Adaptation Noise And Self Organizing Systems

A two--dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities. Each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of the four directions. The flow of cars obeys realistic traffic rules. We investigate the dependence of the average velocity of cars on the global traffic density. At a critical threshold for the density the average velocity reduces drastically caused by jamming. For the low density regime we provide analytical results which agree with the numerical results.

A novel theory for cell differentiation is proposed, based on simulations with interacting artificial cells which have metabolic networks within, and divide into two when the final product is accumulated. Results of simulations with coupled chemical networks and division process lead to the following scenario of the differentiation: Up to some numbers of cells, divisions bring about almost identical cells with synchronized metabolic oscillations. As the number is increased the oscillations lose the synchrony, leading to groups of cells with different phases of oscillations. At later stage this differentiation is fixed in time, and cells spilt into groups with different chemical constituents spontaneously, which are transmitted to daughter cells by cell divisions. Hierarchical differentiation, origin of stem cells, and anomalous differentiation by transplantations are also discussed with relevance to real biological experimental results. (Keywords: differentiation, metabolic network, cell division, clustering, open chaos)

The appropriate choice of the genotype-phenotype mapping in combination with the mutation operator is important for a successful evolutionary search process. We suggest a measure to quantify the quality of this combination by addressing the question whether the relation among distances is carried over from one space to the other. Search processes which do not destroy the neighbourhood structure are termed strongly causal. We apply the proposed measure to parameter and structure optimisation problems in order to assess the combination (mapping, mutation operator) and at the same time to be able to propose improved settings.

The main focus of this work is to understand the dynamics of non regulated markets. The present model can describe the dynamics of any market where the pricing is based on supply and demand. It will be applied here, as an example, for the German stock market presented by the Deutscher Aktienindex (DAX), which is a measure for the market status. The duality of the present model consists of the superposition of the two components - the long and the short term behaviour of the market. The long term behaviour is characterised by a stable development which is following a trend for time periods of years or even decades. This long term growth (or decline) is based on the development of fundamental market figures. The short term behaviour is described as a dynamical evaluation (trading) of the market by the participants. The trading process is described as an exchange between supply and demand. In the framework of this model there the trading is modelled by a system of nonlinear differential equations. The model also allows to explain the chaotic behaviour of the market as well as periods of growth or crashes.

The metaphor of holey adaptive landscapes provides a pictorial representation of the process of speciation as a consequence of genetic divergence. In this metaphor, biological populations diverge along connected clusters of well-fit genotypes in a multidimensional adaptive landscape and become reproductively isolated species when they come to be on opposite sides of a ``hole'' in the adaptive landscape. No crossing of any adaptive valleys is required. I formulate and study a series of simple models describing the dynamics of speciation on holey adaptive landscapes driven by mutation and random genetic drift. Unlike most previous models that concentrate only on some stages of speciation, the models studied here describe the complete process of speciation from initiation until completion. The evolutionary factors included are selection (reproductive isolation), random genetic drift, mutation, recombination, and migration. In these models, pre- and post-mating reproductive isolation is a consequence of cumulative genetic change. I study possibilities for speciation according to allopatric, parapatric, peripatric and vicariance scenarios. The analytic theory satisfactorily matches results of individual-based simulations reported by Gavrilets et al. (1998). It is demonstrated that rapid speciation including simultaneous emergence of several new species is a plausible outcome of the evolutionary dynamics of subdivided populations. I consider effects of population size, population subdivision, and local adaptation on the dynamics of speciation. I briefly discuss some implications of the dynamics on holey adaptive landscapes for molecular evolution.

We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated continuously in the learning process. As the probability distribution evolves, better and better solutions are shown to emerge. The performance of the algorithm is illustrated by the application to the problem of finding the ground state of the Ising spin glass. A simple theoretical understanding of the algorithm is also presented.

We propose a model with heterogeneous interacting traders which can explain some of the stylized facts of stock market returns. In the model synchronization effects, which generate large fluctuations in returns, can arise either from an aggregate exogenous shock or, even in its absence, purely from communication and imitation among traders. A trade friction is introduced which, by responding to price movements, creates a feedback mechanism on future trading and generates volatility clustering.

We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate analytic solution and also by numerical simulation, and use it to make predictions about the distribution of extinctions and species lifetimes that we would expect to see in real ecosystems. It should be possible to test these predictions against the fossil record. The model indicates that a possible mechanism for mass extinction is the coincidence of a large coevolutionary avalanche in the ecosystem with a severe environmental disturbance.

We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are defined purely in terms of the fitness landscapes of each species. Numerical simulations show that the total diversity fluctuates around a natural system size N nat which only weakly depends upon the number of connections per species. This is in agreement with known data for real multispecies communities. The numerical results are confirmed by approximate mean field analysis.

A number of authors have in recent years proposed that the processes of macroevolution may give rise to self-organized critical phenomena which could have a significant effect on the dynamics of ecosystems. In particular it has been suggested that mass extinction may arise through a purely biotic mechanism as the result of so-called coevolutionary avalanches. In this paper we first explore the empirical evidence which has been put forward in favor of this conclusion. The data center principally around the existence of power-law functional forms in the distribution of the sizes of extinction events and other quantities. We then propose a new mathematical model of mass extinction which does not rely on coevolutionary effects and in which extinction is caused entirely by the action of environmental stresses on species. In combination with a simple model of species adaptation we show that this process can account for all the observed data without the need to invoke coevolution and critical processes. The model also makes some independent predictions, such as the existence of ``aftershock'' extinctions in the aftermath of large mass extinction events, which should in theory be testable against the fossil record.