Effects of detrending and rescaling on correspondence analysis: solution stability and accuracy

Detrending and non-linear axis rescaling potentially improve the accuracy of gradient recovery in correspondence analyses but also reduce the stability or consistency of solutions. Variation among bootstrapped ordination solutions was compared across methods in analyses of both field and simulated data. Solution accuracy, measured with mean squared errors from Procrustes analysis, was compared using simulated data with known structure.Standard detrending-by-segments combined with non-linear rescaling entailed some cost in solution stability, but could improve the accuracy of solutions for long gradients. Without non-linear rescaling these solutions were usually less stable and less accurate. Although detrending-by-polynomials might be preferable on other grounds, it did not produce more accurate or stable solutions than detrending-by-segments.Abbreviations CA = correspondence analysis - DCA = detrended correspondence analysis - MSE = Procrustes mean squared error statistic - SD = standard deviation units of species turnover - SRV = scaled variance in species ranks     

Reseating of ecological gradients. III. The effect of scale and niche breath measurements

Abundances of eleven Sphagnum species in 800 sample plots are used to investigate the effect of DCA rescaling on Levins' measure of niche breadth relative to three partitions of the water-table gradient in a boreal Norwegian mire: (1) sample plots classified into 15 categories, each spanning an interval of 2 cm vertical extent, (2) as (1), but sequence of categories rescaled by DCA and sample plots reorganized into 15 categories with uniform beta diversity, and (3), sample plots ordinated by DCA and classified into 15 categories with uniform beta diversity by subdivision of an ordination axis highly correlated with median water-table. Habitat niche breadth is shown to be dependent on four issues (in order of supposedly decreasing importance): (1) scale, (2) noise level of data, (3) homogeneity of individual samples, and (4), weighting function. Six problems relevant to interpretation of measurements of niche breadth are discussed: (1) range of measures, (2) spacing of categories, (3) scale, (4) choice of gradients, (5) number of samples, and (6), comparability of studies. For measures of habitat niche breadth to be biologically meaningful, four conditions have to be satisfied: (1) the gradients studied have important impact on the studied species, (2) sampling is adequate, (3) scaling of gradients is in compositional turnover, and (4), comparability is demonstrated prior to comparison with other studies. Revisions of current methods are proposed. The role of DCA in niche studies is particularly emphasized.     

Rescaling of ecological gradients. I. Calculation of ecological distance between vegetation stands by means of their floristic composition

Geometric models of vegetation (conceptual spaces) are reviewed. Spaces with samples or species as axes are termed flortistic spaces, as opposed to ecological space with environmental gradients as axes. The terms floristic and ecological relationships are defined as relationships in floristic and ecological spaces, respectively. Compositional turnover is pointed out as the essence of ecological gradients, and arguments in favour of measuring ecological distance in units of compositional turnover are given. The most important criteria for evaluation of ecological distance measures are considered to be linear response to separation along ecological gradients and robustness. Theoretical disadvantages of measures of floristic relationships used as ecological distance measures are discussed. A new measure of ecological distance, separation along a DCA ordination axis, is proposed. This measure and four measures of floristic relationships were tested on four simulated coenoclines (high and low beta diversity, high and low noise) using four weighting functions. The new measure was generally superior, particularly with noisy data. The distance measures generally performed best with intermediate weighting of a percentage cover scale. Application of DCA to calculation of ecological distances in multi-gradient systems is briefly discussed. The potential of DCA for rescaling of ecological gradients is emphasized, and some possible applications of rescaling are suggested.     

