Influence Of Spatial Autocorrelation Research Articles

Application of computer geological model in geotechnical engineering investigation

The computer geological model is the approximate model of the actual complex geological phenomenon. During the modeling process, uncertainty from various sources can lead to deterioration of the quality of geological models. In order to ensure the usability of the model, it is necessary to consider the influence of spatial autocorrelation and interrelationship between strata on information transmission and uncertainty when analyzing and predicting multi-layer geological structures. The purpose of this paper is to improve the accuracy and testing breadth of computer modeling by studying geotechnical exploration activities. The calculation formula of information entropy of geological variables is given. At the same time, it introduces how to calculate the maximum information entropy of geological variables under the prior distribution according to the prior information constraints, and how to calculate the results of geological variables under the posterior distribution by using Bayesian updating. This paper introduces the calculation method of formation attribute probability field and iterates formation probability from bottom to top. The results show that the Copula method can improve the geological model in statistical sense. Finally, it is concluded that establishing 3D geological model by computer is helpful to improve the accuracy of geological exploration.

Using multi‐scale spatially explicit frameworks to understand the relationship between functional diversity and species richness

Understanding how ecosystem functioning is impacted by global change drivers is a central topic in ecology and conservation science. We need to assess not only how environmental change affects species richness, but also how the distribution of functional traits (i.e. functional diversity) mediate the relationship between species richness and ecosystem functioning. However, most evidence about the capacity of functional diversity to explain ecosystem functioning has been developed from studies conducted at a single spatial scale. Here, we explore theory, expectations and evidence for why and how species richness and functional diversity relationships vary with spatial scale. Despite the importance of accounting for spatial processes at multiple scales, we show that most studies of the species richness–functional diversity relationship focus on single scale analyses that ignore spatial context. Thus, we discuss the need to establish a spatially explicit, multi‐scale framework for understanding the relationship between species richness and functional diversity. As a starting point to developing such a framework, we detail some expected trajectories and mechanisms by which the diversity of species and functional traits may change across increasing spatial scales. We also explore what is known about two important gaps in the literature about this relationship: 1) the influence of spatial autocorrelation on community assembly processes and 2) the variation in the structure of species interactions across spatial extents. We present some key challenges that could be addressed by integrating approaches from community and landscape ecology. This information will help improve our understanding of the relative influence of local and large‐scale processes on community structure, while providing a foundation for improving biodiversity monitoring, policy and ecosystem function based conservation.

Importance of Spatial Autocorrelation in Machine Learning Modeling of Polymetallic Nodules, Model Uncertainty and Transferability at Local Scale

Machine learning spatial modeling is used for mapping the distribution of deep-sea polymetallic nodules (PMN). However, the presence and influence of spatial autocorrelation (SAC) have not been extensively studied. SAC can provide information regarding the variable selection before modeling, and it results in erroneous validation performance when ignored. ML models are also problematic when applied in areas far away from the initial training locations, especially if the (new) area to be predicted covers another feature space. Here, we study the spatial distribution of PMN in a geomorphologically heterogeneous area of the Peru Basin, where SAC of PMN exists. The local Moran’s I analysis showed that there are areas with a significantly higher or lower number of PMN, associated with different backscatter values, aspect orientation, and seafloor geomorphological characteristics. A quantile regression forests (QRF) model is used using three cross-validation (CV) techniques (random-, spatial-, and cluster-blocking). We used the recently proposed “Area of Applicability” method to quantify the geographical areas where feature space extrapolation occurs. The results show that QRF predicts well in morphologically similar areas, with spatial block cross-validation being the least unbiased method. Conversely, random-CV overestimates the prediction performance. Under new conditions, the model transferability is reduced even on local scales, highlighting the need for spatial model-based dissimilarity analysis and transferability assessment in new areas.

