Universality of citation distributions- a new understanding

Universality of scaled citation distributions was claimed a decade ago (F. Radicchi, S. Fortunato, and C. Castellano, PNAS, 105(45), 17268 (2008)) but its theoretical justification has been lacking so far. Here, we study citation distributions for three disciplines- Physics, Economics, and Mathematics- and assess them using our explanatory model of citation dynamics. The model posits that the citation count of a paper is determined by its fitness- the attribute, which, for most papers, is set at the moment of publication. In addition, the papers’ citation count is related to the process by which the knowledge about this paper propagates in the scientific community. Our measurements indicate that the fitness distribution for different disciplines is nearly identical and can be approximated by the log-normal distribution, while the viral propagation process is discipline-specific. The model explains which sets of citation distributions can be scaled and which can not. In particular, we show that the near-universal shape of the citation distributions for different disciplines and for different citation years traces its origin to the nearly universal fitness distribution, while deviations from this shape are associated with the discipline-specific citation dynamics of papers. Peer Review https://publons.com/publon/10.1162/qss_a_00127

Detecting differences in the topology of scale-free networks grown under time-dynamic topological fitness

The fitness model was introduced in the literature to expand the Barabasi-Albert model’s generative mechanism, which produces scale-free networks under the control of degree. However, the fitness model has not yet been studied in a comprehensive context because most models are built on invariant fitness as the network grows and time-dynamics mainly concern new nodes joining the network. This mainly static consideration restricts fitness in generating scale-free networks only when the underlying fitness distribution is power-law, a fact which makes the hybrid fitness models based on degree-driven preferential attachment to remain the most attractive models in the literature. This paper advances the time-dynamic conceptualization of fitness, by studying scale-free networks generated under topological fitness that changes as the network grows, where the fitness is controlled by degree, clustering coefficient, betweenness, closeness, and eigenvector centrality. The analysis shows that growth under time-dynamic topological fitness is indifferent to the underlying fitness distribution and that different topological fitness generates networks of different topological attributes, ranging from a mesh-like to a superstar-like pattern. The results also show that networks grown under the control of betweenness centrality outperform the other networks in scale-freeness and the majority of the other topological attributes. Overall, this paper contributes to broadening the conceptualization of fitness to a more time-dynamic context.

Dynamics of fitness distributions in the presence of a phenotypic optimum: an integro-differential approach

We propose an integro-differential description of the dynamics of the fitness distribution in an asexual population under mutation and selection, in the presence of a phenotype optimum. Due to the presence of this optimum, the distribution of mutation effects on fitness depends on the parent’s fitness, leading to a non-standard equation with “context-dependent" mutation kernels.Under general assumptions on the mutation kernels, which encompass the standardndimensional Gaussian Fisher’s geometrical model (FGM), we prove that the equation admits a unique time-global solution. Furthermore, we derive a nonlocal nonlinear transport equation satisfied by the cumulant generating function of the fitness distribution. As this equation is the same as the equation derived by Martin and Roques (2016) while studying stochastic Wright-Fisher-type models, this shows that the solution of the main integro-differential equation can be interpreted as the expected distribution of fitness corresponding to this type of microscopic models, in a deterministic limit. Additionally, we give simple sufficient conditions for the existence/non-existence of a concentration phenomenon at the optimal fitness value, i.e, of a Dirac mass at the optimum in the stationary fitness distribution. We show how it determines a phase transition, as mutation rates increase, in the value of the equilibrium mean fitness at mutation-selection balance. In the particular case of the FGM, consistently with previous studies based on other formalisms (Waxman and Peck, 1998, 2006), the condition for the existence of the concentration phenomenon simply requires that the dimensionnof the phenotype space be larger than or equal to 3 and the mutation rateUbe smaller than some explicit threshold.The accuracy of these deterministic approximations are further checked by stochastic individual-based simulations.

Cliff-edge model of obstetric selection in humans

The strikingly high incidence of obstructed labor due to the disproportion of fetal size and the mother’s pelvic dimensions has puzzled evolutionary scientists for decades. Here we propose that these high rates are a direct consequence of the distinct characteristics of human obstetric selection. Neonatal size relative to the birth-relevant maternal dimensions is highly variable and positively associated with reproductive success until it reaches a critical value, beyond which natural delivery becomes impossible. As a consequence, the symmetric phenotype distribution cannot match the highly asymmetric, cliff-edged fitness distribution well: The optimal phenotype distribution that maximizes population mean fitness entails a fraction of individuals falling beyond the “fitness edge” (i.e., those with fetopelvic disproportion). Using a simple mathematical model, we show that weak directional selection for a large neonate, a narrow pelvic canal, or both is sufficient to account for the considerable incidence of fetopelvic disproportion. Based on this model, we predict that the regular use of Caesarean sections throughout the last decades has led to an evolutionary increase of fetopelvic disproportion rates by 10 to 20%.

The non-stationary dynamics of fitness distributions: asexual model with epistasis and standing variation

Various models describe asexual evolution by mutation, selection and drift. Some focus directly on fitness, typically modelling drift but ignoring or simplifying both epistasis and the distribution of mutation effects (travelling wave models). Others follow the dynamics of quantitative traits determining fitness (Fisher’s geometrical model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift. In all cases, predictions are typically obtained in high or low mutation rate limits and for long-term stationary regimes, thus loosing information on transient behaviors and the effect of initial conditions. Here, we connect fitness-based and trait-based models into a single framework, and seek explicit solutions even away from stationarity. The expected fitness distribution is followed over time via its cumulant generating function, using a deterministic approximation that neglects drift. In several cases, explicit trajectories for the full fitness distribution are obtained, for arbitrary mutation rates and standing variance. For non-epistatic mutation, especially with beneficial mutations, this approximation fails over the long term but captures the early dynamics, thus complementing stationary stochastic predictions. The approximation also handles several diminishing return epistasis models (e.g. with an optimal genotype): it can then apply at and away from equilibrium. General results arise at equilibrium, where fitness distributions display a ‘phase transition’ with mutation rate. Beyond this phase transition, in Fisher’s geometrical model, the full trajectory of fitness and trait distributions takes simple form, robust to details of the mutant phenotype distribution. Analytical arguments are explored for why and when the deterministic approximation applies.Significance statementHow fast do asexuals evolve in new environments? Asexual fitness dynamics are well documented empirically. Various corresponding theories exist, to which they may be compared, but most typically describe stationary regimes, thus losing information on the shorter timescale of experiments, and on the impact of the initial conditions set by the experimenter. Here, a general deterministic approximation is proposed that encompasses many previous models as subcases, and shows surprising accuracy when compared to stochastic simulations. It can yield predictions over both short and long timescales, hopefully fostering the quantitative test of alternative models, using data from experimental evolution in asexuals.

Robust Analysis of Preferential Attachment Models with Fitness

The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied by a random fitness. We concentrate on the typical behaviour of the graph by calculating the fitness distribution of a vertex chosen proportional to its degree. For a particular variant of the model, this analysis was first carried out by Borgs, Chayes, Daskalakis and Roch. However, we present a new method, which is robust in the sense that it does not depend on the exact specification of the attachment law. In particular, we show that a peculiar phenomenon, referred to as Bose–Einstein condensation, can be observed in a wide variety of models. Finally, we also compute the joint degree and fitness distribution of a uniformly chosen vertex.