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33
2005) Laws in Darwinian evolutionary theory
 Physics of Life Reviews
"... In the present article the recent works to formulate laws in Darwinian evolutionary dynamics are discussed. Although there is a strong consensus that general laws in biology may exist, opinions opposing such suggestion are abundant. Based on recent progress in both mathematics and biology, another a ..."
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In the present article the recent works to formulate laws in Darwinian evolutionary dynamics are discussed. Although there is a strong consensus that general laws in biology may exist, opinions opposing such suggestion are abundant. Based on recent progress in both mathematics and biology, another attempt to address this issue is made in the present article. Specifically, three laws which form a mathematical framework for the evolutionary dynamics in biology are postulated. The second law is most quantitative and is explicitly expressed in the unique form of a stochastic differential equation. Salient features of Darwinian evolutionary dynamics are captured by this law: the probabilistic nature of evolution, ascendancy, and the adaptive landscape. Four dynamical elements are introduced in this formulation: the ascendant matrix, the transverse matrix, the Wright evolutionary potential, and the stochastic drive. The first law may be regarded as a special case of the second law. It gives the reference point to discuss the evolutionary dynamics. The third law describes the relationship between the focused level of description to
Predatorprey system with strong Allee effect in prey
"... Global bifurcation analysis of a class of general predatorprey models with a strong Allee effect in prey population is given in details. We show the existence of a pointtopoint heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit ..."
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Global bifurcation analysis of a class of general predatorprey models with a strong Allee effect in prey population is given in details. We show the existence of a pointtopoint heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.
Neocybernetics in biological systems
, 2006
"... This report summarizes ten levels of abstraction that together span the continuum from the most elementary to the most general levels when modeling biological systems. It is shown how the neocybernetic principles can be seen as the key to reaching a holistic view of complex processes in general. Pre ..."
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This report summarizes ten levels of abstraction that together span the continuum from the most elementary to the most general levels when modeling biological systems. It is shown how the neocybernetic principles can be seen as the key to reaching a holistic view of complex processes in general. Preface Concrete examples help to understand complex systems. In this report, the key point is to illustrate the basic mechanisms and properties of neocybernetic system models. Good visualizations are certainly needed. It is biological systems, or living systems, that are perhaps the most characteristic examples of cybernetic systems. This intuition is extended here to natural systems in general — indeed, it is all other than manmade ones that seem to be cybernetic. The word “biological ” in the title should be interpreted as “biological ” — referring to general studies of any living systems, independent of the phenosphere. Starting from the concrete examples, connections to more abstract systems are found, and the discussions become more and more allembracing in this text. However, the neocybernetic model framework still makes it possible to conceptually master the complexity. There is more information about neocybernetics available in Internet — also this report is available there in electronic form:
Reliable Computation of Equilibrium States and Bifurcations in Food Chain Models
"... Food chains and webs in the environment can be modeled by systems of ordinary differential equations that approximate species or functional feeding group behavior with a variety of functional responses. We present here a new methodology for computing all equilibrium states and bifurcations of equili ..."
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Food chains and webs in the environment can be modeled by systems of ordinary differential equations that approximate species or functional feeding group behavior with a variety of functional responses. We present here a new methodology for computing all equilibrium states and bifurcations of equilibria in food chain models. The methodology used is based on interval analysis, in particular an intervalNewton/generalizedbisection algorithm that provides a mathematical and computational guarantee that all roots of a nonlinear equation system are enclosed. The procedure is initializationindependent, and thus requires no a priori insights concerning the number of equilibrium states and bifurcations of equilibria or their approximate locations. The technique is tested using several example problems involving tritrophic food chains.
8 Modeling Disease Dynamics: Cholera As a Case Study
"... Disease dynamics are modeled at a population level in order to create a conceptual framework to think about the spread and prevention of disease, to make forecasts and policy decisions, and to ask and answer scientific questions concerning disease mechanisms such as discovering relevant covariates. ..."
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Disease dynamics are modeled at a population level in order to create a conceptual framework to think about the spread and prevention of disease, to make forecasts and policy decisions, and to ask and answer scientific questions concerning disease mechanisms such as discovering relevant covariates. Population models draw on
89 DARWINIAN SELECTION IN ASYMMETRIC WARFARE: THE NATURAL ADVANTAGE OF INSURGENTS AND TERRORISTS
"... I've killed them by the tens of thousands, scoured their countryside at will, pried their allies away, and humiliated them day after day. I have burned their crops and looted their wealth. I've sent a whole generation of their generals into the afterworld... Have I changed nothing? They are stronger ..."
