A Comparative study of germination strategies of two species of genus Allium sect. Allium

Germination experiments were performed with seeds of two species of genus Allium section Allium, a rare and endangered species A. pyrenaicum and a common A. sphaerocephalon. Different pre-treatments and a photoperiod of 24 h darkness were applied in order to simulate different germination conditions. Both species showed a high percentage of viable seeds a part of which were dormant. An elevate percentage of dormant seeds could be caused by a later collection time. Low altitude populations had more mortality than the others, possibly caused by the hard summer conditions during flowering and fruiting time. Comparisons between dates of species coexistence localities only show inter-population variability and it could be caused by the detected dormancy. Darkness accelerates germination, possibly for elongation radicle stimulation. Heat-shock pre-treatments decreased germination time in seeds from localities where fire is a probable event. The rarity of A. Pyrenaicum not seems to be caused by restricted germination requirements but is attributable to distinct habitat preferences, related to his altitudinal range of distribution

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