Fractal analysis of plant spatial patterns: a monitoring tool for vegetation transition shifts

Spatial heterogeneity, like species diversity, is an important ecosystem property. We examine the effects of land use on the diversity and spatial distribution of plants in five semi-arid communities of eastern Spain using non-linear methods to assess the spatialtemporal dynamics of plant populations. Specifically, we are interested in detecting long-term structural changes or drift in an ecosystem before it is too late to prevent irreversible degradation. Fractal analysis is used to characterize the complexity of plant spatial patterns and Information Theory indices are used to measure change in information flow with land use changes and soil substrate. We found that grazing favored diversity and heterogeneity of species distribution on the impoverished gypsum and saline substrate community, as opposed to the detrimental effect of grazing in the Alpha steppe community. Indeed, old-field succession after 30 years of abandonment showed a recovery of species diversity but not the spatial structure of the vegetation. Further, Information Fractal Dimension, representing the unpredictability of plant spatial patterns in the landscape, increased as we moved from a highly diverse to a less diverse community, revealing the change to a more scattered and homogeneous spatial plant distribution. The Information Fractal Dimension is a good estimator of ecosystem disturbance, independent of scale, and thus can be used to monitor ecosystem dynamics.     

Patterns in species associations in plant communities: the importance of scale

Abstract. Present discussions on competitive interactions and the occurrence of predictable patterns in species composition – including assembly rules – are likely to benefit from appropriate analyses of the spatial structure in plant communities. We suggest such an analysis when we specifically want to detect scale regions where fine-scale local processes may affect the spatial pattern of species composition. We combine indirect ordination in the form of Detrended Correspondence Analysis (DCA) and geostatistics in the form of variography. The species abundance data in the sampled quadrats are summarized as positions on the axes in the ordination. Each axis is used as a regionalized variable in the variography to obtain the spatial dependence of the quadrats. The spatial pattern found will suggest the relevant scale region in which to perform an analysis of species associations. A significant spatial dependence (the ‘range’ in geostatistical jargon) will define the size of a sampling plot that will minimize both the problem of being too small and thus having the risk of oversampling of e.g. clonal individuals and of being too large which will risk including individuals that do not interact. We also suggest that plots are spaced at least a ‘range’ apart to insure spatial and statistical independence. Comparisons of species compositions in such plots will reveal any positive or negative associations between species on a scale where these should reflect species-species interactions. To illustrate the method it is applied to three different data sets from two different plant communities.     

Ordination as a tool for analyzing complex data sets

Summary Ordination has proven to be a useful tool for examining relationships between environment and vegetation in data sets with a simple underlying environmental strueture. Complex data sets have proven much less tractable. A strategy is offered for dealing with complex data sets based on progressive removal of sets of stands along identified gradients, and subsequent reordination. This strategy is demonstrated using forests of the North Carolina piedmont.The author gratefully acknowledges the continuing collaboration of Dr. Norman L. Christensen of Duke University. This research was supported by National Science Foundation grants DEB-7708743 and DEB-7804043 to R.K.P. and DEB-7707532 and DEB-7804041 to N.L.C.     

Fractal geometry and root system structures of heterogeneous plant communities

Above-ground plant growth is widely known in terms of structural diversity. Likewise, the below-ground growth presents a mosaic of heterogeneous structures of differing complexity. In this study, root system structures of heterogeneous plant communities were recorded as integral systems by using the trench profile method. Fractal dimensions of the root images were calculated from image files by the box-counting method. This method allows the structural complexity of such associations to be compared between plant communities, with regard to their potentials for soil resource acquisition and utilization. Distinct and partly significant differences are found (fractal dimension between 1.46±0.09 and 1.71±0.05) in the below-ground structural complexity of plant communities, belonging to different biotope types. The size of the heterogeneous plant community to be examined has an crucial influence on the fractal dimension of the root system structures. The structural heterogeneity becomes particularly evident (fractal dimensions between 1.32 and 1.77) when analysing many small units of a complex root system association. In larger plant communities, a broad variety of below-ground structures is recorded in its entirety, integrating the specific features of single sub-structures. In that way, extreme fractal dimensions are lost and the diversity decreases. Therefore, the analysis of larger units of root system associations provides a general knowledge of the complexity of root system structures for heterogeneous plant communities.     

