Description of diffusive and propagative behavior on fractals

The known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes. After that, we propose a description developed in the context of the intrinsic metric of fractals, which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime. We show that our approach has a stronger physical justification than previous works on this field. The most important result we present is the introduction of a dependence on time and space for the conductivity in fractals, which is deduced by scaling arguments and supported by computer simulations. Finally, the diffusion equation is used to introduce the possibility of reaction-diffusion processes on fractals and analyze their properties. Specifically, an analytic expression for the speed of the corresponding travelling fronts, which can be of great interest for application purposes, is derived

Effects of punishment in a mobile population playing the prisoner’s dilemma game

We deal with a system of prisoner’s dilemma players undergoing continuous motion in a two-dimensional plane. In contrast to previous work, we introduce altruistic punishment after the game. We find punishing only a few of the cooperator-defector interactions is enough to lead the system to a cooperative state in environments where otherwise defection would take over the population. This happens even with soft nonsocial punishment (where both cooperators and defectors punish other players, a behavior observed in many human populations). For high enough mobilities or temptations to defect, low rates of social punishment can no longer avoid the breakdown of cooperation

Cohabitation effect on the slowdown of the Neolithic expansion

We introduce the effect of cohabitation between generations to a previous model on the slowdown of the Neolithic transition in Europe. This effect consists on the fact that human beings do not leave their children alone when they migrate, but on the contrary they cohabit until their children reach adulthood. We also use archaeological data to estimate the variation of the Mesolithic population density with distance, and use this information to predict the slowdown of the Neolithic front speed. The new equation leads to a substantial correction, up to 37%, relative to previous results. The new model is able to provide a satisfactory explanation not only to the relative speed but also to the absolute speed of the Neolithic front obtained from archaeological data

Tracing the Origin and Spread of Agriculture in Europe

The origins of early farming and its spread to Europe have been the subject of major interest for some time. The main controversy today is over the nature of the Neolithic transition in Europe: the extent to which the spread was, for the most part, indigenous and animated by imitatio (cultural diffusion) or else was driven by an influx of dispersing populations (demic diffusion). We analyze the spatiotemporal dynamics of the transition using radiocarbon dates from 735 early Neolithic sites in Europe, the Near East, and Anatolia. We compute great-circle and shortest-path distances from each site to 35 possible agricultural centers of origin—ten are based on early sites in the Middle East and 25 arehypothetical locations set at 58 latitude/longitude intervals. We perform a linear fit of distance versus age (and viceversa) for each center. For certain centers, high correlation coefficients (R . 0.8) are obtained. This implies that a steady rate or speed is a good overall approximation for this historical development. The average rate of the Neolithic spread over Europe is 0.6–1.3 km/y (95% confidence interval). This is consistent with the prediction of demic diffusion(0.6–1.1 km/y). An interpolative map of correlation coefficients, obtained by using shortest-path distances, shows thatthe origins of agriculture were most likely to have occurred in the northern Levantine/Mesopotamian area

The Role of the Delay Time in the Modeling of Biological Range Expansions

The time interval between successive migrations of biological species causes a delay time in the reaction-diffusion equations describing their space-time dynamics. This lowers the predicted speed of the waves of advance, as compared to classical models. It has been shown that this delay-time effect improves the modeling of human range expansions. Here, we demonstrate that it can also be important for other species. We present two new examples where the predictions of the time-delayed and the classical (Fisher) approaches are compared to experimental data. No free or adjustable parameters are used. We show that the importance of the delay effect depends on the dimensionless product of the initial growth rate and the delay time. We argue that the delay effect should be taken into account in the modeling of range expansions for biological species

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

It is shown that Lotka-Volterra interaction terms are not appropriate to describe vertical cultural transmission. Appropriate interaction terms are derived and used to compute the effect of vertical cultural transmission on demic front propagation. They are also applied to a specific example, the Neolithic transition in Europe. In this example, it is found that the effect of vertical cultural transmission can be important (about 30%). On the other hand, simple models based on differential equations can lead to large errors (above 50%). Further physical, biophysical, and cross-disciplinary applications are outlined

Time-Delayed Spread of Viruses in Growing Plaques

The spread of viruses in growing plaques predicted by classical models is greater than that measured experimentally. There is a widespread belief that this discrepancy is due to biological factors. Here we show that the observed speeds can be satisfactorily predicted by a purely physical model that takes into account the delay time due to virus reproduction inside infected cells. No free or adjustable parameters are used

Speed of travelling fronts: Two-dimensional and ballistic dispersal probability distributions

The speed of traveling fronts for a two-dimensional model of a delayed reactiondispersal process is derived analytically and from simulations of molecular dynamics. We show that the one-dimensional (1D) and two-dimensional (2D) versions of a given kernel do not yield always the same speed. It is also shown that the speeds of time-delayed fronts may be higher than those predicted by the corresponding non-delayed models. This result is shown for systems with peaked dispersal kernels which lead to ballistic transport