Spatial point pattern analysis of available and exploited resources

A patchy spatial distribution of resources underpins many models of population regulation and species coexistence, so ecologists require methods to analyse spatially‐explicit data of resource distribution and use. We describe a method for analysing maps of resources and testing hypotheses about species' distributions and selectivity. The method uses point pattern analysis based on the L‐function, the linearised form of Ripley's K‐function. Monte Carlo permutations are used for statistical tests. We estimate the difference between observed and expected values of L(t), an approach with several advantages: 1) The results are easy to interpret ecologically. 2) It obviates the need for edge correction, which has largely precluded the use of L‐functions where plot boundaries are “real”. Including edge corrections may lead to erroneous conclusions if the underlying assumptions are invalid. 3) The null expectation can take many forms, we illustrate two models: complete spatial randomness (to describe the spatial pattern of resources in the landscape) and the underlying pattern of resource patches in the landscape (akin to a neutral landscape approach). The second null is particularly useful to test whether spatial patterns of exploited resource points simply reflect the spatial patterns of all resource points. We tested this method using over 100 simulated point patterns encompassing a range of patterns that might occur in ecological systems, and some very extreme patterns. The approach is generally robust, but Type II decision errors might arise where spatial patterns are weak and when trying to detect a clumped pattern of exploited points against a clumped pattern of all points. An empirical example of an intertidal lichen growing on barnacle shells illustrates how this technique might be used to test hypotheses about dispersal mechanisms. This approach can increase the value of survey data, by permitting quantification of natural resource patch distribution in the landscape as well as patterns of resource use by species.     

Fine-scale Microhabitat Heterogeneity in a French Guianan Forest

We examined fine-scale heterogeneity of environmental conditions in a primary rain forest in French Guiana to describe variation in microhabitats that plants may experience during establishment. We characterized both the range as well as the spatial structuring of 11 environmental factors important for seedling establishment in six hexagonal sampling grids, one each in gap and understory sites at three points representing the predominant geomorphic units in this primary forest. Each grid contained 37 sampling points separated by 31 cm–20 m. Monte-Carlo tests of semivariograms against complete spatial randomness indicated that for many variables in all six sampling grids, spatial dependence did not exceed 1 m. A principal component analysis of all sampling points revealed a lack of spatial microhabitat structure, rather than homogeneous patches associated with canopy structure or geomorphology. Our results suggest that ample fine-scale spatial heterogeneity exists to support the coexistence of plant species with differential abiotic requirements for regeneration.     

A test for spatial relationships between neighbouring plants in plots of heterogeneous plant density

Abstract. Maps of plant individuals in (x, y) coordinates (i.e. point patterns) are currently analysed through statistical methods assuming a homogeneous distribution of points, and thus a constant density within the study area. Such an assumption is seldom met at the scale of a field plot whilst delineating less heterogeneous subplots is not always easy or pertinent. In this paper we advocate local tests carried out in quadrats partitioning the plot and having a size objectively determined via a trade‐off between squared bias and variance. In each quadrat, the observed pattern of points is tested against complete spatial randomness (CSR) through a classical Monte‐Carlo approach and one of the usual statistics. Local tests yield maps of p‐values that are amenable to diversified subsequent analyses, such as computation of a variogram or comparison with co‐variates. Another possibility uses the frequency distribution of p‐values to test the whole point pattern against the null hypothesis of an inhomogeneous Poisson process. The method was demonstrated by considering computer‐generated inhomoge‐neous point patterns as well as maps of woody individuals in banded vegetation (tiger bush) in semi‐arid West Africa. Local tests proved able to properly depict spatial relationships between neighbours in spite of heterogeneity/clustering at larger scales. The method is also relevant to investigate interaction between density and spatial pattern in the presence of resource gradients.     

宜昌百里荒草山草坡群落物种分布的空间趋势分析

通过基于CCA的趋势面分析和空间插值方法,研究了宜昌百里荒山地草场的群落结构空间变化,以及群落结构空间趋势与主要环境因子的相关性。结果表明,该群落物种空间中的群落结构面和物理空间中的空间趋势面可以很好地吻合,说明该群落的结构由一种具有强烈空间结构化特征的机制控制。对群落结构和空间趋势影响最显著的环境因素是土壤有效磷。     

A new index of aggregation for animal counts.

A new index is described that is especially appropriate for measuring the aggregation of entomological data in the form of counts per sample unit and that can make use of spatial information when it is available. Calculation of the index is based on a comparison of the effort required of individuals in a sample to achieve complete crowding with that to achieve complete randomness. The power of tests of randomness based on this index is found to be greater than those based on the index of dispersion, especially when spatial information is available.     

