Evaluating range-expansion models for calculating nonnative species' expansion rate

Species range shifts associated with environmental change or biological invasions are increasingly important study areas. However, quantifying range expansion rates may be heavily influenced by methodology and/or sampling bias. We compared expansion rate estimates of Roesel's bush-cricket (Metrioptera roeselii, Hagenbach 1822), a nonnative species currently expanding its range in south-central Sweden, from range statistic models based on distance measures (mean, median, 95th gamma quantile, marginal mean, maximum, and conditional maximum) and an area-based method (grid occupancy). We used sampling simulations to determine the sensitivity of the different methods to incomplete sampling across the species' range. For periods when we had comprehensive survey data, range expansion estimates clustered into two groups: (1) those calculated from range margin statistics (gamma, marginal mean, maximum, and conditional maximum: similar to 3 km/year), and (2) those calculated from the central tendency (mean and median) and the area-based method of grid occupancy (similar to 1.5 km/year). Range statistic measures differed greatly in their sensitivity to sampling effort; the proportion of sampling required to achieve an estimate within 10% of the true value ranged from 0.17 to 0.9. Grid occupancy and median were most sensitive to sampling effort, and the maximum and gamma quantile the least. If periods with incomplete sampling were included in the range expansion calculations, this generally lowered the estimates (range 16-72%), with exception of the gamma quantile that was slightly higher (6%). Care should be taken when interpreting rate expansion estimates from data sampled from only a fraction of the full distribution. Methods based on the central tendency will give rates approximately half that of methods based on the range margin. The gamma quantile method appears to be the most robust to incomplete sampling bias and should be considered as the method of choice when sampling the entire distribution is not possible

An Airborne Gamma Ray Survey of Parts of SW Scotland in February 1993. Final Report

