Covariances among join-count spatial autocorrelation measures

Spatial distributions of biological variables are often well-characterized with pairwise measures of spatial autocorrelation. In this article, the probability theory for products and covariances of join-count spatial autocorrelation measures are developed for spatial distributions of multiple nominal (e.g. species or genotypes) types. This more fully describes the joint distributions of pairwise measures in spatial distributions of multiple (i.e. more than two) types. An example is given on how the covariances can be used for finding standard errors of weighted averages of join-counts in spatial autocorrelation analysis of more than two types, as is typical for genetic data for multiallelic loci.     

Effects of farming practices on spatial behaviour of common voles

This study aimed to reveal changes in spatial behaviour of common voles (Microtus arvalis) after alteration of their habitat by farming practices. Radio-collared common voles were tracked before and after mulching, mowing, harvesting wheat, and ploughing in the flood plain of the river Unstrut in central Germany. Voles undisturbed by agricultural practices were tracked on a mulchland, an abandoned pasture, and a cattle pasture. There was a large decrease in home-range size after harvesting wheat (96%, P<0.001). Changes after mowing (–74%, P=0.06) were almost significant whereas changes after mulching were not (+14%, P=0.60). On the cattle pasture we found a decrease in home-range size (42%, P=0.03) possibly due to increased spatial activity of cattle in autumn. There was a positive correlation of home-range size and vegetation height for plots with and without farming activity but no correlation with vegetation cover, population density, and breeding. Radio-collared common voles did not show evasive movements and farming practices did not cause a shift of centres of activity. Common voles clearly reacted to sudden changes in vegetation height, which may indicate an immediate response to predation risk. Electronic Publication     

The effect of spatial scale on evenness

Abstract. The effect of spatial scale on species evenness has not previously been investigated. As the area of each sample of vegetation (i.e. the spatial grain) increases, evenness could in theory increase, decrease, or stay the same, though the simplest model predicts an increase. We use biomass data from four dune slack sites and two semi-arid grasslands, sampled to allow calculation of evenness at a range of spatial grains. In all six sites, evenness decreases as grain size increases, almost monotonically. It is hypothesized that such a pattern is a result of a general feature of plant species abundance distributions and of vegetation response to environmental microheterogeneity.     

Factors affecting tactile spatial acuity

Tactile spatial acuity on the fingerpad was measured using a grating orientation task. In this task, subjects are required to identify the orientation of square-wave gratings placed on the skin. Previous studies have shown that performance varies as a function of the width of the grooves in the gratings. In the present study, both groove width and the overall size and configuration of the contactors were varied. Sensitivity improved with wider grooves and with larger contactors. Additional measurements showed that the improved sensitivity is not the result of the increase in total area contacted, but rather is due to two other factors associated with larger contactors. One is the greater linear extent of the larger contactors. The other appears to be due to the reduction in the interference produced by the outer edge of the contactor. Specifically, as the contactor increases in size, the distance between the outer edge and the center portion of the grooves also increases. It was also shown that subjects are more sensitive to a single, continuous groove as compared with two grooves of the same total length but spatially discontinuous. Similarly, subjects are more sensitive to a contactor with a continuous groove than to a contactor in which just the end points of the groove are presented. The results are generally consistent with the results of peripheral, neurophysiological recordings. The results are discussed in terms of the way in which both spatial and intensive factors may affect sensitivity to grating orientation.     

Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems

Ecosystems can undergo large-scale changes in their states, known as catastrophic regime shifts, leading to substantial losses to services they provide to humans. These shifts occur rapidly and are difficult to predict. Several early warning signals of such transitions have recently been developed using simple models. These studies typically ignore spatial interactions, and the signal provided by these indicators may be ambiguous. We employ a simple model of collapse of vegetation in one and two spatial dimensions and show, using analytic and numerical studies, that increases in spatial variance and changes in spatial skewness occur as one approaches the threshold of vegetation collapse. We identify a novel feature, an increasing spatial variance in conjunction with a peaking of spatial skewness, as an unambiguous indicator of an impending regime shift. Once a signal has been detected, we show that a quick management action reducing the grazing activity is needed to prevent the collapse of vegetated state. Our results show that the difficulties in obtaining the accurate estimates of indicators arising due to lack of long temporal data can be alleviated when high-resolution spatially extended data are available. These results are shown to hold true independent of various details of model or different spatial dispersal kernels such as Gaussian or heavily fat tailed. This study suggests that spatial data and monitoring multiple indicators of regime shifts can play a key role in making reliable predictions on ecosystem stability and resilience. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A measure of spatial stratified heterogeneity