Scale dependency of diversity components estimated from primary biodiversity data and distribution maps

Different sources of information about biodiversity may lead to unrealistic or biased estimation of its components, with different patterns according to the scale of analysis. In this study, we analyse patterns of species richness at the local (average alpha) and regional (gamma) scales, and the relationship between them (Whittaker's beta), in central Mexico, using as a source of data for the species' distributions: (1) museum specimen occurrence data for birds, and (2) distribution maps based on ecological niche models developed and refined by experts. We performed analyses at five spatial resolutions (1/32°−1/2°). Scale changes (grain and extent) affected significantly the estimates of average alpha, gamma, and beta. Use of raw occurrence data vs. distribution maps yielded contrasting results, with raw data underestimating alpha and overestimating beta, as functions of area. As regards species–area relationships, our results suggest a natural decomposition of factors into an area-invariant component (related to alpha), and an area dependent factor (related to beta). Most of our results are maintained in a null model that randomizes occurrences without changing observed range-size distributions. From this result we argue that average alpha and Whittaker's beta capture little information about the spatial covariation of species distribution patterns.     

Spatial pattern analysis in ecology based on Ripley's K-function: Introduction and methods of edge correction

Abstract. Spatial pattern analysis based on Ripley's K-function is a second-order analysis of point patterns in a twodimensional space. The method is increasingly used in studies of spatial distribution patterns of plant communities, but the statistical methods involved are sometimes poorly understood or have been modified without evaluating the effects on results. The procedures of field data acquisition, statistical analysis, and the test for the null hypothesis of complete spatial randomness are described and the presentation of results is discussed. Different methods of edge correction were tested on a computer-generated random pattern and a mapped distribution of a Mediterranean shrubland. The inclusion of buffer zones around mapped plots describes the spatial pattern most accurately, but may not warrant the additional labour involved. Three variations of the weighted edge correction yielded comparable results for the distribution patterns tested. The toroidal edge correction may give biased results for non-random patterns. Recommendations for standardisation of the statistical procedures and data presentation are given.     

Identifying and correcting spatial bias in opportunistic citizen science data for wild ungulates in Norway

Many publications make use of opportunistic data, such as citizen science observation data, to infer large‐scale properties of species’ distributions. However, the few publications that use opportunistic citizen science data to study animal ecology at a habitat level do so without accounting for spatial biases in opportunistic records or using methods that are difficult to generalize. In this study, we explore the biases that exist in opportunistic observations and suggest an approach to correct for them. We first examined the extent of the biases in opportunistic citizen science observations of three wild ungulate species in Norway by comparing them to data from GPS telemetry. We then quantified the extent of the biases by specifying a model of the biases. From the bias model, we sampled available locations within the species’ home range. Along with opportunistic observations, we used the corrected availability locations to estimate a resource selection function (RSF). We tested this method with simulations and empirical datasets for the three species. We compared the results of our correction method to RSFs obtained using opportunistic observations without correction and to RSFs using GPS‐telemetry data. Finally, we compared habitat suitability maps obtained using each of these models. Opportunistic observations are more affected by human access and visibility than locations derived from GPS telemetry. This has consequences for drawing inferences about species’ ecology. Models naïvely using opportunistic observations in habitat‐use studies can result in spurious inferences. However, sampling availability locations based on the spatial biases in opportunistic data improves the estimation of the species’ RSFs and predicted habitat suitability maps in some cases. This study highlights the challenges and opportunities of using opportunistic observations in habitat‐use studies. While our method is not foolproof it is a first step toward unlocking the potential of opportunistic citizen science data for habitat‐use studies.     

Estimating and controlling for spatial structure in the study of ecological communities

Aim Variation partitioning based on canonical analysis is the most commonly used analysis to investigate community patterns according to environmental and spatial predictors. Ecologists use this method in order to understand the pure contribution of the environment independent of space, and vice versa, as well as to control for inflated type I error in assessing the environmental component under spatial autocorrelation. Our goal is to use numerical simulations to compare how different spatial predictors and model selection procedures perform in assessing the importance of the spatial component and in controlling for type I error while testing environmental predictors. Innovation We determine for the first time how the ability of commonly used (polynomial regressors) and novel methods based on eigenvector maps compare in the realm of spatial variation partitioning. We introduce a novel forward selection procedure to select spatial regressors for community analysis. Finally, we point out a number of issues that have not been previously considered about the joint explained variation between environment and space, which should be taken into account when reporting and testing the unique contributions of environment and space in patterning ecological communities. Main conclusions In tests of species‐environment relationships, spatial autocorrelation is known to inflate the level of type I error and make the tests of significance invalid. First, one must determine if the spatial component is significant using all spatial predictors (Moran's eigenvector maps). If it is, consider a model selection for the set of spatial predictors (an individual‐species forward selection procedure is to be preferred) and use the environmental and selected spatial predictors in a partial regression or partial canonical analysis scheme. This is an effective way of controlling for type I error in such tests. Polynomial regressors do not provide tests with a correct level of type I error.     

