Hierarchical spatial structure in soft-bottom mussel beds

Mussels (Mytilus edulis L.) are unusual because they thrive in both rocky shore and soft-bottom habitats. Despite their ecological and economic importance, little is known about their spatial structure. Mussels do not generally recruit to bare soft substrate because larvae and postlarvae cannot attach to a bottom of small sediment particles. They attach to hard objects on the sediment surface (especially other mussels), so soft-bottom mussel beds may be spatially organized in ways that are fundamentally different from those on rocky shores. The purpose of our study was to characterize the scales of spatial variability for several mussel abundance parameters in soft-bottom, intertidal M. edulis beds in coastal Maine. We used a random factor nested-ANOVA design of 200 cm² Cores within 1 m² Quadrats within 6 m Transects within Positions within bed Sites along 70 km (euclidean distance) of the Maine coast. Based on the literature and our field observations, we hypothesized that Sites and Positions account for most of the spatial variance in soft-botttom mussel beds. We rejected this hypothesis. Sites and Positions were not important in explaining variation in total mussel density, density of new recruits, or density of larger mussels. Although most of the variance in surface silt-clay fraction did occur at these levels, most mussel variation occurred at smaller spatial scales, specifically at the Quadrat scale for new recruits and total mussels and at the Transect scale for larger mussels. Variance in mussel parameters was not closely linked to the silt-clay fraction of surface sediment or to Site rankings of wind exposure and tidal flow. Variance in total mussel density was due primarily to variance in recruitment. No single scale explained more than about half the mussel variance, and no single scale was best at explaining all the mussel parameters. Greater knowledge about mussel bed spatial variability would be useful because it can help direct scale-dependent sampling regimes, field experiments, and coastal management practices.     

毛乌素沙地沙生半灌木群落的空间异质性

在使用 5m× 50 0 0 m样带进行调查获得的植被盖度数据的基础上 ,通过半方差分析和分形分析揭示了毛乌素沙化草地沙生半灌木群落植被盖度的空间变异特点。半方差分析揭示出植被盖度的多尺度变异和等级斑块结构 ,在取样范围内至少存在着 3个等级。分形分析得出毛乌素沙地沙生半木群落植被盖度的分维 D=1 .90 ,接近于 2 ,指示着大部分空间变异发生在较小的尺度上 ;分段分形分析得出不同尺度范围内的分维 ,反映了空间异质性的多尺度变异性。这一结果揭示了荒漠化过程引起的生境破碎化     

Local native plant diversity responds to habitat loss and fragmentation over different time spans and spatial scales

Separating the threats that habitat loss and habitat fragmentation pose to biodiversity is challenging because these processes usually occur simultaneously. Additionally, their importance may be underestimated due to time-delayed extinction. In central Texas savannas, woody plant encroachment reduces the amount of habitat available to herbaceous species while fragmenting remaining habitat. We examined the relationships between present species richness and present and past habitat amount and fragmentation (measured as fractal dimension) using a series of aerial photographs taken over nearly 60 years. We show that woody plant encroachment, a common phenomenon in savannas worldwide, reduces the diversity of herbaceous vegetation through both habitat loss and fragmentation. Habitat loss has the strongest impact on species richness over short time spans and small spatial scales in these savannas. Habitat fragmentation, however, has the strongest impact over longer time spans and larger spatial scales and generates long-term extinction debts. We also demonstrate that examining habitat loss and habitat fragmentation across different time periods and at different spatial scales is essential for understanding their joint and individual effects on plant community composition.     

Mussels matter: postlarval dispersal dynamics altered by a spatially complex ecosystem engineer