Fine-scale patterns of vegetation and environmental factors on an ombrotrophic mire expanse: a numerical approach

The vegetation within an ombrotrophic mire expanse in SE Norway is studied in detail. Percentage cover of 45 species in 436 sample plots (16 ×16 cm), dispersed on 26 transects, are recorded. In addition, species abundance in 6976 subplots (4×4 cm) are recorded. 14 variables are recorded for each of the sample plots, while only distance to the water-table is estimated for the subplots. Spatial co-ordinates are supplied for all sample- and subplots. DCA ordination of a data-set consisting of 412 sample plots reveals two ecologically interpretable vegetational gradients: the hummock-hollow gradient (DCA 1), and a gradient associated with the peat-production of the bottom layer (DCA 2). Passive DCA of subplots is used to get an impression of within sample plot heterogeneity, and shows that the fine-scale compositional turnover may be considerable. Partitioning of the variation in species abundance data is done by use of (partial) CCA. The fraction of unexplained variation is rather large for all the tested data-sets, but within the total variation explained, both distance to the water-table and spatial structure explain large parts.     

Effects of the geomorphometric characteristics of the local terrain on floristic composition in the central Brazilian Amazon

The objective of this study was to identify the effects of local geomorphometry on the abundance, richness and floristic composition of tree species in the central Brazilian Amazon. Forty‐six 0.25‐ha plots in different phyto‐ecologic sites were sampled, and their trees were inventoried. Geomorphometric data (elevation, slope, aspect, plan and profile curvatures) were derived from Shuttle Radar Topography Mission data. A detrended correspondence analysis (DCA) was used to examine the floristic distribution patterns among plots. In addition, geomorphometric variables were submitted to multiple regression analysis to identify the variables influencing floristic composition (represented by the first DCA component), abundance and species richness. Correlation analyses between the number of individuals from each species and the first DCA component were performed to evaluate the contribution of each species. Analysis of the results could not confirm an effect of geomorphometry alone on species richness and abundance, although floristic composition was significantly influenced by profile curvature and elevation. Despite the relatively low variation in altitude at the study site, species were found to be sensitive to terrain peculiarities such as elevation and profile curvature, which can constrain particular ecologic niches and contribute to the spatial distribution patterns of species.     

Measuring compositional change along gradients

A new procedure for measuring compositional change along gradients is proposed. Given a matrix of species-by-samples and an initial ordering of samples on an axis, the ‘gradient rescaling’ method calculates 1) gradient length (beta diversity), 2) rates of species turnover as a function of position on the gradient, and 3) an ecologically meaningful spacing of samples along the gradient. A new unit of beta diversity, the gleason, is proposed. Gradient rescaling is evaluated with both simulated and field data and is shown to perform well under many ecological conditions. Applications to the study of succession, phenology, and niche relations are briefly discussed.     

Instability of ordination results under changes in input data order: explanations and remedies

Abstract. Correspondence analysis (CA) and its Detrended form (DCA) produced by the program CANOCO are unstable under reordering of the species and sites in the input data matrix. In CA, the main cause of the instability is the use of insufficiently stringent convergence criteria in the power algorithm used to estimate the eigenvalues. The use of stricter criteria gives results that are acceptably stable. The divisive classification program TWINSPAN uses CA based on a similar algorithm, but with extremely lax convergence criteria, and is thus susceptible to extreme instability. We detected an order-dependent programming error in the non-linear rescaling procedure that forms part of DCA. When this bug is corrected, much of the instability in DCA disappears. The stability of DCA solutions is further enhanced by the use of strict convergence criteria. In our trials, much of the instability occurred on axes 3 and 4, but one should not assume that published two-dimensional ordinations are sufficiently accurate. Data sets which have pairs of almost equal eigenvalues among the first three axes could suffer from marked instability in the first two dimensions. We recommend that a debugged, strict version of CANOCO be released. Meanwhile, users can check the stability of their CA and DCA ordinations using the software that we have made available on the World Wide Web ( http://www.helsinki.fi/jhoksane/ ). An accurate program for CA, a debugged, strict version of DECORANA (for DCA) and a strict version of TWINSPAN are also available at our site.     

