Avalanche dynamics in Bak-Sneppen evolution model observed with standard distribution width of fitness

We introduce the standard distribution width of fitness to characterize the global and individual features of a ecosystem in the Bak-Sneppen evolution model. Through tracking this quantity in evolution, a different hierarchy of avalanche dynamics, $w_{0}$ avalanche is observed. The corresponding gap equation and the self-organized threshold $w_{c}$ are obtained. The critical exponents $\tau ,$ $\gamma$and $\rho$, which describe the behavior of the avalanche size distribution, the average avalanche size and the relaxation to attractor, respectively, are calculated with numerical simulation. The exact master equation and $\gamma$ equation are derived. And the scaling relations are established among the critical exponents of this new avalanche.Comment: 14 pages, 3 figure

Entropic Sampling and Natural Selection in Biological Evolution

With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this scheme the system evolves continuously into new configurations, yielding non-stationary behavior of the total fitness. Further, both the waiting time distribution of species and the avalanche size distribution display power-law behaviors with exponents close to two, which are consistent with the fossil data. These features are rather robust, indicating the key role of entropy

Punctuated Equilibrium in Software Evolution

The approach based on paradigm of self-organized criticality proposed for experimental investigation and theoretical modelling of software evolution. The dynamics of modifications studied for three free, open source programs Mozilla, Free-BSD and Emacs using the data from version control systems. Scaling laws typical for the self-organization criticality found. The model of software evolution presenting the natural selection principle is proposed. The results of numerical and analytical investigation of the model are presented. They are in a good agreement with the data collected for the real-world software.Comment: 4 pages, LaTeX, 2 Postscript figure

Biological Effects of Stellar Collapse Neutrinos

Massive stars in their final stages of collapse radiate most of their binding energy in the form of MeV neutrinos. The recoil atoms that they produce in elastic scattering off nuclei in organic tissue create radiation damage which is highly effective in the production of irreparable DNA harm, leading to cellular mutation, neoplasia and oncogenesis. Using a conventional model of the galaxy and of the collapse mechanism, the periodicity of nearby stellar collapses and the radiation dose are calculated. The possible contribution of this process to the paleontological record of mass extinctions is examined.Comment: gzipped PostScript (filename.ps.Z), 12 pages. Final version, Phys. Rev. Lett., in pres

Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model

We derive an infinite hierarchy of exact equations for the Bak-Sneppen model in arbitrary dimensions. These equations relate different moments of temporal duration and spatial size of avalanches. We prove that the exponents of the BS model are the same above and below the critical point and express the universal amplitude ratio of the avalanche spatial size in terms of the critical exponents. The equations uniquely determine the shape of the scaling function of the avalanche distribution. It is suggested that in the BS model there is only one independent critical exponent.Comment: Submitted to PRL, 4 two-column pages (revtex), 1 ps figure included with epsf, g-zipped, uuencode

Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model

Infinite hierarchy of exact equations are derived for the newly-observed f-avalanche in the Bak-Sneppen evolution model. By solving the first order exact equation, we found that the critical exponent which governs the divergence of the average avalanche size, is exactly 1 (for all dimensions), confirmed by the simulations. Solution of the gap equation yields another universal exponent, denoting the the relaxation to the attractor, is exactly 1. We also establish some scaling relations among the critical exponents of the new avalanche.Comment: 5 pages, 1 figur

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

Branching Processes and Evolution at the Ends of a Food Chain

In a critically self--organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes, extending previous mean field descriptions and yielding $\nu=1/2$ together with $\tau'=7/4$, as distribution exponent of avalanches starting from species at the ends of a food chain. For the nearest neighbor chain one obtains numerically $\tau'=1.25 \pm 0.01$, and $\tau'_{first}=1.35 \pm 0.01$ for the first return times of activity, again distinct from bulk exponents.Comment: REVTex file, 12 pages, 2 figures in eps-files uuencoded, psfig.st

Mass extinctions and supernova explosions

A nearby supernova (SN) explosion could have negatively influenced life on Earth, maybe even been responsible for mass extinctions. Mass extinction poses a significant extinction of numerous species on Earth, as recorded in the paleontologic, paleoclimatic, and geological record of our planet. Depending on the distance between the Sun and the SN, different types of threats have to be considered, such as ozone depletion on Earth, causing increased exposure to the Sun's ultraviolet radiation, or the direct exposure of lethal x-rays. Another indirect effect is cloud formation, induced by cosmic rays in the atmosphere which result in a drop in the Earth's temperature, causing major glaciations of the Earth. The discovery of highly intensive gamma ray bursts (GRBs), which could be connected to SNe, initiated further discussions on possible life-threatening events in Earth's history. The probability that GRBs hit the Earth is very low. Nevertheless, a past interaction of Earth with GRBs and/or SNe cannot be excluded and might even have been responsible for past extinction events.Comment: Chapter for forthcoming book: Handbook of Supernovae, P. Murdin and A. Alsabeti (eds.), Springer International Publishing (in press

Identifying foundation species in North American forests using long‐term data on ant assemblage structure

Foundation species are locally abundant and uniquely control associated biodiversity, whereas dominant species are locally abundant but are thought to be replaceable in ecological systems. It is important to distinguish foundation from dominant species to direct conservation efforts. Long‐term studies that remove abundant species while measuring community dynamics have the potential to (1) aid in the identification of foundation vs. dominant species and, (2) once a foundation species is identified, determine how long its effects persist within a community after its loss. Long‐term data on ant assemblages within two canopy‐manipulation experiments—the Harvard Forest Hemlock Removal Experiment (HF‐HeRE) and the Black Rock Future of Oak Forests Experiment (BRF‐FOFE)—provide insights into how ant assemblages change and reassemble following the loss of Tsuga canadensis or Quercus spp. Previous research documented foundation species effects on ants in the HF‐HeRE for up to four years after T. canadensis loss. Six additional years of data at HF‐HeRE presented for the first time here show that removal of T. canadensis resulted in taxonomic and some measures of functional shifts in ant assemblages that persisted for ten years, further supporting the hypothesis that T. canadensis is a foundation species at Harvard Forest. In contrast, ant assemblages at BRF‐FOFE varied little regardless of whether oaks or other tree species were removed from the canopy, suggesting that Quercusspecies do not act as foundation species at Black Rock Forest. Deer and moose exclosures within each experiment also allowed for comparisons between effects on ants of foundation or dominant tree species relative to effects of large herbivores. At HF‐HeRE, effects of T. canadensis were stronger than effects of large herbivores on taxonomic and functional diversity of ant assemblages. At BRF‐FOFE, in contrast, effects of Quercus species were weaker than effects of large herbivores on ant taxonomic diversity and some measures of ant functional diversity. These findings illustrate the importance of distinguishing between the roles of irreplaceable foundation species and replaceable dominant ones in forested ecosystems along with other drivers of biodiversity (e.g., herbivory)