Dynamics of a Simple Evolutionary Process

We study the simple evolutionary process in which we repeatedly find the least fit agent in a population of agents and give it a new fitness, which is chosen independently at random from a specified distribution. We show that many of the average properties of this process can be calculated exactly using analytic methods. In particular, we find the distribution of fitnesses at arbitrary time, and the distribution of the lengths of runs of hits on the same agent, the latter being found to follow a power law with exponent -1, similar to the distribution of times between evolutionary events in the Bak–Sneppen model and models based on the so-called record dynamics. We confirm our analytic results with extensive numerical simulations.

[1]  Kenton K. Yee.  Introduction to Spin and Lattice Models in the Social Sciences , 2001, nlin/0106028.

[2]  G. Cuniberti,et al.  Effects of regulation on a self-organized market , 2001, cond-mat/0108533.

[3]  Paulo Murilo Castro de Oliveira,et al.  Why do evolutionary systems stick to the edge of chaos , 2001, Theory in Biosciences.

[4]  Stefan Boettcher,et al.  Optimization with Extremal Dynamics , 2000, Complex..

[5]  D. Stauffer,et al.  DIRECTED BAK–SNEPPEN MODEL FOR FOOD CHAINS , 2000 .

[6]  M. Newman,et al.  Decline in extinction rates and scale invariance in the fossil record , 1998, Paleobiology.

[7]  William A. Tozier,et al.  Comment on _Self-organized criticality in living systems_ by C. Adami , 1997, adap-org/9702001.

[8]  Alstrom,et al.  Fitness Optimization and Decay of Extinction Rate Through Biological Evolution. , 1995, Physical review letters.

[9]  Ray,et al.  Anomalous approach to the self-organized critical state in a model for "life at the edge of chaos" , 1994, Physical review letters.

[10]  Bak,et al.  Punctuated equilibrium and criticality in a simple model of evolution. , 1993, Physical review letters.

[11]  Littlewood,et al.  Slow dynamics from noise adaptation. , 1993, Physical review letters.

[12]  W. Feller.  An Introduction to Probability Theory and Its Applications , 1959 .

[13]  Mamta Mittal.  An Introduction To Probability Theory And Its Application , 2003 .

[14]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[15]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[16]  Feder,et al.  Dynamics of invasion percolation. , 1988, Physical review letters.