桂林岩溶石山青冈栎群落的数量分析

应用双向指示种分析(TWINSPAN)和除趋势对应分析(DCA)方法对桂林岩溶石山青冈栎群落进行数量分类与排序。通过TWINSPAN分类,将青冈栎群落60个样方划分为8个群丛类型,探讨了各群丛类型的基本特征。结果表明:DCA排序与TWINSPAN分类结果较一致,DCA排序较好地体现了各群丛类型与环境因子的相互关系,DCA第一排序轴主要反映了坡度的变化梯度;DCA排序图的对角线基本体现了坡向的变化梯度。坡度的变化是影响岩溶石山青冈栎群落物种组成与分布的重要生态因子。     

SPATIAL PARADIGMS OF LOTIC DIATOM DISTRIBUTION: A LANDSCAPE ECOLOGY PERSPECTIVE

Spatial distributional patterns of benthic diatoms and their relation to current velocity were investigated in an unshaded cobble-bottom reach of White Creek (Washington County, NY). On 27 August 1999, diatoms were sampled and current velocity and depth were measured on a regular square sampling grid with a grain size of 0.01 m², interval of 0.5 m, and extent of 16 m². The relative abundance of the 18 common diatom species enumerated in the 81 samples was subjected to detrended correspondence analysis (DCA). The first axis (DCA1) explained 51% of the variance in diatom data and separated the samples according to current regimes. The spatial autocorrelation of DCA1 sample scores in deposition and erosion regions of White Creek was determined by Moran's I statistic to indicate patch size. In White Creek the patch length of all diatom communities was more than 3.1 m, whereas the patch width was 1 m in the deposition region and 0.5 m in the erosion region. There were 5 dominant diatom taxa, Achnanthes minutissima Kütz. et vars, Fragilaria capucina Dezmazières et vars, F. crotonensis Kitt., Diatoma vulgaris Bory, and Synedra ulna (Nitz.) Ehr. et vars. The patch length of the dominant species varied from 1 to more than 4.1 m, whereas the patch width, if defined, was 0.5 m. Achnanthes minutissima and F. capucina, the two diatom species with the highest relative abundance, displayed spatially structured patches of low abundance and comparatively random patches of high abundance, suggesting broad scale abiotic control of species performance in low abundance regions and finer scale biotic control of high abundance areas. Another objective of this study was to test the hypothesis that higher current velocities, which generally impede immigration, would increase randomness and complexity (i.e. homogeneity of diatom distributional patterns). The spatial complexity in low versus high velocity transects was determined by calculating the respective fractal dimension (D) of DCA1 scores. D of DCA1 was higher in the higher current velocity transects, suggesting that spatial complexity and homogeneity of diatom communities increased in faster currents. Partial canonical correspondence analysis was conducted on diatom, environmental, and spatial data to assess how much of the variance in species distribution could be attributed to environmental (current velocity and depth) versus spatial factors. The variance of species data, explained by the environment (exclusively current velocity), was 38%; whereas space alone contributed only 10%, indicating that 1) current velocity was the major factor that controlled diatom distribution in streams and 2) there were other spatially dependent variables, most likely biotic, but their role in shaping diatom communities was minor.     

The influence of multi‐scale environmental variables on the distribution of terricolous lichens in a fog desert

Question: How do environmental variables in a hyper‐arid fog desert influence the distribution patterns of terricolous lichens on both macro‐ and micro‐scales? Location: Namib Desert, Namibia. Methods: Sites with varying lichen species cover were sampled for environmental variables on a macro‐scale (elevation, slope degree, aspect, proximity to river channels, and fog deposition) and on a micro‐scale (soil structure and chemistry). Macro‐scale and micro‐scale variables were analysed separately for associations with lichen species cover using constrained ordination (DCCA) and unconstrained ordination (DCA). Explanatory variables that dominated the first two axes of the constrained ordinations were tested against a lichen cover gradient. Results: Elevation and proximity to river channels were the most significant drivers of lichen species cover in the macro‐scale DCCA, but results of the DCA suggest that a considerable percentage of variation in lichen species cover is unexplained by these variables. On a micro‐scale, sediment particle size explained a majority of lichen community variations, followed by soil pH. When both macro and micro‐scale variables were tested along a lichen cover gradient, soil pH was the only variable to show a significant relationship to lichen cover. Conclusion: The findings suggest that landscape variables contribute to variations in lichen species cover, but that stronger links occur between lichen growth and small‐scale variations in soil characteristics, supporting the need for multi‐scale approaches in the management of threatened biological soil crust communities and related ecosystem functions.     