Use of precise spatial data for describing spatial patterns and plant interactions in a diverse Great Basin shrub community

Community-structuring processes continue to be of great interest to plant ecologists, and plant spatial patterns have been linked to processes including disturbance, dispersal, environmental heterogeneity, and plant interactions. Under the assumption that the analysis of the spatial structure of plant communities can help to elucidate the type and importance of the predominant community-structuring processes, many studies have analyzed point pattern data on various plant species. A variety of methods have been devised to acquire point pattern data for individual plants, however, the classic tradeoff between the speed of acquisition and the precision of spatial data has meant that large and precise datasets on plant locations are difficult to obtain. The primary goal of this study was to develop a GPS-based methodology for the rapid collection of precise spatial data on plant locations in a semi-arid shrubland in the Great Basin, USA. The secondary goal was to demonstrate a potential application of this approach by using recently developed univariate and bivariate spatial statistics to test for aggregation within the shrub community, as observed in other semi-arid shrublands. We efficiently mapped 2,358 individuals of five shrub species with a spatial error of ≤0.02 m, and found strong statistical evidence of fine-scale aggregation (1) independent of species, (2) within species, and (3) between two species pairs. Our approach is useful for rapidly collecting precise point pattern data in plant communities, and has other applications related to population modeling, GIS analysis, and conservation.     

Adaptive leaf structures in a Myrica-Erica stand on Tenerife (Canary Islands)

This study is based on a phytosociological table and a matrix of species and morphological characters. The relevés were taken along a transect in a Myrica faya-Erica arborea formation on Tenerife (Canary Islands). The analysis of the phytosociological table reveals a vegetational succession and a corresponding ecological gradient. The study of correlations between morphological and ecological data leads to the creation of groups of species with different combinations of characters, and to a discussion of the adaptive values of each character combination. The species of each group occupy similar niches.Abbreviations AOC= Analysis of Concentration - P/C= index ratio between the perimeter of a leaf and the circumference of a circle having the same area as the leaf     

莲花山主要森林群落空间格局的分形特征

应用信息维数对莲花山主要森林群落的空间格局进行了研究.结果表明:森林群落的格局强度尺度变化程度由高至低的次序为:岷江冷杉一糙皮桦一白桦群落(Q4)1.84＞云杉-紫果云杉-糙皮桦群落(Q2)1.53＞岷江冷杉群落(Q3)1.14＞紫果云杉-云杉-岷江冷杉群落(Q7)1.10＞华山松群落(Q5)0.99＞岷江冷杉人工林(Q1)0.82＞辽东栎群落(Q6)0.45;群落格局信息维数的差异反映了更新状况的差异,揭示出群落个体分布的非均匀性状况.综合3种分形维数,确定各亚高山寒温性森林群落生长与更新状况的次序为Q4＞Q2＞Q3＞Q7＞Q5＞Q1＞Q6.各群落总体平均记盒维数为1.76,关联维数为1.71,信息维数为1.12;各森林群落生长状况较好,个体聚集程度较低,更新状况一般.分形维数谱将不同森林群落的空间结构特征明确区分开来.     

Direct measurement of spatial autocorrelation at the community level in four plant communities

Abstract. Four sites were sampled to determine spatial autocorrelation in vegetation at the community level. All were in western New Zealand, but on different substrates and of different physiognomy: a terrace forest, a floodplain forest, a mire and the middle of a logging road. In ‘dissimograms’the four communities all showed steady increases in dissimilarity with distance, but with shoulders in the curve for some sites, which could be related to plant morphology. Most of the increase in dissimilarity occurred over very short distances: less than 0.5 m in the forests, less than 1 m in the mire and less than 2 m in the road. Separate analyses of the woody and herbaceous guilds in the floodplain forest showed that herbaceous dissimilarities remained low at distances up to 20 m, probably because of clonal structure in some species. The mire showed low overall dissimilarity, which is attributed to the uniform substrate and the small species pool. Simulations showed that the approach is capable of indicating structure when it is present. Although the dissimogram was clearest when analysing a simulated grid of patches, other types of simulated patchiness showed dissimograms that were clearly distinguishable from those obtained from the vegetation studied. The almost continuous rise in dissimilarity with distance found in the four sites offers no support to the Hierarchy theory, fitting much more closely the alternative Continuum theory.     