Uphill shifts in distribution of butterflies in the Czech Republic: effects of changing climate detected on a regional scale

Aim To assess whether altitude changes in the distribution of butterflies during the second half of the 20th century are consistent with climate warming scenarios. Location The Czech Republic. Methods Distributional data were taken from a recent butterfly distribution atlas, which maps all Czech butterflies using a grid of 10′ longitude to 6′ latitude, equivalent to about 11.1 × 12 km. Cell altitude was used as an independent variable, and altitudinal ranges of individual species (less migrants, extinct species, recent arrivals and extremely rare species) in 1950–80 vs. 1995–2001 and in 1950–80, 1981–94, 1995–2001 were compared using U‐tests and linear regressions. Results Of 117 (U‐tests) and 119 (regressions) species, we found significant uphill increases in 15 and 12 species, respectively. The two groups were nested; none (U‐test) and one (regression) species showed a significant altitudinal decrease. Binomial tests of frequencies of signs of the U‐tests and regression coefficients, including nonsignificant ones, also showed that the increases prevailed. The mean and median of the significant shifts were 60 and 90 m, respectively, and the maximum shift per species was 148 m. The recording effort in individual time periods was not biased with respect to altitude. Main conclusion Altitude shifts in the distribution of Czech butterflies are already detectable on the coarse scales of standard distribution maps. The increasing species do not show any consistent pattern in habitat affiliations, conservation status and mountain vs. nonmountain distribution, which renders climatic explanation as the most likely cause of the distributional shifts.     

边缘效应带和保留带内红松幼林水分生态的差异

 以一个经过12年边缘效应带处理的14年生红松(Pinus koraiensis)(1998年)幼林生态系统为研究对象,对处于不同宽度的边缘效应带和保留带的红松幼树木质部水势、叶片蒸腾强度、气孔导度、叶片温度、空气相对湿度和光合有效辐射的日变化以及土壤相对含水量进行了分析,结合叶片净光合速率探讨了效应带宽度对红松幼林生态系统中红松幼树水分生态及红松生长状况的可能影响模式。结果表明：1）边缘效应带的开拓降低了效应带内红松幼树木质部水势、空气相对湿度和叶片气孔导度,显著提高了叶片蒸腾强度、叶片温度和光合有效辐射     

Connecting species’ geographical distributions to environmental variables: range maps versus observed points of occurrence

Connecting the geographical occurrence of a species with underlying environmental variables is fundamental for many analyses of life history evolution and for modeling species distributions for both basic and practical ends. However, raw distributional information comes principally in two forms: points of occurrence (specific geographical coordinates where a species has been observed), and expert-prepared range maps. Each form has potential short-comings: range maps tend to overestimate the true occurrence of a species, whereas occurrence points (because of their frequent non-random spatial distribution) tend to underestimate it. Whereas previous comparisons of the two forms have focused on how they may differ when estimating species richness, less attention has been paid to the extent to which the two forms actually differ in their representation of a species’ environmental associations. We assess such differences using the globally distributed avian order Galliformes (294 species). For each species we overlaid range maps obtained from IUCN and point-of-occurrence data obtained from GBIF on global maps of four climate variables and elevation. Over all species, the median difference in distribution centroids was 234 km, and median values of all five environmental variables were highly correlated, although there were a few species outliers for each variable. We also acquired species’ elevational distribution mid-points (mid-point between minimum and maximum elevational extent) from the literature; median elevations from point occurrences and ranges were consistently lower (median −420 m) than mid-points. We concluded that in most cases occurrence points were likely to produce better estimates of underlying environmental variables than range maps, although differences were often slight. We also concluded that elevational range mid-points were biased high, and that elevation distributions based on either points or range maps provided better estimates.     

