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A traditional grid model for soil sampling may suffer from poor efficiency and low accuracy. With a nonferrous metal processing plant as the study area, a three-dimensional kriging interpolation model was built based on this plant's preliminary investigation data for arsenic (As), and a detailed survey sampling programme was proposed. The sampling density at the pollution interval of the surface soil was estimated by the coefficient of variation method, and the sampling depth was determined by the pollution interval of the vertical prediction results. The results showed that the encrypted soil sampling distribution optimisation method obtains greater pointing accuracy with fewer points. The sampling accuracy was 87.62% after optimising the depth of pointing. Moreover, this approach could save 66.13% of the sampling costs and 56.93% of the testing costs compared to a full deployment programme. This study provides a new and cost-effective method for predicting the extent of contamination exceedance at a site and provides valuable information to guide post-remediation strategies for contaminated sites.

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Large-effect loci-those statistically significant loci discovered by genome-wide association studies or linkage mapping-associated with key traits segregate amidst a background of minor, often undetectable, genetic effects in wild and domesticated plants and animals. Accurately attributing mean differences and variance explained to the correct components in the linear mixed model analysis is vital for selecting superior progeny and parents in plant and animal breeding, gene therapy, and medical genetics in humans. Marker-assisted prediction and its successor, genomic prediction, have many advantages for selecting superior individuals and understanding disease risk. However, these two approaches are less often integrated to study complex traits with different genetic architectures. This simulation study demonstrates that the average semivariance can be applied to models incorporating Mendelian, oligogenic, and polygenic terms simultaneously and yields accurate estimates of the variance explained for all relevant variables. Our previous research focused on large-effect loci and polygenic variance separately. This work aims to synthesize and expand the average semivariance framework to various genetic architectures and the corresponding mixed models. This framework independently accounts for the effects of large-effect loci and the polygenic genetic background and is universally applicable to genetics studies in humans, plants, animals, and microbes.

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The coefficient of determination (R2 ) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlated. This paper proposes a new coefficient of determination for this setting that accounts for any such correlation. A key advantage of the proposed method is that it only requires the fit of the model under consideration, with no need to also fit a null model. Also, the approach entails a bias correction in the estimator assessing the variance explained by fixed effects. Three examples are used to illustrate new measure. A simulation shows that the proposed estimator of the new coefficient of determination has only minimal bias.

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Many important traits in plants, animals, and microbes are polygenic and challenging to improve through traditional marker-assisted selection. Genomic prediction addresses this by incorporating all genetic data in a mixed model framework. The primary method for predicting breeding values is genomic best linear unbiased prediction, which uses the realized genomic relationship or kinship matrix (K) to connect genotype to phenotype. Genomic relationship matrices share information among entries to estimate the observed entries' genetic values and predict unobserved entries' genetic values. One of the main parameters of such models is genomic variance (σg2), or the variance of a trait associated with a genome-wide sample of DNA polymorphisms, and genomic heritability (hg2); however, the seminal papers introducing different forms of K often do not discuss their effects on the model estimated variance components despite their importance in genetic research and breeding. Here, we discuss the effect of several standard methods for calculating the genomic relationship matrix on estimates of σg2 and hg2. With current approaches, we found that the genomic variance tends to be either overestimated or underestimated depending on the scaling and centering applied to the marker matrix (Z), the value of the average diagonal element of K, and the assortment of alleles and heterozygosity (H) in the observed population. Using the average semivariance, we propose a new matrix, KASV, that directly yields accurate estimates of σg2 and hg2 in the observed population and produces best linear unbiased predictors equivalent to routine methods in plants and animals.

