Prediction of the upper tail of concentration distributions of a continuous point source release in urban environments

The peak values observed in a measured concentration time series of a dispersing gaseous pollutant released continuously from a point source in urban environments, and the hazard level associated with them, demonstrate the necessity of predicting the upper tail of concentration distributions. For the prediction of concentration distributions statistical models are preferably employed which provide information about the probability of occurrence. In this paper a concentration database pertaining to a field experiment is used for the selection of the statistical distribution. The inverses of the gamma cumulative distribution function (cdf) for 75th–99th percentiles of concentration are found to be more consistent with the experimental data than those of the log-normal distribution. The experimental values have been derived from measured high frequency time series by sorting first the concentrations and then finding the concentration which corresponds to each probability. Then the concentration mean and variance that are predicted with Computational Fluid Dynamics-Reynolds Averaged Navier–Stokes (RANS) methodology are used to construct the gamma distribution. The proposed model (“RANS-gamma”) is included in the framework of a computational code (ADREA-HF) suitable for simulating the dispersion of airborne pollutants over complex geometries. The methodology is validated by comparing the inverses of the model cdfs with the observed ones from two wind tunnel experiments. The evaluation is performed in the form of validation metrics such as the fractional bias, the normalized mean square error and the factor-of-two percentage. From the above comparisons it is concluded that the overall model performance for the present cases is satisfactory.     

Species abundance distributions result from body size-energetics relationships

Abundance distributions are a central characteristic of ecosystems. Certain distributions have been derived from theoretical models of community organization, and therefore the fit of data to these distributions has been proposed as a test of these theories. However, it is shown here that the geometric sequence distribution can be derived directly from the empirical relationship between population density and body size, with the assumption of random or uniform body size distributions on a log scale (as holds at local scales). The geometric sequence model provides a good to excellent fit to empirical data. The presence of noise in the relationship between population density and body size creates a curve that begins to approximate a lognormal species abundance distribution as the noise term increases. For continental-scale data in which the body size distribution is not flat, the result of sampling tends again toward the lognormal. Repeat sampling over time smooths out species population fluctuations and damps out the noise, giving a more precise geometric sequence abundance distribution. It is argued that the direct derivation of this distribution from empirical relationships gives it priority over distributions derived from complex theoretical community models.     

Sensitivity of normal theory methods to model misspecification in the calculation of upper confidence limits on the risk function for continuous responses

Normal theory procedures for calculating upper confidence limits (UCL) on the risk function for continuous responses work well when the data come from a normal distribution. However, if the data come from an alternative distribution, the application of the normal theory procedures may lead serious over- or under-coverage depending upon the alternative distribution. In this paper we conduct simulation studies to investigate the sensitivity of three normal theory UCL procedures to departures from normality. Data from several gamma, reciprocal gamma, and lognormal distributions are considered. The normal theory procedures are applied to both the raw data and the log-transformed data.     

Power-law behaviour and parametric models for the size-distribution of forest fires

This paper examines the distribution of areas burned in forest fires. Empirical size distributions, derived from extensive fire records, for six regions in North America are presented. While they show some commonalities, it appears that a simple power-law distribution of sizes, as has been suggested by some authors, is too simple to describe the distributions over their full range. A stochastic model for the spread and extinguishment of fires is used to examine conditions for power-law behaviour and deviations from it. The concept of the extinguishment growth rate ratio (EGRR) is developed. A null model with constant EGRR leads to a power-law distribution, but this does not appear to hold empirically for the data sets examined. Some alternative parametric forms for the size distribution are presented, with a four-parameter ‘competing hazards’ model providing the overall best fit.     

On the place of origin of deep-sea lsopods

Biogeographic and phylogenetic data on the deep-sea isopod family Ilyarachnidae (Paraselloidea) document its origin and evolutionary radiation in the deep sea. The distribution of eyes among paraselloidean families suggests an in situ evolution for all those families which have primarily deep-sea distributions. Present-day distributions of paraselloidean isopods provide no hints to their ultimate sources in shallow water. These findings contrast to recent suggestions in the literature that the deep-sea isopod fauna has been derived from shallow Antarctic waters.     

