Components Of Spatial Variation Research Articles

Spatial and temporal effects of heat waves on the diversity of European stream invertebrate communities

The frequency and magnitude of extreme events, such as heat waves, are predicted to increase with climate change. However, assessments of the response of biological communities to heat waves are often inconclusive. We aimed to assess the responses in abundance, taxonomic and functional diversity indices of stream invertebrate communities to heat waves using long-term monitoring data collected across Europe. We quantified the heat waves' magnitude, analyzed the spatial (i.e., long-term mean) and temporal (anomaly around the long-term mean) components of variation in the magnitude of heat waves, and their interaction with anthropogenic stressors (ecological quality and land cover). For the spatial component of variation, we found a negative association of the community indices to the increasing magnitude of heat waves. Sites undergoing heat waves of higher magnitude showed fewer species and lower trait diversity compared with sites experiencing lower magnitude heat waves. However, we could not detect an immediate temporal response of the communities to heat waves (i.e., the temporal component). Furthermore, we found that the effects of heat waves interacted with the ecological quality of the streams and their surrounding land cover. Diversity declined with increasing heat waves' magnitude in streams with higher ecological quality or surrounded by forest, which may be due to a higher proportion of sensitive species in the community. Heat waves' impacts on diversity were also exacerbated by increasing urban cover. The interaction between heat waves' magnitude and anthropogenic stressors suggests that the effects of extreme events can compromise the recovery of communities. Further, the predicted increase in heat waves will likely have long-term effects on stream invertebrate communities that are currently undetected.

Spatial organisation of the soil macrofauna community of an oak forest in the steppe zone of Ukraine

Background. Environmental impact assessments and the development of measures for the protection and sustainable use of ecosystems should take into account that not only steppe ecosystems but also forest, marsh, salt marsh and meadow ecosystems are referenced for the steppe zone. A comparative approach requires the study of reference ecosystems to understand how much a particular ecosystem has been transformed or how far it is from natural patterns in the restoration process. The soil macrofaunal community of the forest ecosystem of the right bank of the Samara River can be considered a reference for many forest ecosystems in the region. The aim of this study was to identify patterns of spatial organization of the soil macrofaunal community of an oak forest on the right bank of the Samara River. Materials and Methods. A study was conducted in a deciduous woodland located in an oak forest on the right bank of the Samara River. The study area was divided into 5 transects, each consisting of 20 sampling points with a 2 m distance between rows. The samples of the soil macrofauna were taken from a single block of soil that was 25×25×30 cm deep and removed quickly. Vascular plant species lists were recorded for each 2×2 m subplot. The soil penetration resistance and electrical conductivity were measured. Soil faunal trophic activity was assessed by means of a bait lamina test. Results and Discussion. The spatial structure of the community is complex in terms of hierarchy. The driver of the broad-scale component of spatial variation in the community is the properties of the topsoil, mainly the density of the litter. Vegetation cover forms a broad component of the spatial variation in soil macrofauna. An important factor in structuring ecological space is the location of trees. The pure spatial pattern is represented by broad-, medium-, and fine-scale components. Conclusion. The soil macrofaunal community of an oak forest on the slope of the right bank of a steppe river has a high level of abundance and taxonomic and ecological diversity. The spatial distribution of trees forms a broad-scale component of variation in the soil macrofaunal community, and herbaceous cover forms a medium-scale component. The fine-scale component of community variation is due to neutral factors.

Beta diversity of restored river dike grasslands is strongly influenced by uncontrolled spatio‐temporal variability

