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Social, biological and economic networks grow and decline with occasional fragmentation and re-formation, often explained in terms of external perturbations. We show that these phenomena can be a direct consequence of simple imitation and internal conflicts between ‘cooperators’ and ‘defectors’. We employ a game-theoretic model of dynamic network formation where successful individuals are more likely to be imitated by newcomers who adopt their strategies and copy their social network. We find that, despite using the same mechanism, cooperators promote well-connected highly prosperous networks and defectors cause the network to fragment and lose its prosperity; defectors are unable to maintain the highly connected networks they invade. Once the network is fragmented it can be reconstructed by a new invasion of cooperators, leading to the cycle of formation and fragmentation seen, for example, in bacterial communities and socio-economic networks. In this endless struggle between cooperators and defectors we observe that cooperation leads to prosperity, but prosperity is associated with instability. Cooperation is prosperous when the network has frequent formation and fragmentation., Mathematics, Other Research Unit

As an example of life at high Reynolds number, we investigate the dynamics of the Fisher equation for the spreading of micro-organisms in one dimension subject to both turbulent convection and diffusion. We show that for strong enough turbulence, bacteria, for example, track, in a quasilocalized fashion (with remarkably long persistence times), sinks in the turbulent field. An important consequence is a large reduction in the carrying capacity of the fluid medium. We analytically determine the regimes where this quasi-localized behavior occurs and test our predictions by numerical simulations., Physics

Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a population undergoing a continual range expansion in one dimension. During such a colonization period, lineages can fix at the wave front by means of a "surfing" mechanism [Edmonds C.A., Lillie A.S. & Cavalli-Sforza L.L. (2004) Proc Natl Acad Sci USA 101: 975-979]. We quantify this phenomenon in terms of (i) the spatial distribution of lineages that reach fixation and, closely related, (ii) the continual loss of genetic diversity (heterozygosity) at the wave front, characterizing the approach to fixation. Our simulations show that an effective population size can be assigned to the wave that controls the (observable) gradient in heterozygosity left behind the colonization process. This effective population size is markedly higher in pushed waves than in pulled waves, and increases only sub-linearly with deme size. To explain these and other findings, we develop a versatile analytical approach, based on the physics of reaction-diffusion systems, that yields simple predictions for any deterministic population dynamics., Physics