Methodische Aspekte probabilistischer Modellierung

The main topic of probabilistic modelling is to introduce the subject of variability into exposure assessment. Instead of fixed parameters (means, percentiles), each variable will be expressed in the mathematical form of a distribution of their realisations in the population of interest. The technique of Monte Carlo simulations also makes complex models computable. The results are expressions of variation and uncertainty in exposure assessment. The text discusses the principle and new methodical efforts in modelling: The fit of input distributions, the technical realizations and possibilities in documentation of the results.     

Inference about the ratio of means from Negative Binomial paired count data

We derive some statistical properties of the distribution of two Negative Binomial random variables conditional on their total. This type of model can be appropriate for paired count data with Poisson over-dispersion such that the variance is a quadratic function of the mean. This statistical model is appropriate in many ecological applications including comparative fishing studies of two vessels and or gears. The parameter of interest is the ratio of pair means. We show that the conditional means and variances are different from the more commonly used Binomial model with variance adjusted for over-dispersion, or the Beta-Binomial model. The conditional Negative Binomial model is complicated because it does not eliminate nuisance parameters like in the Poisson case. Maximum likelihood estimation with the unconditional Negative Binomial model can result in biased estimates of the over-dispersion parameter and poor confidence intervals for the ratio of means when there are many nuisance parameters. We propose three approaches to deal with nuisance parameters in the conditional Negative Binomial model. We also study a random effects Binomial model for this type of data, and we develop an adjustment to the full-sample Negative Binomial profile likelihood to reduce the bias caused by nuisance parameters. We use simulations with these methods to examine bias, precision, and accuracy of estimators and confidence intervals. We conclude that the maximum likelihood method based on the full-sample Negative Binomial adjusted profile likelihood produces the best statistical inferences for the ratio of means when paired counts have Negative Binomial distributions. However, when there is uncertainty about the type of Poisson over-dispersion then a Binomial random effects model is a good choice.     

Bimodal distribution of organochlorine insecticide levels in soil due to emulsion spraying

Concentrations (c) of lindane and technical DDT have been determined in about 60 soil samples, randomly taken from a 10 × 10 m² plot of bare soil one day after spraying. These experimental c, log c data, and literature data for dieldrin are used to examine the various residue distributions in cultivated and uncultivated soil plots. The normality of these distributions is examined with some statistical tests. All c distribution curves are more or less skew to higher c levels. From the pooled cumulative distribution curve and frequency histogram it is concluded that the found c distributions can be characterized best as bimodal.

Finally, some practical recommendations are given for cost‐effective soil sampling.     

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.     

Difficulties with the lognormal model in mean estimation and testing

A frequent assumption in environmental risk assessment is that the underlying distribution of an analyte concentration is lognormal. However, the distribution of a random variable whose log has a t-distribution has infinite mean. Because of the proximity of the standard normal and t-distribution, this suggests that a distribution such as the gamma or truncated normal, with smaller right tail probabilities, might make a better statistical model for mean estimation than the lognormal. In order to assess the effect of departures from lognormality on lognormal-based statistics, we simulated complete lognormal, truncated normal, and gamma data for various sample sizes and coefficients of variation. In these cases, departures from lognormality were not easily detected with the Shapiro-Wilk test. Various lognormal-based estimates and tests were compared with alternate methods based on the ordinary sample mean and standard error. The examples were also considered in the presence of random left censoring with the mean and standard error of the product limit estimate replacing the ordinary sample mean and standard error. The results suggest that in the estimation of or tests about a mean, if the assumption of lognormality is at all suspect, then lognormal-based approaches may not be as good as the alternative methods.     

Income inequality and willingness to pay for environmental public goods

We study how the distribution of income among members of society, and income inequality in particular, affects social willingness to pay (WTP) for environmental public goods. We find that social WTP for environmental goods decreases (increases) with income inequality if and only if environmental goods and manufactured goods are substitutes (complements). We derive adjustment factors for benefit transfer to control for differences in income distributions between a study site and a policy site. For illustration, we quantify how social WTP for environmental public goods depends on the respective income distributions for empirical case studies in Sweden and the World at large. We find that the adjustment for income inequality can be substantial.     

Extinction times in experimental populations

Predicting population extinctions is a key element of quantitative conservation biology and population ecology. Although stochastic population theories have long been used to obtain theoretical distributions of population extinction times, model-based predictions have rarely been tested. Here I report results from a quantitative analysis of extinction time in 281 experimental populations of water fleas (Daphnia magna) in variable environments. To my knowledge, this is the first quantitative estimate of the shape of the distribution of population extinction times based on extinction data for any species. The finding that the distribution of population extinction times was extraordinarily peaked is consistent with theoretical predictions for density-independent populations, but inconsistent with predictions for density-dependent populations. The tail of the extinction time distribution was not exponential. These results imply that our current theories of extinction are inadequate. Future work should focus on how demographic stochasticity scales with population size and effects of nonrandom variable environments on population growth and decline.     