Spatial stratified heterogeneity, referring to the within-strata variance less than the between strata-variance, is ubiquitous in ecological phenomena, such as ecological zones and many ecological variables. Spatial stratified heterogeneity reflects the essence of nature, implies potential distinct mechanisms by strata, suggests possible determinants of the observed process, allows the representativeness of observations of the earth, and enforces the applicability of statistical inferences. In this paper, we propose a q-statistic method to measure the degree of spatial stratified heterogeneity and to test its significance. The q value is within [0,1] (0 if a spatial stratification of heterogeneity is not significant, and 1 if there is a perfect spatial stratification of heterogeneity). The exact probability density function is derived. The q-statistic is illustrated by two examples, wherein we assess the spatial stratified heterogeneities of a hand map and the distribution of the annual NDVI in China.     

Hierarchical spatial modeling of additive and dominance genetic variance for large spatial trial datasets

Summary .  This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets. Direct application of such models to large spatial datasets are, however, computationally infeasible because of cubic-order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein–Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, genetic effects and anisotropic spatial residuals, and a large dataset from a Scots pine ( Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial, which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability.     

Persistent spatial patterns for semi-discrete models of excitable media

Excitable media have the property that in the spatially homogeneous configuration there is a globally asymptotically stable equilibrium, and no sustained non-decaying oscillations are possible. If diffusion effects are present, however, experiments seem to indicate the possibility of persistent oscillations. In more than one space dimension this may occur, apparently, even if the initial disturbance is restricted to a compact subset of an open domain in the medium. In this paper we discuss a mathematical model of this phenomenon. The model consists of a doubly infinite coupled system of ordinary differential equations, and therefore is intended to represent a spatially discrete network of interconnected cells.     

中国壳斗科植物空间多样性格局研究

采用地理信息系统技术,制作空间分布图、从空间上计算多样性格局指数,研究中国壳斗科植物属、种的空间多样性分布格局。结果显示,云南南部、广西北部和广东北部的属、种数量均较多,是中国壳斗科植物多样性的重要分布地区,甘肃南部、陕西南部、河南西部及南部是壳斗科植物向南、向北扩散的重要通道;从多样性指数来看,种的多样性指数值均比属的值高,但均匀度指数却是属的值高;当属或种的数量为1时,其所占面积、占景观的比例、斑块数量、最大斑块指数、景观形状指数均最大,随着属或种的数量逐渐增加,其多样性明显提高,但其各项指标基本呈依次降低的趋势。通过对壳斗科植物空间多样性格局进行量化研究,获取了中国壳斗科植物空间多样性分布规律及多样性格局数量特点,利用地理信息系统技术可以使多样性研究体现出空间性和定量化的特征。     

Bacteriophage evolution given spatial constraint

Spatial structure can impede mixing, diffusion, and motility. In microbiology laboratories, spatial structure is commonly achieved via formation of agar gels, within which bacteriophage (phage) replication results in localized clearings called plaques. Developing a better understanding of phage plaque formation is relevant because of the ubiquity of phage plaquing in the laboratory; because plaque size has been employed as a measure of phage fitness; because many bacteria exist within environments that display significant spatial structure (e.g., biofilms, soils, sediments, and in or on plant or animal tissues); and because spatial structure could impede phage exploitation of bacterial communities. There is, however, a relative dearth of experimentation and analysis considering phage plaque formation from the perspective of selection acting on individual phage growth parameters-latent period, burst size, and adsorption rate. Here we consider the impact of these parameters on rates of plaque wavefront velocity (rates of radial plaque enlargement), especially as functions of existing phage and environmental properties. We do so based on analyses of published equations which predict plaque enlargement rates. These indicate that greater wavefront velocities should be associated with (i) latent period reductions, (ii) larger burst sizes, or (iii) faster virion binding to bacteria. We suggest, however, that deviations could occur, respectively, (i) if virion adsorption is "slow" or if burst sizes are large, (ii) if burst sizes are already large, or (iii) if virion binding rates are already fast, bacterial densities are especially high, or burst sizes are large. Higher initial lawn bacterial densities could also contribute to faster plaque expansion, but only if adsorption is otherwise slow or burst sizes are large. By contrast, faster virion diffusion is always expected to result in greater plaque wavefront velocities. Overall, we provide a snapshot of how phage populations may respond evolutionarily to selection for more-rapid propagation during spatially constrained growth.     