AbstractAimsUnderstanding the spatio‐temporal patterns of restoration outcomes is crucial to improve predictability of restoration. High beta diversity of species‐rich communities is sought because it increases overall biodiversity and improves ecosystem stability and multifunctionality. For predictive restoration, it is important to identify the significance of drivers like site characteristics but also uncontrolled factors such as spatial effects, historical factors, and year effects.LocationDikes at river Danube, SE Germany.MethodsWe studied dike grasslands 4–19 years after restoration over five years (2017–2021, 41 plots in 12 sites). We calculated beta diversity indices to describe spatial variation and temporal turnover, including their additive components ‘replacement’ and ‘nestedness’, or ‘gains’ and ‘losses’. We analysed the main drivers of beta diversity like local site characteristics, landscape, and historical factors.ResultsSpatial variation of the restored dike grasslands was dominated by the replacement component and showed no homogenisation despite a significant temporal turnover. The replacement drivers changed over time, although replacement was mainly affected by slope aspect and landscape factors. Historical factors were inconsistent over time, and no statistically clear drivers of nestedness were found. The dike grasslands exhibited a year‐to‐year turnover in species composition of 37 ± 11%. Gains and losses were balanced over time, although the ratio changed and was most pronounced on south‐facing slopes.ConclusionsThe restored grasslands exhibited spatial variation by site characteristics but also by spatial factors which were not controlled by restorations. Moreover, high non‐directional temporal turnover occurred, caused most likely by weather fluctuations, slightly varying management, and stochastic biotic dynamics. Thus, flexible targets are recommended for restoration monitoring, by defining a set of desired states within a certain range. Furthermore, the dominance of the replacement component of spatial variation should move the focus from defining one precise restoration approach to defining a set of possible methods which together would foster beta diversity.

Spatial Heterogeneity of Mechanical Impedance of Atypical Chernozem: The Ecological Approach

Abstract In this research paper, the spatial heterogeneity of mechanical impedance of a typical chernozem was investigated. The distance between experimental points in the mechanical impedance space was explained by means of multidimensional scaling. Spearman’s rank correlation coefficients between dissimilarity indices and gradient separation with different data transformation methods revealed that the use of log-transformed data and Horn-Morisita distance was the most appropriate approach to reflect the relationship between the mechanical impedance of soil and ecological factors. A three dimensional variant of multidimensional scaling procedure was selected as the most appropriate decision. Environmental factors were estimated with the use of phytoindicator scales. Broad, medium and fine-scale components of spatial variation of mechanical impedance of soil were extracted using the principal coordinates of neighbour matrices method (PCNM). In the extracted dimensions, statistically significant phytoindicator scales were found to describe variability from 8 to 33%. Dimension 1 correlated with a thermal climate indicator value, a hygromorphs index, an abundance of steppe species and meadow species. Dimension 2 correlated with a continental climate indicator value, carbonate content in the soil and the soil trophicity index (capacity of the soil for plant nutrition). Dimension 3 correlated with acidity, humidity and cryoclimate indicator values. Variation partitioning results revealed that environmental factors and spatial variables explained 47.8% of the total variation of the dimensions. Purely environmental component explained 18.2% of total variation. The spatial component and spatially structured environmental fractions explained 43.6%. The broad-scale spatial component explained 26.4% of dimensional variation, medium-scale – 6.7% and fine-scale – 5.7%. As a result of regression analysis, the broad-scale spatially structured environmental fractions were found to be connected with variability of moisture and thermal climate indicator values. The medium-scale component was revealed to be connected with variability of moisture, thermal climate, total salt regime and aeration of soil indicator value. The fine-scale component was connected with carbonate content in the soil, acidity and humidity indicator values.

