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.     

Scales of spatial patterns of distribution of intertidal invertebrates

Few comparative studies of spatial patterns at different scales have examined several species in the same habitat or the same species over a range of habitats. Therefore, variability in patterns among species or among habitats has seldom been documented. This study quantifies spatial patterns of a suite of intertidal snails and a species of barnacle using a range of statistical techniques. Variability in densities was quantified from the scale of adjacent quadrats (over a distance of centimeters) to tens of kilometers. Significant differences in abundances occurred primarily at two spatial scales. Small-scale differences were found at the scales of centimeters or 1–2 m and, for many species on many shores, these accounted for most of the variability in abundances from place to place. These are likely to be determined by behavioural responses to small-scale patches of microhabitat. Large-scale differences in abundance were also found in most species at the scale of hundreds of meters alongshore. These are likely to be due to variation in recruitment (and/or mortality) because of limited dispersal by adults of these species. There was little or no additional variation among shores, separated by tens of kilometers, than was shown among patches of shore separated by hundreds of meters. Identification of the scale(s) at which significant differences in abundance are found focus attention on the processes (and the scales at which these processes operate) that influence patterns of distribution and abundance. Some of the advantages and disadvantages of various procedures are discussed.     

Downscaling indicators of forest habitat structure from national assessments

Downscaling is an important problem because consistent large-area assessments of forest habitat structure, while feasible, are only feasible when using relatively coarse data and indicators. Techniques are needed to enable more detailed and local interpretations of the national statistics. Using the results of national assessments from land-cover maps, this paper demonstrates downscaling in the spatial domain, and in the domain of the habitat model. A moving window device was used to measure structure (habitat amount and connectivity), and those indicators were then analyzed and combined with other information in various ways to illustrate downscaling.     

Population structure and spatial patterns for trees in a temperate old-growth evergreen broad-leaved forest in Japan

The population structure and spatial pattern of major tree species in a warm-temperate old-growth evergreen broad-leaved forest in the Tatera Forest Reserve of Japan were investigated. All stems 5 cm in diameter at breast height (DBH) were mapped on a 4 ha plot and analyses were made of population structure and the spatial distribution and spatial association of stems in different vertical layers for nine species. This was done in the context of scale dependency. The plot was located on a very gentle slope and 17.1% of its canopy layer was in gaps. It contained 45 woody plant species and 4570 living stems with a basal area of 63.9 m² ha^–1. Castanopsis cuspidata var. sieboldii, the most dominant species for the basal area, had the maximum DBH among the species present, fewer smaller stems and a lower coefficient of statistical skewness of the DBH distribution. The second most dominant species, Dystilium racemosum, had the highest stem density (410 ha^–1), more abundant smaller stems and a relatively higher coefficient of skewness. Most stems in different vertical layers showed a weakly aggregated distribution with loose colonies as basic units. Gap dependency for the occurrence of stems under the canopy layer was weak. Maximum slope degree of the plot also weakly affected the occurrence of stems. Spatial associations varied among intra- and interspecific cohorts in the different layers and spatial scales examined, and positive associations among cohorts were found more frequently as the scales examined became larger. This tendency suggests that key factors forming observed spatial associations might vary with the spatial scales.     

A spatial model of forest dynamics

Effects of spatial processes on temperate deciduous forest structure and dynamics were investigated with a spatial simulator derived from a forest gap model. The multi-species neighborhood model accounted for competitive interactions and endogenous disturbance in the form of small canopy gaps. Simulated and actual spatial pattern of old-growth stands were compared. The 400 yr simulations produced a pattern scale (0.07–0.2 ha patches) similar to that of an actual stand; simulated pattern intensity was greater than actual intensity, however. Distances to nearest neighbor were somewhat similar for trees in the simulated and actual stands; yet the frequency distributions of distance to nearest neighbor values differed substantially. The simulated stand patterns were generally less random than the actual patterns. Spatial pattern changed markedly during the course of simulated succession. Pattern approached a random dispersion in early succession. Intensity peaked at mid-succession (ca. 150 yr) with a hyperdispersed overstory and a strongly clumped understory. Pattern intensity diminished in late succession as a mixed size structure developed. Old-growth patch size was greater than the neighborhood (or gap) size, suggesting the gap-sized areas do not behave independently.     