An airborne gamma ray survey was conducted for the Scottish Office Environment Department of coastal and inland parts of SW Scotland to define existing background levels, to locate features worthy of further attention, and to demonstrate the emergency response capabilities of radiometric methods. Coastal areas were surveyed with 500 m line spacing. Inland areas were specified to 2 km line spacing, however it was possible to achieve 1 km line spacing in the majority of the inland zone. Fieldwork was conducted between the 1st and 16th February 1993. A total of over 17,000 gamma ray spectra were recorded, using a 16 litre NaI spectrometer mounted in a helicopter flying at 50-75m ground clearance and 120kph. A total area of 3650 km2 was surveyed in 41.6 flying hours, from roughly 4370 line kilometres. The data were reduced in the field using standard SURRC procedures for background subtraction, stripping of spectral interferences, altitude correction, and calibration. Preliminary maps of the distribution of 137Cs, 40K, 214Bi, 208Tl, and estimated ground level gamma dose rate were produced during the fieldwork period using working calibration values derived from previous surveys. A set of core samples was collected from Wigtown Merse, Longbridgemuir and Caerlaverock merse for calibration purposes, and aerial observations were performed at these sites. Further soil sampling and ground level in-situ gamma spectrometry was performed in the summer of 1993 to investigate the applicability of the calibration to a range of upland soil types and topographical environments. These locations received peak deposition from the Chernobyl accident, are vulnerable to wet deposition, and are difficult to monitor rapidly using ground based methods. A total of 76 soil cores, subdivided into 168 separate samples was thus collected for high resolution gamma spectrometry in the laboratory. This was conducted from April to November 1993. For the terrestrial sites the aerial survey estimates based on the working calibration, were in good agreement with both in-situ gamma spectrometry and the results of core analysis. This validates the preliminary maps in these contexts, and confirms that a general calibration is sufficient for fallout mapping under emergency response conditions. On coastal salt marsh sites (merse), where aged deposits of Sellafield derived activity have accumulated, subsurface activity profiles for 137Cs and 241Am and the presence of superficial levels of 134Cs were observed from the soil cores. Similar features have been observed in previous surveys. In these cases the effects of source burial must be taken into account to avoid underestimation of activity levels by both ground-based and aerial gamma spectrometry. A separate set of detailed maps for the principal merse sites was therefore prepared using a calibration factor derived from the soil cores from this context. There are prospects for developing spectral analysis procedures to account for source depth in aerial surveys. Source burial on the merse also has implications for sampling techniques, and for dose rate measurement, which would merit further consideration. The radiometric maps show clearly the distributions of each individual nuclide and indicate the contribution which individual localised features make to the overall gamma ray dose rate. Naturally occurring nuclides reflect the underlying geological and geomorphological contexts of the landscape. The main granite intrusions, most notably at Cairnsmore of Fleet, the Loch Doon Granodiorite, Glencairn of Carsphairn, the Dalbeattie granite, and Criffel Pluton are readily visible in 40K, 214Bi and 208Tl maps, and control their local radiation environments. A number of areas of enhanced 214Bi, which may reflect radon potential, were noted. A transient radon associated 214Bi signal was observed on the west of the Wigtown peninsular during the survey. Examination of spectral data in the vicinity of Dundrennan has confirmed that there is no evidence of widespread terrestrial contamination arising from the use of depleted uranium projectiles on the range. The 137Cs map indicates the environmental distribution of this nuclide in considerable detail. Levels of 137Cs range from approximately 2 kBq m-2, a level consistent with global weapons’ testing fallout, from 2-40kBq m-2 on terrestrial sites affected by deposition from the Chernobyl accident, and from 40 kBq m-2 to over 200 kBq m-2 on tide washed pastures which have accumulated marine sediments from the Irish Sea. All three levels are represented within the survey zone, in a manner which is consistent with the findings of previous aerial surveys in adjacent areas, and with ground based studies. The main Chernobyl deposition in Dumfries and Galloway appears to have occurred between an area just east of the Nith, and Glenluce. The northern limit has not yet been defined, and there may be grounds for considering extension of the northern and particularly eastern limits of the inland survey zone. Within the survey zone the deposition pattern is complex, including both upland and lowland components. The plume trajectories for deposition inferred from these observations are oriented northwards rather than in the NW directions predicted by meteorological derived estimates. This may explain the contradiction between results from the Central Highlands and the estimated fallout patterns. The data presented here both add to previous knowledge, and serve as a baseline against which any future changes can be measured. The survey provides systematic coverage of the sedimentary and terrestrial coastal system for the first time, and has identified a number of merse sites which have accumulated radioactivity from past marine discharges from Sellafield, and which are not routinely monitored under existing Scottish Office arrangements. Some of these locations are extensive and fall within SSI’s; furthermore they are key sites for studying future deposition trends. It would seem prudent to review radiological assessments in the light of this work to ensure that the patterns of occupancy and sensitive ecologies of the merse are taken fully into account. The emergency response potential of aerial radiometrics has been clearly demonstrated in this project. It provides the only practical means of providing comprehensive environmental measurements of remote and upland landscapes on a short time scale, with an effective area sampling density some 106-107 times greater than soil sampling. Results are compatible with ground based approaches, and could focus ground based efforts effectively under emergency conditions. Modern approaches to data recording and analysis are able to produce maps during the survey period. National baseline mapping in Scotland, at 1 km resolution, would require less than 800 flying hours; 20 km line spacing would take roughly 40 hours of flight time. A long term programme of high resolution national baseline mapping, coupled to an emergency response standby arrangement, would provide an extremely cost effective way of preserving the capability developed since the Chernobyl accident, while producing high quality environmental data for research purpos

