A generalized Chao estimator with measurement error and external information

We present a generalized Chao (GC) estimator based on a subject-occasion-specific design matrix. We then extend the GC estimator to (i) external information, in the form of non-linear constraints on subpopulation sizes and (ii) measurement error. For the first, we propose a reparameterization of the estimating equations. As a result, the constrained MLE can be found with no additional computational efforts. For the second we generalize SIMEX procedure to multiple measurement methods. In simulation we show that (even incorrect) external information can substantially decrease the MSE. We illustrate with an application to a whale shark (Rhincodon typus) population, where mostly jouvenile males are observed. We use external information on gender ratio of whale sharks to correct for low catchability of females, and our multivariate SIMEX procedure to correct for measurement error in assessment of shark length. The resulting population size estimates are about 60% larger than the unconstrained–uncorrected counterparts.     

Robust optimal observation of a metapopulation

We consider a two-parameter continuous-time Markovian model for patch occupancy in metapopulation, and address the question of when to observe the population in order to obtain the most accurate and precise estimator of the parameters. Using the likelihood obtained from a diffusion approximation we derive a robust procedure for determining the optimal observation schedule, which is considerably simpler than would otherwise be possible. We investigate the performance of two optimality criteria, ED-optimality and a particular form of maximin-optimality. Both allow one to incorporate prior belief about the parameter values before any data is collected. Kernel density estimates of the maximum likelihood estimator are compared under the various combinations of optimality criteria and prior distributions. Our methods are illustrated with reference to a model for the spread of crown of thorns starfish (Acanthaster planci) among the 55 islands comprising the Ryukyu group in Japan.     

Laboratory evaluation of kinetic parameters for lake sediment denitrification models

Laboratory experiments using the acetylene blockage technique showed that denitrification rates in sediments from Lake Okeechobee, Florida, are described by Michaelis-Menten nitrate dependence and Arrhenius temperature dependence (E_act = 15.5 kcal, but do not appear to be affected by seasonal differences in the supply of carbon substrates in this eutrophic lake. Peak nitrate concentrations in the sediments are in the range of the half-saturation constant, and thus, for a given temperature, k_d varies by a factor of approximately two over the typical range of nitrate concentrations. Most diagenetic sediment denitrification models employ a single-valued rate constant k_d, to describe nitrate dependence. However, the use of a constant k_d for eutrophic lake sediments may result in a significantly erroneous estimate of annual denitrification loss.     

The use of measurable coefficients in process formulations—zooplankton grazing

This paper redefines a construct previously used to model phytoplankton—zooplankton interactions in such a way as to permit the use of measurable quantities as contruct coefficients. The new construct can use unaltered values of the half-saturation constant for zooplankton grazing on total available food (k_s) and the minimum food concentration necessary to stimulate effective feeding (BMIN) reported in the literature. Typical values for these coefficients are 0.1–15 and 0.016–0.19, respectively.     

Diffusional mass transfer coefficient at the water–sediment interface for wind-induced flow in very shallow lagoons

Very shallow lagoons that are a few centimeters deep are common in the arid Andes of Northern Chile, Argentina, Bolivia and Perú. The dynamics of these lagoons are dominated by the water–sediment interface (WSI) and strong afternoon winds. Although many studies have examined the diffusional mass transfer coefficients (k _t ) of open channel flows, estimates for wind-induced flows are still unknown. The aim of this article is to propose and validate an analytical expression for computing k _t at the WSI for wind-induced flow. The laboratory measurements were conducted in a wind tunnel with a water tank of variable depth located at its downwind end. Natural muddy sediments were placed in the middle of the tank so that the dissolved oxygen (DO) was consumed in the sediments. The diffusional mass transfer coefficient that characterizes the DO uptake in the sediment was obtained from DO micro-profiles measured with an OX-25 Unisense microelectrode. Water velocity profiles were measured with a 2D side-view Sontek acoustic doppler velocimetry (ADV), and the wind shear velocity was computed based on wind velocity profiles that were measured with an Extech hot-wire anemometer. A total of 16 experiments were conducted with different water depths and wind shear stresses. The constants required by the model were determined from these experiments, and the analytical expression was successfully validated by the laboratory observations. The analytical expression obtained for computing k _t was also validated with field observations that were conducted in October, 2012, in Salar del Huasco, Northern Chile (20.274° S, 68.883° W, 3800 m above sea level). The comparison between the observed and predicted values of k _t provides a determination coefficient of r ² = 0.48 and a p value < 0.01. The results show that the value of k _t for wind-induced flow is proportional to the wind shear velocity and the inverse of the Reynolds number of the wind-induced current.     

