Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)

Generació Einstein 3.0. La comunicació en un món nou

Imaginem-nos que volem vendre alguna cosa a un jove: un producte, una idea o potser unes pràctiques a la nostra empresa. Com ho faríeu? Quins mètodes podríeu fer servir? Ho faríeu de la mateixa manera que ho heu fet sempre? Penseu que els vostres anuncis, textos publicitaris, llocs web o cartells encara serien vàlids? Creieu que tots els diners invertits en comunicació i màrqueting us ajudarien a assolir l’objectiu? Si la resposta a aquestes preguntes és que sí, aleshores no cal que continueu llegint. Podeu continuar comunicant-vos amb els joves com ho heu fet fins ara, perquè us funciona. Però si us passa com a tots nosaltres i reconeixeu que la comunicació amb els joves no és tan fàcil, que de vegades us sembla que no us veuen o no us senten, aleshores us convidem a continuar llegint. No pretenem oferir totes les respostes, ja que no tenim la clau dels seus cors, però sí que volem mirar d’entendre el seu comportament, la seva manera de pensar i les seves accions