Implications from ASKAP Fast Radio Burst Statistics

Although there has recently been tremendous progress in studies of fast radio bursts (FRBs), the nature of their progenitors remains a mystery. We study the fluence and dispersion measure (DM) distributions of the ASKAP sample to better understand their energetics and statistics. We first consider a simplified model of a power-law volumetric rate per unit isotropic energy dN/dE ~ E^{-gamma} with a maximum energy E_max in a uniform Euclidean Universe. This provides analytic insights for what can be learnt from these distributions. We find that the observed cumulative DM distribution scales as N(>DM) ~ DM^{5-2*gamma} (for gamma > 1) until a maximum value DM_max above which bursts near E_max fall below the fluence threshold of a given telescope. Comparing this model with the observed fluence and DM distributions, we find a reasonable fit for gamma ~ 1.7 and E_max ~ 10^{33} erg/Hz. We then carry out a full Bayesian analysis based on a Schechter rate function with cosmological factor. We find roughly consistent results with our analytical approach, although with large errors on the inferred parameters due to the small sample size. The power-law index and the maximum energy are constrained to be gamma = 1.6 +/- 0.3 and log(E_max) [erg/Hz] = 34.1 +1.1 -0.7 (68% confidence), respectively. From the survey exposure time, we further infer a cumulative local volumetric rate of log N(E > 10^{32} erg/Hz) [Gpc^{-3} yr^{-1}] = 2.6 +/- 0.4 (68% confidence). The methods presented here will be useful for the much larger FRB samples expected in the near future to study their distributions, energetics, and rates.Comment: ApJ accepted. Expanded beyond the scope of the earlier version into 8 pages, 7 figures. Following referees' comments, we included a full Bayesian analysis based on a Schechter rate function with cosmological factor. The PDF of the inferred model parameters are presented by MCMC sampling in Figure 4 (the most important result). We also discussed the completeness of ASKAP sample in Section

The VIMOS Public Extragalactic Redshift Survey (VIPERS): On the correct recovery of the count-in-cell probability distribution function

We compare three methods to measure the count-in-cell probability density function of galaxies in a spectroscopic redshift survey. From this comparison we found that when the sampling is low (the average number of object per cell is around unity) it is necessary to use a parametric method to model the galaxy distribution. We used a set of mock catalogues of VIPERS, in order to verify if we were able to reconstruct the cell-count probability distribution once the observational strategy is applied. We find that in the simulated catalogues, the probability distribution of galaxies is better represented by a Gamma expansion than a Skewed Log-Normal. Finally, we correct the cell-count probability distribution function from the angular selection effect of the VIMOS instrument and study the redshift and absolute magnitude dependency of the underlying galaxy density function in VIPERS from redshift $0.5$ to $1.1$. We found very weak evolution of the probability density distribution function and that it is well approximated, independently from the chosen tracers, by a Gamma distribution.Comment: 14 pages, 11 figures, 2 table

An Aerial Gamma Ray Survey of Torness Nuclear Power Station on 27-30 March 1994

<p>An aerial gamma-ray survey of the environment of Torness Nuclear Power Station was commissioned by Scottish Nuclear Limited, and conducted by the Scottish Universities Research and Reactor Centre. The area surveyed encloses a 31km square, with Torness Nuclear Power Station at the centre, flown with a line spacing of 500m. A secondary area, in closer proximity to the nuclear site, was flown with 250m spacing.</p> <p>Over 6000 gamma ray spectra were recorded with a high volume spectrometer operated from a helicopter over a three day period in March 1994. Spectral data were recorded together with satellite navigation (GPS) and radar altimetry data. The results provide a comprehensive record of the radiation environment around Torness and have been used to map the distribution of natural and man-made radionuclides, forming a baseline to enable future environmental changes may be assessed.</p> <p>The natural radionuclides 40K, 214Bi and 208Tl are highly correlated with each other and show a distribution which reflects both the underlying geological and geomorphological features of the area. The main structural boundaries of the Dunbar-Gifford and Lammermuir faults can be partly discerned in the maps, as can some igneous intrusions. Areas with peat or alluvium cover appear as negative features in the radiometric maps.</p> <p>Radiocaesium 137Cs levels range from below 4 kBq m-2 to over 20 kBq m-2. Upland areas near Coldingham Common, Black Castle Hill and Dunbar Common show the highest values, similar in deposition pattern and level to Chernobyl activity observed in the West of Scotland and elsewhere. Published national maps derived from meteorological and ground sampling data predicted much lower levels for these locations. However core samples taken after the survey have confirmed the presence of the activity, and the attribution to Chernobyl. This finding demonstrates both the effectiveness of the method for rapid location of radioactive deposition, and the need for baseline studies to determine present levels. Count rates from a spectral window corresponding to 60Co were also mapped. The results are close to detection limits and show a slight correlation with natural sources. Therefore they are more probably due to residuals remaining after separation of spectral interferences than to low level 60Co contamination.</p> <p>Gamma ray dose rates range from approximately 0.1 to 0.6 mGy a-1 with a mean value of 0.34 mGy a-1, and are derived mainly from natural sources. Ground level measurements were taken at nine district monitoring points within the area using a 3x3" NaI spectrometer and a survey meter (Series 6/80) used routinely by SNL. Both ground based data sets were in good agreement with each other and with the aerial survey after accounting for instrumental and cosmic ray background contributions.</p> <p>There is no evidence that Torness Power Station has affected the surrounding radiation environment, within the operational and sensitivity limits of the aerial survey.</p> <p>The longer term impact of the site can be assessed by future surveys. Moreover under emergency conditions it would be possible to utilise this method for rapid mapping of the area on a timescale which cannot be matched using alternative approaches. </p&gt

