Average survival rates after 50 years for networked nodes as a function of the correlation strength among disasters.

<p>Solid lines describe networks that are very inhomogeneous (<i>β</i> = 0.8), dashed lines describe networks that are more homogeneous (<i>β</i> = 0.2). Red curves describe spatial correlations among disasters, black curves represent spatial-temporal correlations and blue curves represent temporal correlations.</p

Samples of random events for four correlation scenarios.

<p>The horizontal axis represents time up to 50 years. The vertical axis represents a spatial grid. The total number of events is 500 for each panel. <i>σ</i>_<i>t</i> and <i>σ</i>_<i>x</i> are the variances in the spatial and temporal domain defining the level of correlation (see the detailed discussion in Section 2).</p

Node Survival in Networks under Correlated Attacks

<div><p>We study the interplay between correlations, dynamics, and networks for repeated attacks on a socio-economic network. As a model system we consider an insurance scheme against disasters that randomly hit nodes, where a node in need receives support from its network neighbors. The model is motivated by gift giving among the Maasai called Osotua. Survival of nodes under different disaster scenarios (uncorrelated, spatially, temporally and spatio-temporally correlated) and for different network architectures are studied with agent-based numerical simulations. We find that the survival rate of a node depends dramatically on the type of correlation of the disasters: Spatially and spatio-temporally correlated disasters increase the survival rate; purely temporally correlated disasters decrease it. The type of correlation also leads to strong inequality among the surviving nodes. We introduce the concept of disaster masking to explain some of the results of our simulations. We also analyze the subsets of the networks that were activated to provide support after fifty years of random disasters. They show qualitative differences for the different disaster scenarios measured by path length, degree, clustering coefficient, and number of cycles.</p></div

Four typical gift giving networks for <i>β</i> = 0.2 for a single simulation of 50 years.

<p>Red nodes are nodes that have survived, black nodes are dead. Directed links indicate one or more gift giving event in the course of a 50 year simulation.</p

Average herd size per surviving node after 50 years as a function of the correlation strength among disasters.

<p>Solid lines describe networks that are very inhomogeneous (<i>β</i> = 0.8), dashed lines describe networks that are more homogeneous (<i>β</i> = 0.2). Red curves describe spatial correlations among disasters, black curves represent spatial-temporal correlations and blue curves represent temporal correlations.</p

Gift giving events as a function of time.

<p>Solid lines describe networks that are very inhomogeneous (<i>β</i> = 0.8), dashed lines describe networks that are more homogeneous (<i>β</i> = 0.2). Red curves describe spatial correlations among disasters, black curves represent spatial-temporal correlations and blue curves represent temporal correlations.</p

Average survival rates after 50 years for isolated nodes as a function of changing disaster variances and different disaster correlations.

<p>Red curves describe spatial correlations among disasters, black curves represent spatial-temporal correlations and blue curves represent temporal correlations. The correlation strength is defined in detail in the main text in Section 4.</p

Node Survival in Networks under Correlated Attacks - Fig 7

<p>a) Average path length and b) average degree of the cattle flow networks for the four different disaster correlation cases.</p

Additional file 2: Fig. S1. of The absence of reproductive isolation between non-sister and deeply diverged mitochondrial lineages of the black-throated tit (Aegithalos concinnus) revealed by a multilocus genetic analysis in a contact zone

Plots of the best K identified by the method of ΔK. (DOCX 163 kb

Additional file 1: Table S1. of The absence of reproductive isolation between non-sister and deeply diverged mitochondrial lineages of the black-throated tit (Aegithalos concinnus) revealed by a multilocus genetic analysis in a contact zone

Sampling locations, sample size, geographic information and mitochondrial divergence of the black-throated tit for this study. (DOCX 18 kb