Invasion and effective size of graph-structured populations

摘要

Author summary Evolving populations, companies, social circles are networks in which genes, resources and ideas circulate. Imagine a useful novelty is introduced in the network: a favorable mutation, a new product concept or a smart idea. Will this novelty be retained and propagated through the network or rather lost? Using tools originally devised for demographic research, we model the dynamics of the very initial spread of a useful novelty in a network. The network structure has a strong impact on these dynamics by affecting the effective network size through random effects. This effective network size, which correlates with the probability that a novelty spreads and is different from the actual size (i.e. number of nodes), varies with network structure. The effective size can even become independent of the actual network size and thus remain very small even for huge networks.