Can we trust gradients extracted by Detrended Correspondence Analysis?

Abstract. In this study, data from dry temperate grassland vegetation in Denmark are used to compare the predictive power of gradients obtained by ordination. One of the problems of ordination methods based on weighted averaging, namely the assumption of symmetric, unimodal response curves, is investigated by smoothing species responses to simple and complex gradients respectively. It was found that species response types to a pH gradient are diverse and often deviate from a unimodal, symmetrical shape. Bimodal responses were also found, but they disappeared when more influential gradients were considered. Many species showed truncated responses with optima near gradient ends. In order to assess the impact of unrealistic response assumptions and reported problems with instability on the performance of DCA, the predictive potentials of measured variables and coenoclines extracted by DCA were compared. Despite field data violating the assumption of unimodal response, DCA was found to extract gradients predicting species abundance better than the environmental variables available. Shortcomings and advantages of indirect and direct methods in plant ecology are discussed.     

Relative importance of spatial processes and environmental factors in shaping alpine meadow communities

Aims Spatial processes and environmental control are the two distinct, yet not mutually exclusive forces of community structuring, but the relative importance of these factors is controversial due to the species-specific dispersal ability, sensitivity towards environmental variables, organism's abundance and the effect of spatial scale. In the present paper, we explored spatial versus environmental control in shaping community composition (i.e. β-diversity) and species turnover (i.e. change of β-diversity) at an alpine meadow along a slope aspect gradient on the Qinghai–Tibetan Plateau at different spatial scales of sampling (quadrats and plots), by taking account of seed dispersal mode and abundance.Methods We examined the relative importance of spatial processes and environmental factors using all species and four additional subsets of selected species. Moreover, we attempted to explore the effect of scale (quadrat refers to scale of ~0.3 m and plot of ~8 m) on their counter balance. The data were analyzed both by variation partitioning and multiple regressions on distance matrices. The spatial structure was modelled using Moran's eigenvector maps (MEM).Important findings Both spatial processes and environmental factors were important determinants of the community composition and species turnover. The community composition in the alpine meadow was controlled by spatially structured environment (17.6%), space independent of environment (18.0%) and a negligible effect of environment independent of space (4.4%) at the scale of quadrats. These three components contributed 21.8, 9.9 and 13.9%, respectively, at the scale of plots. The balance between the forces at different spatial scales drove community structures along the slope aspect gradient. The importance of environmental factors on β-diversity at alpine meadow increased with scale while that of spatial processes decreased or kept steady, depending on dispersal mode and abundance of species comprising the subset. But the 'pure' effect of spatial processes on species turnover increased with scale while that of environmental factors decreased. This discrepancy highlights that β-diversity and species turnover were determined jointly by spatial processes and environmental factors. We also found that the relative roles of these processes vary with spatial scale. These results underline the importance of considering species-specific dispersal ability and abundance of species comprising the communities and the appropriate spatial scale in understanding the mechanisms of community assembly.     

Effects of sampling teams and estimation methods on the assessment of plant cover

Abstract. We evaluated variability in cover estimation data obtained by (1) two sampling teams who double sampled plots and (2) one team that used two methods (line intercepts and visual estimation of cover classes) to characterize vegetation of herbaceous wetlands. Species richness and cover estimates were similar among teams and among methods, but one sampling team scored cover higher than the other. The line intercept technique yielded higher cover estimates but lower species richness estimates than the cover class method. Cluster analyses of plots revealed that 36% and 11% of plots sampled consecutively by two teams or using two methods, respectively, were similar enough in species composition and abundance to be paired together in the resulting clustering tree. Simplifying cover estimate data to presence/absence increased the similarity among both teams and methods at the plot scale. Teams were very similar in their overall characterization of sites when cover estimation data were used, as assessed by cluster analysis, but methods agreed best on their overall characterization of sites when only presence/absence data were considered. Differences in abundance estimates as well as pseudoturnover contribute to variability. For double sampled plots, pseudoturnover was 19.1%, but 57.7% of pseudo‐turnover cases involved taxa with ≤ 0.5% cover while only 3.4% involved taxa with > 8% cover. We suggest that vegetation scientists incorporate quality control, calibrate observers and publish their results.     