Estimation of some parameters of large fish populations by capture-recapture experiments

A certain number of tagged fish is liberated and assumed to be distributed randomly among a natural fish population. The fish are subjected to a number of fishing experiments within relatively short periods, and lie between equal intervening periods of durationT. Untagged fish are retained, while tagged fish are released during the fishing experiments. Denoting the catchability of untagged fish byq _u and that for tagged fish byq _t , it is assumed that they are related by the equation “q _u =cq _t ” wherec is a constant. Denoting the survival rates of tagged fish and the effective fishing effort of commerical fisheries per unit time from the (k-1)^th to thek ^th experiments by _t S _k andf _k , respectively, it is assumed that they vary from period to period. Assuming that during thek ^th experiment, the number of untagged fish captured and the experimental fishing rate of tagged fish are denoted by _u X _k and _t P _k , respectively, then $$\begin{array}{*{20}c} {\frac{{(_u X_k )^2 }}{{[_u X_{(k - 1)} ][_u X_{(k + 1)} ]}} = \frac{{_t S_k }}{{_t S_{(k + 1)} }} \cdot \frac{{e^{ - (1 - c)q_t f_{(k + 1)} T} }}{{e^{ - (1 - c)q_t f_k T} }} \cdot } \\ {\frac{{1 - c_t P_{(k - 1)} }}{{1 - c_t P_k }} \cdot \frac{{(_t P_k )^2 }}{{[_t P_{(k - 1)} ][_t P_{(k + 1)} ]}}.} \\ \end{array}$$ The above equation containsc as a single unknown, while all other terms are supplied by the capture-recapture experiments, exceptf _k andf _(k+1) which may be obtained from fisheries statistics. A number of the above equations are obtained from several experiments and can be combined into a single equation to obtain an overall estimate forc which can be used to derive estimates for experimental fishing rates, abundance, and instantaneous natural and fishing mortality rates for natural fish populations. These estimates are free from type (A) tagging errors, and have the advantage of taking into consideration the probable different behaviour of tagged and untagged fish.     

RANS simulation of neutral atmospheric boundary layer flows over complex terrain by proper imposition of boundary conditions and modification on the k-ε model

In this study, a modelling methodology is proposed for RANS simulations of neutral Atmospheric Boundary Layer (ABL) flows on the basis of the standard k-ε model, which allows the adoption of an arbitrary shear stress model. This modelling methodology is first examined in the context of an open flat terrain in an empty domain to ascertain there are no substantial changes in the prescribed profiles. The results show that relatively good homogeneity can be achieved with this modelling methodology for various sets of inflow boundary profiles. In addition, to extend the solutions derived from the standard k-ε model to RNG k-ε model, the RNG k-ε model is in detail assembly and tuned. Finally, the topographic effects on surface wind speeds over a complex terrain are assessed with the combined use of the proposed methodology and the modified RNG model. The numerical results are in good agreement with wind tunnel testing results and long-term field observations. A discussion of the effects of horizontal homogeneity and turbulence models on the simulated wind flows over a complex terrain is also given.     

