The main theories of biodiversity either neglect species interactions or assume that species interact randomly with each other. However, recent empirical work has revealed that ecological networks are highly structured, and the lack of a theory that takes into account the structure of interactions precludes further assessment of the implications of such network patterns for biodiversity. Here we use a combination of analytical and empirical approaches to quantify the influence of network architecture on the number of coexisting species. As a case study we consider mutualistic networks between plants and their animal pollinators or seed dispersers. These networks have been found to be highly nested, with the more specialist species interacting only with proper subsets of the species that interact with the more generalist. We show that nestedness reduces effective interspecific competition and enhances the number of coexisting species. Furthermore, we show that a nested network will naturally emerge if new species are more likely to enter the community where they have minimal competitive load. Nested networks seem to occur in many biological and social contexts, suggesting that our results are relevant in a wide range of fields.

Within the context of a first-order phase transition in the early Universe, we study the collision process for vacuum bubbles expanding in a plasma. The effects of the plasma are simulated by introducing a damping term in the equations of motion for a U (1) global field. We find that Lorentz-contracted spherically symmetric domain walls adequately describe the overdamped motion of the bubbles in the thin wall approximation, and study the process of collision and phase equilibration both numerically and analytically. With an analytical model for the phase propagation in 1+1 dimensions, we prove that the phase waves generated in the bubble merging are reflected by the walls of the true vacuum cavity, giving rise to a long-lived oscillating state that delays the phase equilibration. The existence of such a state in the 3+1 dimensional model is then confirmed by numerical simulations, and the consequences for the formation of vortices in three-bubble collisions are considered. 98.80.Cq

One possible way in which phase transitions in the early universe may have occurred is via nucleation of bubbles of the new phase (true vacuum) in the old phase (false vacuum). The technique most widely used to compute the probability of bubble nucleation is based on instanton methods in the context of the semiclassical approximation. At zero temperature in 3+1 dimensions the nucleation rate is dominated by the O(4) symmetric instanton, a sphere of radius R, while a t temperatures T >> R-' the decay is dominated by a "cylindrical" (static) instanton with O (3) invariance. There has been discussion in the literature as to whether the transition between these two regimens would be first order (discontinuity in the first derivative of the nucleation rate a t the transition temperature T,), or second order (continuity of the first derivative, but discontinuity of the second derivative a t T,). In this paper we obtain the finite temperature solutions corresponding t o the quantum and the thermal regimes, and compute their action as a function of the temperature for different values of the wall thickness in a p4 potential. Our results indicate that only for the cases of very large wall thickness a second-order transition takes place, while for all the other cases a first-order transition occurs.

No abstract

(20/12/96) Within the context of first order phase transitions in the early universe, we study the influence of a coupling between the (global U(1)) scalar driving the transition and the rest of the matter content of the theory. The effect of the coupling on the scalar is simulated by introducing a damping term in its equations of motion, as suggested by recent results in the electroweak phase transition. After a preceeding paper, in which we studied the influence that this coupling has in the dynamics of bubble collisions and topological defect formation, we proceed in this paper to quantify the impact of this new effects on the probability of defect creation per nucleating bubble.