This study investigated postlarval dispersal of soft-bottom macrofauna at a spatially complex intertidal mudflat comprising patches of bare sediment and an ecosystem engineer, the mussel Mytilus edulis. At each of four sites in Guard Point Cove, Maine, USA, we took core samples and deployed bedload traps in bare sediment and mussel bed habitats to estimate ambient densities, rates of sediment flux, and several measures of postlarval dispersal. Univariate and multivariate nonmetric multidimensional scaling (nMDS) results showed few significant site effects and no habitat×site interactions. In contrast, there were numerous significant habitat effects. Compared to the bare sediment, the mussel bed habitat had: fewer species; higher ambient density and proportional abundance of the oligochaete Tubificoides benedeni (the dominant species in both habitats); lower ambient densities and proportional abundances of major taxa and the nonoligochaetes as a group; and higher sediment flux and relative (i.e., per capita) dispersal of nonoligochaetes. Macrofauna species dispersed in relative proportions that were different from those in the ambient assemblage. Per capita T. benedeni transport rates were low in mussel beds compared to those for nonoligochaetes, consistent with the view that beds represent favorable habitat for oligochaetes. The number of total macrofauna individuals trap⁻¹ day⁻¹ was negatively correlated with ambient density and positively correlated with sediment flux in both habitats, but these relationships were significant only in the mussel bed. The results indicate that altered transport rates of sediment and postlarvae are important mechanisms by which mussels act as ecosystem engineers to modify soft-bottom habitats. Differential transport rates caused by aggregations of mussels and other foundation species must be considered in explanations of spatial pattern in soft-bottom communities.     

The area-independent effects of habitat complexity on biodiversity vary between regions

Potential explanatory variables often co‐vary in studies of species richness. Where topography varies within a survey it is difficult to separate area and habitat‐diversity effects. Topographically complex surfaces may contain more species due to increased habitat diversity or as a result of increased area per se. Fractal geometry can be used to adjust species richness estimates to control for increases in area on complex surfaces. Application of fractal techniques to a survey of rocky shores demonstrated an unambiguous area‐independent effect of topography on species richness in the Isle of Man. In contrast, variation in species richness in south‐west England reflected surface availability alone. Multivariate tests and variation in limpet abundances also demonstrated regional variation in the area‐independent effects of topography. Community composition did not vary with increasing surface complexity in south‐west England. These results suggest large‐scale gradients in the effects of heterogeneity on community processes or demography.     

Does macrophyte fractal complexity drive invertebrate diversity,biomass and body size distributions?

Habitat structure is one of the fundamental factors determining the distribution of organisms at all spatial scales, and vegetation is of primary importance in shaping the structural environment for invertebrates in many systems. In the majority of biotopes, invertebrates live within vegetation stands of mixed species composition, making estimates of structural complexity difficult to obtain. Here we use fractal indices to describe the structural complexity of mixed stands of aquatic macrophytes, and these are employed to examine the effects of habitat complexity on the composition of free-living invertebrate assemblages that utilise the habitat in three dimensions. Macrophytes and associated invertebrates were sampled from shallow ponds in southwest England, and rapid digital image analysis was used to quantify the fractal complexity of all plant species recorded, allowing the complexity of vegetation stands to be reconstructed based on their species composition. Fractal indices were found to be significantly related to both invertebrate biomass–body size scaling and overall invertebrate biomass; more complex stands of macrophytes contained a greater number of small animals. Habitat complexity was unrelated to invertebrate taxon richness and macrophyte surface area and species richness were not correlated with any of the invertebrate community parameters. The biomass–body size scaling relationship of lentic macroinvertebrates matched those predicted by models incorporating both allometric scaling of resource use and the fractal dimension of a habitat, suggesting that both habitat fractal complexity and allometry may control density–body size scaling in lentic macroinvertebrate communities.     

Large-Scale Spatial Dynamics of Intertidal Mussel (Mytilus edulis L.) Bed Coverage in the German and Dutch Wadden Sea

Intertidal blue mussel beds are important for the functioning and community composition of coastal ecosystems. Modeling spatial dynamics of intertidal mussel beds is complicated because suitable habitat is spatially heterogeneously distributed and recruitment and loss are hard to predict. To get insight into the main determinants of dispersion, growth and loss of intertidal mussel beds, we analyzed spatial distributions and growth patterns in the German and Dutch Wadden Sea. We considered yearly distributions of adult intertidal mussel beds from 36 connected tidal basins between 1999 and 2010 and for the period 1968–1976. We found that in both periods the highest coverage of tidal flats by mussel beds occurs in the sheltered basins in the southern Wadden Sea. We used a stochastic growth model to investigate the effects of density dependence, winter temperature and storminess on changes in mussel bed coverage between 1999 and 2010. In contrast to expectation, we found no evidence that cold winters consistently induced events of synchronous population growth, nor did we find strong evidence for increased removal of adult mussel beds after stormy winter seasons. However, we did find synchronic growth within groups of proximate tidal basins and that synchrony between distant groups is mainly low or negative. Because the boundaries between synchronic groups are located near river mouths and in areas lacking suitable mussel bed habitat, we suggest that the metapopulation is under the control of larval dispersal conditions. Our study demonstrates the importance of moving from simple habitat suitability models to models that incorporate metapopulation processes to understand spatial dynamics of mussel beds. The spatio-dynamic structure revealed in this paper will be instrumental for that purpose.     