Riparian disturbance and community structure of a Quercus-Ulmus forest in central Japan

Population structure and ecological characteristics of component species of a riparian Ulmus-Quercus forest in central Japan were analyzed with special reference to riparian disturbance regime. Though the dbh distribution of the whole community was L-shaped, those of several component tree populations had several modes, suggesting intermittent regeneration periods in the past. Correlation of spatial distributions among tree populations and subpopulations showed 6 major groups reflecting riparian disturbances in the past and different establishment patterns among species. A cluster of small-sized tree populations (Salix sachalinensis, Alnus hirsuta and Populus maximowiczii <30 cm dbh) were distributed on the lower terrace along the active river channel, while large-sized subpopulations (dbh 60 cm) of Quercus crispula and Ulumus davidiana var. japonica occurred on the higher terrace. The Phellodendron amurense population also occurred on the higher terrace in small clumps though the trees were small (less than 55 cm dbh). Subpopulations of intermediate-sized individuals (30 dbh < 60 cm) of Q. crispula and U. davidiana var. japonica, together with Betula and Acer spp. populations occurred on the intermediate terrace. Dendrochronological analyses indicated that the large and intermediate-sized tree groups were established about 330 and 90 years ago, respectively, while the small-sized tree group established about 35 years ago. A survey of historical disturbances showed that these periods of establishment of the former two groups almost coincided with the historically major floods occurring in 1662 and 1902. However, the disturbance that resulted in the establishment of the youngest group could not be precisely identified. Thus, the forest is a mosaic of three differently-aged patches, which is closely related to the frequency and scale of riparian disturbances. Longevity of trees and the preferred conditions for seed germination and/or seedling establishment were particularly important for the guild structure in this forest community.     

Predicting forest grouse distribution taking account of spatial autocorrelation

Spatially explicit, multi-scale models for predictions of species potential distribution can be useful tools for integrating biodiversity considerations in planning and strategic environmental assessment. In such models, the occurrences of focal species are related to habitat and landscape variables, which in urbanising areas should also include effects of urban disturbances. Moreover, the accuracy of the spatial predictive models may be affected by spatial autocorrelation, which means that a part of the variance is explained by neighbouring values. The aim of this study was to explore the effects of habitat and disturbance patterns on the distribution of two forest grouse species, Tetrao urogallus and Bonasa bonasia, and to detect and model the effects of spatial autocorrelation. The distribution of the two species could be explained in terms of reduction of a main predator, habitat quality, quantity and connectivity, including urban disturbances. The residuals of the initial regressions showed positive spatial autocorrelation that could be quantified by using a spatial probit model. The application of the spatial probit model revealed strongly significant spatial dependencies for both species. Furthermore, the model fit could be increased for T. urogallus by applying this model. The results implied that both species distributions might be affected by both reactions to the underlying land-use pattern, but also by interaction with neighbours. The use of the spatial probit model is a way to incorporate spatial interactions that otherwise cannot be captured by the independent variables.     

分形及其在植物研究中的应用

本文着重介绍了非线性科学热点之一的分形理论,并综述了分形理论在植物结构模拟、植物群落研究、景观格局研究、树木冠层特征研究、木材学研究、作物根系研究等方面的应用进展以及分维数求算方法研究进展,最后,对非线性理论在植物研究领域应用前景进行了展望。     

Fractal dimension of humic acids

Small-angle neutron scattering experiments have been made on solutions of humic acid aggregates with an acidity corresponding to pH 5.0 and at 0.1 M ionic strength. We observe power-law decay of the intensity over one decade of the scattering vector, Q, indicating that the aggregates are fractal. We explain the normalized intensity in the entire Q-range by assuming that the humic acid particles can be described by building units of a radial size, 25 Å, aggregated into clusters with an average radius of 400–500 Å. For humic acids obtained from two different sources, we determine the fractal dimension, D = 2.3 ± 0.1. For small values of Q, the measured data of one of the samples extend into the Guinier range giving an average radius of gyration of 320 ± 20 Å. Correspondence to: R. Österberg     

