Multiscale ordination: a method for detecting pattern at several seales

Multivariate analyses of vegetation data have been restricted to a single scale of sampling, or multiscale sampling has been restricted to a single species. However, vegetation scientists need to be able to explore spatial relationships of many species over many scales. We present a modification of Noy-Meir & Anderson's (1971) method of multiscale ordination by summing two-term local covariance matrices and smoothing the component profiles. The advantages of our method are: 1) results are less subject to the starting position of the transect, 2) matrices may be added at any block size, and 3) plots of factor scores are smoothed by a moving weighted average to better reveal patterns at a prescribed scale.This procedure provides statistical associations of species over a range of scales. The scales which exhibit the association to the maximum extent are then determined from multiscale ordination. The relationships of different associations and their scales can then be examined. The application of the method to fabricated data proved successful in recovering the structure built into the data. When used on real vegetation data, from a community and a landscape, the method revealed the details of species associations over a range of scales, and of the relationships among associations.Abbreviations PCA = Principal Components Analysis - DCA = Detrended Correspondence Analysis - TTLC = Two-Term Local Covariance     

Permutation of Two-Term Local Quadrat Variance Analysis: General concepts for interpretation of peaks

Abstract. Many ecological studies use Two-Term Local Quadrat Variance Analysis (TTLQV) and its derivatives for spatial pattern analysis. Currently, rules for determining variance peak significance are arbitrary. Variance peaks found at block size 1 and at > 50 % of the transect length are the only peaks whose use is explicitly prohibited. Although the use of variance peaks found at block sizes > 10 % of the transect length have also been warned against, many researchers interpret them regardless. We show in this paper that variance peaks derived from TTLQV are subject to additional ‘rules of thumb’. Through the use of randomization and permutation analyses on real and simulated data of species abundance in contiguous plots along a single transect, we show that variance peaks found at block sizes 1, 2 and 3 occur frequently by chance and thus likely do not indicate biologically meaningful patterns. The use of multiple replicate transects decreases the probability of Type II error.     

Transect-based patch size frequency analysis

Abstract. A new, transect-based patch size detection method for species pattern is proposed which improves results obtained with methods described earlier. The method was tested on an extensive artificial data set together with three of the existing methods considered best: Two and Three Term Local Quadrat Variance (T2LQV and T3LQV) and New Local Variance (NLV). The TLQV methods recovered only some of the existing patterns and were heavily dependent on inter-patch distances, whereas NLV almost always produced curves with oscillations. In addition a significance test is proposed, while such a test is seldom found in the earlier methods. Our method, PASFRAN, determines the frequencies of runs with 1, 2, 3, etc. quadrats containing a certain species and compares those with frequencies based on Monte Carlo simulated random configurations. The comparison is performed for each run length and the significance of the deviation between observed and expected frequencies can be calculated on the basis of a large number of simulations. Because this approach may be considered a case of multiple testing, a Bonferroni correction on the significance level was applied. The method can also be used for the detection of inter-patch distances. In addition, run lengths can be grouped and the test can be applied to the frequencies of combinations of run lengths. The method can detect dominance patches when quantitative data on the occurrence of plant species are available. In the same way, it can detect multi-species patterns using sample scores from an ordination analysis such as correspondence analysis. An extension towards composite, higher-order patterns is under investigation. The new method appeared to be effective in recovering artificial patterns, while it is not influenced by the relative values of patch size and inter-patch distance. When applied to the distribution of cow dung patches and certain plant species along a transect of 500 quadrats of 10 cm × 10 cm in an alvar limestone grassland, it produced straightforward and realistic results as compared with other methods and field impressions.     