Random effects compound Poisson model to represent data with extra zeros

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and predict species counts (discrete data) or abundance distributions (continuous data). Standard methods for modeling such data include mixture and two-part conditional models. Conversely to these methods, the stochastic models proposed here behave coherently with regards to a change of scale, since they mimic the harvesting of a marked Poisson process in the modeling steps. Random effects are used to account for inhomogeneity. In this paper, model design and inference both rely on conditional thinking to understand the links between various layers of quantities : parameters, latent variables including random effects and zero-inflated observations. The potential of these parsimonious hierarchical models for zero-inflated data is exemplified using two marine macroinvertebrate abundance datasets from a large scale scientific bottom-trawl survey. The EM algorithm with a Monte Carlo step based on importance sampling is checked for this model structure on a simulated dataset : it proves to work well for parameter estimation but parameter values matter when re-assessing the actual coverage level of the confidence regions far from the asymptotic conditions.Comment: 4

An Airborne and Vehicular Gamma Survey of Greenham Common, Newbury District and Surrounding Areas

The airborne gamma ray survey recorded more than 40,000 scintillation spectra and 20,000 spectra from semiconductor detectors. The vehicular survey produced a further 1346 and 763 spectral sets respectively. The installation, calibration, recording and analysis followed SURRC procedures which have been developed and validated over many years and are fully documented. Pre flight checks on detector performance for energy calibration, energy resolution and sensitivity were performed on a daily basis. Background readings over water were taken on a daily basis. All data were registered and backed up in duplicate to form a digital archive of the survey. Subsequent analysis and mapping has used a combination of standard procedures established over many years, and new techniques developed to analyse the low energy spectra. All results have been retained to facilitate traceability and further analysis in the future. The sensitivity of the aircraft and vehicle were also checked at Greenham Common by collecting a set of 31 core samples for independent laboratory analysis. The key points arising from the airborne survey of the entire area show that there has been sufficient sensitivity to record variations in the natural background. The levels of 137Cs are consistent with weapons' testing fallout, and are substantially lower than in other parts of the UK and Europe. The average levels of K (0.5%), U (1 ppm) and Th (3 ppm) are lower than national averages and show variations within the area which reflect local geology and landcover. The area as a whole therefore is one of low environmental radiation background compared with national averages. There is no evidence of signals at Greenham Common or in its vicinity which would present a local radiation hazard. However, signals were detected in the vicinity of Harwell and the Rutherford laboratory which would, at the time of the survey, represent radiation projected off-site as a result of materials stored on-site or on-site activities. Examination of the low energy gamma ray spectra recorded from the semiconductor detectors reveals no evidence, within the sensitivity limits of the method, for excess gamma ray signals at the energies associated with 235U around Greenham Common, Newbury and Thatcham. The low energy data are sufficiently sensitive to record variations in the distribution of natural activity in the area. There is tentative evidence for 241Am in the vicinity of AWE Aldermaston. The vehicular survey demonstrated that the grass areas in between the runway and taxi lanes, and around the hardstand associated with the 1958 fire have retained weapons' testing 137Cs. This supports the view that these represent authentic undisturbed areas for sampling. The built surfaces remaining at the time of the survey were of lower natural activity and 137Cs content than their surroundings. High resolution gamma ray spectra at selected sites were also consistent with the known sources of background radioactivity. On the basis of the results, Newbury District and surrounding areas represent an area with low environmental radioactivity compared with national and European averages. There is no evidence to substantiate fears about the quality of the radiation environment in the vicinity of Greenham Common