东灵山濒危植物刺五加生存群落的数量分析

在样方调查的基础上,分别采用双向指示种分类法(TWINSPAN)、除趋势对应分析法(DCA)和典范对应分析(CCA)对东灵山地区濒危植物刺五加的生存群落进行数量分析。TWINSPAN分类将刺五加生存群落分为9类,分类结果在DCA二维排序图上得到了较好的验证,其中第一轴反映的是海拔梯度,第二轴反映了坡向、坡度的变化。刺五加多分布在位于海拔较高、光照较少的杂木林中,除在少数群落中成为灌木层的优势种外,相对分布较少。CCA排序结果与DCA的排序结果基本一致,反映出植物群落分布随环境因子梯度变化的趋势,揭示了海拔和光照是限制刺五加生长的主要环境因子。     

Quantitative analysis of endangered Acanthopanax senticosus communities in Dongling Mountain of Beijing

Based on the survey of community plots, a quantitative analysis of endangered Acanthopanax senti-cosus communities in Dongling Mountain was performed with two way indicator species analysis (TWINSPAN), detrended correspondence analysis (DCA) and canonical correspondence analysis (CCA). The communities of A. senticosus were classified into 9 types by TWINSPAN and the results were validated by DCA. On the DCA graph, the first axis reflected the gradient of altitude and the second axis reflected the aspect and slope. Most of A. senticosus were distributed in the thick forests at a high altitude with little light. With the exception of being a dominant species of shrub layers in a few communities, A. senticosus has a relatively scarce distribution. In accordance with DCA, the results of CCA also show the trend that the distribution of A. senticosus communities varied along with the gradient change of environmental factors. Altitude and light are the main factors affecting A. senticosus growth.     

A better way to estimate population trends

Estimation of a population trend from a time series of abundance data is an important task in ecology, yet such estimation remains logistically and conceptually challenging in practice. First, the extent to which unequal intervals in the time series, due to missing observations or irregular sampling, compromise trend estimation is not well‐known. Furthermore, the predominant trend estimation method (loglinear regression of abundance data against time) ignores the possibility of process noise, while an alternative method (the ‘diffusion approximation’) ignores observation error in the abundance data. State‐space models that account for both process noise and observation error exist but have been little used. We study an adaptation of the exponential growth state‐space (EGSS) model for use with missing data in the time series, and we compare its trend estimation to the status quo methods. The EGSS model provides superior estimates of trend across wide ranges of time series length and sources of variation. The performance of the EGSS model even with half of the counts in the time series missing implies that trend estimates may be improved by diverting effort away from annual monitoring and towards increasing time series length or improving precision of the abundance estimates for years that data are collected.     

Fine‐scale five‐year vegetation change in boreal bog vegetation

Abstract. Within an ombrogenous part of N. Kisselbergmosen, Rødenes, SE Norway, fine‐scale changes in species abundance, successional trends relative to the main gradients (as represented by DCA axes), and co‐ordinated change within pairs of the bottom layer species are studied. Data sets were sampled twice with a five‐year interval, and included species abundance and cover of mud bottom, naked peat and litter in 436 sample plots (16 cm× 16 cm), and species abundance in 6976 subplots (4 cm× 4 cm). Depth from the surface of subplots to the water table was estimated in 1991. Most summers and growing seasons were somewhat drier than normal in the 5‐yr period. The area covered by mud‐bottom, naked peat and litter increased significantly, as did the frequencies of the dwarf shrubs Calluna vulgaris and Andromeda polifolia in hummocks and upper lawn. Sample plots were significantly displaced downward the peat productivity gradient (DCA 2), reflecting the reduced cover of many bottom layer species, including all Sphagnum spp. Significant coordinated changes in cover of bottom layer species are described. The changes observed in hummocks support the existence of a local regeneration cycle, as suggested by other researchers. Some of the vegetation changes seem parallel to those reported from areas with a higher nitrogen deposition, but it is not likely that nitrogen deposition alone is the major cause of the observed changes. Between‐year variation in population size and climatic fluctuations may as well explain the observed changes.     