Predicting habitat distribution and frequency from plant species co-occurrence data

Aim Species frequency data have been widely used in nature conservation to aid management decisions. To determine species frequencies, information on habitat occurrence is important: a species with a low frequency is not necessarily rare if it occupies all suitable habitats. Often, information on habitat distribution is available for small geographic areas only. We aim to predict grid‐based habitat occurrence from grid‐based plant species distribution data in a meso‐scale analysis. Location The study was carried out over two spatial extents: Germany and Bavaria. Methods Two simple models were set up to examine the number of characteristic plant species needed per grid cell to predict the occurrence of four selected habitats (species data from FlorKart, http://www.floraweb.de ). Both models were calibrated in Bavaria using available information on habitat distribution, validated for other federal states, and applied to Germany. First, a spatially explicit regression model (generalized linear model (GLM) with assumed binomial error distribution of response variable) was obtained. Second, a spatially independent optimization model was derived that estimated species numbers without using spatial information on habitat distribution. Finally, an additional uncalibrated model was derived that calculated the frequencies of 24 habitats. It was validated using NATURA2000 habitat maps. Results Using the Bavarian models it was possible to predict habitat distribution and frequency from the co‐occurrence of habitat‐specific species per grid cell. As the model validations for other German federal states were successful, the models were applied to all of Germany, and habitat distribution and frequencies could be retrieved for the national scale on the basis of habitat‐specific species co‐occurrences per grid cell. Using the third, uncalibrated model, which includes species distribution data only, it was possible to predict the frequencies of 24 habitats based on the co‐occurrence of 24% of formation‐specific species per grid cell. Predicted habitat frequencies deduced from this third model were strongly related to frequencies of NATURA2000 habitat maps. Main conclusions It was concluded that it is possible to deduce habitat distributions and frequencies from the co‐occurrence of habitat‐specific species. For areas partly covered by habitat mappings, calibrated models can be developed and extrapolated to larger areas. If information on habitat distribution is completely lacking, uncalibrated models can still be applied, providing coarse information on habitat frequencies. Predicted habitat distributions and frequencies can be used as a tool in nature conservation, for example as correction factors for species frequencies, as long as the species of interest is not included in the model set‐up.     

A Computer Programme Package for the Statistical Analysis of Spatial Point Processes in a Square

A computer programme for the statistical analysis of point data in a square is described. Several tests for randomness of the distribution of points are possible. The most comprehensive of these are comparisons of the empirical distributions of the inter-point and closest neighbour distances with their respective expected distributions under complete randomness, and tests based on Ripley' L function; using these, significant aggregation or regularity can be identified. It is also possible to calculate statistics of properties (“attributes”) associated with each spatial point, as well as to compare statistics for sub-areas of the experimental square. Several measures of spatial autocorrelation are available, amongst them correlograms and variograms. The programme can also find the tesselation of the study area and correlate tile properties with the point attributes. The procedures are illustrated by references to the spatial distribution and mound heights of Trinevitermes trinervoides on a study area in South Africa. Although the programme was developed specifically for application in entomology, it could be used to analyse data from many other disciplines.     

Accounting for spatial autocorrelation in null models of tree species association

A commonly used null model for species association among forest trees is a well‐mixed community (WMC). A WMC represents a non‐spatial, or spatially implicit, model, in which species form nearest‐neighbor pairs at a rate equal to the product of their community proportions. WMC models assume that the outcome of random dispersal and demographic processes is complete spatial randomness (CSR) in the species’ spatial distributions. Yet, stochastic dispersal processes often lead to spatial autocorrelation (SAC) in tree species densities, giving rise to clustering, segregation, and other nonrandom patterns. Although methods exist to account for SAC in spatially‐explicit models, its impact on non‐spatial models often remains unaccounted for. To investigate the potential for SAC to bias tests based upon non‐spatial models, we developed a spatially‐heterogeneous (SH) modelling approach that incorporates measured levels of SAC. Using the mapped locations of individuals in a tropical tree community, we tested the hypothesis that the identity of nearest‐neighbors represents a random draw from neighborhood species pools. Correlograms of Moran's I confirmed that, for 50 of 51 dominant species, stem density was significantly autocorrelated over distances ranging from 50 to 200 m. The observed patterns of SAC were consistent with dispersal limitation, with most species occurring in distinct patches. For nearly all of the 106 species in the community, the frequency of pairwise association was statistically indistinguishable from that projected by the null models. However, model comparisons revealed that non‐spatial models more strongly underestimated observed species‐pair frequencies, particularly for conspecific pairs. Overall, the CSR models projected more significant facilitative interactions than did SH models, yielding a more liberal test of niche differences. Our results underscore the importance of accounting for stochastic spatial processes in tests of association, regardless of whether spatial or non‐spatial models are employed.     

