Ecological model of extinctions

We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the others, that reproduces and evolves in time. Each species is simultaneously a predator and a prey in a food chain. Mutations that change the interactions are supposed to occur randomly at a low rate. Extinctions of populations result naturally from the predator-prey dynamics. The model is not pinned in a fitness variable, and natural selection arises from the dynamics.Comment: 16 pages (LaTeX type, RevTeX style), including 6 figures in gif format. To be published in Phys. Rev. E (prob. Dic. 96

The stackelberg minimum spanning tree game

We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or STACKMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor's prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game. We analyze the complexity and approximability of the first player's best strategy in STACKMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most min{k, 3 + 2 In 6,1 + In W}, where k is the number of distinct red costs, b is the number of blue edges, and W is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm. © Springer-Verlag Berlin Heidelberg 2007.Frank Dehne, Jörg-Rüdiger Sack, and Norbert Zeh, editors, Algorithms and Data StructuresSpringer Berlin / Heidelberg10th International Workshop on Algorithms and Data Structures, WADS 2007; Halifax; Canada; 15 August 2007 through 17 August 2007.info:eu-repo/semantics/publishe