Assessing isotropy for spatial point processes

A common assumption while analyzing spatial point processes is direction invariance, i.e., isotropy. In this article, we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second-order intensity function. We derive an L(2) consistent subsampling estimator for the asymptotic covariance matrix of the sample second-order intensity function and use this to construct a test statistic with a chi(2) limiting distribution. We demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set, where our approach confirms suspected directional effects in the spatial distribution of the desert plant species.     

Characterizing spatial extinction in an abbreviated version of the Barnes maze

Adult male Wistar rats were trained to find an escape box in the Barnes maze in order to characterize the extinction process of a learned spatial preference. To do so, once they had fully acquired the spatial task, they were repeatedly exposed to the maze without the escape box. Multiple behavioral measurements (grouped into motor skill and spatial preference indicators) were followed up throughout the complete training process. Animals gained efficiency in finding the escape box during acquisition, as indicated by the reduction in the time spent escaping from the maze, the number of errors, the length of the traveled path, and by the increase in exploration accuracy and execution speed. When their retention and preference were tested 24 h later, all the subjects retained their enhanced performance efficiency and accuracy and displayed a clear-cut preference for the escape hole and its adjacent holes. Almost all motor skill indicators followed an inverse, though not monotonic, pattern during the extinction training, returning to basal levels after three trials without escape box, displaying a transient relapse during the fifth extinction trial. Preference indicators also followed a reverse pattern; however, it took seven trials for them to return to basal levels, relapsing during the eighth extinction trial. The abbreviated Barnes maze acquisition, evaluation, and extinction procedures described herein are useful tools for evaluating the effects of behavioral and/or pharmacological treatment on different stages of spatial memory, and could also be used for studying the neurophysiological and neurobiological underpinnings of this kind of memory.     

Colonization rules and spatial distributions in ecology

Because they are intuitive and mathematically straight-forward, colonization rules are often used to model spatial patterns in ecology. Colonization rules assign individuals to categories according to the locations of previous colonists. In this note, a compact introduction to colonization rules in ecology is presented with implications for autocorrelation and spatial distributions. I use the colonization rule approach to unify a diverse set of spatial and species diversity analyses, exploring future extensions to incorporate greater realism.     

Grating orientation as a measure of tactile spatial acuity

Recent studies have used grating orientation as a measure of tactile spatial acuity on the fingerpad. In this task subjects identify the orientation of a grooved surface presented in either the proximal-distal or lateral-medial orientation. Other recent results have suggested that there might be a substantial anisotropy on the fingerpad related to spatial sensitivity. This anisotropy was revealed using a task in which subjects discriminated between a smooth and a grooved surface presented at different orientations on the fingerpad. The anisotropy was substantial enough that it might permit subjects to discriminate grating orientation on the basis of intensive rather than spatial cues. The present study examined the possibility that anisotropy on the fingerpad might provide cues in a spatial acuity task. The ability of subjects to discriminate between a smooth and a grooved surface was measured under conditions that are typically used in grating orientation tasks. No evidence of anisotropy was found. Also, using a grating orientation task, separate estimates were made of sensitivity in the proximal-distal and lateral-medial orientations. Again no evidence of anisotropy was found. Consistent with changes in the density of innervation, grating orientation sensitivity was found to vary as a function of location on the fingerpad. The results support the view that grating orientation is a valid measure of spatial acuity reflecting underlying neural, spatial mechanisms.     