Будова дерново-літогенного ґрунту на червоно-бурій глині в екологічному аспекті

The dynamics of spatial heterogeneity of the sod-lithogenic soil on red-clay burіh clays has been studied in the environmental aspect in terms of hardness. The ecomorphic analysis of vegetation of the section was carried ont. The ordination of data of soil hardness has been realized by the non-metric multidimensional scaling. The three-dimensional variant of multidimensional scaling was applied. The relationship of varying the hardness of the soil and environmental factors has been determined using phytoindicative scales. Using the technique of spatial data analysis (PCNM) the elements of spatial autocorrelation data of soil hardness and defined processes underlying its formation have been highlighted. It was established that statistically significant phytoindicative scales describe from 7 to 49% of the variability of the multidimensional measurements. Temperature value of soil and cryoregime have a value for the formation of the first coordinate axis. The axis marks the conditions distinguishing soil hardness in layers of 10–35 cm from those located above and below of the selected block. The second coordination axis reflects the opposite phenomenon in soil structure above and below the level of 20 cm and describes the representation of gigromorphes in plant community. The highest values in the formation of the third coordination axis have light scales and ombroregime. Measurement selects the contrast on the basis of hardness at the level 10–35 cm from the surrounding soil layers. During fractionation of variations hardness of the studied soil site it was established that environmental factors determine 56 % of the total variability of the results. PCNM-variables describe 7 % of the variation of indicators of soil hardness and spatial patterns deterministic environment – 10 % of feature variability. Herewith the most important environmental factors for describing of large-scale spatial component of variation of soil hardness are the content of carbonate salts, digestible forms of nitrogen, thermo- and ombroregime, salt regime and continentality climate. The components of the spatial variability of the hardness of a long-period fluctuations are associated with the distribution of plant gigromorphes. Spatial variability of detailed scale components is dependent on soil aeration and ombroregime. High-frequency periodic oscillations of hardness are related to such factors as aeration of the soil, ombroclimate and also distribution structure of trophomorphes, gigromorphes and heliomorphes.

Positional plasticity in regenerating Amybstoma mexicanum limbs is associated with cell proliferation and pathways of cellular differentiation

BackgroundThe endogenous ability to dedifferentiate, re-pattern, and re-differentiate adult cells to repair or replace damaged or missing structures is exclusive to only a few tetrapod species. The Mexican axolotl is one example of these species, having the capacity to regenerate multiple adult structures including their limbs by generating a group of progenitor cells, known as the blastema, which acquire pattern and differentiate into the missing tissues. The formation of a limb regenerate is dependent on cells in the connective tissues that retain memory of their original position in the limb, and use this information to generate the pattern of the missing structure. Observations from recent and historic studies suggest that blastema cells vary in their potential to pattern distal structures during the regeneration process; some cells are plastic and can be reprogrammed to obtain new positional information while others are stable. Our previous studies showed that positional information has temporal and spatial components of variation; early bud (EB) and apical late bud (LB) blastema cells are plastic while basal-LB cells are stable. To identify the potential cellular and molecular basis of this variation, we compared these three cell populations using histological and transcriptional approaches.ResultsHistologically, the basal-LB sample showed greater tissue organization than the EB and apical-LB samples. We also observed that cell proliferation was more abundant in EB and apical-LB tissue when compared to basal-LB and mature stump tissue. Lastly, we found that genes associated with cellular differentiation were expressed more highly in the basal-LB samples.ConclusionsOur results characterize histological and transcriptional differences between EB and apical-LB tissue compared to basal-LB tissue. Combined with our results from a previous study, we hypothesize that the stability of positional information is associated with tissue organization, cell proliferation, and pathways of cellular differentiation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12861-015-0095-4) contains supplementary material, which is available to authorized users.

Partitioning the variation in African vertebrate distributions into environmental and spatial components – exploring the link between ecology and biogeography

There has been a proliferation of studies aimed at predicting the distributions of species from environmental variables despite evidence that spatial interpolation or spatially‐constrained mechanistic models have comparable explanatory power. Moreover, the processes behind environmental and spatial correlations – and their interactions – remain elusive. Here, we examined geographic patterns in the amount of variation explained by environmental correlation and exogenous or endogenous spatial autocorrelation for 4423 terrestrial vertebrate species in Africa using variation partitioning analysis. We also tested the effects of range size and taxonomic class on the relative importance of environmental and spatial correlations, and contrasted empirical patterns to two environmentally‐neutral models to identify potential underlying environmental and spatial mechanisms. Results showed that geographic range size was associated with environmental and spatial variation components in ways that where qualitatively indistinguishable from environmentally‐neutral species with constrained dispersal, suggesting that proportions of variation are due to range cohesiveness rather than other ecological processes. As a consequence, large‐scale patterns of biodiversity should be studied cautiously due to the difficulty of obtaining evidence of causal mechanistic links between species distributions and spatio‐environmental gradients. However, we also uncovered ecologically‐meaningful patterns in the residuals of the relationship between range size and the respective variation components, which differed among vertebrate classes. Moreover, these patterns coincided with contemporary biogeographical regions. This study, therefore, demonstrates that it is possible to extract meaningful environmental and spatial associations that potentially link ecological and biogeographical processes.

