Darwinian Selection and Non-existence of Nash Equilibria

We study selection acting on phenotype in a collection of agents playing local games lacking Nash equilibria. After each cycle one of the agents losing most games is replaced by a new agent with new random strategy and game partner. The network generated can be considered critical in the sense that the lifetimes of the agents is power law distributed. The longest surviving agents are those with the lowest absolute score per time step. The emergent ecology is characterized by a broad range of behaviors. Nevertheless, the agents tend to be similar to their opponents in terms of performance.Comment: 4 pages, 5 figure

APPLICATION OF THE ECONOMIC THRESHOLD FOR INTERSEASONAL PEST CONTROL

We show how an interseasonal pest control problem can be simplified to enable an intraseasonal model to be empirically applied, extending the range of application of the intraseasonal model. Three alternative economic thresholds are compared. The optimal solution requires repeated computations by the farmer to compute the profit maximizing dose, with a corresponding threshold, for each pest infestation. Two alternative decision rules require a single computation by the farmer for the threshold and dosage rate. An empirical illustration shows that, relative to the optimal solution which is computationally burdensome to the farmer, little net revenue is lost by using one of the thresholds based upon a simpler decision rule.Farm Management,

The maximum density droplet to lower density droplet transition in quantum dots

We show that, Landau level mixing in two-dimensional quantum dot wave functions can be taken into account very effectively by multiplying the exact lowest Landau level wave functions by a Jastrow factor which is optimized by variance minimization. The comparison between exact diagonalization and fixed phase diffusion Monte Carlo results suggests that the phase of the many-body wave functions are not affected much by Landau level mixing. We apply these wave functions to study the transition from the maximum density droplet state (incipient integer quantum Hall state with angular momentum L=N(N-1)/2) to lower density droplet states (L>N(N-1)/2).Comment: 8 pages, 5 figures, accepted for publication in Phys. Rev.

The measure and significance of Bateman's principles

Bateman's principles explain sex roles and sexual dimorphism through sex-specific variance in mating success, reproductive success and their relationships within sexes (Bateman gradients). Empirical tests of these principles, however, have come under intense scrutiny. Here, we experimentally show that in replicate groups of red junglefowl, Gallus gallus, mating and reproductive successes were more variable in males than in females, resulting in a steeper male Bateman gradient, consistent with Bateman's principles. However, we use novel quantitative techniques to reveal that current methods typically overestimate Bateman's principles because they (i) infer mating success indirectly from offspring parentage, and thus miss matings that fail to result in fertilization, and (ii) measure Bateman gradients through the univariate regression of reproductive over mating success, without considering the substantial influence of other components of male reproductive success, namely female fecundity and paternity share. We also find a significant female Bateman gradient but show that this likely emerges as spurious consequences of male preference for fecund females, emphasizing the need for experimental approaches to establish the causal relationship between reproductive and mating success. While providing qualitative support for Bateman's principles, our study demonstrates how current approaches can generate a misleading view of sex differences and roles

ECONOMIC THRESHOLDS UNDER UNCERTAINTY WITH APPLICATION TO CORN NEMATODE MANAGEMENT

An economic threshold of agricultural pest management is derived. Results provide a method for researchers to use in making improved pest control recommendations to farmers without farm level decision-making. An empirical illustration for lesion nematode management in irrigated corn is given and directions for further research are indicated.Crop Production/Industries, Risk and Uncertainty,

The weakly perturbed Schwarzschild lens in the strong deflection limit

We investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang & Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining point-like to the lowest order.Comment: 12 pages, 1 figure