Finding a common ordination for several data sets by individual differences scaling

Individual differences scaling is a multidimensional scaling method for finding a common ordination for several data sets. An individual ordination for each data set can then be derived from the common ordination by adjusting the axis lengths so as to maximize the correlations between observed proximities and individual ordination distances. The importance of the various axes for each data set and the mutual similarities and goodness of fit for the individual data sets are described by weight plots. As an example, 46 soft-water lakes in eastern Finland are ordinated on two dimensions according to 3 chemical data sets (water in summer and autumn, sediment) and 4 biological sets (major phytoplankton groups, phytoplankton, surface sediment diatom and cladoceran assemblages). The method seems to be effective as a means of ordination for obtaining the common ordination for the data sets. The major taxonomic groups gave the ordination which differed most clearly from the ordinations of the other data sets. Phytoplankton was most poorly ordinated in all the analyses. The other data sets were fairly coherent. When only biological data sets were ordinated, the diatoms and cladocerans showed rather different patterns. It seems that the cladocerans are best correlated with water chemistry, both according to weights in the joint analysis, and according to correlation between the axes from the biological data sets and the chemical variables.Abbreviations CCA = Canonical correspondence analysis - IDS = Individual differences scaling - MDS = multidimensional scaling - PCA = Principal components analysis     

Community pattern analysis: A method for quantifying community mosaic structure

A method of quantifying community spatial patterns, community pattern analysis, is described. It is proposed that ordination analysis is used to obtain an integrated score for each quadrat from transect data. For the data presented here, separate ordinations were made of both floristic and environmental (soils) data. The ordination axis scores are then analysed using two or three-term local variance analysis to quantify the scales of community pattern. Correlation analyses allow the relationship between the vegetation and soils data (as represented by ordination axis scores), and other environmental data to be investigated at defined scales. The advantages of this method, that employs the joint application of conventional methods, are that it includes the influence of all species in the analysis, and that multiple uncorrelated scales of pattern within a community are identified.     

Approaching the serpentine factor at a local scale—a study in an ultramafic area in northern Greece

We explore factors responsible for vegetation differentiation in a small-scale serpentine area, and attempt to provide new insights in the complexity of the serpentine factor at community level. We sampled 49 quadrats. From each quadrat physical and chemical soil parameters were measured and species composition, altitude, inclination, aspect and coordinates were recorded. Quadrats were classified and ordination analyses were used to explore the environmental gradients and to estimate the explanatory power of the variables. Generalized linear models were used to investigate the response of species to environmental factors. Variance partitioning was applied to calculate the proportion of variance attributed to different groups of explanatory variables. The gradients revealed were related to soil texture, nutrient contents, calcium deficiency, chromium content, climatic parameters and grazing and disturbance intensity. Variance partitioning showed that the highest proportions of variance were attributed to the nutrients and physiographic (including soil texture) variables, while smaller but notable proportions of variance were attributed to geographical coordinates and to metal contents. Our study shows that vegetation differentiation at a local scale is determined by a complex factor of soil properties and climatic parameters, together with variation in disturbance and succession.     

The use of wavelets for spatial pattern analysis in ecology

Abstract. We investigate the characteristics of the wavelet transform as an approach to analyzing spatial pattern. Compared to the familiar methods of paired quadrat or blocked quadrat variance calculations, the wavelet method seems to offer several advantages. First, when wavelet variance is plotted as a function of scale, the peak variance height is determined by pattern intensity and does not increase with scale and, depending on the wavelet chosen, the position of the variance peak matches the scale exactly. Second, the method produces only faint resonance peaks, if any, and third, by using several different wavelet forms, different characteristics of the pattern can be investigated. Fourth, the method is able to portray very clearly trends in the data, when the pattern is non-stationary. Lastly, the wavelet position variance can be used to identify patches and gaps in data with random error. We demonstrate these characteristics using artificial data and data from previously published studies for comparison. We show that two versions of the familiar blocked quadrat variance technique are forms of wavelet analysis.     

Diversity and Community Quantitative Characteristics ofFloor Lichen in Yaoluoping National NatureReserve of Anhui,China

Twenty nine quadrats belonging to various habitats were sampled in Yaoluoping National Nature Reserve, lichen species in each quadrat were identified and the lichen coverage of each quadrat was measured, combined with several environmental indices, with the purpose of understanding the lichen distributing pattern and community quantitative characteristics. Factor analysis was used to appraise relationships among ecological factors, cluster analysis and Spearman rank correlation coefficient test were employed for ordination and Fisher’s exact test was applied to evaluate interspecific correlation. Factor analysis showed that the number of species decreased as the altitude increased, and there was significant positive correlation between dominant species quantity and coverage (P=0.034), very significant positive correlation between humidity and habitat type (P=0.001). Based on cluster analysis data, twenty nine quadrats were divided into 5 types of association. Fisher’s exact test indicates 10 species pairs were very significant positive association and four species pairs significant positive, but no species pair was negative significant association. Fisher’s exact test demonstrated that the competition between the species was low.     