Contrasting spatial heterogeneity of sessile organisms within mussel (Perna perna L.) beds in relation to topographic variability

We examined the spatial heterogeneity in three sessile rocky shore organisms, the mussel Perna perna, the barnacle Octomeris angulosa (Sowerby) and the red alga Gelidium pristoides (Turn.) at a range of continuous local scales along horizontal transects within mid- and upper mussel beds of South African shores. We also examined the relationships between variability of organisms and topographic features (rock depressions, slope, aspect), and between mussel, barnacle and algal variability over the same scales. To estimate spatial heterogeneity, we analyzed scaling properties of semivariograms using a fractal approach. Relationships between different variables at the different scales were examined by cross-semivariograms. Spatial dependence of P. perna variability increased with spatial dependence of topographic variability, so that scaling regions of mussel and topographic distributions corresponded well. This relationship often improved with larger local scales (mussel cover increased with depressions, steeper slope and aspect towards waves), while at smaller spatial scales, variability in mussel cover was less well explained by variability in topography. The variability of the barnacle O. angulosa exhibited spatial dependence, even on topographically unstructured shores. In contrast, the distribution of the alga G. pristoides revealed high fractal dimensions, showing spatial independence on topographically unstructured shores. Algae also showed a very strong negative relationship with mussels at most local scales, and a negative relationship with barnacles in upper zones, especially at larger local scales. Barnacles may show clear spatial dependence because of hydrodynamics (at larger local scales) and the need to find a future mate in close proximity (at smaller local scales), while algae may show a strong negative relationship with mussels because of competition for space.     

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.     

恢复演替中草地斑块动态及尺度转换分析

研究了９ａ草地恢复油潜系列中斑块边界形状和斑块面积分布动态,并进行了凡度转换分析。獐茅斑块的边界分维数和斑块化指数最高,羊草斑块的较低,碱蓬斑块的斑块化指数略小于羊草斑块,边界分维数大于洋草斑块。共他类型斑块的两种指数基本上介于獐茅斑块之间,斑块化指数的年限变动滞后于斑块边界分维数,斑块边发维数在整个试验的尺度范围内符合同一自相似规律,斑块的面积分布格局在不同的尺度上有不同的自相似规律。     

The use of fractal image statistics in the estimation of lateral spatial extent

It has been argued that the characteristics of many commonly occurring surface textures are such that the resulting luminance distributions have the statistical properties of fractals, over a wide range of spatial scales. We show that, when fractal luminance distributions are spatially filtered, the spatial density of zero-crossings obtained is inversely proportional to the scale of filtering, and is not strongly dependent on the fractal dimension of the pattern used. We propose that this predictable property of natural images could provide a basis for the estimation of lateral spatial extent by counting zero-crossings within an interval at a variety of spatial scales, and averaging over spatial scale. We carried out experiments to compare the relative apparent lateral extents of fractal patterns and patterns of equally spaced bars, as a function of the number of bars. The results are in good agreement with theory.     

