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.

A multivariate analysis of beta diversity across organisms and environments

We examined variability in hierarchical beta diversity across ecosystems, geographical gradients, and organism groups using multivariate spatial mixed modeling analysis of two independent data sets. The larger data set comprised reported ratios of regional species richness (RSR) to local species richness (LSR) and the second data set consisted of RSR: LSR ratios derived from nested species-area relationships. There was a negative, albeit relatively weak, relationship between beta diversity and latitude. We found only relatively subtle differences in beta diversity among the realms, yet beta diversity was lower in marine systems than in terrestrial or freshwater realms. Beta diversity varied significantly among organisms' major characteristics such as body mass, trophic position, and dispersal type in the larger data set. Organisms that disperse via seeds had highest beta diversity, and passively dispersed organisms showed the lowest beta diversity. Furthermore, autotrophs had lower beta diversity than organisms higher up the food web; omnivores and carnivores had consistently higher beta diversity. This is evidence that beta diversity is simultaneously controlled by extrinsic factors related to geography and environment, and by intrinsic factors related to organism characteristics.

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.

On the Multivariate Gamma-Gamma (ΓΓ) Distribution with Arbitrary Correlation and Applications in Wireless Communications

The statistical properties of the multivariate GammaGamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the su m of ΓΓ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.

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.

Slow Release Drug Dissolution Profile Prediction in Pharmaceutical Manufacturing: a Multivariate and Machine Learning Approach

Slow release drugs must be manufactured to meet target specifications with respect to dissolution curve profiles. In this paper we consider the problem of identifying the drivers of dissolution curve variability of a drug from historical manufacturing data. Several data sources are considered: raw material parameters, coating data, loss on drying and pellet size statistics. The methodology employed is to develop predictive models using LASSO, a powerful machine learning algorithm for regression with high-dimensional datasets. LASSO provides sparse solutions facilitating the identification of the most important causes of variability in the drug fabrication process. The proposed methodology is illustrated using manufacturing data for a slow release drug.

The determination of optimal processing conditions for PLA and PLA/CaCO3 in twin screw extrusion using DoE and multivariate analysis

Biodegradable polymers, such as PLA (Polylactide), come from renewable resources like corn starch and if disposed of correctly, degrade and become harmless to the ecosystem making them attractive alternatives to petroleum based polymers. PLA in particular is used in a variety of applications including medical devices, food packaging and waste disposal packaging. However, the industry faces challenges in melt processing of PLA due to its poor thermal stability which is influenced by processing temperatures and shearing.
Identification and control of suitable processing conditions is extremely challenging, usually relying on trial and error, and often sensitive to batch to batch variations. Off-line assessment in a lab environment can result in high scrap rates, long lead times and lengthy and expensive process development. Scrap rates are typically in the region of 25-30% for medical grade PLA costing between €2000-€5000/kg.
Additives are used to enhance material properties such as mechanical properties and may also have a therapeutic role in the case of bioresorbable medical devices, for example the release of calcium from orthopaedic implants such as fixation screws promotes healing. Additives can also reduce the costs involved as less of the polymer resin is required.
This study investigates the scope for monitoring, modelling and optimising processing conditions for twin screw extrusion of PLA and PLA w/calcium carbonate to achieve desired material properties. A DAQ system has been constructed to gather data from a bespoke measurement die comprising melt temperature; pressure drop along the length of the die; and UV-Vis spectral data which is shown to correlate to filler dispersion. Trials were carried out under a range of processing conditions using a Design of Experiments approach and samples were tested for mechanical properties, degradation rate and the release rate of calcium. Relationships between recorded process data and material characterisation results are explored.

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.

A Conditional Approach for Modelling Patient Re-admissions in Hospital using a mixture of Coxian phase-type distributions incorporating Bayes Theorem

The number of elderly patients requiring hospitalisation in Europe is rising. With a greater proportion of elderly people in the population comes a greater demand for health services and, in particular, hospital care. Thus, with a growing number of elderly patients requiring hospitalisation competing with non-elderly patients for a fixed (and in some cases, decreasing) number of hospital beds, this results in much longer waiting times for patients, often with a less satisfactory hospital experience. However, if a better understanding of the recurring nature of elderly patient movements between the community and hospital can be developed, then it may be possible for alternative provisions of care in the community to be put in place and thus prevent readmission to hospital. The research in this paper aims to model the multiple patient transitions between hospital and community by utilising a mixture of conditional Coxian phase-type distributions that incorporates Bayes' theorem. For the purpose of demonstration, the results of a simulation study are presented and the model is applied to hospital readmission data from the Lombardy region of Italy.

Prognostic role of lemur tyrosine kinase-3 germline polymorphisms in adjuvant gastric cancer in Japan and the United States

Lemur tyrosine kinase-3 (LMTK3) was recently identified as an estrogen receptor (ER)-α modulator related to endocrine therapy resistance, and its polymorphisms rs9989661 (T>C) T/T genotype and rs8108419 (G>A) G/G or A/G genotype predicted improved outcomes in breast cancer. Because different predominant ER distributions link to breast and gastric cancer and little is known of the prognostic role of LMTK3 in gastric cancer, this study was carried out to clarify the prognostic role of these polymorphisms in gastric cancer. One-hundred and sixty-nine Japanese and 137 U.S. patients with localized gastric adenocarcinoma were enrolled. Genomic DNA was extracted from blood or tissue, and all samples were analyzed by PCR-based direct DNA sequencing. Overall, these polymorphisms were not associated with survival in both cohorts. When gender was considered, in multivariate analysis, harboring rs9989661 T/T genotype was associated with disease-free survival [HR, 4.37; 95% confidence interval (CI), 2.08-9.18; P < 0.0001] and overall survival (OS; HR, 3.69; 95% CI, 1.65-8.24; P = 0.0014) in the Japanese males and time to recurrence (HR, 7.29; 95% CI, 1.07-49.80; P = 0.043) in the U.S. females. Meanwhile, harboring rs8108419 G/G genotype was associated with OS in the Japanese females (HR, 3.04; 95% CI, 1.08-8.56; P = 0.035) and the U.S. males (HR, 3.39; 95% CI, 1.31-8.80; P = 0.012). The prognostic role of these polymorphisms may be negative in gastric cancer. These findings suggest that the estrogen pathway may play a prognostic role in patients with gastric cancer but this may be dependent on the regional differences both in physiology and genetic alterations of gastric cancer.