Positive interactions in plant communities and the individualistic-continuum concept

The individualistic nature of communities is held as a fundamental ecological tenet by many ecologists. The empirical rationale for the individualistic hypothesis is largely based on gradient analyses in which plant species are almost always found to be arranged independently of one another in “continua” along environmental gradients. However, continua are correlative patterns and do not identify the processes that determine them, and so they do not necessarily preclude the possibility of interdependent interactions within plant communities. For example, the common occurrence of positive interactions suggests that plant species may not always be distributed independently of each other. If the distributions and abundances of species are enhanced by the presence of other species, their organization is not merely a coincidence of similar adaptation to the abiotic environment. Interpretations of gradient analyses also appear to assume that interactions among species should be similar at all points along environmental axes, and that groups of species should be associated at all points on a gradient if interdependence is to be accepted. However, virtually all types of ecological interactions have been shown to vary with changes in the abiotic environment, and a number of field experiments indicate that positive effects become stronger as abiotic stress increases. Furthermore, interactions among plants have been shown to shift from competition to facilitation along environmental continua. Thus, significant interdependence may occur even when species do not fully overlap in distribution. Higher-order, indirect interactions between animals and plants, and among plants, also suggest that interdependence within communities occurs. Eliminating a species involved in an indirect interaction may not necessarily mean that its beneficiary will be eliminated from a community, but the prospect that the distribution and abundance of any species in a plant community may be positively affected by the effects that other species have on their competitors suggests that communities are organized by much more than “the fluctuating and fortuitous immigration of plants and an equally fluctuating and variable environment” as stated by Henry Gleason. The ubiquity of direct and indirect positive interactions within plant communities provides a strong argument that communities are more interdependent than current theories allow. Received: 17 February 1997 / Accepted: 23 May 1997     

Extended dissimilarity: a method of robust estimation of ecological distances from high beta diversity data

It is widely accepted that reliable ordination of ecological data requires a strong linear or ordinal relationship between the dissimilarity of sites, based on species composition, and the ecological distance between them. Certain dissimilarity measures, having the property that they take a fixed maximum value when sites have no species in common, have been shown to be strongly correlated with ecological distance. For ecological gradients of moderate length (moderate beta diversity), such measures, in conjunction with non-metric multidimensional scaling, will reliably yield successful ordinations. However, as beta diversity increases, more sites have no species in common, and such measures invariably under-estimate ecological distance for such sites. Thus ordinations of data with high species turnover (high beta diversity) may fail.Extended dissimilarities are defined using an iterative adaptation of flexible shortest path adjustment applied to the matrix of dissimilarities with fixed maximum values. By means of theoretical argument and simulations, this is shown to lead to far stronger correlations between the adjusted site dissimilarity and ecological distance for ecological gradients of greater length than previously considered. Hence ordinations of extended dissimilarities, by means of either metric or non-metric scaling techniques, are shown to outperform corresponding ordinations of unadjusted dissimilarities, with the difference increasing with increasing beta diversity.     

Multiscale patterns of spatial variation in stream macroinvertebrate communities

Our ability to detect patterns of variation of communities depends on the spatial scale of observation. I examined the spatial variation of macroinvertebrate community structure: abundance, richness, evenness, percentage of Ephemeroptera, Plecoptera and Trichoptera (EPT), and taxonomic composition across a wide range of spatial scales in two mountain streams. In a nested design, three segments were selected within each basin, three riffles within each segment, three sections within each riffle, and three samples within each section. Significant variation of communities occurred mainly at sample and riffle scales, although different community characteristics may vary at different scales. Environmental factors were strongly related to communities, but these relationships depended on spatial scale in many cases, suggesting that the influence of the environment is ultimately regulated by the grain and extent of organisms. This study highlights the importance of multiscale studies to obtain a complete understanding of the spatial variation of macroinvertebrate communities and their relationship with the environment.     