Modelling of the spatio-temporal distribution of rat sightings in an urban environment

The brown rat lives with man in a wide variety of environmental contexts and adversely affects public health by transmission of diseases, bites, and allergies. Understanding behavioural aspects of pest species can contribute to their effective management and control. We report an analysis of the spatio-temporal distribution of rat sightings, which are directly related to rat infestation, in a district of Madrid (Spain). We first consider an empirical analysis of the first-order for the first and second order properties of the spatio-temporal point process of rat sightings, in which we model the first-order intensity function as a product of two intensity functions, one spatial and the other temporal, and use the inhomogeneous spatio-temporal K-function to estimate second order properties. We then formulate a more mechanistic model in which the conditional intensity of the point process depends explicitly on its past history. We have found that the sightings show strong seasonal variation and are strongly influenced by environmental factors related to human behaviour. We have also identified spatio-temporal clustering and interaction over and above the separate temporal and spatial components of variation in risk, and have estimated the spatial scale on which the interaction operates.

Spatial extent, regional specificity and metacommunity structuring in lake macrophytes

AbstractAimSpatial extent is inherently related to the potential roles of the main mechanisms structuring metacommunities. We examined the effects of varying spatial extent (ecological province, region and subregion) on the environmental and spatial components of variation in lake macrophyte communities. We also studied these effects separately for three macrophyte functional groups.LocationThe US state of Minnesota.MethodsWe examined average and heterogeneity differences in macrophyte community composition and environmental variation among the subregions of Minnesota using canonical analysis of principal coordinates (CAP) and homogeneity of multivariate dispersion (PERMDISP), respectively. We further used partial redundancy analysis (pRDA) to decompose variation in macrophyte community composition between environmental variables and spatial location at each spatial extent and geographical region. Spatial variables were derived using principal coordinates of neighbour matrices (PCNM) analysis.ResultsCAP and PERMDISP analyses showed that the subregions differed both in average community composition and in the heterogeneity of community composition for all macrophyte taxa, for emergent and submerged macrophytes, but not for non‐rooted macrophytes. We did not, however, find significant differences in overall environmental heterogeneity among the subregions. Variation partitioning using pRDAs showed that species sorting is more important than spatial processes for macrophytes, although these patterns were relatively weak. There was, however, much regional specificity, with the environmental and spatial fractions of community composition varying widely at different spatial extents, among different geographical regions and among functional groups. Contrary to our initial expectations, we did not find increasing spatial structuring and decreasing environmental control with increasing spatial extent.Main conclusionsOur findings indicate that, in macrophyte metacommunities, the relative contribution of spatial processes and environmental control varies rather unpredictably with spatial extent and geographical region. Our findings are thus of importance in advancing metacommunity ecology by showing that drawing wide‐ranging conclusions based on a single spatial extent or a single geographical region may be unwise.

Measurements of spatial variations in response of ionization chambers

Measurements of the spatial variations in the response of three ionization chamber (IC) designs were tested as a function of chamber bias voltage, incident X-ray flux and fill gas. Two components of spatial variation are seen. When the ionization chambers are near saturation, spatial variations exist that are tied to the chamber geometry. While the response of some chambers is relatively flat, others show significant variation across the IC. These variations appear to be inherent in the response of each IC at saturation. When the chamber is far from saturation, large spatial variations in response are present when N(2) is used as a fill gas, but not when ambient air is used as a fill gas. These appear to be tied to space charge effects.

