We explore the hypothesis that the relative abundance of feedback loops in many empirical complex networks is severely reduced owing to the presence of an inherent global directionality. Aimed at quantifying this idea, we propose a simple probabilistic model in which a free parameter gamma controls the degree of inherent directionality. Upon strengthening such directionality, the model predicts a drastic reduction in the fraction of loops which are also feedback loops. To test this prediction, we extensively enumerated loops and feedback loops in many empirical biological, ecological and socio-technological directed networks. We show that, in almost all cases, empirical networks have a much smaller fraction of feedback loops than network randomizations. Quite remarkably, this empirical finding is quantitatively reproduced, for all loop lengths, by our model by fitting its only parameter gamma. Moreover, the fitted value of gamma correlates quite well with another direct measurement of network directionality, performed by means of a novel algorithm. We conclude that the existence of an inherent network directionality provides a parsimonious quantitative explanation for the observed lack of feedback loops in empirical networks.
Bianco, Giuseppe; Mariani, Patrizio; Visser, André W.; Mazzocchi, Maria Grazia; Pigolotti, Simone Journal of the Royal Society Interface Vol. 11, num. 96, p. 1-9 DOI: 10.1098/rsif.2014.0164 Date of publication: 2014-07-06 Journal article
Movement is a fundamental behaviour of organisms that not only brings about beneficial encounters with resources and mates, but also at the same time exposes the organism to dangerous encounters with predators. The movement patterns adopted by organisms should reflect a balance between these contrasting processes. This trade-off can be hypothesized as being evident in the behaviour of plankton, which inhabit a dilute three-dimensional environment with few refuges or orienting landmarks. We present an analysis of the swimming path geometries based on a volumetric Monte Carlo sampling approach, which is particularly adept at revealing such trade-offs by measuring the self-overlap of the trajectories. Application of this method to experimentally measured trajectories reveals that swimming patterns in copepods are shaped to efficiently explore volumes at small scales, while achieving a large overlap at larger scales. Regularities in the observed trajectories make the transition between these two regimes always sharper than in randomized trajectories or as predicted by random walk theory. Thus, real trajectories present a stronger separation between exploration for food and exposure to predators. The specific scale and features of this transition depend on species, gender and local environmental conditions, pointing at adaptation to state and stage-dependent evolutionary trade-offs.
We study a stochastic spatial model of biological competition in which two species have the same birth and death rates, but different diffusion constants. In the absence of this difference, the model can be considered as an off-lattice version of the voter model and presents similar coarsening properties. We show that even a relative difference in diffusivity on the order of a few percent may lead to a strong bias in the coarsening process favoring the more agile species. We theoretically quantify this selective advantage and present analytical formulas for the average growth of the fastest species and its fixation probability.
We study a stochastic community model able to interpolate from a neutral regime to a niche partitioned regime upon varying a single parameter tuning the intensity of niche stabilization, namely the difference between intraspecific and interspecific competition. By means of a self-consistent approach, we obtain an analytical expression for the species abundance distribution, in excellent agreement with stochastic simulations of the model. In the neutral limit, the Fisher log-series is recovered, while upon increasing the stabilization strength the species abundance distribution develops a maximum for species at intermediate abundances, corresponding to the emergence of a carrying capacity. Numerical studies of species extinction-time distribution show that niche-stabilization strongly affects also the dynamical properties of the system by increasing the average species lifetimes, while suppressing their fluctuations. The results are discussed in view of the niche-neutral debate and of their potential relevance to field data.
We introduce a stochastic model describing aggregation of misfolded proteins and degradation by the protein quality control system in a single cell. Aggregate growth is contrasted by the cell quality control system, that attacks them at different stages of the growth process, with an efficiency that decreases with their size. Model parameters are estimated from experimental data. Two qualitatively different behaviors emerge: a homeostatic state, where the quality control system is stable and aggregates of large sizes are not formed, and an oscillatory state, where the quality control system periodically breaks down, allowing for formation of large aggregates. We discuss how these periodic breakdowns may constitute a mechanism for the development of neurodegenerative diseases
We study stochastic copying schemes in which discrimination between a right and a wrong match is achieved via different kinetic barriers or different binding energies of the two matches. We demonstrate that, in single-step reactions, the two discrimination mechanisms are strictly alternative and cannot be mixed to further reduce the error fraction. Close to the lowest error limit, kinetic discrimination results in a diverging copying velocity and dissipation per copied bit. On the other hand, energetic discrimination reaches its lowest error limit in an adiabatic regime where dissipation and velocity vanish. By analyzing experimentally measured kinetic rates of two DNA polymerases, T7 and Pol¿, we argue that one of them operates in the kinetic and the other in the energetic regime. Finally, we show how the two mechanisms can be combined in copying schemes implementing error correction through a proofreading pathway.