Two methods of sampling fish larvae over reefs: a comparison from the Gulf of California

I compared the sampling properties of two methods for collecting fish larvae over reefs: nighttime collecting with a light trap, and daytime collecting with a small plankton net that could be steered by a diver. Samples were collected in the Gulf of California during summer, 1989 and 1990. The 90 light-trap samples yielded 9406 larvae from 31 families, while the 75 plankton-net samples yielded 17852 larvae from 43 families plus unidentified anguilliforms. Four families were collected only in the light trap, and 16 families plus the anguilliforms were collected only with the plankton net. With one exception, the families that were collected by only one method were rare. Twenty-seven families were collected by both methods, but only 13 were collected at least five times by each. The average catch per sample differed significantly between methods for 9 of these 13 families. In each case, the plankton net yielded more larvae per sample. The distribution of larvae among families was less equitable in light-trap samples than in planktonnet collections, primarily because clupeids were so dominant in the former. However, the taxonomic composition of light-trap and plankton-net collections was broadly similar. Seven families were shared among the ten most abundant families for each method, and the relative abundances of taxa (47 families plus anguilliforms) were strongly correlated between methods. A comparison of larval size-distributions for 12 families indicated that the size structure of catches usually differed between collecting methods. In four families there was little overlap in the size classes collected, in five families the distributions overlapped broadly but had different shapes, and in three families the size distributions were similar. Although the light trap collected larger larvae on average, its catches were not limited to settlement-stage or transition larvae. Larvae of at least ten families were present over reefs in all size classes, but the combination of both sampling methods was usually required to detect this. Based on their abundance and wide size distribution over reefs, at least some larvae from these ten families may remain over reefs throughout development. However, additional data are required to determine the importance of water over reefs as a larval habitat.     

Effects of connectivity and spatial resolution of analyses on conservation prioritization across large extents

The outcome of analyses that prioritize locations for conservation on the basis of distributions of species, land cover, or other elements is influenced by the spatial resolution of data used in the analyses. We explored the influence of data resolution on prioritization of Finnish forests with Zonation, a software program that ranks the priority of cells in a landscape for conservation. We used data on the distribution of different forest types that were aggregated to nine different resolutions ranging from 0.1 × 0.1 km to 25.6 × 25.6 km. We analyzed data at each resolution with two variants of Zonation that had different criteria for prioritization, with and without accounting for connectivity and with and without adjustment for the effect on the analysis of edges between areas at the project boundary and adjacent areas for which data do not exist. Spatial overlap of the 10% of cells ranked most highly when data were analyzed at different resolutions varied approximately from 15% to 60% and was greatest among analyses with similar resolutions. Inclusion of connectivity or edge adjustment changed the location of areas that were prioritized for conservation. Even though different locations received high priority for conservation in analyses with and without accounting for connectivity, accounting for connectivity did not reduce the representation of different forest types. Inclusion of connectivity influenced most the outcome of fine-resolution analyses because the connectivity extents that we based on dispersal distances of typical forest species were small. When we kept the area set aside for conservation constant, representation of the forest types increased as resolution increased. We do not think it is necessary to avoid use of high-resolution data in spatial conservation prioritization. Our results show that large extent, fine-resolution analyses are computationally feasible, and we suggest they can give more flexibility to implementation of well-connected reserve networks.     

Wet and dry epoch durations of spatially averaged rain rate,their probability distributions and scaling properties

This article is concerned with the notion of duration of wet and dry epochs in stochastic processes of spatially averaged (instantaneous) rain rate over a given region. Gamma, Lognormal, and Inverse Gaussian parametric families of probability distributions have been considered as candidate models for the distribution of such durations. Goodness of these model's fit to data of dry and wet epoch durations obtained from real time series of spatially averaged rain rate, has been tested with Pearson's -test. The parameters of each of these models have been estimated by maximum likelihood and method of moments, based on TOGA-COARE measurements of tropical rainfall. The hypotheses of independence and identical distribution (i.i.d.) among durations of dry or wet epochs have also been tested using a certain version of the Wald-Wolfowitz test. Finally, the effect of spatial scale on the moments of dry and wet epoch durations has also been investigated, pointing to self-similarity of the underlying random structures over space. The main result of this study is that among the three candidate models, Inverse Gaussian is the one conforming most adequately with all the classical testing criteria implemented here, and also with the newly established scaling behavior of both dry and wet epoch duration processes over space. This is a remarkable finding, considering that the Inverse Gaussian family has recently been also justified from a theoretical viewpoint as a reasonable model for the probability distributions of dry and wet epoch durations.     