Using animal movement paths to measure response to spatial scale

Animals live in an environment that is patchy and hierarchical. I present a method of detecting the scales at which animals perceive their world. The hierarchical nature of habitat causes movement path structure to vary with spatial scale, and the patchy nature of habitat causes movement path structure to vary throughout space. These responses can be measured by a combination of path tortuousity (measured with fractal dimension) versus spatial scale, the variation in tortuousity of small path segments along the movement path, and the correlation between tortuousities of adjacent path segments. These statistics were tested using simulated animal movements. When movement paths contained no spatial heterogeneity, then fractal D and variance continuously increased with scale, and correlation was zero at all scales. When movement paths contained spatial heterogeneity, then fractal D sometimes showed a discontinuity at transitions between domains of scale, variation showed peaks at transitions, and correlations showed a statistically significant positive value at scales smaller than patch size, decreasing to below zero at scales greater than patch size. I illustrated these techniques with movement paths from deer mice and red-backed voles. These new analyses should help understand how animals perceive and react to their landscape structure at various spatial scales, and to answer questions about how habitat structure affects animal movement patterns.     

Fine-scale spatial patterns in populations of the clonal moss Hylocomium splendens partly reflect structuring processes in the boreal forest floor

Spatial patterns of important population or individual characteristics are expected to reflect structuring ecosystem processes to the extent that populations with strikingly different spatial patterns most likely have been structured by different processes. Few studies of spatial pattern in plant assemblages, bryophyte assemblages in particular, still exist and pattern has only vaguely been linked with process. In this study we describe fine-scale spatial variation in size and the occurrence of terminated (non-branching) segments in 21 Norwegian populations of the dominant boreal forest moss Hylocomium splendens, in search for general patterns of spatial structure. All Hylocomium splendens segments in the investigated plots were followed for a 10-year period; their size (dry mass, estimated from in situ measurements) and fate (terminated or ramifying) were recorded annually. The spatial structure of size and terminating segments at scales from 0.5 to 16 cm was described for each population as fractal dimension profiles, derived from semi-variograms. For about one half of the populations size and terminating segments could be assigned to a specific spatial pattern, the predicted outcome of one of three main structuring processes: (i) negative spatial dependence (fractal dimension F>3.0) on the scale of individuals (below 2 cm), indicative of negative interactions; (ii) positive spatial dependence (F<3.0) on the scale of individuals, indicative of positive interactions; and (iii) positive spatial dependence on broader (4–8 cm) scales, indicative of structuring by environmental factors or patchy disturbance. Patterns (i) and (iii) were observed both for size and terminated segments more often than expected. Fractal dimension profiles for size obtained separately for each year revealed temporal patterns of spatial structure that tended to be invariant over years. Negative spatial dependence of size, possibly due to large size difference between buried segments and other segments during self thinning, was typical of populations rapidly growing in number. Positive spatial dependence with a range of influence by the spatial process of 4–8 cm was observed in plots with sparse bryophyte cover and high cover of deciduous litter, probably due to accumulation of litter in depressions between shoots or groups of shoots. The main finding of this study is that different populations of the same species in the same type of ecosystem can be spatially structured in different ways. This accords with a model for the studied system as consisting of a mosaic of cells, of spatial extent of a few cm or larger, intergrading in space and temporally dynamic, the population characteristics of each cell being shaped by several structuring processes that vary, temporally and spatially, in their relative importance.     

Influence of aquatic macrophyte habitat complexity on invertebrate abundance and richness in tropical lagoons

1. Aquatic plants are a key component of spatial heterogeneity in a waterscape, contributing to habitat complexity and helping determine diversity at various spatial scales. Theoretically, the more complex a habitat, the higher the number of species present. 2. Few empirical data are available to test the hypothesis that complexity increases diversity in aquatic communities (e.g. Jeffries, 1993 ). Fractal dimension has become widely applied in ecology as a tool to quantify the degree of complexity at different scales. 3. We investigated the hypothesis that complexity in vegetated habitat in two tropical lagoons mediates littoral invertebrate number of taxa (S) and density (N). Aquatic macrophyte habitat complexity was defined using a fractal dimension and a gradient of natural plant complexities. We also considered plant area, plant identity and, only for S, invertebrate density as additional explanatory variables. 4. Our results indicate that habitat complexity provided by the different architectures of aquatic plants, significantly affects both S and total N. However, number of individuals (as a result of passive sampling) also helps to account for S and, together with plant identity and area, contributes to the determination of N. We suggest that measurements of structural complexity, measured through fractal geometry, should be included in studies aimed at explaining attributes of attached invertebrates at small (e.g. plant or leaf) scales.     

