Seasonal environmental heterogeneity is cyclic, persistent and geographically widespread. In species that reproduce multiple times annually, environmental changes across seasonal time may create different selection regimes that may shape the population ecology and life history adaptation in these species. Here, we investigate how two closely related species of Drosophila in a temperate orchard respond to environmental changes across seasonal time. Natural populations of Drosophila melanogaster and Drosophila simulans were sampled at four timepoints from June through November to assess seasonal change in fundamental aspects of population dynamics as well as life history traits. D. melanogaster exhibit pronounced change across seasonal time: early in the season, the population is inferred to be uniformly young and potentially represents the early generation following overwintering survivorship. D. melanogaster isofemale lines derived from the early population and reared in a common garden are characterized by high tolerance to a variety of stressors as well as a fast rate of development in the laboratory environment that declines across seasonal time. In contrast, wild D. simulans populations were inferred to be consistently heterogeneous in age distribution across seasonal collections; only starvation tolerance changed predictably over seasonal time in a parallel manner as in D. melanogaster. These results suggest fundamental differences in population and evolutionary dynamics between these two taxa associated with seasonal heterogeneity in environmental parameters and associated selection pressures.

[1] Narrow bipolar pulses (NBPs) are a class of highaltitude, high-energy discharges that occur during some thunderstorms. We use a modified transmission line model (called MTLEI) with a current that increases exponentially along the propagation channel to test mechanisms that might produce NBPs. Model outputs were compared to measured E data from a single NBP collected at near and far field locations. We were unable to fit the measured data using the fast current propagation speeds appropriate for a runaway breakdown/extensive air shower mechanism. Instead, by using currents that travel relatively slowly (6 Â 10 7 m/s), the MTLEI model fit the data reasonably well. This result is compatible with a mechanism that uses runaway breakdown to produce charge carriers along with a moving electric field to drive the main NBP current. Using this model for the measured NBP, we estimate a charge moment of 0.6 CÁkm.

We discuss a family of random fields indexed by a parameter s ∈ R which we call the fractional Gaussian fields, given bywhere W is a white noise on R d and (−∆) −s/2 is the fractional Laplacian. These fields can also be parameterized by their Hurst parameter H = s − d/2. In one dimension, examples of FGF s processes include Brownian motion (s = 1) and fractional Brownian motion (1/2 < s < 3/2). Examples in arbitrary dimension include white noise (s = 0), the Gaussian free field (s = 1), the bi-Laplacian Gaussian field (s = 2), the log-correlated Gaussian field (s = d/2), Lévy's Brownian motion (s = d/2 + 1/2), and multidimensional fractional Brownian motion (d/2 < s < d/2 + 1). These fields have applications to statistical physics, early-universe cosmology, finance, quantum field theory, image processing, and other disciplines.We present an overview of fractional Gaussian fields including covariance formulas, Gibbs properties, spherical coordinate decompositions, restrictions to linear subspaces, local set theorems, and other basic results. We also define a discrete fractional Gaussian field and explain how the FGF s with s ∈ (0, 1) can be understood as a long range Gaussian free field in which the potential theory of Brownian motion is replaced by that of an isotropic 2s-stable Lévy process.

The conformal loop ensemble $\operatorname {CLE}_{\kappa}$ with parameter $8/3<\kappa<8$ is the canonical conformally invariant measure on countably infinite collections of noncrossing loops in a simply connected domain. Given $\kappa$ and $\nu$, we compute the almost-sure Hausdorff dimension of the set of points $z$ for which the number of CLE loops surrounding the disk of radius $\varepsilon$ centered at $z$ has asymptotic growth $\nu\log (1/\varepsilon )$ as $\varepsilon \to0$. By extending these results to a setting in which the loops are given i.i.d. weights, we give a CLE-based treatment of the extremes of the Gaussian free field.Comment: Published at http://dx.doi.org/10.1214/14-AOP995 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

In 1990, Schnyder used a 3-spanning-tree decomposition of a simple triangulation, now known as the Schnyder wood, to give a fundamental grid-embedding algorithm for planar maps. We show that a uniformly sampled Schnyder-wood-decorated triangulation with n vertices converges as n → ∞ to the Liouville quantum gravity with parameter 1, decorated with a triple of SLE 16 's of angle difference 2π/3 in the imaginary geometry sense. Our convergence result provides a description of the continuum limit of Schnyder's embedding algorithm via Liouville quantum gravity and imaginary geometry.