Estimating Population Size with Noninvasive Capture-Mark-Recapture Data

Abstract:  Estimating population size of elusive and rare species is challenging. The difficulties in catching such species has triggered the use of samples collected noninvasively, such as feces or hair, from which genetic analysis yields data similar to capture-mark-recapture (CMR) data. There are, however, two differences between classical CMR and noninvasive CMR. First, capture and recapture data are gathered over multiple sampling sessions in classical CMR, whereas in noninvasive CMR they can be obtained from a single sampling session. Second, because of genotyping errors and unlike classical CMR, there is no simple relationship between (genetic) marks and individuals in noninvasive CMR. We evaluated, through simulations, the reliability of population size estimates based on noninvasive CMR. For equal sampling efforts, we compared estimates of population size N obtained from accumulation curves, a maximum likelihood, and a Bayesian estimator. For a closed population and without sampling heterogeneity, estimates obtained from noninvasive CMR were as reliable as estimates from classical CMR. The sampling structure (single or multiple session) did not alter the results, the Bayesian estimator in the case of a single sampling session presented the best compromise between low mean squared error and a 95% confidence interval encompassing the parametric value of N in most simulations. Finally, when suitable field and lab protocols were used, genotyping errors did not substantially bias population size estimates (bias < 3.5% in all simulations). The ability to reliably estimate population size from noninvasive samples taken during a single session offers a new and useful technique for the management and conservation of elusive and rare species.     

Using enhanced dasymetric mapping techniques to improve the spatial accuracy of sea level rise vulnerability assessments

This article reports on the application of dasymetric mapping techniques to interpolate and disaggregate block group population counts to smaller areal units (i.e., tax parcels) and derive surface population models with more realistic representations of population distributions in our residential study area in Miami-Dade, Florida. Three methods of dasymetric interpolation were tested: (i) binary, (ii) three-class, and (iii) limiting variable. Our enhanced limiting variable approach introduced an adjustment factor for parcel vacancy rates in the dasymetric calculations, and applied dasymetric mapping techniques to disaggregate future population projections to the tax lot level of analysis. The limiting variable interpolation generated the lowest coefficient of variation (0.188), followed by the three-class interpolation (0.645). We also found that population densities vary substantially within land use classes of single family, medium density and high density classes, and these variations also highlighted the importance of incorporating vacancy rates when interpolating population counts to categorical land use data. Overall, the enhanced dasymetric mapping technique is particularly useful for examining the impact of sea-level rise as its derivatives are compatible with high resolution LiDAR and orthoimagery data. Coastal counties can also benefit from such high resolution surface population models to enhance the accuracy of hazard-related vulnerability assessments and to guide the development of relevant shore zone conservation and adaptation strategies.     

Estimation of the density of a clustered point pattern using a distance method

Distance-based methods use point-to-point distances or random-location-to-point distances in a cloud of points to estimate characteristics of the point pattern. One such characteristics is the density of points. The difficulty with distance-based density estimators is that their distribution depends on the spatial pattern of points. In particular, the distribution of distances is untractable for usual clustered patterns, that are often observed in natural systems. Here, we propose a density estimator for clustered patterns, based on the random-location-to-pth-point distance X _p . An approximate expression for the distribution function, F _p , of X _p was obtained by identifying the first two moments of the count of individuals in disks for a given point process with the first two moments of a negative binomial distribution. The approximate expression of F _p was then used to derive a maximum-likelihood estimator of the intensity of the point process. The quality of the approximation of F _p was assessed for homogeneous Poisson processes (for which the expression of F _p is exact) and for Matérn processes. The intensity estimator based on Matérn processes was then used to estimate tree density in a tree savanna in Mali, and it compared favorably with six robust estimators found in the literature.     

Multi-metric evaluation of the models WARM,CropSyst, and WOFOST for rice

WARM (Water Accounting Rice Model) simulates paddy rice (Oryza sativa L.), based on temperature-driven development and radiation-driven crop growth. It also simulates: biomass partitioning, floodwater effect on temperature, spikelet sterility, floodwater and chemicals management, and soil hydrology. Biomass estimates from WARM were evaluated and compared with the ones from two generic crop models (CropSyst, WOFOST). The test-area was the Po Valley (Italy). Data collected at six sites from 1989 to 2004 from rice crops grown under flooded and non-limiting conditions were split into a calibration (to estimate some model parameters) and a validation set. For model evaluation, a fuzzy-logic based multiple-metrics indicator (MQI) was used: 0 (best) ≤ MQI ≤ 1 (worst). WARM estimates compared well with the actual data (mean MQI = 0.037 against 0.167 and 0.173 with CropSyst and WOFOST, respectively). On an average, the three models performed similarly for individual validation metrics such as modelling efficiency (EF > 0.90) and correlation coefficient (R > 0.98). WARM performed best in a weighed measure of the Akaike Information Criterion: (worst) 0<wk<1$0<w_k<1$ (best), considering estimation accuracy and number of parameters required to achieve it (mean wk=0.983$w_k=0.983$ against 0.007 and ∼0.000 with CropSyst and WOFOST, respectively). WARM results were sensitive to 30% of the model parameters (ratio being lower with both CropSyst, <10%, and WOFOST, <20%), but appeared the easiest model to use because of the lowest number of crop parameters required (10 against 15 and 34 with CropSyst and WOFOST, respectively). This study provides a concrete example of the possibilities offered using a range of assessment metrics to evaluate model estimates, predictive capabilities, and complexity.     