Elements of metacommunity structure of Paraguayan bats: multiple gradients require analysis of multiple ordination axes

Techniques to evaluate elements of metacommunity structure (EMS; coherence, species turnover and range boundary clumping) have been available for several years. Such approaches are capable of determining which idealized pattern of species distribution best describes distributions in a metacommunity. Nonetheless, this approach rarely is employed and such aspects of metacommunity structure remain poorly understood. We expanded an extant method to better investigate metacommunity structure for systems that respond to multiple environmental gradients. We used data obtained from 26 sites throughout Paraguay as a model system to demonstrate application of this methodology. Using presence–absence data for bats, we evaluated coherence, species turnover and boundary clumping to distinguish among six idealized patterns of species distribution. Analyses were conducted for all bats as well as for each of three feeding ensembles (aerial insectivores, frugivores and molossid insectivores). For each group of bats, analyses were conducted separately for primary and secondary axes of ordination as defined by reciprocal averaging. The Paraguayan bat metacommunity evinced Clementsian distributions for primary and secondary ordination axes. Patterns of species distribution for aerial insectivores were dependent on ordination axis, showing Gleasonian distributions when ordinated according to the primary axis and Clementsian distributions when ordinated according to the secondary axis. Distribution patterns for frugivores and molossid insectivores were best described as random. Analysis of metacommunities using multiple ordination axes can provide a more complete picture of environmental variables that mold patterns of species distribution. Moreover, analysis of EMS along defined gradients (e.g., latitude, elevation and depth) or based on alternative ordination techniques may complement insights based on reciprocal averaging because the fundamental questions addressed in analyses are contingent on the ordination technique that is employed.     

鹞落坪自然保护区地面生地衣多样性及群落数量特征

在鹞落坪保护区设置样方,调查样方内地面生地衣种类和生境指标,探讨森林地面生地衣的分布模式和群落特征。对地衣群落进行了因子分析和排序;应用2×2联表的Fisher精确检验和Spearman秩相关系数进行了种间关联分析。因子分析表明随海拔上升,种类趋于减少,优势种的数目和盖度之间存在显著的正相关（P=0.034）,样方湿度和样方生境类型存在极其显著的正相关（P=0.001）。根据组平均分析结果并综合生境特征,将保护区地面生地衣划分为5个群丛类型。Fisher精确检验表明仙人掌绵腹衣Anzia opuntiella与红心黑蜈蚣衣Phaeophyscia erythrocardia等10个种对呈极显著正相关,4个种对呈显著正相关,无显著负相关种对出现。各个地衣种之间的竞争很小。     

Quadrat variance analysis and pattern development during primary succession

Abstract. The interpretation of Hill's ‘Two Term Local Quadrat Variance’ analysis to detect the scale of spatial pattern in vegetation is improved by an equation that relates the block size of a variance peak to the scale of the pattern that gave rise to it. (Contrary to previous belief, the two are not the same, especially for large block sizes.) Deviations of pattern from a perfectly regular alternation of equally sized gaps and patches of uniform density cause changes in the variance. To aid in the interpretation of these changes, two indices of pattern regularity are proposed, one based on density and one based onpresence/absence, in orderte distinguish the effects of irregularities of patch density from irregularities of patch size and position. These methods are applied to a study of primary succession on glacial moraines near Mt. Robson, British Columbia, Canada, in order to evaluate certain hypotheses about the development of pattern. Other researchers have proposed that during succession, the pattern at first intensifies at the scales initially observed, then as succession proceeds some scales of pattern are lost due to coalescence of patches and eventually the intensity of those that remain decreases as the patterns become more and more irregular. The vegetation on the Mt. Robson moraines confirms this sequence of changes in vegetation pattern, only to the extent that patterns intensify initially in the chronosequence; the number of scales of pattern in the vegetation remains about the same throughout and there is no evidence that the patterns become more irregular. The variance-block size graphs derived from presence / absence data matched those from density data well, indicating that the simpler data, in this case, are almost as informative about pattern as the more detailed data.     

Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis

Indirect gradient analysis, or ordination, is primarily a method of exploratory data analysis. However, to support biological interpretations of resulting axes as vegetation gradients, or later confirmatory analyses and statistical tests, these axes need to be stable or at least robust into minor sampling effects. We develop a computer-intensive bootstrap (resampling) approach to estimate sampling effects on solutions from nonlinear ordination.We apply this approach to simulated data and to three forest data sets from North Carolina, USA and examine the resulting patterns of local and global instability in detrended correspondence analysis (DCA) solutions. We propose a bootstrap coefficient, scaled rank variance (SRV), to estimate remaining instability in species ranks after rotating axes to a common global orientation. In analysis of simulated data, bootstrap SRV was generally consistent with an equivalent estimate from repeated sampling. In an example using field data SRV, bootstrapped DCA showed good recovery of the order of common species along the first two axes, but poor recovery of later axes. We also suggest some criteria to use with the SRV to decide how many axes to retain and attempt to interpret.Abbreviations DCA= detrended correspondence analysis - SRV= scaled rank variance     

河西走廊盐化草甸主要植物群落分布特点及其土壤环境特征

 采用系统网格法调查河西走廊盐化草甸典型地段的植被和土壤环境因素,用DCA排序技术进行定量分析,来划分该区植物群落的分布格局,并以土壤环境指标(有机质、全盐含量、pH值、潜水位埋深)解释其所形成的5个样方组,反映出内陆干旱次生盐渍化区土壤水盐分布的差别同潜水位的关系。     

Diallel genetic analysis of the elements of paradise fish's (Macropodus opercularis L.) behavior in familiar and novel situations

Elements of the paradise fish's ethogram were recorded in 1 familiar and 3 different unfamiliar situations and the inheritance of these behavioral elements was investigated employing a five times replicated diallel cross between 3 inbred strains. A generalized Hayman Analysis of Variance and a Variance Covariance Analysis were performed to estimate genetic effects and parameters, such as, additive genetic variance, different sorts of dominance variance, reciprocal effects, direction and degree of dominance, ratio between the frequency of dominant and of recessive alleles, minimum number of effective factors and heritabilities, etc. Knowing the genetic architecture, we make inferences about the possible evolutionary past of the behavioral elements and explain why selection might favor certain types of paradise fish's behavior in particular circumstances. In several cases a possibility of "monogenic" inheritance emerged. We explain this finding and conclude that in a cross experiment where the inheritance of phenotypical units are investigated by employing only a few genetically different strains this result may be expected.     

Finding essential scales of spatial variation in ecological data: a multivariate approach

The identification of spatial structures is a key step in understanding the ecological processes structuring the distribution of organisms. Spatial patterns in species distributions result from a combination of several processes occuring at different scales: identifying these scales is thus a crucial issue. Recent studies have proposed a new family of spatial predictors (PCNM: principal coordinates of neighbours matrices; MEMs: Moran's eigenvectors maps) that allow for modelling of spatial variation on different scales. To assess the multi-scale spatial patterns in multivariate data, these variables are often used as predictors in constrained ordination methods. However, the selection of the appropriate spatial predictors is still troublesome, and the identification of the main scales of spatial variation remains an open question. This paper presents a new statistical tool to tackle this issue: the multi-scale pattern analysis (MSPA). This ordination method uses MEMs to decompose ecological variability into several spatial scales and then summarizes this decomposition using graphical representations. A canonical form of MSPA can also be used to assess the spatial scales of the species-environment relationships. MSPA is compared to constrained ordination using simulated data, and illustrated using the famous oribatid mites dataset. The method is implemented in the free software R.     