Multi-scale variation in spatial heterogeneity for microbial community structure in an eastern Virginia agricultural field

To better understand the distribution of soil microbial communities at multiple spatial scales, a survey was conducted to examine the spatial organization of community structure in a wheat field in eastern Virginia (USA). Nearly 200 soil samples were collected at a variety of separation distances ranging from 2.5 cm to 11 m. Whole-community DNA was extracted from each sample, and community structure was compared using amplified fragment length polymorphism (AFLP) DNA fingerprinting. Relative similarity was calculated between each pair of samples and compared using geostatistical variogram analysis to study autocorrelation as a function of separation distance. Spatial autocorrelation was found at scales ranging from 30 cm to more than 6 m, depending on the sampling extent considered. In some locations, up to four different correlation length scales were detected. The presence of nested scales of variability suggests that the environmental factors regulating the development of the communities in this soil may operate at different scales. Kriging was used to generate maps of the spatial organization of communities across the plot, and the results demonstrated that bacterial distributions can be highly structured, even within a habitat that appears relatively homogeneous at the plot and field scale. Different subsets of the microbial community were distributed differently across the plot, and this is thought to be due to the variable response of individual populations to spatial heterogeneity associated with soil properties.     

Identifying spatial patterns in the tropical rain forest structure using hemispherical photographs

This work emphasises the usefulness of hemispherical photography for identifying spatial patterns in the tropical rain forest structure. Structural variability was investigated at a local (intra-site) scale, in relation to the forest mosaic, and at a regional (inter-sites) scale, for its implication in forest typology. Four primary forest sites, from 0.6 to 1 ha, were investigated in Central Sumatra, Indonesia.In a first instance, a qualitative analysis of the forest 3-D structure was found to be very helpful in the interpretation of quantitative results related to forest dynamics. The quantitative analysis was undertaken through the assessment of three structural characteristics: (1) the canopy openness (CO), or visible sky as seen from all directions of the hemisphere, (2) the spherical variance (SV), which quantifies the spatial dispersion of gaps and, (3) the plant area index (L_p), defined as half the surface area of canopy elements per unit ground area. At the local scale, maps of the CO values gave an indication about disturbance location and extent, providing an interesting document for studies on forest dynamics. At the regional scale, between-sites comparisons of CO, SV and L_p values added new information on forest structural differences when compared to dendrometric measurements. These results emphasised the fact that rain forest may exhibit high structural variability, even within a same bioclimatic region and a narrow altitude range. Hemispherical photographs could be a quick means of further investigating this spatial variability and it's relation to physical environment, thus providing information that is crucial for the refining of forest typology in the area.     

基于分形理论的木材顺纹理断裂研究

研究5种木材顺纹理断裂性质和断面分形特征,测量断口表面的分形维数,建立了分形维数与断裂韧性间的关系.研究结果表明：（1）不同树种因其构造差异对裂纹扩展的阻力不同,这种差异同样也表现在材料断裂表面的形貌特征上;（2）木材顺纹理断裂韧性K（IC）^（TL）与分形维数D之间有很高的正比关系：y=0.036x＋2.162,（R^2=0.98）,揭示了断口分形维数与材料性能之间的内在联系.     

基于盒维数的心音信号分形特征研究

在传统盒维数的基础上,从尺度变化的角度,提出一种计算心音信号时域波形分形维数的新的二进盒维数算法,并给出了算法思想和估算方法;然后用该方法对正常心音和几种典型的病态心音的分形维数进行计算,并对其分形特征进行了研究．研究结果表明：心音信号具有明显的分形特征,分形维数能够反映心音信号的复杂程度,并且能够明显地区分正常心音和病态心音．     

Extinction threshold for spatial forest dynamics with height structure

We present a pair-approximation model for spatial forest dynamics defined on a regular lattice. The model assumes three possible states for a lattice site: empty (gap site), occupied by an immature tree, and occupied by a mature tree, and considers three nonlinearities in the dynamics associated to the processes of light interference, gap expansion, and recruitment. We obtain an expression of the basic reproduction number R₀ which, in contrast to the one obtained under the mean-field approach, uses information about the spatial arrangement of individuals close to extinction. Moreover, we analyze the corresponding survival-extinction transition of the forest and the spatial correlations among gaps, immature and mature trees close to this critical point. Predictions of the pair-approximation model are compared with those of a cellular automaton.     

