Evolution and extinction dynamics in rugged fitness landscapes

Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness landscapes. As a consequence, the average fitness in the system increases logarithmically with time, while the rate of extinction steadily decreases. This dynamics is studied by numerical simulations and, in a simpler mean field version, analytically. We also study the effect of externally added `mass' extinctions. The predictions for various quantities of paleontological interest (life-time distributions, distribution of event sizes and behavior of the rate of extinction) are robust and in good agreement with available data. Brief version of parts of this work have been published as Letters. (PRL 75, 2055, (1995) and PRL, 79, 1413, (1997))Comment: 30 pages 9 figures LaTe

Extremal dynamics on complex networks: Analytic solutions

The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold $x_c$ to be 1/(_f+1), where _f=/ (=) in the quenched (annealed) updating case, where is the n-th moment of the degree distribution. Thus, the threshold is zero (finite) for the degree exponent \gamma 3) for the quenched case in the thermodynamic limit. The theoretical value x_c fits well to the numerical simulation data in the annealed case only. Avalanche size, defined as the duration of successive mutations below the threshold, exhibits a critical behavior as its distribution follows a power law, P_a(s) ~ s^{-3/2}.Comment: 6 pages, 2 figure

Wealth redistribution with finite resources

We present a simplified model for the exploitation of finite resources by interacting agents, where each agent receives a random fraction of the available resources. An extremal dynamics ensures that the poorest agent has a chance to change its economic welfare. After a long transient, the system self-organizes into a critical state that maximizes the average performance of each participant. Our model exhibits a new kind of wealth condensation, where very few extremely rich agents are stable in time and the rest stays in the middle class.Comment: 4 pages, 3 figures, RevTeX 4 styl

Theoretical size distribution of fossil taxa: analysis of a null model

BACKGROUND: This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution. MODEL: New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate. CONCLUSION: The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family

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

Improving estimation of glacier volume change: a GLIMS case study of Bering Glacier System, Alaska

International audienceThe Global Land Ice Measurements from Space (GLIMS) project has developed tools and methods that can be employed by analysts to create accurate glacier outlines and resultant measures of glacier extent. To illustrate the importance of accurate glacier outlines and the effectiveness of GLIMS standards we have conducted a case study on Bering Glacier System (BGS), Alaska. BGS is a complex glacier system aggregated from multiple drainage basins, numerous individual ice streams, and many accumulation areas. Published measurements of BGS surface area vary from 1740 to 6200 km2, depending on how the boundaries of this system have been defined. Utilizing GLIMS tools and standards we have completed a new outline and analysis of the area-altitude distribution (hypsometry) of BGS using Landsat images from 2000 and 2001. We compared this new outline (3632 km2) with three previous outlines to illustrate the errors that result from the widely varying estimates used in previous analysis of BGS area. The use of different BGS outlines results in highly variable measures of volume change and net balance (bn). Outline variability alone results in a net balance rate range of ?1.0 to ?3.2 m/yr water equivalent (W.E.), a volume change range of ?4.2 to ?8.2 km3/yr, and a near doubling in contributions to sea level equivalent (SLE), 0.0122 mm/yr to 0.0236 mm/yr. A study of three different models of BGS net balance leads us to favor estimates of bn of ?1.2 m/yr W.E. and total volume change of ?4.2 km3/yr for the period 1950?2004. These estimates result in a near doubling of contributions to sea level equivalent when compared with previous studies. While current inaccuracies in glacier outlines hinder our ability to fully understand glacier change, there is no reason why our understanding of glacier extents should not be comprehensive and accurate. Such accuracy is possible with the increasing volume of satellite imagery of glacierized regions, and recent advances in tools and standards

Self-organized criticality in deterministic systems with disorder

Using the Bak-Sneppen model of biological evolution as our paradigm, we investigate in which cases noise can be substituted with a deterministic signal without destroying Self-Organized Criticality (SOC). If the deterministic signal is chaotic the universality class is preserved; some non-universal features, such as the threshold, depend on the time correlation of the signal. We also show that, if the signal introduced is periodic, SOC is preserved but in a different universality class, as long as the spectrum of frequencies is broad enough.Comment: RevTex, 8 pages, 8 figure

Constraints on planet X/Nemesis from Solar System's inner dynamics

We put full 3D constraints on a putative planet X by using the dynamics of the inner planets of the solar system. In particular, we compute the mimium distance of X as a function of its heliocentric latitude and longitude for different values of its mass.Comment: LaTex, MNRAS macros. 12 pages, 4 figures, 3 tables. To appear in Monthly Notices of the Royal Astronomical Society (MNRAS). Some typos fixe

Considering the Case for Biodiversity Cycles: Reexamining the Evidence for Periodicity in the Fossil Record

Medvedev and Melott (2007) have suggested that periodicity in fossil biodiversity may be induced by cosmic rays which vary as the Solar System oscillates normal to the galactic disk. We re-examine the evidence for a 62 million year (Myr) periodicity in biodiversity throughout the Phanerozoic history of animal life reported by Rohde & Mueller (2005), as well as related questions of periodicity in origination and extinction. We find that the signal is robust against variations in methods of analysis, and is based on fluctuations in the Paleozoic and a substantial part of the Mesozoic. Examination of origination and extinction is somewhat ambiguous, with results depending upon procedure. Origination and extinction intensity as defined by RM may be affected by an artifact at 27 Myr in the duration of stratigraphic intervals. Nevertheless, when a procedure free of this artifact is implemented, the 27 Myr periodicity appears in origination, suggesting that the artifact may ultimately be based on a signal in the data. A 62 Myr feature appears in extinction, when this same procedure is used. We conclude that evidence for a periodicity at 62 Myr is robust, and evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous.Comment: Minor modifications to reflect final published versio

Self-Organized Criticality Driven by Deterministic Rules

We have investigated the essential ingredients allowing a system to show Self Organized Criticality (SOC) in its collective behavior. Using the Bak-Sneppen model of biological evolution as our paradigm, we show that the random microscopic rules of update can be effectively substituted with a chaotic map without changing the universality class. Using periodic maps SOC is preserved, but in a different universality class, as long as the spectrum of frequencies is broad enough.Comment: 4 pages, RevTex (tar.gz), 4 eps-figures include