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The distribution of soil pollutants is receiving increasing attention. The accurate determination of the soil pollution distribution in an area is becoming more important. To date, many soil quality surveys have already been carried out in China, and the use of these surveys to reflect soil pollution is worth examining. This article provides an example of the application of combined two-phase data to assess soil contamination in a region. Based on data acquired during two soil sampling phases in 2005 and 2015, we chose a typical watershed in southeast China as the study area. We analysed the data using spatial interpolation analysis, compared the results, and extracted points to perform point combination based on site conditions. Ultimately, these analyses allowed us to develop a new method involving the use of multi-period data to evaluate the soil quality on a regional scale. In the ten years from 2005 to 2015, apparent changes in soil pollution occurred. We found that the area with no change in soil pollution accounts for 46.98% of the total basin and the area demonstrating a soil pollution increase accounts for 47.25% of the total basin, while the area exhibiting a soil pollution reduction only accounts for 5.78% of the whole area. The average accuracy of the combined points increased to 89% from 76 and 81%. The analysis of the land-use types and spatial locations during the two periods revealed no direct relationship between the soil contamination changes and the changes in the total number of land-use types, but a correlation was observed with the intensity of human activities at the spatial locations. This paper proposes a new method for the spatial assessment of soil pollution based using multiple periods of existing data on the above analysis.

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We generalize Taylor's law for the variance of light-tailed distributions to many sample statistics of heavy-tailed distributions with tail index α in (0, 1), which have infinite mean. We show that, as the sample size increases, the sample upper and lower semivariances, the sample higher moments, the skewness, and the kurtosis of a random sample from such a law increase asymptotically in direct proportion to a power of the sample mean. Specifically, the lower sample semivariance asymptotically scales in proportion to the sample mean raised to the power 2, while the upper sample semivariance asymptotically scales in proportion to the sample mean raised to the power [Formula: see text] The local upper sample semivariance (counting only observations that exceed the sample mean) asymptotically scales in proportion to the sample mean raised to the power [Formula: see text] These and additional scaling laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the Omega index, the upside potential ratio, and the Farinelli-Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. Such power-law scaling relationships are known in ecology as Taylor's law and in physics as fluctuation scaling. We find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of α based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators of α.

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As an important ecological barrier for the North China Plain, research on the spatial variations of soil nutrients in the southern foot of the Taihang Mountains is of great significance for the forestry ecological construction in this rocky mountainous area. With the typical slopes (the artificial forestland and the natural wild slope) of the southern foot of the Taihang Mountains as the research objects, we used the grid method to arrange sampling points, and combined classical statistics, geostatistics and constrained sorting methods to analyze the spatial variations of soil nutrients. The results showed that: 1) soil total carbon (TC) contents were 6.80-57.05 g·kg-1, and the total nitrogen (TN) contents were 0.74-3.93 g·kg-1. The coefficients of variation of both soil TC and TN were 25.0%-52.8%, belonging to the moderate degree of variation, which were caused by the combination of random and structural factors. The spatial aggregation of soil nutrients decreased with increasing lag distances. 2) The contents of soil nutrients had increasing trends from the top to the bottom of the slopes, with high nutrient values appearing at the bottom of the slopes. 3) The soil bulk density, gravel content, vegetation coverage, and soil water content were the main factors affecting the spatial variability of soil TC and TN on the southern foot of the Taihang Mountains. 4) Soil water content was the main factor affecting soil nutrients at the natural wild slope, but not at the artificial forestland.

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We conducted an experiment to test the characteristics and differences of the spatial distribution of constructive species Stipa breviflora at different scales under different stocking rates in the S. breviflora desert steppe in Siziwang Banner, Inner Mongolia. The spatial distribution of S. breviflora under four treatments (control, light grazing, moderate grazing, and heavy grazing) at different scales (small scale as 1 m×1 m and mesoscale as 5 m×10 m) were analyzed. The results showed that the population density of S. breviflora at mesoscale in the control and light grazing was significantly lower than that at the small scale. Grazing significantly increased the population density of S. breviflora in the meso- and small scales. At the small scale, the population distribution of S. breviflora in the control, light grazing, moderate grazing, and heavy grazing treatments conformed to linear, exponential, exponential and exponential models, respectively, and Gaussian, exponential, Gaussian and exponential models at mesoscale fitted by semi-variance function. The spatial distribution pattern at small scales in the control was simple and better but was more complex and poorer under the heavy grazing. At the mesoscale, it was simple and better under the heavy grazing but complex and poor under the moderate grazing. The spatial heterogeneity of S. breviflora population reduced and were more uniform under the moderate and heavy grazing at meso- and small scales. In addition, the trend of population distribution in the enclosure, moderate and heavy grazing were generally the same, while light grazing showed inconsistent trend at different scales.