Spatial heterogeneity of leaf area index in a temperate old-growth forest: Spatial autocorrelation dominates over biotic and abiotic factors

Leaf area index (LAI) controls many eco-physiological processes and can be widely used to scale-up leaf processes to ecosystem, landscape and regional levels. However, the macro-scale spatial heterogeneity of LAI and its controlling factors are not fully understood. We estimated annual maximum LAI using an LAI-2200 plant canopy analyzer in a 9-ha, old-growth, mixed broadleaved-Korean pine (Pinus koraiensis) forest in China. We analyzed the spatial heterogeneity of LAI and mapped its distribution using geostatistical methods; then, through variance partitioning, we examined the influences of several biotic factors, abiotic factors and spatial autocorrelation on the LAI distribution. Variance partitioning showed that these factors altogether explained 59% of the variation in the distribution of LAI. Compared to biotic and abiotic factors, spatial autocorrelation controlled more spatial heterogeneity of LAI by explaining 51.4% of the total variation in LAI. For biotic and abiotic factors, the mean diameter at breast height (DBH) of large trees (DBH > 10 cm), elevation, soil temperature and soil mass moisture content significantly affected the LAI distribution (P < 0.01). Notably, spatial autocorrelation unexpectedly explained the most variation in the LAI values, and it also varies with cardinal direction and is a key descriptor of LAI spatial variability. These results suggest that the influence of spatial autocorrelation on LAI distribution should attract more attention and that both the relative importance of and interactions among different determining factors is helpful for better understanding the mechanistic determinants of LAI distributions in temperate mixed forests.

Assemblage of immature Odonata (Insecta, Anisoptera) in streams of the Mato Grosso do Sul State: spatial implications

ABSTRACT This study investigated the assemblages attributes (composition, abundance, richness, diversity and evenness) and the most representative genera of Odonata, Anisoptera at Água Boa and Perobão Streams, Iguatemi River basin, Brazil. Both are first order streams with similar length that are impacted by riparian forest removal and silting. Quarterly samplings were conducted from March to December 2008 in the upper, intermediate and lower stretch of each stream. The Mantel test was used to check the influence of spatial autocorrelation on the Odonata composition. Spatial variations in the composition were summarized by the Principal Coordinates Analysis (PCoA) using Mantel test residuals. The effects of spatial correlation on richness and abundance were investigated by the spatial correlogram of Moranʼs I coefficients. The most representative genera in each stream were identified by the Indicator Value Method. The spatial variations in the attributes of the assemblages were assessed using analysis of variance of null models. We collected 500 immature individuals of 23 genera and three families. Among the attributes analyzed only the composition and abundance showed significant spatial differences, with the highest mean abundance found in the Perobão Stream. Miathyria and Zenithoptera were the indicator genera of the Água Boa Stream and Erythrodiplax, Libellula, Macrothemis, Progomphus and Tramea were the indicator genera of the Perobão Stream.

Impacts of Multi Resolution Species Distributional Information Analyzing Macroecological Patterns

In this brief report, a simple scaling algorithm was developed for reconstructing range cells upon the original pixellevel distributional points of species. The algorithm could generate the distributional cells of species that covers all the original distributional points of species, but being with varying spatial resolutions (i.e., different sizes of the smallest operative area unit). As such, I could quantitatively evaluate the macroecological patterns (including richness, rarity hotspots, and the influence of spatial autocorrelation on structuring species’ richness and rarity patterns) on the basis of these varying-resolution species distributional layers. Resultant diversity patterns thus could be compared to the true patterns directly derived from species’ original distributional points. The present theoretical results showed that, the macroecological patterns identified from varying-resolution data could be basically consistent to those from the true distributional data, as long as there were not many multi-scaling distributional layers inside the whole dataset. However, the estimated macroecological patterns would be far departed from the true ones when there were a remarkable number of multi-scaling layers inside. Thus, I argued that the varying-resolution data could be utilized but with some cautions so as to accurately reveal ecological patterns and interpret the relationship between species diversity, distribution and environment.

Chironomid-based water depth reconstructions: an independent evaluation of site-specific and local inference models