Demography of a dormancy-prone geophyte: influence of spatial scale on interpretation of dynamics

Both temporal and spatial scales are important in the evaluation of population dynamics, but the latter often receives less attention in demographic analyses. We used a 5-year demographic data set for a long-lived geophyte, Calochortus lyallii, to investigate the pattern and components of spatial variation at two scales (population and microsite). We found that neither the projected population structure nor asymptotic population growth rate (λ) varied greatly across either scale, although the underlying contributors to the variation in λ, V(λ), did differ between scales. Life table response experiment analyses showed that V(λ) among populations came primarily from variation in seedling survival and progression of non-reproductive plants, whereas V(λ) among microsites was primarily due to the variable fertility of large adults. Prolonged dormancy was important in reducing V(λ) among quadrats at both the scales, partly countering fluctuations in other transitions such as recruitment. This result represents some of the first evidence that underground “bulb banks” could function to offset the effects of a spatially heterogeneous environment in a manner analogous to seed banks. Future work is needed to isolate the specific, sometimes idiosyncratic, life history phenomena acting to modulate plant population dynamics in a spatial context.

Geostatistical modelling of regional bird species richness: exploring environmental proxies for conservation purpose

Identifying spatial patterns in species diversity represents an essential task to be accounted for when establishing conservation strategies or monitoring programs. Predicting patterns of species richness by a model-based approach has recently been recognised as a significant component of conservation planning. Finding those environmental predictors which are related to these patterns is crucial since they may represent surrogates of biodiversity, indicating in a fast and cheap way the spatial location of biodiversity hotspots and, consequently, where conservation efforts should be addressed. Predictive models based on classical multiple linear regression or generalised linear models crowded the recent ecological literature. However, very often, problems related with spatial autocorrelation in observed data were not adequately considered. Here, a spatially-explicit data-set on birds presence and distribution across the whole Tuscany region was analysed. Species richness was calculated within 1 × 1 km grid cells and 10 environmental predictors (e.g. altitude, habitat diversity and satellite-derived landscape heterogeneity indices) were included in the analysis. Integrating spatial components of variation with predictive ecological factors, i.e. using geostatistical models, a general model of bird species richness was developed and used to obtain predictive regional maps of bird diversity hotspots. A meaningful subset of environmental predictors, namely habitat productivity, habitat heterogeneity, combined with topographic and geographic information, were included in the final geostatistical model. Conservation strategies based on the predicted hotspots as well as directions for increasing sampling effort efficiency could be extrapolated by the proposed model.

The behaviour of soil process models of ammonia volatilization at contrasting spatial scales

SummaryProcess models are commonly used in soil science to obtain predictions at a spatial scale that is different from the scale at which the model was developed, or the scale at which information on model inputs is available. When this happens, the model and its inputs require aggregation or disaggregation to the application scale, and this is a complex problem. Furthermore, the validity of the aggregated model predictions depends on whether the model describes the key processes that determine the process outcome at the target scale. Different models may therefore be required at different spatial scales. In this paper we develop a diagnostic framework which allows us to judge whether a model is appropriate for use at one or more spatial scales both with respect to the prediction of variations at those scale and in the requirement for disaggregation of the inputs. We show that spatially nested analysis of the covariance of predictions with measured process outcomes is an efficient way to do this. This is applied to models of the processes that lead to ammonia volatilization from soil after the application of urea.We identify the component correlations at different scales of a nested scheme as the diagnostic with which to evaluate model behaviour. These correlations show how well the model emulates components of spatial variation of the target process at the scales of the sampling scheme. Aggregate correlations were identified as the most pertinent to evaluate models for prediction at particular scales since they measure how well aggregated predictions at some scale correlate with aggregated values of the measured outcome. There are two circumstances under which models are used to make predictions. In the first case only the model is used to predict, and the most useful diagnostic is the concordance aggregate correlation. In the second case model predictions are assimilated with observations which should correct bias in the prediction, and errors in the variance; the aggregate correlations would be the most suitable diagnostic.