Factors influencing the spatial distribution of forest plant species in hedgerows of North-western Germany

In North-western Germany woodland fragmentation has caused a decline in many forest plant species. Hedgerows partly offer a similar environment as forests and have been identified as potential habitats for forest plants in various studies from North America and Western Europe. The objective of this study was to examine whether this applies also to Central Europe and which variables affect the spatial distribution and abundance of forest plant species in hedgerows on a local scale. Three hedgerow networks north of the city of Bremen, Germany, were selected as study areas and divided into totally 515 hedgerow segments. In each segment we recorded all vascular plants and a large number of explanatory variables relating to structure, spatial configuration, environment and management. Averaged across species there was a predominant effect of environmental factors on the occurrence of forest species in the hedgerows, followed by spatial configuration and management. Hedgerow structure was found to be less important. In general, forest species were favored by low nutrient and light availability as well as high connectivity with other hedgerows or forest; they avoided hedgerows with a west-easterly orientation and an adjacent land use in the form of fields or grasslands. Forest species found and not found in hedgerows did not differ in their environmental preferences or life history traits. The number of threatened forest species in the hedgerows, however, was lower than expected with respect to their overall proportion to the total number of forest species in the region.     

A geostatistical analysis of small-scale spatial variability in bacterial abundance and community structure in salt marsh creek bank sediments

Small-scale variations in bacterial abundance and community structure were examined in salt marsh sediments from Virginia's eastern shore. Samples were collected at 5 cm intervals (horizontally) along a 50 cm elevation gradient, over a 215 cm horizontal transect. For each sample, bacterial abundance was determined using acridine orange direct counts and community structure was analyzed using randomly amplified polymorphic DNA fingerprinting of whole-community DNA extracts. A geostatistical analysis was used to determine the degree of spatial autocorrelation among the samples, for each variable and each direction (horizontal and vertical). The proportion of variance in bacterial abundance that could be accounted for by the spatial model was quite high (vertical: 60%, horizontal: 73%); significant autocorrelation was found among samples separated by 25 cm in the vertical direction and up to 115 cm horizontally. In contrast, most of the variability in community structure was not accounted for by simply considering the spatial separation of samples (vertical: 11%, horizontal: 22%), and must reflect variability from other parameters (e.g., variation at other spatial scales, experimental error, or environmental heterogeneity). Microbial community patch size based upon overall similarity in community structure varied between 17 cm (vertical) and 35 cm (horizontal). Overall, variability due to horizontal position (distance from the creek bank) was much smaller than that due to vertical position (elevation) for both community properties assayed. This suggests that processes more correlated with elevation (e.g., drainage and redox potential) vary at a smaller scale (therefore producing smaller patch sizes) than processes controlled by distance from the creek bank.     

Mapping tropical forest fractional cover from coarse spatial resolution remote sensing imagery

At regional to global scales the only feasible approach to mapping and monitoring forests is through the use of coarse spatial resolution remotely sensed imagery. Significant errors in mapping may arise as such imagery may be dominated by pixels of mixed land cover composition which cannot be accommodated by conventional mapping approaches. This may lead to incorrect assessments of forest extent and thereby processes such as deforestation which may propagate into studies of environmental change. A method to unmix the class composition of image pixels is presented and used to map tropical forest cover in part of the Mato Grosso, Brazil. This method is based on an artificial neural network and has advantages over other techniques used in remote sensing. Fraction images depicting the proportional class coverage in each pixel were produced and shown to correspond closely to the actual land cover. The predicted and actual forest cover were, for instance, strongly correlated (up to r = 0.85, significant at the 99% level of confidence) and the predicted extent of forest over the test site much closer to the actual extent than that derived from a conventional approach to mapping from remotely sensed imagery.