A quantitative and statistically robust method for the determination of xylem conduit spatial distribution

? Premise of the study: Because of their limited length, xylem conduits need to connect to each other to maintain water transport from roots to leaves. Conduit spatial distribution in a cross section plays an important role in aiding this connectivity. While indices of conduit spatial distribution already exist, they are not well defined statistically. ? Methods: We used point pattern analysis to derive new spatial indices. One hundred and five cross-sectional images from different species were transformed into binary images. The resulting point patterns, based on the locations of the conduit centers-of-area, were analyzed to determine whether they departed from randomness. Conduit distribution was then modeled using a spatially explicit stochastic model. ? Key results: The presence of conduit randomness, uniformity, or aggregation depended on the spatial scale of the analysis. The large majority of the images showed patterns significantly different from randomness at least at one spatial scale. A strong phylogenetic signal was detected in the spatial variables. ? Conclusions: Conduit spatial arrangement has been largely conserved during evolution, especially at small spatial scales. Species in which conduits were aggregated in clusters had a lower conduit density compared to those with uniform distribution. Statistically sound spatial indices must be employed as an aid in the characterization of distributional patterns across species and in models of xylem water transport. Point pattern analysis is a very useful tool in identifying spatial patterns.     

Predicting the distribution of four species of raptors (Aves: Accipitridae) in southern Spain: statistical models work better than existing maps

Aim To test the effectiveness of statistical models based on explanatory environmental variables vs. existing distribution information (maps and breeding atlas), for predicting the distribution of four species of raptors (family Accipitridae): common buzzard Buteo buteo (Linnaeus, 1758), short‐toed eagle Circaetus gallicus (Gmelin, 1788), booted eagle Hieraaetus pennatus (Gmelin, 1788) and black kite Milvus migrans (Boddaert, 1783). Location Andalusia, southern Spain. Methods Generalized linear models of 10 × 10 km squares surveyed for the presence/absence of the species by road census. Statistical models use as predictors variables derived from topography, vegetation and land‐use, and the geographical coordinates (to take account of possible spatial trends). Predictions from the models are compared with current distribution maps from the national breeding atlas and leading reference works. Results The maps derived from statistical models for all four species were more predictive than the previously published range maps and the recent national breeding atlas. The best models incorporated both topographic and vegetation and land‐use variables. Further, in three of the four species the inclusion of spatial coordinates to account for neighbourhood effects improved these models. Models for the common buzzard and black kite were highly predictive and easy to interpret from an ecological point of view, while models for short‐toed eagle and, particularly, booted eagle were not so easy to interpret, but still predicted better than previous distribution information. Main conclusions It is possible to build accurate predictive models for raptor distribution with a limited field survey using as predictors environmental variables derived from digital maps. These models integrated in a geographical information system produced distribution maps that were more accurate than previously published ones for the study species in the study area. Our study is an example of a methodology that could be used for many taxa and areas to improve unreliable distribution information.     

Isolation and characterization of polymorphic microsatellite loci in the Australian smelt,Retropinna semoni

Five polymorphic microsatellite loci were isolated from the Australian smelt, Retropinna semoni, in order to study levels of connectivity among populations at various spatial scales. Screening of one natural population (n = 30) from central Victoria, southeastern Australia, yielded nine to 14 alleles per locus with observed levels of heterozygosity ranging from 0.40 to 0.80. All loci were in Hardy–Weinberg equilibrium after Bonferroni correction for multiple tests. These loci should provide a useful tool in further understanding the population genetics of this species.     

Anthropogenic activity expressed as ‘artificial light at night’ improves predictive density distribution in bird populations

Artificial Light At Night (ALAN) is one of the most important anthropogenic environmental components that affects biodiversity worldwide. Despite extensive knowledge on ALAN, being a measure of human activity that directly impacts numerous aspects of animal behaviour, such as orientation and distribution, little is known about its effects on density distribution on a large spatial scale. That is why we decided to explore by means of the Species Distribution Modelling approach (SDM) how ALAN as one of 33 predictors determines farmland and forest bird species densities. In order to safeguard study results from any inconsistency caused by the chosen method, we used two approaches, i.e. the Generalised Additive Model (GAM) and the Random Forest (RF). Within each approach, we developed two models for two bird species, the Black woodpecker and the European stonechat: the first with ALAN, and the second without ALAN as an additional predictor. Having used out-of-bag procedures in the RF approach, information-theoretic criteria for the GAM, and evaluation models based on an independent dataset, we demonstrated that models with ALAN had higher predictive density power than models without it. The Black woodpecker definitely and linearly avoids anthropogenic activity, defined by the level of artificial light, while the European stonechat tolerates human activity to some degree, especially in farmland habitats. What is more, a heuristic analysis of predictive maps based on models without ALAN shows that both species reach high densities in regions where they are deemed rare. Hence, the study proves that urbanisation processes, which can be reflected by ALAN, are among key predictors necessary for developing Species Density Distribution Models for both farmland and forest bird species.