Beta diversity as the variance of community data: dissimilarity coefficients and partitioning

Beta diversity can be measured in different ways. Among these, the total variance of the community data table Y can be used as an estimate of beta diversity. We show how the total variance of Y can be calculated either directly or through a dissimilarity matrix obtained using any dissimilarity index deemed appropriate for pairwise comparisons of community composition data. We addressed the question of which index to use by coding 16 indices using 14 properties that are necessary for beta assessment, comparability among data sets, sampling issues and ordination. Our comparison analysis classified the coefficients under study into five types, three of which are appropriate for beta diversity assessment. Our approach links the concept of beta diversity with the analysis of community data by commonly used methods like ordination and anova . Total beta can be partitioned into Species Contributions (SCBD: degree of variation of individual species across the study area) and Local Contributions (LCBD: comparative indicators of the ecological uniqueness of the sites) to Beta Diversity. Moreover, total beta can be broken up into within‐ and among‐group components by manova , into orthogonal axes by ordination, into spatial scales by eigenfunction analysis or among explanatory data sets by variation partitioning.     

Spatial models for spatial statistics: some unification

A general statistical framework is proposed for comparing linear models of spatial process and pattern. A spatial linear model for nested analysis of variance can be based on either fixed effects or random effects. Greig-Smith (1952) originally used a fixed effects model, but there are also examples of random effects models in the soil science literature. Assuming intrinsic stationarity for a linear model, the expectations of a spatial nested ANOVA and two term local variance (TTLV, Hill 1973) are functions of the variogram, and several examples are given. Paired quadrat variance (PQV, Ludwig & Goodall 1978) is a variogram estimator which can be used to approximate TTLV, and we provide an example from ecological data. Both nested ANOVA and TTLV can be seen as weighted lag-1 variogram estimators that are functions of support, rather than distance. We show that there are two unbiased estimators for the variogram under aggregation, and computer simulation shows that the estimator with smaller variance depends on the process autocorrelation.     

Fractal geometry: a tool for describing spatial patterns of plant communities

Vegetation is a fractal because it exhibits variation over a continuum of scales. The spatial structure of sandrim, bryophyte, pocosin, suburban lawn, forest tree, and forest understory communities was analyzed with a combination of ordination and geostatistical methods. The results either suggest appropriate quadrat sizes and spacings for vegetation research, or they reveal that a sampling design compatible with classical statistics is impossible. The fractal dimensions obtained from these analyses are generally close to 2, implying weak spatial dependence. The fractal dimension is not a constant function of scale, implying that patterns of spatial variation at one scale cannot be extrapolated to other scales.     

Effects of plot size on the ordination of vegetation samples

Questions: Do ordination patterns differ when based on vegetation samples recorded in plots of different size? If so, how large is the effect of plot size relative to the effects of data set heterogeneity and of using presence/absence or cover‐abundance data? Can we combine plots of different size in a single ordination? Methods: Two homogeneous and two heterogeneous data sets were sampled in Czech forests and grasslands. Cover‐abundances of plant species were recorded in series of five or six nested quadrats of increasing size (forest 49‐961 m2; grassland 1‐49 m²). Separate ordinations were computed for plots of each size for each data set, using either species presences/absences or cover‐abundances recorded on an ordinal scale. Ordination patterns were compared with Procrustean analysis. Also, ordinations of data sets jointly containing plots of different size were calculated; effects of plot size were evaluated using a Monte Carlo test in constrained ordination. Results: The results were consistent between forest and grassland data sets. In homogeneous data sets, the effect of presence/absence vs. cover‐abundance was similar to, or larger than, the effect of plot size; for presence/absence data the differences between ordinations of differently sized plots were smaller than for cover‐abundance data. In heterogeneous data sets, the effect of plot size was larger than the effect of presence‐absence vs. cover‐abundance. The plots of smaller size (= 100 m2 in forests, = 4 m² in grasslands) yielded the most deviating ordination patterns. Joint ordinations of differently sized plots mostly did not yield patterns that would be artifacts of different plot size, except for plots from the homogeneous data sets that differed in size by a factor of four or higher. Conclusions: Variation in plot size does influence ordination patterns. Smaller plots tend to produce less stable ordination patterns, especially in data sets with low ß‐diversity and species cover‐abundances. Data sets containing samples from plots of different sizes can be used for ordination if they represent vegetation with large ß‐diversity. However, if data sets are homogeneous, i.e. with low ß‐diversity, the differences in plot sizes should not be very large, in order to avoid the danger of plot size differences distorting the real vegetation differentiation in ordination patterns.