Water depth is an important environmental variable that explains a significant portion of the variation in the chironomid fauna of shallow lakes. We developed site-specific and local chironomid water-depth inference models using 26 and 104 surface-sediment samples, respectively, from seven kettlehole lakes in the Plymouth Aquifer, southeast Massachusetts, USA. Our site-specific model spans a depth gradient of 5.6 m, has an \( {\text{r}}_{\text{jack}}^{2} \) of 0.90, root mean square error of prediction (RMSEP) of 0.5 m and maximum bias of 0.7 m. Our local model has a depth gradient of 11.7 m, an \( {\text{r}}_{\text{jack}}^{2} \) of 0.71, RMSEP of 1.6 m and maximum bias of 2.9 m. Principal coordinates of neighbourhood matrices (PCNM) analysis showed that there is no influence of spatial autocorrelation on the site-specific model, but PCNM variables explained a significant amount of variance (4.8%) in the local model. This variance, however, is unique from the variance explained by water depth. We applied the inference models to a Holocene chironomid record from Crooked Pond, a site for which multiple, independent palaeohydrological reconstructions are available. The chironomid-based reconstructions are remarkably similar and show stable water depths of ~5 m, interrupted by a 2-m decrease between 4,200 and 3,200 cal a BP. Sedimentological evidence of water level fluctuations at Crooked Pond, obtained using the so-called Digerfeldt approach, also shows a drop in water depths around that time. The period of reconstructed lower water levels coincides with the abrupt decline in moisture-dependent hemlock in this region, providing further evidence for this major palaeohydrological event. The site-specific model has the best performance statistics, but the high percent abundance of fossil taxa from the long core that are absent or rare in the training set makes the site-specific reconstruction unreliable for the period before 4,400 cal a BP. The fossil taxa are well represented in the local model, making it the preferred inference model. The strong similarity between the chironomid-based reconstructions and the independent palaeohydrological records highlights the potential for using chironomid-based inference models to determine past lake depths at sites where temperature was not an influencing factor.

Null models reveal preferential sampling, spatial autocorrelation and overfitting in habitat suitability modelling

Nowadays, species are driven to extinction at a high rate. To reduce this rate it is important to delineate suitable habitats for these species in such a way that these areas can be suggested as conservation areas. The use of habitat suitability models (HSMs) can be of great importance for the delineation of such areas. In this study MaxEnt, a presence-only modelling technique, is used to develop HSMs for 223 nematode species of the Southern Bight of the North Sea. However, it is essential that these models are beyond discussion and they should be checked for potential errors. In this study we focused on two categories (1) errors which can be attributed to the database such as preferential sampling and spatial autocorrelation and (2) errors induced by the modelling technique such as overfitting, In order to quantify these adverse effects thousands of nulls models were created. The effect of preferential sampling (i.e. some areas where visited more frequenty than others) was investigated by comparing model outcomes based from null models sampling the actual sampling stations and null models sampling the entire mapping area ( Raes and ter Steege, 2007). Overfitting is exposed by a fivefold cross-validation and the influence of spatial autocorrelation is assessed by separating test and training sets in space. Our results clearly show that all these effects are present: preferential sampling has a strong effect on the selection of non-random species models. Crossvalidation seems to have less influence on the model selection and spatial autocorrelation is also strongly present. It is clear from this study that predefined thresholds are not readily applicable to all datasets and additional tests are needed in model selection.

Revealing biogeographical patterns by nonlinear ordinations and derived anisotropic spatial filters

ABSTRACTAim Spatial floristic and faunistic data bases promote the investigation of biogeographical gradients in relation to environmental determinants on regional to continental scales. Our aim was to extract major gradients in the distribution of vascular plant species from a grid‐based inventory (the German FLORKART data base) and relate them to long‐term precipitation and temperature records as well as soil conditions. We present an ordination technique capable of coping with this complex data array. The goal was also to sort out the influence of spatial autocorrelation, assuming floristic autocorrelation is anisotropic.Location Germany, at a spatial resolution of 6′ × 10′.Methods Isometric feature mapping (Isomap) was applied as a nonlinear ordination method. Isomap was coupled to ‘eigenvector‐based filters’ for generating spatial reference models representing spatial autocorrelation. What is novel here is that the derived filters are not based on the assumption of equidirectional autocorrelation. Instead, the so‐called ‘principal coordinates of anisotropic neighbour matrices’ build filters to test the influence of geographical vicinity in directions of high similarity among observations.Results The Isomap ordination of floristic data explained more than 95% of the data variance in six dimensions. The leading two dimensions (representing about 80% of the FLORKART data variance) revealed clear spatial gradients that could be related to independent effects of temperature, precipitation and soil observations. By contrast, the third and higher FLORKART dimensions were dominated by an antagonism of anisotropic spatial autocorrelation and soil conditions. A subsequent cluster analysis of the floristic Isomap coordinates educed the spatial organization of the floristic survey, indicating a considerable sampling bias.Conclusions We showed that Isomap provides a consistent methodical framework for both ordination and derived spatial filters. The technique is useful for tracing the often nonlinear features of species occurrence data to environmental drivers, taking into account anisotropic spatial autocorrelation. We also showed that sampling biases are a conspicuous source of variance in a frequently used floristic data base.