Use of ecological groups in analysis and classification of plant communities in a section of western Quebec

A plant community analysis and classification were done for an integrated ecological study, in the lake Abitibi region, Quebec. Two levels of vegetation analysis were used: the ecological group level and the community level. Species were first grouped according to their sociological affinities. The ecological significance of those groupings was studied by principal component analysis, with the inclusion of abiotic variables, and by the study of ecological profiles. Secondly, the concurrent use of ecological groups permitted the definition and characterization of noda. The relationships between the noda, in the space defined by the ecological groups, were analyzed by principal coordinate analysis on which is superimposed the shortest spanning tree. Those combined analyses permitted the identification of 35 community types which vary mainly according to surficial deposits (organic or mineral), drainage, relative richness of soils in bases, flooding, presence of bedrock outcrops. fire perturbations and microclimate. Those variations are discussed according to the exlusive or non-exclusive character of the ecological groups.     

麦长管蚜及蚜茧蜂空间格局的地学统计学研究

应用地学统计学的原理和方法研究了不同时期麦长管蚜及蚜茧蜂种群的空间结构和空间相关性,结果表明,不同时期麦长管蚜种群的半变异函数曲线皆为球型,其空间格局为聚集型,变程在33－57cm之间;蚜茧蜂种群的拟合半变异函数曲线也表现为球型,呈聚集空间格局,空间变程在36－55cm之间,并与麦长管蚜种群在数量和空间上有较强的追随关系,说明蚜茧蜂种群是麦长管蚜种群的优势种天敌。     

棉蚜及龟纹瓢虫空间格局的地学统计学研究

应用地学统计学的原理和方法研究了不同时期棉蚜及龟纹瓢虫种群的空间结构和空间生。结果表明,不同时期棉蚜种群的关变异函数曲线皆为球型,其空间格局为聚集型,变程在８．２１￣１０．８１ｍ之间;龟纹瓢虫种群的拟合半变异函数曲线也表现为球型,呈聚集空间格局,空间变程在８．０１￣１４．２５ｍ之间,并与棉蚜种群在数量和空间上有较强的追随关系,说明龟纹瓢虫种群是棉蚜种群的优势种天敌。     

Fractal geometry of bean root systems: correlations between spatial and fractal dimension

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. The objective of this work was to determine if fractal geometry might be useful in estimating the three-dimensional complexity of root architecture from more accessible measurements. A set of results called projection theorems predict that the fractal dimension (FD) of a projection of a root system should be identical to the FD of roots in three-dimensional space (three-dimensional FD). To test this prediction we employed SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean (Phaseolus vulgaris L.). We computed the three-dimensional FD, FD of horizontal plane intercepts (planar FD), FD of vertical line intercepts (linear FD), and FD of orthogonal projections onto planes (projected FD). Three-dimensional FD was found to differ from corresponding projected FD, suggesting that the analysis of roots grown in a narrow space or excavated and flattened prior to analysis is problematic. A log-linear relationship was found between FD of roots and spatial dimension. This log-linear relationship suggests that the three-dimensional FD of root systems may be accurately estimated from excavations and tracing of root intersections on exposed planes.     

棉蚜和草间小黑蛛种群空间格局的地统计学研究

应用地统计学的原理和方法研究了石榴园不同时期棉蚜及草间小黑蛛种群的空间结构和空间相关性．结果表明,不同时期棉蚜种群的半变异函数曲线皆为球型,其空间格局为聚集型,变程在7．33～12．40cm之间;草间小黑蛛种群的拟合半变异函数曲线也表现为球型,呈聚集空间格局,空间变程在6．47～20．88cm之间,并与棉蚜种群在数量和空间上有较强的追随关系,说明草间小黑蛛种群是棉蚜种群的优势种天敌．