Global patterns of speciation and diversity.

In recent years, strikingly consistent patterns of biodiversity have been identified over space, time, organism type and geographical region. A neutral theory (assuming no environmental selection or organismal interactions) has been shown to predict many patterns of ecological biodiversity. This theory is based on a mechanism by which new species arise similarly to point mutations in a population without sexual reproduction. Here we report the simulation of populations with sexual reproduction, mutation and dispersal. We found simulated time dependence of speciation rates, species-area relationships and species abundance distributions consistent with the behaviours found in nature. From our results, we predict steady speciation rates, more species in one-dimensional environments than two-dimensional environments, three scaling regimes of species-area relationships and lognormal distributions of species abundance with an excess of rare species and a tail that may be approximated by Fisher's logarithmic series. These are consistent with dependences reported for, among others, global birds and flowering plants, marine invertebrate fossils, ray-finned fishes, British birds and moths, North American songbirds, mammal fossils from Kansas and Panamanian shrubs. Quantitative comparisons of specific cases are remarkably successful. Our biodiversity results provide additional evidence that species diversity arises without specific physical barriers. This is similar to heavy traffic flows, where traffic jams can form even without accidents or barriers.

Semiclassical approximations based on complex trajectories.

The semiclassical limit of the coherent state propagator involves complex classical trajectories of the Hamiltonian H(u,v) = satisfying u(0) = z' and v(T) = z"*. In this work we study mostly the case z' = z". The propagator is then the return probability amplitude of a wave packet. We show that a plot of the exact return probability brings out the quantal images of the classical periodic orbits. Then we compare the exact return probability with its semiclassical approximation for a soft chaotic system with two degrees of freedom. We find two situations where classical trajectories satisfying the correct boundary conditions must be excluded from the semiclassical formula. The first occurs when the contribution of the trajectory to the propagator becomes exponentially large as Planck's over 2 pi goes to zero. The second occurs when the contributing trajectories undergo bifurcations. Close to the bifurcation the semiclassical formula diverges. More interestingly, in the example studied, after the bifurcation, where more than one trajectory satisfying the boundary conditions exist, only one of them in fact contributes to the semiclassical formula, a phenomenon closely related to Stokes lines. When the contributions of these trajectories are filtered out, the semiclassical results show excellent agreement with the exact calculations.

Stability and instability of polymorphic populations and the role of multiple breeding seasons in phase III of Wright's shifting balance theory.

It is generally difficult for a large population at a fitness peak to acquire the genotypes of a higher peak, because the intermediates produced by allelic recombination between types at different peaks are of lower fitness. In his shifting-balance theory, Wright proposed that fitter genotypes could, however, become fixed in small isolated demes by means of random genetic fluctuations. These demes would then try to spread their genome to nearby demes by migration of their individuals. The resulting polymorphism, the coexistence of individuals with different genotypes, would give the invaded demes a chance to move up to a higher fitness peak. This last step of the process, namely, the invasion of lower fitness demes by higher fitness genotypes, is known as phase III of Wright's theory. Here we study the invasion process from the point of view of the stability of polymorphic populations. Invasion occurs when the polymorphic equilibrium, established at low migration rates, becomes unstable. We show that the instability threshold depends sensitively on the average number of breeding seasons of individuals. Iteroparous species (with many breeding seasons) have lower thresholds than semelparous species (with a single breeding season). By studying a particular simple model, we are able to provide analytical estimates of the migration threshold as a function of the number of breeding seasons. Once the threshold is crossed and polymorphism becomes unstable, any imbalance between the different demes is sufficient for invasion to occur. The outcome of the invasion, however, depends on many parameters, not only on fitness. Differences in fitness, site capacities, relative migration rates, and initial conditions, all contribute to determine which genotype invades successfully. Contrary to the original perspective of Wright's theory for continuous fitness improvement, our results show that both upgrading to higher fitness peaks and downgrading to lower peaks are possible.

Periodic orbits of nonscaling Hamiltonian systems from quantum mechanics.

Quantal (E,tau) plots are constructed from the eigenvalues of the quantum system. We demonstrate that these representations display the periodic orbits of the classical system, including bifurcations and the transition from stable to unstable. (c) 1995 American Institute of Physics.

The mind of the analyst: from listening to interpretation.

The analyst demands two somewhat contradictory attitudes of himself: on the one hand, he listens and interprets on the basis of his theoretical knowledge, experiences and scheme of reference and, on the other, he must open himself to the new, the unforeseen and the surprising. His work, from listening to interpretation, is situated within a context that includes the history of the treatment as well as the history of the analysand, which is in the process of reconstruction. This context determines the moment of the interpretation (which may vary), i.e. the point ot urgency of a given session. This point denotes the moment when something emerges from the unconscious of the analysand and the analyst believes that it must be interpreted. It is something that occurs within the intersubjective field, which embraces both participants and has its own, partly unconscious, dynamics. This configuration or unconscious fantasy of the field constitutes the common source from which both the discourse of one partner and the other's interpretation spring. The moments of blockage in the dynamics of the field, the obstacles in the analytic process, invite every analyst to take a 'second look' at the field, focusing on the unconscious intersubjective relationship which determines it. Focused either on the analysand or on the field, the interpretation can perform its two dialectically complementary functions: it may irrupt into the disguises of the patient's unconscious, or it may allow him to synthesise and reconstruct his history and identity.

Calculations of periodic trajectories for the Henon-Heiles Hamiltonian using the monodromy method.

The monodromy method, for calculating classical periodic trajectories, is applied to the famous Henon-Heiles potential, which is invariant under the group D(3). The monodromy method is computationally very efficient and is used to find many families of periodic trajectories, including a number of simple bifurcations from the main families of the Henon-Heiles potential.

The infantile psychic trauma from us to Freud: pure trauma, retroactivity and reconstruction.

In the works of Freud, the concept of childhood psychic trauma evolves in the direction of increasing complexity. The authors maintain that this expansion corresponds to a new conception of retroactive temporality (Nachträglich), which is precisely the one we use in the analytic process of reconstruction and historicization from the present toward the past. We are thus led to differentiate the extreme form of the unassimilable 'pure' Trauma, nearly pure death drive, from the retroactively historicized forms which are reintegrated into the continuity of a vital flow of time that we 'invent' in analytic work.

Process and non-process in analytic work.

The 'talking cure', named by Anna O. and discovered by Freud, has been widely expanded and diversified throughout our century. Our objective in this paper is to underline several points which seem to define the analytic process. We believe that forthcoming progress in psychoanalysis must arise from the study of clinical experience at its frontiers, at its topmost limits, in its failures. For this reason, we have concentrated our search on the analytic non-process, in the very places where the process stumbles or halts. This has led us to propose the introduction of several terms: 'field', 'bastion', 'second look'. When the process stumbles or halts, the analyst must question himself about the obstacle. The obstacle involves the analysand's transference and the analyst's countertransference, and poses rather confusing problems. The arrest of the process introduces us fully into the nature of its movement, its inherent temporality. If the process is to continue, then by what main-spring can we accomplish it? We describe this particular dialectic of processes and non-process as a task of overcoming the obstacles which describe its success or failure.