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Bacteria, in contrast to eukaryotic cells contain two types of genes: chromosomal genes that are fixed to the cell, and plasmids that are mobile genes, easily shared to other cells. The sharing of plasmid genes between individual bacteria and between bacterial lineages has contributed vastly to bacterial evolution, allowing specialized traits to `jump ship' between one lineage or species and the next. The benefits of this generosity from the point of view of both recipient and plasmid are generally understood, but come at the expense of chromosomal genes in the donor cell, which share potentially advantageous genes with their competition while receiving no benefit. Using both continuous models and agent based simulations, we demonstrate that `secretive' genes which restrict horizontal gene transfer are favored over wide range of models and parameter values. Our findings lead to a peculiar paradox: given the obvious benefits of keeping secrets, why do bacteria share information so freely?, Comment: 27 pages, 8 figures, 1 table

The rise of the World Airline Network over the past century has lead to sharp changes in our notions of `distance' and `closeness' - both in terms of trade and travel, but also (less desirably) with respect to the spread of disease. When novel pathogens are discovered, countries, cities and hospitals are caught trying to predict how much time they have to prepare. In this paper, by considering the early stages of epidemic spread as a simple branching process, we derive the full probability distribution of arrival times. We are able to re-derive a number of past arrival time results (in suitable limits), and demonstrate the robustness of our approach, both to parameter values far outside the traditionally considered regime, and to errors in the parameter values used. The branching process approach provides some theoretical justification to the `effective distance' introduced by Brockmann & Helbing (2013), however we also observe that when compared to real world data, the predictive power of all methods in this class is significantly lower than has been previously reported., Comment: 27 pages, 15 figures

Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with escape time sensitive to noise. When the model is extended to include space, this leads to different points in space "escaping from zero" at different times, and uniform initial conditions nucleate into sharp peaks spread randomly across a nearly uniform background, a phenomena closely resembling nucleation during phase transition. We use Large Deviation Theory to determine burst shape and temporal scaling with respect to noise amplitude. These results give a prototype for a particular form of patternless symmetry breaking in the vicinity of a stability boundary, and demonstrates how microscopic noise can lead to macroscopic effects in such a region.

Population structures can be crucial determinants of evolutionary processes. For the Moran process on graphs certain structures suppress selective pressure, while others amplify it (Lieberman et al. 2005 Nature 433 312-316). Evolutionary amplifiers suppress random drift and enhance selection. Recently, some results for the most powerful known evolutionary amplifier, the superstar, have been invalidated by a counter example (D\'iaz et al. 2013 Proc. R. Soc. A 469 20130193). Here we correct the original proof and derive improved upper and lower bounds, which indicate that the fixation probability remains close to $1-1/(r^4 H)$ for population size $N\to\infty$ and structural parameter $H\gg1$. This correction resolves the differences between the two aforementioned papers. We also confirm that in the limit $N,H\to\infty$ superstars remain capable of eliminating random drift and hence of providing arbitrarily strong selective advantages to any beneficial mutation. In addition, we investigate the robustness of amplification in superstars and find that it appears to be a fragile phenomenon with respect to changes in the selection or mutation processes., Comment: 29 pages, 4 figures, Major Revision