The spatial correlation and interaction between manufacturing agglomeration and environmental pollution

Using statistical data from 285 cities in China, this paper studies the spatial correlation and interaction between manufacturing agglomeration and environmental pollution. Using a widely used spatial correlation index, bivariate Moran's I, we first estimate the spatial correlation between manufacturing agglomeration and environmental pollution. We show that there is significant spatial correlation between them, and distinct patterns of local spatial concentration are identified. Then, we use a spatial simultaneous equations (SSE) model to analyze the interaction between manufacturing agglomeration and environmental pollution. We show that manufacturing agglomeration aggravates environmental pollution, while environmental pollution restrains manufacturing agglomeration. In addition, manufacturing agglomeration and environmental pollution in any one city can be affected by manufacturing agglomeration and environmental pollution in surrounding cities through spatial spillover. Finally, we put forward specific suggestions based on the conclusions for more sustainable development.     

Structural segregation and scales of spatial dependency in Abies amabilis forests

Question: Is a mosaic structure apparent in the spatial distribution of trees in old‐growth Abies amabilis forests? Location: Montane forests of the western Cascade Range, Washington, USA. Methods: Maps of tree locations were created for study areas located in two, 300‐year old stands and a single 600‐year old stand. Stand structure parameters were calculated using several subsample quadrats sizes (56.25 ‐ 306.25 m²), which were drawn randomly with replacement at a density of 250 quadrats per ha from the stem maps in the computing environment. Spatial cross‐covariance functions between different canopy strata were estimated using the spline cross‐correlogram. Results: Negative spatial correlation (segregation) between subcanopy tree density and areas of high overstorey occupancy was detected. Understorey and midstorey tree densities were positively spatially correlated. These general trends were apparent across the range of observational scales investigated. Significant spatial correlation between canopy strata was observed at spatial scales of 12 ‐ 44 m and extended to the largest scales in the 600‐year old stand. Conclusion: The observed spatial segregation between canopy strata supports the hypothesis that old A. amabilis forests form fine‐scale structural mosaics. Structural segregation at small scales may be due to competitive interactions as well as exogenous forcing of tree locations (e.g. by mortality due to pathogens or disturbance), however segregation at large scales in the 600‐year old stand is likely due to exogenous factors alone. This study reinforces the idea that horizontal heterogeneity is an emergent property of old‐growth forests.     

Fish-habitat associations across multiple spatial scales

Important to the study of reef fish ecology is understanding the degree to which fish community structure varies across space, what factors can account for such variation, and whether these factors are scale dependent. This study examined the structure of reef fish communities across four spatial scales (1, 10 100, and 200 m²) visually censused from seven sites within Tague Bay, St. Croix, U.S. Virgin Islands. Relative differences in the number of individuals and species among sites indicated a pattern that was consistent across spatial scales. Spearmans rank correlation revealed significant positive correlation in site rankings, in terms of species richness, between 1 and 10 m², and 100 and 200 m²; and for the abundance of individuals between 100 and 200 m². In order to understand the degree to which quantified habitat variables account for patterns in the abundance of individuals and species, and whether these fish-habitat relationships were consistent regardless of spatial scale, separate canonical correlation analyses were conducted at each scale. Independent of scale, the total number of individuals and species were correlated with specific habitat variables, either negatively (with areas of pavement, sand, no algae, and low structural complexity) or positively (with areas of Amphiroa rigida, Halimeda incrassata, high structural complexity, and diverse algae/seagrass communities). These habitat variables explained 31–81% (at scales of 1–200 m²) of the variation in the number of individuals and species. Similar analyses were also performed on the abundances of the nine most common species, and whether their specific habitat associations were independent of scale. Results indicated that habitat variables explained 19–73% (at scales of 1–200 m²) of the variation in abundances of each species. Unique fish-habitat relationships were observed for each species, and most such relationships were consistent across spatial scales. The structure of reef fish communities of Tague Bay was explained in large part by the composition of coral and algae communities present. Both the spatial variation in community structure and the fish-habitat relationships, at the community and population level, appeared to be largely independent of the spatial scale examined. This suggests that generalizations across Tague Bay are possible. Similar habitat associations reported in the literature are discussed with regard to the possibility for generalizations across regions.