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Ecosystem services (ESs) are a diverse range of environmental properties that have significant effects on both landscape characteristics and human well-being, an understanding of the spatial variation of which is required for effective ecosystem management and conservation. In this study, we aimed to identify the geographical variation in ESs and examine the factors impacting ESs in Punjab Province, Pakistan. We evaluated ecosystem service intensity (ESI) by using the benefit transfer method and investigated the spatial heterogeneity of ESIs at the tehsil level by using an exploratory spatial data analysis (ESDA) model and semivariance analysis. This analysis indicated that spatial distribution of ESI shows significant and optimal spatial heterogeneity of ESs, revealing several hot and cold spots for ESI transformation in the study area. The ESI decreased from east to west and north to south, with a trough in the metropolitan zones, including Lahore, Sheikhupura, Faisalabad, and Multan, which was in accordance with the land use/cover pattern. Furthermore, using geographically weighted regression (GWR) analysis, we also identified geographical clusters within which land use/cover pressure and population growth were significantly positively associated with ESI across the province, based on a lag distance scale. The findings of this study have functional economic implications with respect to highlighting areas worthy of conservation and designing ecological corridors to enhance the delivery of ESs for regional benefits.

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To evaluate the spatial distribution characteristics of soil heavy metal content in Xiwuzhumuqin Banner, Inner Mongolia, we analyzed the spatial heterogeneity of soil Cu, Cr, Pb, and Mn contents within 8 km distance of the mining area. Results showed that the contents of Cu, Cr, Pb and Mn in soil were 12.7, 32.6, 29.9 and 201.3 mg·kg-1, and their coefficients of variation were 26.8%, 33.9%, 27.1% and 45.7%, respectively. According to the model fitting by semi-variance function, the spatial distribution of Cu, Cr, Pb and Mn were consistent with the Gaussian model, Gaussian model, Gaussian model and linear model, respectively. Results of the spatial distribution pattern analysis showed that the spatial correlation levels of Mn, Cr and Cu were high, which were mainly affected by structural factors, but little affected by random factors. The spatial correlation level of Pb element was moderate, which was affected by both structural factors and random factors. Results of the fractal dimension analysis showed that the spatial distribution of four heavy metal contents was simple. Combined with 2D and 3D views, the four types of heavy metals all presented gradient distribution, which decreased with the increases of distance. The contents of Cu and Mn were mainly concentrated within 1.5 km from the mining area, while Cr and Pb were mainly concentrated within 2.0 km and 3.0 km from the mining area, respectively.

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Spatial and scale effects have barely been considered in forensic entomology, despite their pervasive influence on most of the parameters affecting the development of insect larval stages and the progression of insect succession on cadavers. Here, we used smoothing/interpolation techniques and semivariograms to document the spatial dynamics of sarcosaprophageous Calliphoridae, an important forensic taxon, in the Greater Moncton area in New Brunswick, Canada. Results indicated that the spatial dynamics of Calliphoridae differed between species, some species showing strong patterns of regional aggregation while others did not. Multivariate spatial correlations indicated that interspecific relationships in space varied widely, ranging from local and large-scale aggregation to spatial anticorrelation between species. Overall, this study suggested that even within a restricted timescale, the spatial dynamics of Calliphoridae can operate at many scales, manifest in different patterns, and be attributed to multiple different causes. We stress that forensic entomology has much to benefit from the use of spatial analysis because many important forensic questions, both at the fundamental and practical levels, require a spatial solution.

