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There is empirical evidence from a range of disciplines that as theconnectivity of a network increases, we observe an increase in the averagefitness of the system. But at the same time, there is an increase in theproportion of failure/extinction events which are extremely large. Theprobability of observing an extreme event remains very low, but it is markedlyhigher than in the system with lower degrees of connectivity. We give examplesfrom complex systems such as outages in the US power grid, the robustnessproperties of cell biology networks, and trade links and the propagation ofboth currency crises and disease. We consider networks which are populated byagents which are heterogeneous in terms of their fitness for survival. Thenetwork evolves over time, and in each period agents take self-interesteddecisions to increase their fitness for survival to form alliances whichincrease the connectivity of the network. The network is subjected to externalnegative shocks both with respect to the size of the shock and the spatialimpact of the shock. We examine the size/frequency distribution of extinctionsand how this distribution evolves as the connectivity of the network grows. Theresults are robust with respect to the choice of statistical distribution ofthe shocks. We find that increasing the number of connections causes anincrease in the average fitness of agents, yet at the same time makes thesystem as whole more vulnerable to catastrophic failure/extinction events on annear-global scale.Comment: 15 pages, 5 figure

Cascades of failure and extinction in dynamically evolving complex systems