological systems are complex assemblies of large numbers of individuals, interacting competitively under multifaceted environmental conditions. Recent studies using microbial laboratory communities have revealed some of the selforganization principles underneath the complexity of these systems. A ..."
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Ecological systems are complex assemblies of large numbers of individuals, interacting competitively under multifaceted environmental conditions. Recent studies using microbial laboratory communities have revealed some of the selforganization principles underneath the complexity of these systems. A major role of the inherent stochasticity of its dynamics and the spatial segregation of different interacting species into distinct patterns has thereby been established. It ensures viability of microbial colonies by allowing for species diversity, cooperative behavior and other kinds of “social ” behavior. A synthesis of evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes provides the mathematical tools and conceptual framework for a deeper understanding of these ecological systems. We give an introduction into the modern formulation of these theories and illustrate their effectiveness focussing on selected examples of microbial
Small mammals in young forests: implications for management for sustainability. For. Ecol. Manage
, 2001
"... Small mammals have been proposed as indicators of sustainability in forests in the Pacific Northwest and elsewhere. Mammal community composition and species abundances purportedly result from interactions among species, forestfloor characteristics, large coarse woody debris, understory vegetation, ..."
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Small mammals have been proposed as indicators of sustainability in forests in the Pacific Northwest and elsewhere. Mammal community composition and species abundances purportedly result from interactions among species, forestfloor characteristics, large coarse woody debris, understory vegetation, and overstory composition. Coarse woody debris is thought to be particularly important because of its diverse ecological functions; covers from 10 to 15 % have been recommended based on retrospective studies of forests and small mammals. Unfortunately, ecological correlations are not necessarily indicative of causal relationships and magnitudes depend on composition of finite, usually nonrandom, crosssectional samples. Retrospective studies must be replicated to confirm relationships. We conducted a largescale, crosssectional survey of 30 to 70yearold coniferous forests in western Washington to determine if previously reported relationships would hold with an unrelated, larger sample. Coarse woody debris cover was 8.3 ± 0.6 % (0 ± S.E., n = 8 blocks of forest, range 413%). Understory cover was too low (18 ± 8% for shrubs) to allow examining interactions between understory and coarse woody debris. Overstory composition covaried with coarse woody debris. One or two of four statistically extracted habitat factors (overstory composition, herbaceous cover, abundance of Acer circinatum, and abundance of Acer macrophyllum) accounted for 1870 % of variance in abundance of 11 mammal species. Our results support hypotheses that: (1) biocomplexity resulting from interactions of decadence, understory development, and overstory composition provides preinteractive niche diversification with predictable, diverse, smallmammal