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This study evaluated the changes of spatial distribution of the constructive species Stipa breviflora in the desert steppe under different grazing intensities (control, light, moderate, and heavy grazing) in Siziwang, Inner Mongolia. The small-scale spatial distribution of S. breviflora was measured. Results showed that population density of S. breviflora was following the order: heavy grazing (27.81 individuals·m-2) > moderate grazing (22.17 individuals·m-2) > control (11.31 individuals·m-2) > light grazing (10.76 individuals·m-2). The moderate and heavy grazing significantly increased population density of S. breviflora. According to the model fitting by semi-variance function, the population density of S. breviflora under the control, light, moderate and heavy gra-zing treatments were consistent with the exponential model, spherical model, exponential model and spherical model, respectively. Results from spatial distribution pattern analysis showed that structural ratio of S. breviflora population was control (99.7%) > heavy grazing (94.7%) > light grazing (92.7%) > moderate grazing (87.9%). Such a result indicated that the spatial autocorrelation of the four treatments was high, which were mainly affected by structural factors. In comparison, S. breviflora population structure ratio under moderate grazing treatment was the smallest, and partly affected by random factors. Based on fractal dimension analysis, spatial structure of the four treatments was good with simple spatial distribution. With the increases of grazing intensity, the spatial distribution was simpler and more homogeneous. Combined with 2D and 3D views, both light and heavy grazing changed spatial distribution of S. breviflora population from gradient distribution to patch distribution and resulted in the reduction of spatial heterogeneity.

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Based on a grid (25 m X 25 m) equidistant sampling, the spatial variability of pH, organic matter, total nitrogen, available phosphorus, CEC and three typical heavy metal elements Cd, As and Pb in soil tillage layer (0-20 cm) were analyzed by using GIS and Geostatistics in the paddy field of 3.56 hm2 in Beishan Town, Changsha County, Hunan Province. The results showed that soil pH value and Pb content showed weak variation, and other indexes showed moderate variation. The order of variation was following available phosphorus ＞ Cd ＞ total nitrogen ＞ organic matter ＞ CEC ＞ As ＞ Pb ＞ pH. Results of the semi-variance test showed that the best fitting model of the semi-variance function of organic matter, available phosphorus and As was exponential, and the best semi-variance function of pH, total nitrogen, CEC, Cd, Pb was spherical. All the indicators had a strong spatial correlation except for CEC, which showed moderate spatial correlation. Kriging interpolation analysis showed that pH, total nitrogen, CEC, Pb were plaque distribution, while organic matter, available phosphorus, Cd and As were block and banded distribution. Vegetation, topography and human activities were the main factors driving the variation of soil nutrients and heavy metals in the study area. The correlation between soil nutrients and heavy metals content was significant, among which pH and organic matter, Cd and Pb reached a very significant correlation level.

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Taking Quercus mongolica population in the secondary forest of Q. mongolica as the research object, two plots in different stages of succession (A and B) were set up in Tazigou Forest Farm of Wangqing Forestry Bureau, Jilin Province. By applying the method of adjacent grid survey, each plot was divided into 100 units of 10 m×10 m and the spatial coordinates of each tree in the unit were accurately located to survey all the basic information of trees with diameter at breast height (DBH)≥1 cm. The degree, composition, scale and pattern of spatial heterogeneity of individual tree of Q. mongolica were analyzed by means of semi-variance function and fractal dimension of geostatistics. By using Kriging interpolation method, unbiased estimation of tree attribute with spatial autocorrelation was carried out, distribution map was drawn and spatial distribution pattern was analyzed. The results showed that the best semi-variance function of tree attributes in two plots was mainly distributed in an exponential model and a spherical model with an aggregated distribution. The degree of spatial autocorrelation and continuity of plot A were higher than that of plot B. The DBH and the east-west crown (CEW) had strong spatial heterogeneity and autocorrelation in the two plots. The tree attributes of both plots showed strong spatial heterogeneity in the north-south direction. In addition, there was strong spatial heterogeneity in the northwest-southeast direction of plot A and in the northeast-southwest of plot B. The strength of the spatial heterogeneity was higher and the scale being larger in plot A. The variations of DBH and CEW were obvious in plot A, while the variations of CEW and south-north crown (CSN) were obvious in plot B. The fractal dimension and semi-variogram function showed the same result. The tree attributes of plot A were mainly patchy and stripe, and the variation trend of spatial distribution pattern was obvious. The tree attributes of plot B was broken, with complex pattern. Those results indicated that the characteristics of population, community development, spatial scale and spatial horizontal direction might affect the spatial pattern of populations. The geostatistical analysis method is helpful to quantitatively and directly describe population growth and development trend, which can provide a theoretical basis for the sustainable management of Q. mongolica secondary forests in Northeast China.

