Phylogeographical analysis of two cold-tolerant plants with disjunct Lusitanian distributions does not support in situ survival during the last glaciation

Aim: We used a combination of modelling and genetic approaches to investigate whether Pinguicula grandiflora and Saxifraga spathularis, two species that exhibit disjunct Lusitanian distributions, may have persisted through the Last Glacial Maximum (LGM, c. 21 ka) in separate northern and southern refugia.

Location: Northern and eastern Spain and south-western Ireland.

Methods: Palaeodistribution modelling using maxent was used to identify putative refugial areas for both species at the LGM, as well as to estimate their distributions during the Last Interglacial (LIG, c. 120 ka). Phylogeographical analysis of samples from across both species' ranges was carried out using one chloroplast and three nuclear loci for each species.

Results: The palaeodistribution models identified very limited suitable habitat for either species during the LIG, followed by expansion during the LGM. A single, large refugium across northern Spain and southern France was postulated for P. grandiflora. Two suitable regions were identified for S. spathularis: one in northern Spain, corresponding to the eastern part of the species' present-day distribution in Iberia, and the other on the continental shelf off the west coast of Brittany, south of the limit of the British–Irish ice sheet. Phylogeographical analyses indicated extremely reduced levels of genetic diversity in Irish populations of P. grandiflora relative to those in mainland Europe, but comparable levels of diversity between Irish and mainland European populations of S. spathularis, including the occurrence of private hapotypes in both regions.

Main conclusions: Modelling and phylogeographical analyses indicate that P. grandiflora persisted through the LGM in a southern refugium, and achieved its current Irish distribution via northward dispersal after the retreat of the ice sheets. Although the results for S. spathularis are more equivocal, a similar recolonization scenario also seems the most likely explanation for the species' current distribution.

Angular distributions in two-colour two-photon ionization of He

We present R-Matrix with time dependence (RMT) calculations for the photoionization of helium irradiated by an EUV laser pulse and an overlapping IR pulse with an emphasis on the anisotropy parameters of the sidebands generated by the dressing laser field. We investigate how these parameters depend on the amount of atomic structure included in the theoretical model for two-photon ionization. To verify the accuracy of the RMT approach, our theoretical results are compared with experiment.

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Dust-acoustic supersolitons in a three-species dusty plasma with kappa distributions

Supersolitons are a form of soliton characterised, inter alia, by additional local extrema superimposed on the usual bipolar electric field signature. Previous studies of supersolitons supported by three-component plasmas have dealt with ion-acoustic structures. An analogous problem is now considered, namely, dust-acoustic supersolitons in a plasma composed of fluid negative dust grains and two kappa-distributed positive ion species. Calculations illustrating some supersoliton characteristics are presented. © Cambridge University Press 2013.

A new statistical framework for the quantification of covariate associations with species distributions

Identifying processes that shape species geographical ranges is a prerequisite for understanding environmental change. Currently, species distribution modelling methods do not offer credible statistical tests of the relative influence of climate factors and typically ignore other processes (e.g. biotic interactions and dispersal limitation). We use a hierarchical model fitted with Markov Chain Monte Carlo to combine ecologically plausible niche structures using regression splines to describe unimodal but potentially skewed response terms. We apply spatially explicit error terms that account for (and may help identify) missing variables. Using three example distributions of European bird species, we map model results to show sensitivity to change in each covariate. We show that the overall strength of climatic association differs between species and that each species has considerable spatial variation in both the strength of the climatic association and the sensitivity to climate change. Our methods are widely applicable to many species distribution modelling problems and enable accurate assessment of the statistical importance of biotic and abiotic influences on distributions.

Fractal species distributions do not produce power-law species-area relationships

We derive the species-area relationship (SAR) expected from an assemblage of fractally distributed species. If species have truly fractal spatial distributions with different fractal dimensions, we show that the expected SAR is not the classical power-law function, as suggested recently in the literature. This analytically derived SAR has a distinctive shape that is not commonly observed in nature: upward-accelerating richness with increasing area (when plotted on log-log axes). This suggests that, in reality, most species depart from true fractal spatial structure. We demonstrate the fitting of a fractal SAR using two plant assemblages (Alaskan trees and British grasses). We show that in both cases, when modelled as fractal patterns, the modelled SAR departs from the observed SAR in the same way, in accord with the theory developed here. The challenge is to identify how species depart from fractality, either individually or within assemblages, and more importantly to suggest reasons why species distributions are not self-similar and what, if anything, this can tell us about the spatial processes involved in their generation.

The geographical structure of British bird distributions:diversity, spatial turnover and scale

1. Using data on the spatial distribution of the British avifauna, we address three basic questions about the spatial structure of assemblages: (i) Is there a relationship between species richness (alpha diversity) and spatial turnover of species (beta diversity)? (ii) Do high richness locations have fewer species in common with neighbouring areas than low richness locations?, and (iii) Are any such relationships contingent on spatial scale (resolution or quadrat area), and do they reflect the operation of a particular kind of species-area relationship (SAR)?

2. For all measures of spatial turnover, we found a negative relationship with species richness. This held across all scales, with the exception of turnover measured as beta (sim).

3. Higher richness areas were found to have more species in common with neighbouring areas.

4. The logarithmic SAR fitted better than the power SAR overall, and fitted significantly better in areas with low richness and high turnover.

5. Spatial patterns of both turnover and richness vary with scale. The finest scale richness pattern (10 km) and the coarse scale richness pattern (90 km) are statistically unrelated. The same is true of the turnover patterns.

6. With coarsening scale, locations of the most species-rich quadrats move north. This observed sensitivity of richness 'hotspot' location to spatial scale has implications for conservation biology, e.g. the location of a reserve selected on the basis of maximum richness may change considerably with reserve size or scale of analysis.

7. Average turnover measured using indices declined with coarsening scale, but the average number of species gained or lost between neighbouring quadrats was essentially scale invariant at 10-13 species, despite mean richness rising from 80 to 146 species (across an 81-fold area increase). We show that this kind of scale invariance is consistent with the logarithmic SAR.

Stress and Strain Distributions During Compressive Deformation of Titanium Alloy Affected by Microstructure

In the research of the microstructural influence on dynamic compression, an assumption that the α and the β phases in titanium alloys were linearly strengthened was proposed, and a two-dimensional model using ANSYS (ANSYS, Inc., Canonsburg, PA) focusing on the role of microgeometrical structure was developed. By comparing the stress and strain distributions of different microstructures, the roles of cracks and phase boundaries in titanium compression were studied.

Brightness variation distributions among main belt asteroids from sparse light curve sampling with Pan-STARRS 1

The rotational state of asteroids is controlled by various physical mechanisms including collisions, internal damping and the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. We have analysed the changes in magnitude between consecutive detections of ∼ 60,000 asteroids measured by the PanSTARRS 1 survey during its first 18 months of operations. We have attempted to explain the derived brightness changes physically and through the application of a simple model. We have found a tendency toward smaller magnitude variations with decreasing diameter for objects of 1 < D < 8 km. Assuming the shape distribution of objects in this size range to be independent of size and composition our model suggests a population with average axial ratios 1: 0.85 ± 0.13: 0.71 ± 0.13, with larger objects more likely to have spin axes perpendicular to the orbital plane.