The Tangled Nature model as an evolving quasi-species model

We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold, consistent with the simulation results, that provides a valuable insight into how the microscopic dynamics of the model determine the observed macroscopic phenomena published previously. The dynamics of the Tangled Nature model is defined on the microevolutionary time scale via reproduction, with heredity, variation, and natural selection. Each organism reproduces with a rate that is linked to the individuals' genetic sequence and depends on the composition of the population in genotype space. Thus the microevolutionary dynamics of the fitness landscape is regulated by, and regulates, the evolution of the species by means of the mutual interactions. At low mutation rate, the macro evolutionary pattern mimics the fossil data: periods of stasis, where the population is concentrated in a network of coexisting species, is interrupted by bursts of activity. As the mutation rate increases, the duration and the frequency of bursts increases. Eventually, when the mutation rate reaches a certain threshold, the population is spread evenly throughout the genotype space showing that natural selection only leads to multiple distinct species if adaptation is allowed time to cause fixation.Comment: Paper submitted to Journal of Physics A. 13 pages, 4 figure

The species-area relationship and evolution

Models relating to the Species-Area curve are usually defined at the species level, and concerned only with ecological timescales. We examine an individual-based model of co-evolution on a spatial lattice based on the Tangled Nature model, and show that reproduction, mutation and dispersion by diffusion in an interacting system produces power-law Species-Area Relations as observed in ecological measurements at medium scales. We find that co-evolutionary habitats form, allowing high diversity levels in a spatially homogenous system, and these are maintained for exponentially increasing time when increasing system size.Comment: 21 pages, 5 figures. This is the final, accepted draf

Unified "micro"- and "macro-" evolution of eco-systems: Self-organization of a dynamic network

Very recently we have developed a dynamic network model for eco-systems that achieved ``unification'' of ``micro'' and ``macro''-evolution. We now propose an extension of our model so as to stabilize the eco-system and describe {\it speciation} in a more realistic manner.Comment: 7 pages with 3 figures; for Max Born Symposium, Poland, Sept. 200

Computer simulations of history of life: speciation, emergence of complex species from simpler organisms, and extinctions

We propose a generic model of eco-systems, with a {\it hierarchical} food web structure. In our computer simulations we let the eco-system evolve continuously for so long that that we can monitor extinctions as well as speciations over geological time scales. {\it Speciation} leads not only to horizontal diversification of species at any given trophic level but also to vertical bio-diversity that accounts for the emergence of complex species from simpler forms of life. We find that five or six trophic levels appear as the eco-system evolves for sufficiently long time, starting initially from just one single level. Moreover, the time intervals between the successive collections of ecological data is so short that we could also study ``micro''-evolution of the eco-system, i.e., the birth, ageing and death of individual organisms.Comment: 7 pages, including 4 EPS figures, REVTE

Fluctuations and correlations in an individual-based model of biological coevolution

We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in previous investigations. The stationary states of the mutationless model are generally well approximated by Gaussian distributions, so that the fluctuations and correlations of the populations can be computed analytically. Several specific cases are studied by Monte Carlo simulations, and there is excellent agreement between the data and the theoretical predictions.Comment: 25 pages, 2 figure

Evolutionary ecology in-silico:evolving foodwebs, migrating population and speciation

We have generalized our ``unified'' model of evolutionary ecology by taking into account the possible movements of the organisms from one ``patch'' to another within the same eco-system. We model the spatial extension of the eco-system (i.e., the geography) by a square lattice where each site corresponds to a distinct ``patch''. A self-organizing hierarchical food web describes the prey-predator relations in the eco-system. The same species at different patches have identical food habits but differ from each other in their reproductive characteristic features. By carrying out computer simulations up to $10^9$ time steps, we found that, depending on the values of the set of parameters, the distribution of the lifetimes of the species can be either exponential or a combination of power laws. Some of the other features of our ``unified'' model turn out to be robust against migration of the organisms.Comment: 12 pages of PS file, including LATEX text and 9 EPS figure

Tangled Nature: A model of emergent structure and temporal mode among co-evolving agents

Understanding systems level behaviour of many interacting agents is challenging in various ways, here we'll focus on the how the interaction between components can lead to hierarchical structures with different types of dynamics, or causations, at different levels. We use the Tangled Nature model to discuss the co-evolutionary aspects connecting the microscopic level of the individual to the macroscopic systems level. At the microscopic level the individual agent may undergo evolutionary changes due to mutations of strategies. The micro-dynamics always run at a constant rate. Nevertheless, the system's level dynamics exhibit a completely different type of intermittent abrupt dynamics where major upheavals keep throwing the system between meta-stable configurations. These dramatic transitions are described by a log-Poisson time statistics. The long time effect is a collectively adapted of the ecological network. We discuss the ecological and macroevolutionary consequences of the adaptive dynamics and briefly describe work using the Tangled Nature framework to analyse problems in economics, sociology, innovation and sustainabilityComment: Invited contribution to Focus on Complexity in European Journal of Physics. 25 page, 1 figur

Complex dynamics in coevolution models with ratio-dependent functional response

We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The underlying individual-based population dynamics are based on a ratio-dependent functional response [W.M. Getz, J. Theor. Biol. 108, 623 (1984)]. Analytical results for fixed-point population sizes in some simple communities are derived and discussed. In long kinetic Monte Carlo simulations we find quite robust, approximate 1/f noise in species diversity and population sizes, as well as power-law distributions for the lifetimes of individual species and the durations of periods of relative evolutionary stasis. Adaptive foraging enhances coexistence of species and produces a metastable low-diversity phase and a stable high-diversity phase.Comment: 19 page