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This paper introduces a Semivariance-Transinformation (S-T) based method for designing an optimum bay water nutrients monitoring network in San Francisco bay (S.F. bay), USA. Phosphorus and nitrogen are the most important nutrients that lead to eutrophic condition. The monthly phosphate and nitrate+nitrite data recorded during September 2006 to August 2015 was obtained over 14 active stations located at S.F. bay and was used in the research. Semivariance and discrete transinformation entropy have been applied to calculate the optimum range of the monitoring distance. The study indicated the ranges of 28 to 82 and 37 to 50km for the phosphate and nitrate+nitrite respectively. Useful information can be obtained from the monitoring network, if the monitoring distance is included in the mentioned intervals. The findings of the research introduce a new approach in the field of water quality monitoring networks design.

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Often spatiotemporal resolution/scale of environmental and health data do not align. Therefore, researchers compute exposure by interpolation or by aggregating data to coarse spatiotemporal scales. The latter is often preferred because of sparse geographic coverage of environmental monitoring, as interpolation method cannot reliably compute exposure using the small sample of sparse data points. This paper presents a methodology of diagnosing the levels of uncertainty in exposure at a given distance and time interval, and examines the effects of particulate matter (PM) ≤2.5 µm and ≤10 µm in diameter (PM2.5 and PM10, respectively) on birth weight (BW) and low birth weight (LBW), i.e., birth weight <2500 g in Chicago (IL, USA), accounting for exposure uncertainty. Two important findings emerge from this paper. First, uncertainty in PM exposure increases significantly with the increase in distance from the monitoring stations, e.g., 50.6% and 38.5% uncertainty in PM10 and PM2.5 exposure respectively for 0.058° (~6.4 km) distance from the monitoring stations. Second, BW was inversely associated with PM2.5 exposure, and PM2.5 exposure during the first trimester and entire gestation period showed a stronger association with BW than the exposure during the second and third trimesters. But PM10 did not show any significant association with BW and LBW. These findings suggest that distance and time intervals need to be chosen with care to compute exposure, and account for the uncertainty to reliably assess the adverse health risks of exposure.

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Soil phosphorus is an important indicator to measure the soil fertility, because the content of soil phosphorus has an important effect on physical and chemical properties of soil, plant growth, and microbial activity in soil. In this study, the soil samples collecting and indoor analysis were conducted in Zhoukou City located in the flooded area of the Yellow River. By using GIS combined with geo-statistics, we tried to analyze the spatial variability and content distribution of soil total phosphorus (TP) and soil available phosphorus (AP) in the study area. Results showed that TP and AP of both soil layers (0-20 cm and 20-40 cm) were rich, and the contents of TP and AP in surface layer (0-20 cm) were higher than in the second layer (20-40 cm). TP and AP of both soil layers exhibited variation at medium level, and AP had varied much higher than TP. TP of both layers showed medium degree of anisotropy which could be well modeled by the Gaussian model. TP in the surface layer showed strong spatial correlation, but that of the second layer had medium spatial correlation. AP of both layers had a weaker scope in anisotropy which could be simulated by linear model, and both soil layers showed weaker spatial correlations. TP of both soil layers showed a slowly rising change from southwest to northeast of the study area, while it gradually declined from northwest to southeast. AP in soil surface layer exhibited an increase tendency firstly and then decrease from southwest to the northeast, while it decreased firstly and then increased from southeast to the northwest. AP in the second soil layer had an opposite change in the southwest to the northeast, while it showed continuously increasing tendency from northwest to the southeast. The contents of TP and AP in the surface layer presented high grades and the second layer of TP belonged to medium grade, but the second layer of AP was in a lower grade. The artificial factors such as land use type, cropping system, irrigation and fertilization were the main factors influencing the distribution and spatial variation of soil phosphorus in this area.