A novel approach to understanding bird communities using informed diversity estimates at local and regional scales in northern California and southern Oregon

Assessment and preservation of biodiversity has been a central theme of conservation biology since the discipline's inception. However, when diversity estimates are based purely on measures of presence–absence, or even abundance, they do not directly assess in what way focal habitats support the life history needs of individual species making up biological communities. Here, we move beyond naïve measures of occurrence and introduce the concept of “informed diversity” indices which scale estimates of avian species richness and community assemblage by two critical phases of their life cycle: breeding and molt. We tested the validity of the “informed diversity” concept using bird capture data from multiple locations in northern California and southern Oregon to examine patterns of species richness among breeding, molting, and naïve (based solely on occurrence) bird communities at the landscape and local scales using linear regression, community similarity indices, and a Detrended Correspondence Analysis (DCA). At the landscape scale, we found a striking pattern of increased species richness for breeding, molting, and naïve bird communities further inland and at higher elevations throughout the study area. At the local scale, we found that some sites with species‐rich naïve communities were in fact species‐poor when informed by breeding status, indicating that naïve richness may mask more biologically meaningful patterns of diversity. We suggest that land managers use informed diversity estimates instead of naïve measures of diversity to identify ecologically valuable wildlife habitat.     

Reseating of ecological gradients. II. The effect of scale on symmetry of species response curves

Response curves are presented for 15 species of vascular plants, bryophytes, and lichens relative to the water-table gradient in a boreal Norwegian mire. The gradient is scaled in two ways; position of median water-table in cm below the surface of the bottom layer, and in units of compositional turnover (rescaled by DCA). The two scalings produce quite different curves above the maximum water-level, which corresponds to median water-level 10–14 cm below the surface of the bottom layer. The significant drop in compositional turnover above this level can be ascribed to vertical differences in water-table having a lesser effect on plants in aerated hummocks than on plants in temporarily water-logged hollows. Skewness of response curves was reduced by gradient rescaling, most strongly after removal of influence of other gradients. It is argued that response curves will generally be Gaussian if: (1) the response is with respect to a dominant ecological factor, (2) the range of variation along the gradient is sufficient, (3) the distribution of samples is adequate, and (4), the gradient is scaled in units of compositional turnover.     

Use of detrended correspondence analysis to evaluate factors controlling spatial distribution of benthic insects

Detrended correspondence analysis (DCA) was evaluated for its effectiveness in displaying factors controlling the spatial distribution of benthic insects in an oligotrophic stream where an experimental gradient (copper) that selectively affects population abundances was imposed. DCA proved to be highly sensitive to differences among samples and consistently provided ecologically meaningful species ordinations.Seasonality of taxa was the major gradient displayed by DCA prior to copper exposure when data for all sampling dates were included. Sensitivity of taxa to copper was a more important factor affecting community structure than was seasonality during periods of continuous exposure to copper (2.5 to 15 µg l^-1 Cu_T; approximately 12 to 75 ng l^-1 Cu²⁺. When pre-dose data for each sampling date were ordinated independently, substratum composition and biological interactions were the major gradients displayed in species ordinations. During periods of exposure, sensitivity of taxa to copper was the primary gradient. This gradient also reflected a generally greater sensitivity to copper of herbivorous than of detritivorous or predatory benthic insects. DCA revealed the persistence, eleven months after dosing ceased, of differences in community structure between the control and high treatment (5 and 10 µg l^-1 Cu_T) sections. Differences between sections were not evident on this sampling date from total biomass or total density (numerical) estimates.