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I've killed them by the tens of thousands, scoured their countryside at will, pried their allies away, and humiliated them day after day. I have burned their crops and looted their wealth. I've sent a whole generation of their generals into the afterworld... Have I changed nothing? They are stronger now than before. They are more than before. They fight more sensibly than before. They win when they used to lose. —Hannibal in David Anthony Durham’s “Pride of Carthage” Never engage the same enemy for too long, or he will adapt to your tactics. —Clausewitz Models of human conflict tend to focus on military power, predicting that—all else equal—the stronger side will prevail. This overlooks a key insight from the evolutionary dynamics of competing populations: the process of adaptation by natural selection. Darwinian selection weeds out poor performers and propagates good performers, thus leading to a cumulative increase in effective
Elastic systems: Another view at complexity
 In Proceedings of SCAI ’06
"... Elastic systems study complex systems in a cybernetic perspective, assuming that it is the internal feedbacks and interactions that are responsible for the observed functionalities. What is more, in the neocybernetic framework there are some additional assumptions — like balance and linearity pursui ..."
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Elastic systems study complex systems in a cybernetic perspective, assuming that it is the internal feedbacks and interactions that are responsible for the observed functionalities. What is more, in the neocybernetic framework there are some additional assumptions — like balance and linearity pursuit — that make it possible to apply efficient theoretical tools for model construction. It turns out that the very simple starting points are enough to assure selfregulation and selforganization. This selforganization can be interpreted in terms of multivariate statistics: The system implements principal subspace compression of the input resources. This optimality makes it possible to make evolutionary hypotheses, and generalize the models to different phenospheres. 1
Information and Entropy in Cybernetic Systems
"... Abstract. It has been shown that the cybernetic approaches can efficiently be used for analysis and design of complex networked systems. Still, the earlier discussions were bound to the actual application domain at hand. This paper gives more intuition in what truly takes place in a cybernetic syste ..."
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Abstract. It has been shown that the cybernetic approaches can efficiently be used for analysis and design of complex networked systems. Still, the earlier discussions were bound to the actual application domain at hand. This paper gives more intuition in what truly takes place in a cybernetic system from another point of view. Information theory, and specially the concept of entropy, offer a yet more general perspective to such analyses. 1
Scenario Based Analysis of Linear Computations
"... In this paper we consider the following task: given an abstract state machine, characterize the subsets of initial values corresponding to di#erent typical scenarios of the system behavior. In order to solve it we suggest formalization of the notion of scenario and then discuss possible approach ..."
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In this paper we consider the following task: given an abstract state machine, characterize the subsets of initial values corresponding to di#erent typical scenarios of the system behavior. In order to solve it we suggest formalization of the notion of scenario and then discuss possible approaches to the classification of the computations.
Ecology 2004
, 2004
"... this paper we use these shooting records to address the following questions: 769 grouse cycles 2004 British . What proportion of grouse timeseries are asymmetrical and/or nonlinear? . How does asymmetry manifest itself within the timeseries? . Is there geographical variation in patterns ..."
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this paper we use these shooting records to address the following questions: 769 grouse cycles 2004 British . What proportion of grouse timeseries are asymmetrical and/or nonlinear? . How does asymmetry manifest itself within the timeseries? . Is there geographical variation in patterns of asymmetry and nonlinearity? . Are variations in patterns of asymmetry and nonlinearity related to variations in grouse population density, growth and decline rates or with anticipated patterns in intensity of parasitism as predicted by rainfall? Methods The timeseries used came from moors located in all the major regions of grouse habitats in the United Kingdom where shooting has occurred for at least 32 years. Two hundred and eightynine grouse timeseries were included, detrended and patched or split, as described in Haydon et al. (2002). We excluded from subsequent analyses those timeseries that were not distinguishable (at the 5% level) either from white noise using the LjungBox test, or from a zeroth order autoregressive process (AR0, see below). For nine populations there were multiple timeseries of which nonewere either white noise or AR0, and in these cases the longest timeseries was selected for analysis. For the purposes of model fitting and nonlinear analysis, timeseries were normalized using BoxCox transformations by taking the value of the exponent that was the maximum likelihood for each timeseries (see Results) as described by Sokal &Rohlf (1981) and then standardized to zero mean and unit variance. Time reversibility We applied Rothman's (1992) TR test to timeseries to determine timereversibility, which examines the equality of the bicovariances for various values of lag, k (where x t is the transformed timeseries, an...