Robust Extraction of Spatial Correlation

The increased variability of process parameters makes it important yet challenging to extract the statistical characteristics and spatial correlation of process variation. Recent progress in statistical static-timing analysis also makes the extraction important for modern chip designs. Existing approaches extract either only a deterministic component of spatial variation or these approaches do not consider the actual difficulties in computing a valid spatial-correlation function, ignoring the fact that not every function and matrix can be used to describe the spatial correlation. Applying mathematical theories from random fields and convex analysis, we develop: 1) a robust technique to extract a valid spatial-correlation function by solving a constrained nonlinear optimization problem and 2) a robust technique to extract a valid spatial-correlation matrix by employing a modified alternative-projection algorithm. Our novel techniques guarantee to extract a valid spatial-correlation function and matrix from measurement data, even if those measurements are affected by unavoidable random noises. Experiment results, obtained from data generated by a Monte Carlo model, confirm the accuracy and robustness of our techniques and show that we are able to recover the correlation function and matrix with very high accuracy even in the presence of significant random noises

Interpolating Soil Properties Using Kriging Combined with Categorical Information of Soil Maps

Kriging interpolation is frequently used for mapping soil properties in the analysis and interpretation of spatial variation of soil. Mapping quality could affect the performance of site‐specific management. Soil map–delineation in existing soil maps showing abrupt changes at the boundaries between different soil types can provide valuable categorical information for interpreting variation in soil properties. In this study, map units were used to group sampled observations, and the variation in soil properties was separated into two parts: (i) between soil types (i.e., soil type effect) and (ii) within each soil type (i.e., residual). A kriging model combined with soil map–delineation, taking into account the variation components of soil type effect and residual, was proposed. A comparison of performance of kriging combined with soil map–delineation (KSMD) and ordinary kriging (OK) was performed to assess the feasibility of KSMD for improving the interpolation of soil properties. Real data of soil properties (sand, silt, and clay contents; pH; and Mehlich‐3 Ca and P) in a field of midwestern Taiwan were used for illustration. The analysis of variance table revealed that the contribution of soil types is a significant source of the spatial variation of soil. The spatial variation components of soil type effect and residual were thus determined for KSMD. When comparing KSMD and OK, the mean errors of KSMD and OK estimations were similar. However, decreases in estimation of imprecision for KSMD relative to OK (DIP %) for the 127 validation locations for sand, silt, and clay contents; pH; and Mehlich‐3 Ca and P were 34, 40, 48, 20, 42, and 3%, respectively. These results suggested that the proposed KSMD method could use the information of soil map–delineation to increase precision of the interpolation of soil properties.

Vegetation heterogeneity and ditches create spatial variability in methane fluxes from peatlands drained for forestry

Drainage of peatlands for forestry starts a succession of ground vegetation in which mire species are gradually replaced by forest species. Some mire plant communities vanish quickly following the water-level drawdown; some may prevail longer in the moister patches of peatland. Drainage ditches, as a new kind of surface, introduce another component of spatial variation in drained peatlands. These variations were hypothesized to affect methane (CH4) fluxes from drained peatlands. Methane fluxes from different plant communities and unvegetated surfaces, including ditches, were measured at the drained part of Lakkasuo mire, Central Finland. The fluxes were found to be related to peatland site type, plant community, water-table position and soil temperature. At nutrient-rich fen sites fluxes between plant communities differed only a little: almost all plots acted as CH4 sinks (−0.9 to −0.4 mg CH4 m−2 d−1), with the exception of Eriophorum angustifolium Honck. communities, which emitted 0.9 g CH4 m−2 d−1. At nutrient-poor bog site the differences between plant communities were clearer. The highest emissions were measured from Eriophorum vaginatum L. communities (29.7 mg CH4 m−2 d−1), with a decreasing trend to Sphagna (10.0 mg CH4 m−2 d−1) and forest moss communities (2.6 mg CH4 m−2 d−1). CH4 emissions from different kinds of ditches were highly variable, and extremely high emissions (summertime averages 182–600 mg CH4 m−2 d−1) were measured from continuously water-covered ditches at the drained fen. Variability in the emissions was caused by differences in the origin and movement of water in the ditches, as well as differences in vegetation communities in the ditches. While drainage on average greatly decreases CH4 emissions from peatlands, a great spatial variability in fluxes is emerged. Emissions from ditches constantly covered with water, may in some cases have a great impact on the overall CH4 emissions from drained peatlands.