Application of k-means clustering to environmental risk zoning of the chemical industrial area

The homogeneous risk characteristics within a sub-area and the heterogeneous from one sub-area to another are unclear using existing environmental risk zoning methods. This study presents a new zoning method by determining and categorizing the risk characteristics using the k-means clustering data mining technology. The study constructs indices and develops index quantification models for environmental risk zoning by analyzing the mechanism of environmental risk occurrence. We calculate the source risk index, air risk field index, water risk field index, and target vulnerability of the study area with Nanjing Chemical Industrial Park using a 100 m - 100 m mesh grid as the basic zoning unit, and then use k-means clustering to analyze the environmental risk in the area. We obtain the optimal clustering number with the largest average silhouette coefficient by calculating the average silhouette coefficients of clustering at different k-values. The clustering result with the optimal clustering number is then used for the environmental risk zoning, and the zoning result is mapped using the geographic information system. The study area is divided into five sub-areas. The common environmental risk characteristics within the same sub-area, as well as the differences between sub- areas, are presented. The zoning is helpful in risk management and is convenient for decision makers to distribute limited resources to different sub-areas in the design of risk reducing intervention.     

Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.     

Estimating abundance: a non parametric mark recapture approach for open and closed systems

We present a novel, non-parametric, frequentist approach for capture-recapture data based on a ratio estimator, which offers several advantages. First, as a non-parametric model, it does not require a known underlying distribution for parameters nor the associated assumptions, eliminating the need for post-hoc corrections or additional modeling to account for heterogeneity and other violated assumptions. Second, the model explicitly deals with dependence of trials by considering trials to be dependent; therefore, cluster sampling is handled naturally and additional adjustments are not necessary. Third, it accounts for ordering, utilizing the fact that a system with a small population will have a greater frequency of recaptures “early” in the survey work compared to an identical system with a larger population. We provide mathematical proof that our estimator attains asymptotic minimum variance under open systems. We apply the model to a data set of bottlenose dolphins (Tursiops truncatus) and compare results to those from classic closed models. We show that the model has an impressive rate of convergence and demonstrate that there’s an inverse relationship between population size and the proportion of the population that need to be sampled, while achieving the same degree of accuracy for abundance estimates. The model is flexible and can apply to ecological situations as well as other situations that lend themselves to capture recapture sampling.     

Estimation of rare and clustered population mean using stratified adaptive cluster sampling

For many clustered populations, the prior information on an initial stratification exists but the exact pattern of the population concentration may not be predicted. Under this situation, the stratified adaptive cluster sampling (SACS) may provide more efficient estimates than the other conventional sampling designs for the estimation of rare and clustered population parameters. For practical interest, we propose a generalized ratio estimator with the single auxiliary variable under the SACS design. The expressions of approximate bias and mean squared error (MSE) for the proposed estimator are derived. Numerical studies are carried out to compare the performances of the proposed generalized estimator over the usual mean and combined ratio estimators under the conventional stratified random sampling (StRS) using a real population of redwood trees in California and generating an artificial population by the Poisson cluster process. Simulation results show that the proposed class of estimators may provide more efficient results than the other estimators considered in this article for the estimation of highly clumped population.