遗传算法支持下土地利用空间分形特征尺度域的识别

针对土地利用空间分形特征只存在于有限尺度域的现象,采用无标度区内离散点拟合的离差平方和平均值最小作为目标函数,提出了一种基于遗传算法的土地利用空间分形特征尺度域的识别方法,用于准确计算分形维数的有效区间范围。以武汉市武昌区水域空间分形特征为例,利用Quickbird多光谱遥感影像提取土地利用空间信息,重点讨论了基于遗传算法识别土地利用空间分形特征尺度域范围的总体思路、适应度函数和遗传算子等环节;然后分别从测定系数、标准差和无标度区间3个角度,将其同人工判断法、相关系数法以及强化系数法进行对比讨论;并结合研究区域实际的水域空间分布格局,分析不同方法计算所得半径维数的合理性。结果表明,土地利用分形特征尺度域的范围对分形维数计算结果有较大影响;相对于传统计算方法来说,遗传算法在尺度无标度区间识别上具有更高的精度,可以为土地利用空间格局分形特征的研究提供客观指导意见。     

Spatial patterns and scaling behaviors of Steller sea lion (Eumetopias jubatus) distributions and their environment

Fractal geometry and other multi-scale analyses have become popular tools for investigating spatial patterns of animal distributions in heterogeneous environments. In theory, changes in patterns of animal distributions with changes in scale reflect transitions between the controlling influences of one environmental factor or process over another. In an effort to find linkages between Steller sea lions (Eumetopias jubatus) and their environment, the objective of this study was to determine if the spatial distribution of Steller sea lions at sea displayed similar scaling properties to the variation of two environmental features, including bathymetry and sea surface temperature (SST). Additionally, distributions of Steller sea lion point patterns were examined with respect to measurements of bathymetric complexity. From February 2000 to May 2004, satellite transmitters were deployed on 10 groups of juvenile Steller sea lions (n=52) at eight different locations within the Aleutian Islands and Gulf of Alaska. Indices of fractal dimension were calculated for each group of sea lions using a unit square box-counting method, whereas indices of bathymetry and SST patchiness were derived by conducting a variance ratio analysis over the same scales. Distributions of Steller sea lions at sea displayed self-similar fractal patterns, suggesting that individuals were distributed in a continuous hierarchical set of clumps within clumps across scales, and foraging behavior was likely influenced by a scale invariant mechanism. Patterns of bathymetric variability also were self-similar, whereas patterns of SST variability were scale dependent and failed to retain self-similar spatial structure at larger scales. These results indicate that the distributions of Steller sea lions at sea were more influenced by bathymetry than SST at the scales examined, but scale-dependent patterns in the distribution of Steller sea lions at sea or linkages with SST may have been apparent if analyses were conducted at finer spatial scales.     

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。     

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。     

Large scale patterns in mussel beds: stripes or spots?

Journal of Mathematical Biology - An aerial view of an intertidal mussel bed often reveals large scale striped patterns aligned perpendicular to the direction of the tide; dense bands of mussels...     

Scale-dependent foraging and patch choice in fractal environments

Many spatially complex environments are fractal, and consumers in these environments face scale-dependent trade-offs between encountering high densities of small resource patches versus low densities of large resource patches. I address the effects of these trade-offs on foraging by incorporating scale-dependent encounter of resources in fractal landscapes into classical optimal foraging theory. This model is then used to predict optimal scales of perception (foraging scale) and patch choice in response to spatial features of landscapes. The model predicts that, for a given density of resources, landscapes with greater extent and fractal dimension and that contain patchy (low fractal dimension) resources favour large foraging scales and specialization on a small proportion of resource patches. Fragmented (low fractal dimension) landscapes of small extent with dispersed (high fractal dimension) resources favour smaller foraging scales and generalists that use a large proportion of available resource patches. These predictions synthesize the results of other spatially explicit consumer–resource models into a simple framework and agree reasonably well with results of several empirical studies. This study thus places optimal foraging theory in a spatial context and suggests evolutionary mechanisms of consumers' responses to important spatial phenomena (e.g. habitat fragmentation, resource aggregation). This revised version was published online in July 2006 with corrections to the Cover Date.