We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space is continuous and the total density of competing individuals fluctuates due to demographic stochasticity. By means of analytics and numerical simulations, we study the behavior of fixation probabilities, fixation times, and heterozygosity, in a neutral setting and in cases where the two species can compete or cooperate. By concluding with examples in which individuals are transported by fluid flows, we argue that this model is a natural choice to describe competition in marine environments.
Juul, Jeepe; Kianercy, Ardeshir; Bernhardsson, Sebastian; Pigolotti, Simone Bulletin of the American Physical Society Vol. 88, num. 2, p. 1-99 DOI: 10.1103/PhysRevE.88.022806 Date of publication: 2013 Journal article
We study adaptive dynamics in games where players abandon the population at a given rate and are replaced by naive players characterized by a prior distribution over the admitted strategies. We demonstrate how such a process leads macroscopically to a variant of the replicator equation, with an additional term accounting for player turnover. We study how Nash equilibria and the dynamics of the system are modified by this additional term for prototypical examples such as the rock-paper-scissors game and different classes of two-action games played between two distinct populations. We conclude by showing how player turnover can account for nontrivial departures from Nash equilibria observed in data from lowest unique bid auctions.
As a model for cell-to-cell communication in biological tissues, we construct repressor lattices by repeating a regulatory three-node motif on a hexagonal structure. Local interactions can be unidirectional, where a node either represses or activates a neighbor that does not communicate backwards. Alternatively, they can be bidirectional where two neighboring nodes communicate with each other. In the unidirectional case, we perform stability analyses for the transitions from stationary to oscillating states in lattices with different regulatory units. In the bidirectional case, we investigate transitions from oscillating states to ordered patterns generated by local switches. Finally, we show how such stable patterns in two-dimensional lattices can be generalized to three-dimensional systems.
Understanding factors that shape biodiversity and species coexistence across scales is of utmost importance in ecology, both theoretically and for conservation policies. Species-area relationships (SARs), measuring how the number of observed species increases upon enlarging the sampled area, constitute a convenient tool for quantifying the spatial structure of biodiversity. While general features of species-area curves are quite universal across ecosystems, some quantitative aspects can change significantly. Several attempts have been made to link these variations to ecological forces. Within the framework of spatially explicit neutral models, here we scrutinize the effect of varying the local population size (i.e. the number of individuals per site) and the level of habitat saturation (allowing for empty sites). We conclude that species-area curves become shallower when the local population size increases, while habitat saturation, unless strongly violated, plays a marginal role. Our findings provide a plausible explanation of why SARs for microorganisms are flatter than those for larger organisms.
In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid,
provided that it is also unique. We use a grand canonical approach to derive an analytical expression for
the equilibrium distribution of strategies. We then study the properties of the solution as a function of the
mean number of players, and compare them with a large data set of internet auctions. The theory agrees
with the data with striking accuracy for small population-size N, while for larger N a qualitatively
different distribution is observed.We interpret this result as the emergence of two different regimes, one in
which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large
population to adapt and find the optimal strategy when participating in a collective game.
Bernacchia, Alberto; Pigolotti, Simone Journal of the Royal Statistical Society: Series B (Statistical Methodology) Vol. 73, num. 3, p. 407-422 DOI: 10.1111/j.1467-9868.2011.00772.x Date of publication: 2011-06-01 Journal article
The estimation of a density profile from experimental data points is a challenging problem, which is usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow the design of more accurate estimation procedures, such as maximum likelihood. Our aim is to construct a procedure that makes no explicit assumptions, but still providing an accurate estimate of the density. We introduce the self-consistent estimate: the power spectrum of a candidate density is given, and an estimation procedure is constructed on the assumption, to be released a posteriori, that the candidate is correct.
We present and discuss particle based algorithms to numerically study the dynamics of population subjected to an advecting flow condition. We discuss few possible variants of the algorithms and compare them in a model compressible flow. A comparison against appropriate versions of the continuum stochastic Fisher equation (sFKPP) is also presented and discussed. The algorithms can be used to study populations genetics in fluid environments.