EFFECTS OF SPATIAL STRUCTURES ON THE RESULTS OF FIELD EXPERIMENTS

Field experiments have been designed to account for spatial structures since the inception of randomized complete block designs by R. A. Fisher. In recent years, our understanding of spatial structures led to refinements in the design and analysis of field experiments in the face of spatial patterning. In the presence of spatial autocorrelation in the response variable, is it possible to optimize the experimental design to maximize the response to the experimental factors? The questions addressed in this paper are: (1) What is the effect of spatial autocorrelation on type I error of the tests of significance commonly used to analyze the results of field experiments? (2) How effectively can we control for the effect of spatial autocorrelation by the design of the experiment? (3) Which experimental designs lead to tests of significance that have greater power? (4) What is the influence of spatial autocorrelation on power of ANOVA tests of significance? This paper attempts to answer these questions through numerical simulations with known spatial autocorrelation. Response variable were simulated to represent the sum of separate effects: (1) an explanatory environmental variable (which could be used as a covariable in the analysis) with a deterministic structure plus spatial autocorrelation, (2) an effect of the experimental treatments, (3) spatial autocorrelation in the response (e.g., biological) variable, and (4) a random error. The program repeatedly generated and analyzed surfaces with given parameters (1000 replicates). The rejection rate of the null hypothesis of no effect of the treatment onto the response variable provided estimates of type I error and power. The simulations showed the following: (1) In the presence of spatial autocorrelation, or if repetitive deterministic structures are present in the variables influencing the response, experimental units should not be positioned at random. (2) ANOVA that takes blocking into account is an efficient way of correcting for deterministic structures or spatial autocorrelation. (3) For constant effort, experimental designs that have more, smaller blocks, broadly spread across the experimental area, lead to tests that have more power in the presence of spatial autocorrelation. (4) Short-ranged spatial autocorrelation affects the power of ANOVA tests more than large-ranged spatial autocorrelation.

Influence of spatial autocorrelation on a fixed-effect model used to evaluate treatment of oil spills

A study was conducted during 1989 by the EPA to evaluate the effectiveness of two methods of nitrogen fertilizer application to treat the Exxon oil spill on beaches of Alaska. The current study, using the data, was to determine the spatial relationship of oil residue on these beaches and to evaluate the influence of spatial autocorrelation on the power of a fixed-effect model used by EPA investigators. The distribution of residual dry weight (mg oil residue/kg of beach material), was found to be spatially independent on individual beaches and for individual sampling times. The presence of spatial autocorrelation resulted in an overestimation of treatment means and an underestimation of their respective standard errors. In turn, an increase in the significance of differences in individual treatments and in the power of the test resulted. A spatial autoregressive model was used to correct for the presence of spatially autocorrelated residuals and the model was used to obtain the best linear unbiased estimates of parameters. Analysis of variance showed that oil residue concentration was significantly higher on the control beach (Raven Beach) than on either of the beaches fertilized with two different nitrogen treatment applications (Kittiwake Beach or Tern Beach). These results also showed that the two fertilizer treatments reduced the concentration of oil residue significantly faster than would have occurred without treatment. The power of the experimental design, a randomized block design used by the EPA, adequately detected significant differences among treatments. A fixed-effect model was used to analyze the data. Furthermore, the current study also found that increasing the sampling intensity or replicating the experimental design could have decreased the power of the test because of the presence of spatially autocorrelated data. In general, the power of the fixed-effect model for the design to detect a significant difference among treatments increased over time. In contrast, the power of the fixed-effect model to detect a specified difference across all times decreased over time because of decreases in means and their associated standard errors.

Spatial structure, sampling design and scale in remotely-sensed imagery of a California savanna woodland

This article describes research related to sampling techniques for establishing linear relations between land surface parameters and remotely-sensed data. Predictive relations are estimated between percentage tree cover in a savanna environment and a normalized difference vegetation index (NDVI) derived from the Thematic Mapper sensor. Spatial autocorrelation in original measurements and regression residuals is examined using semi-variogram analysis at several spatial resolutions. Sampling schemes are then tested to examine the effects of autocorrelation on predictive linear models in cases of small sample sizes. Regression models between image and ground data are affected by the spatial resolution of analysis. Reducing the influence of spatial autocorrelation by enforcing minimum distances between samples may also improve empirical models which relate ground parameters to satellite data.