Using habitat suitability index and particle dispersion models for early detection of marine invaders.

Eradication and control of invasive species are often possible only if populations are detected when they are small and localized. To be efficient, detection surveys should be targeted at locations where there is the greatest risk of incursions. We examine the utility of habitat suitability index (HSI) and particle dispersion models for targeting sampling for marine pests. Habitat suitability index models are a simple way to identify suitable habitat when species distribution data are lacking. We compared the performance of HSI models with statistical models derived from independent data from New Zealand on the distribution of two nonindigenous bivalves: Theora lubrica and Musculista senhousia. Logistic regression models developed using the HSI scores as predictors of the presence/absence of Theora and Musculista explained 26.7% and 6.2% of the deviance in the data, respectively. Odds ratios for the HSI scores were greater than unity, indicating that they were genuine predictors of the presence/ absence of each species. The fit and predictive accuracy of each logistic model were improved when simulated patterns of dispersion from the nearest port were added as a predictor variable. Nevertheless, the combined model explained, at best, 46.5% of the deviance in the distribution of Theora and correctly predicted 56% of true presences and 50% of all cases. Omission errors were between 6% and 16%. Although statistical distribution models built directly from environmental predictors always outperformed the equivalent HSI models, the gain in model fit and accuracy was modest. High residual deviance in both types of model suggests that the distributions realized by Theora and Musculista in the field data were influenced by factors not explicitly modeled as explanatory variables and by error in the environmental data used to project suitable habitat for the species. Our results highlight the difficulty of accurately predicting the distribution of invasive marine species that exhibit low habitat occupancy and patchy distributions in time and space. Although the HSI and statistical models had utility as predictors of the likely distribution of nonindigenous marine species, the level of spatial accuracy achieved with them may be well below expectations for sensitive surveillance programs.     

Assessing the effects of pseudo-absences on predictive distribution model performance

Modelling species distributions with presence data from atlases, museum collections and databases is challenging. In this paper, we compare seven procedures to generate pseudo-absence data, which in turn are used to generate GLM-logistic regressed models when reliable absence data are not available. We use pseudo-absences selected randomly or by means of presence-only methods (ENFA and MDE) to model the distribution of a threatened endemic Iberian moth species (Graellsia isabelae). The results show that the pseudo-absence selection method greatly influences the percentage of explained variability, the scores of the accuracy measures and, most importantly, the degree of constraint in the distribution estimated. As we extract pseudo-absences from environmental regions further from the optimum established by presence data, the models generated obtain better accuracy scores, and over-prediction increases. When variables other than environmental ones influence the distribution of the species (i.e., non-equilibrium state) and precise information on absences is non-existent, the random selection of pseudo-absences or their selection from environmental localities similar to those of species presence data generates the most constrained predictive distribution maps, because pseudo-absences can be located within environmentally suitable areas. This study shows that if we do not have reliable absence data, the method of pseudo-absence selection strongly conditions the obtained model, generating different model predictions in the gradient between potential and realized distributions.     

Geochemical mapping in Jamaica

A high-precision regional geochemical data base of Jamaica is being developed as a basis for a wide variety of economic and environmental applications. These include pollution studies, resource identification and management, agriculture, land use, and the relationship between geochemistry and the health of crops, animals, and man. The acquisition of analytical data is mainly by instrumental neutron activation analysis using a SLOWPOKE reactor and by energy dispersive X-ray fluorescence. Concentration ranges and means in soil are presented for 31 elements and maps illustrating the distributions of Al, Br, Co, and the -ray intensities are presented as examples. Compared with world averages the levels of many heavy metals in Jamaican soils are found to be relatively high and in the main strongly correlated with bauxite occurrences. The high content of bromine in the soils appears to reflect the impact of sea-spray.