MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Preferential attachment renders an evolving network of populations robust against crashes

Areejit Samal and Hildegard Meyer-Ortmanns


We study a model for the evolution of chemical species under a combination of population dynamics on a short time scale and a selection mechanism on a larger time scale. Least fit nodes are replaced by new nodes whose links are attached to the nodes of the given network via preferential attachment.

In contrast to a random attachment of newly incoming nodes that as used in previous work, this preferential attachment mechanism accelerates the generation of a so-called autocatalytic set after a start from a random geometry and the growth of this structure until it saturates in a stationary phase in which the whole system is an autocatalytic set. Moreover, the system in the stationary phase becomes much more stable against crashes in the population size as compared to random attachment. We explain in detail in terms of graph theoretical notions which structure of the resulting network is responsible for this stability. Essentially it is a very dense core with many loops and less nodes playing the role of a keystone that prevent crashes almost completely.

89.75.Fb, 89.75.Hc,
complex networks, network evolution, population dynamics, selection, autocatalytic set

Related publications

2009 Repository Open Access
Areejit Samal and Hildegard Meyer-Ortmanns

Preferential attachment renders an evolving network of populations robust against crashes

In: Physica / A, 388 (2009) 8, pp. 1535-1545