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Modeling groundwater properties is an important tool by means of which water resources management can judge whether these properties are within the safe limits or not. This is usually done regularly and in the aftermath of crises that are expected to reflect negatively on groundwater properties, as occurred in Jordan due to crises in neighboring countries. In this study, specific capacity and salinity of groundwater of B2/A7 aquifer in Amman Zarqa Basin were evaluated to figure out the effect of population increase in this basin as a result of refugee flux from neighboring countries to this heavily populated basin after Gulf crises 1990 and 2003. Both properties were found to exhibit a three-parameter lognormal distribution. The empirically calculated ß parameter of this distribution mounted up to 0.39 m(3)/h/min for specific capacity and 238 ppm for salinity. This parameter is suggested to account for the global changes that took place all over the basin during the entire period of observation and not for local changes at every well or at certain localities in the basin. It can be considered as an exploratory result of data analysis. Formal and implicit evaluation followed this step using structural analysis and construction of experimental semivariograms that represent the spatial variability of both properties. The adopted semivariograms were then used to construct maps to illustrate the spatial variability of the properties under consideration using kriging interpolation techniques. Semivariograms show that specific capacity and salinity values are spatially dependent within 14,529 and 16,309 m, respectively. Specific capacity semivariogram exhibit a nugget effect on a small scale (324 m). This can be attributed to heterogeneity or inadequacies in measurement. Specific capacity and salinity maps show that the major changes exhibit a northwest southeast trend, near As-Samra Wastewater Treatment Plant. The results of this study suggest proper management practices.

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Ecosystem services are strongly influenced by the landscape configuration of natural and human systems. So they are heterogeneous across landscapes. However lack of the knowledge of spatial variations of ecosystem services constrains the effective management and conservation of ecosystems. We presented a spatially explicit and quantitative assessment of the geographic variations in ecosystem services for the Fuzhou City in 2009 using exploratory spatial data analysis (ESDA) and semivariance analysis. Results confirmed a significant and positive spatial autocorrelation, and revealed several hot-spots and cold-spots for the spatial distribution of ecosystem service intensity (ESI) in the study area. Also the trend surface analysis indicated that the level of ESI tended to be reduced gradually from north to south and from west to east, with a trough in the urban central area, which was quite in accordance with land-use structure. A more precise cluster map was then developed using the range of lag distance, deriving from semivariance analysis, as neighborhood size instead of default value in the software of ESRI ArcGIS 10.0, and geographical clusters where population growth and land-use pressure varied significantly and positively with ESI across the city were also created by geographically weighted regression (GWR). This study has good policy implications applicable to prioritize areas for conservation or construction, and design ecological corridor to improve ecosystem service delivery to benefiting areas.

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Soil conditions and microclimate are important determinants of the fine-scale distribution of plant species in the Arctic, creating locally heterogeneous vegetation. We hypothesize that root-associated fungal (RAF) communities respond to the same fine-scale environmental gradients as the aboveground vegetation, creating a coherent pattern between aboveground vegetation and RAF. We explored how RAF communities of the ectomycorrhizal (ECM) plant Bistorta vivipara and aboveground vegetation structure of arctic plants were affected by biotic and abiotic variables at 0.3-3.0-m scales. RAF communities were determined using pyrosequencing. Composition and spatial structure of RAF and aboveground vegetation in relation to collected biotic and abiotic variables were analysed by ordination and semi-variance analyses. The vegetation was spatially structured along soil C and N gradients, whereas RAF lacked significant spatial structure. A weak relationship between RAF community composition and the cover of two ECM plants, B. vivipara and S. polaris, was found, and RAF richness increased with host root length and root weight. Results suggest that the fine-scale spatial structure of RAF communities of B. vivipara and the aboveground vegetation are driven by different factors. At fine spatial scales, neighbouring ECM plants may affect RAF community composition, whereas soil nutrients gradients structure the vegetation.

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