     

Spatial trends in abundance of long-finned pilot whales, white-beaked dolphins and harbour porpoises in West Greenland

Data from an aerial line transect survey conducted off West Greenland during August–September 2007 were used to estimate the abundance of long-finned pilot whales (Globicephala melas), white-beaked dolphins (Lagenorhynchus albirostris) and harbour porpoises (Phocoena phocoena). The abundance of each species was estimated using mark-recapture distance sampling techniques to correct for perception bias, and correction factors for time spent at the surface were applied. The fully corrected abundance estimates were 8,133 long-finned pilot whales, 11,984 white-beaked dolphins and 33,271 harbour porpoises. Based on density surface modelling methods, a count model with a generalised additive model formulation was used to relate abundance to spatial variables. Response curves indicated that the preferred habitats were deep offshore areas in Midwest Greenland for pilot whales, deep water over steep seabed slopes in South Greenland for white-beaked dolphins and relatively shallow inshore waters in Midwest–South Greenland for harbour porpoises. The abundance estimates and spatial trends for the three species are the first obtained from Greenland.     

Bootstrap confidence intervals for adaptive cluster sampling design based on Horvitz–Thompson type estimators

Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) introduced several bootstrap methods under adaptive cluster sampling using a Horvitz–Thompson type estimator. Using a simulation study, they showed that their proposed methods provide confidence intervals with highly understated coverage rates. In this article, we first show that their bootstrap methods provide biased bootstrap estimates. We then define two bootstrap methods, based on the method of Gross (Proceeding of the survey research methods section. American Statistical Association, Alexandria, VA, pp 181–184, 1980) and Bootstrap With Replacement, that provide unbiased bootstrap estimates of the population mean with bootstrap variances matching the corresponding unbiased variance estimator. Using a simulation study, we show that the bootstrap confidence intervals based on our proposed methods have better performance than those based on available bootstrap methods, in the sense of having coverage proportion closer to the nominal coverage level. We also compare the proposed intervals to empirical likelihood based intervals in small samples.     

Flow and drag force around a free surface piercing cylinder for environmental applications

This paper investigates flows around a free surface piercing cylinder with Froude number F > 0.5 and Reynolds number around Re = 50,000. The aim of this work is to gain a better understanding of the flow behaviour in environmental systems such as fishways. The advances are based upon experimental and numerical results. Several flow discharges and slopes are tested to obtain both subcritical and supercritical flows. The drag force exerted on the cylinder is measured with the help of a torque gauge while the velocity field is obtained using particle velocimetry. For the numerical part, two URANS turbulence models are tested, the k-\(\omega\) SST and the RNG k-\(\varepsilon\) models using the OpenFOAM software suite for subcritical cases, and then compared with the corresponding experimental results. With fishways applications in mind, the changes in drag coefficient \(C_d\) versus Froude number and water depth are studied and experimental correlations proposed. We conclude that the most suitable URANS turbulence model for reproducing this kind of flow is the k-\(\omega\) SST model.     

Shifts of the feeding niche along the size dimension of three juvenile fish species in a tidal mudflat in southeastern Brazil

The diet of three cooccurring abundant fish species (Eucinostomus argenteus, Diapterus rhombeus and Micropogonias furnieri) and its ontogenetic changes in a mudflat area of a tropical bay in southeastern Brazil were described. The working hypothesis is that these three species shift the use of the available resources throughout their growth. Early juveniles of D. rhombeus and M. furnieri fed mainly on Cyclopoida copepods, shifting to Nematoda (D. rhombeus) and errant Polychaeta (M. furnieri) as they increased in size. In contrast, the early life stages of E. argenteus fed mainly on errant Polychaeta and Calanoida copepods, with increasing niche breadth as they grew. The relative degree of individual specialisation in resource use indicated specialism for M. furnieri and E. argenteus, and generalism for D. rhombeus. The largest intraspecific overlap was found for the smallest size classes. Niche breadth increased during ontogeny, with a higher average niche breadth at lower prey length/predator length ratios. Therefore, species-specific differences in diet across the resource gradient and increased niche breadth during ontogeny characterised the shifts of resource use, and probably account for the coexistence of these species in zones of sympatry in mudflat areas of southeastern Brazil.