Assessing the influence of environmental heterogeneity on bird spacing patterns: a case study with two raptors

Testing for aggregation or regularity in point patterns is difficult in the presence of spatial variation in abundance due to environmental heterogeneity. Using a recently developed method generalizing Ripley's K function for non homogeneous point patterns, we test the aggregation of the nests in two species of birds (little owl and Montagu's harrier) exhibiting heterogeneous distributions in response to landscape structure. We compare the results obtained under different null models accounting for environmental heterogeneity at large and/or small spatial scales.Whereas both species were initially found to form clusters at some scale, taking spatial heterogeneity into account revealed that 1) territorial little owls showed no clustering of territories when habitat availability was considered; 2) semi‐colonial harriers still formed significant clusters, but part of the aggregation in this species could be explained by landscape structure alone. Our results highlight that it is feasible and highly recommended to account for non‐stationarity when testing for aggregation. Further, provided that sufficient knowledge of the study system is available, this approach helps to identify behavioural and environmental components of spatial variation in abundance. Additionally, we demonstrate that accounting for large or small‐scale heterogeneity affects the perception of spacing behaviours differently, so that both need to be considered.

Environmental and spatial controls of palm (Arecaceae) species richness across the Americas

ABSTRACTAim To determine the main factors that control the distribution of palm species richness across the Americas, to understand the relative importance of climatic and other environmental factors vs. spatial variables (as substitutes for non‐environmental factors such as history), and to evaluate how robust the patterns found are to changes in spatial scale.Location Tropical and subtropical America (34°N−34°S; 33°W−120°W).Methods We provide a GIS‐based analysis of spatial variation in species richness at 10 grain sizes (1°−10° square grid cells). We use multiple regressions and variation partitioning to test patterns of species richness in relation to five environmental descriptors [mean annual temperature (°C), mean annual precipitation (mm year−1), number of wet days year−1, topographical range (maximum–minimum elevation), number of vegetation types] and nine spatial variables (the terms of a cubic trend‐surface polynomial).Results We observe peaks in palm species richness in southern Mesoamerica, the Chocó area, western and eastern Amazon basin, and east Andean slopes, and a strong latitudinal richness gradient even within the tropical zone. Pure environmental and pure spatial variation components are of equal magnitude through all spatial scales analysed. Water‐related variables such as annual rainfall and number of wet days are the main richness predictors. Spatial variables, notably latitude squared are also important, whereas temperature‐ and habitat‐related variables are relatively unimportant.Main conclusions Our analysis suggests that in the Americas, palm species richness at spatial scales from 1° to 10° is most strongly controlled by water availability, although unknown broad‐scale factors, perhaps soil, historical processes or geometric constraints, are also important.

Detecting the spatial component of variation in the weed community at the farm scale with variation partitioning by canonical correspondence analysis

SummaryVariation partitioning by canonical correspondence analysis (CCA) was applied to analyse spatial variation in the species composition of a weed community for an area of farmland in southern Finland. The farmland, covering 450 ha, was sampled with a 60 m × 60 m grid. Data on weed species were collected along with the following groups of explanatory variables: spatial variables (the terms of second‐order polynomial trend surface regression equation generated on the x and y co‐ordinates of sample quadrats: x, y, x2, xy, y2, x2y and xy2), farmer variables (nine farms), soil variables (four soil types and pH value), crop variables (barley, oats, sugarbeet, potato and turnip rape) and physical variables (area of field, altitude, slope and aspect in four directions). The main variation in species composition along the first and second CCA axes was caused by interplay between farmer and crop variables. Farmer and crop variables explained more of the variation than did soil or physical variables. All the variables were to some extent spatially structured. The spatial variables contributed 54.5% of the total variation, of which pure spatial variation accounted for 12.2%. The highest covariation with spatial variables was detected with farmer (33.7%) and crop variables (25.7%). Variation partitioning by CCA is recommended for studying the relationship between the spatial variation in weed communities and explanatory variables.

Spatial filtering using media with indefinite permittivity and permeability tensors

Bilayers of media for which the permittivity and permeability tensors are indefinite—that is, not all principle elements possess the same sign—can be used to construct low-, high-, and bandpass spatial filters. These filters possess sharp adjustable roll-offs, and can operate both below and above free-space cutoff to select specific spatial variation components or beam angles from a source or image.