Foraging in nature: Contrasting responses to resource heterogeneity at small‐ and large‐spatial scales

A key problem faced by foragers is how to forage when resources are distributed heterogeneously in space. This heterogeneity and associated trade‐offs may change with spatial scale. Furthermore, foragers may also have to optimize acquiring multiple resources. Such complexity of decision‐making while foraging is poorly understood. We studied the butterfly Ypthima huebneri to examine how foraging decisions of adults are influenced by spatial scale and multiple resources. We predicted that, at a small‐spatial scale, the time spent foraging in a patch should be proportional to resources in the patch, but at large‐spatial scales, due to limitations arising from large travel costs, this relationship should turn negative. We also predicted that both adult and larval resources should jointly affect foraging butterflies. To test these predictions, we laid eleven plots and sub‐divided them into patches. We mapped nectar and larval resources and measured butterfly behavior in these patches and plots. We found that adult foraging behavior showed contrasting relationships with adult resource density at small versus large‐spatial scales. At the smaller‐spatial scale, butterflies spent more time feeding in resource‐rich patches, whereas at the large‐scale, butterflies spent more time feeding in resource‐poor plots. Furthermore, both adult and larval resources appeared to affect foraging decisions, suggesting that individuals may optimize search costs for different resources. Overall, our findings suggest that the variation in foraging behavior seen in foragers might result from animals responding to complex ecological conditions, such as resource heterogeneity at multiple spatial scales and the challenges of tracking multiple resources.     

Spatial pattern of distribution of marine invertebrates within a subtidal community: do communities vary more among patches or plots?

Making links between ecological processes and the scales at which they operate is an enduring challenge of community ecology. Our understanding of ecological communities cannot advance if we do not distinguish larger scale processes from smaller ones. Variability at small spatial scales can be important because it carries information about biological interactions, which cannot be explained by environmental heterogeneity alone. Marine fouling communities are shaped by both the supply of larvae and competition for resources among colonizers—these two processes operate on distinctly different scales. Here, we demonstrate how fouling community structure varies with spatial scale in a temperate Australian environment, and we identify the spatial scale that captures the most variability. Community structure was quantified with both univariate (species richness and diversity) and multivariate (similarity in species composition) indices. Variation in community structure was unevenly distributed between the spatial scales that we examined. While variation in community structure within patch was usually greater than among patch, variation among patch was always significant. Opportunistic taxa that rely heavily on rapid colonization of free space spread more evenly among patches during early succession. In contrast, taxa that are strong adult competitors but slow colonizers spread more evenly among patches only during late succession. Our findings show significant patchiness can develop in a habitat showing no systematic environmental spatial variation, and this patchiness can be mediated through different biological factors at different spatial scales.     

A negative heterogeneity–diversity relationship found in experimental grassland communities

Recent meta-analyses and simulation studies have suggested that the relationship between soil resource heterogeneity and plant diversity (heterogeneity–diversity relationship; HDR) may be negative when heterogeneity occurs at small spatial scales. To explore different mechanisms that can explain a negative HDR, we conducted a mesocosm experiment combining a gradient of soil nutrient availability (low, medium, high) and scale of heterogeneity (homogeneous, large-scale heterogeneous, small-scale heterogeneous). The two heterogeneous treatments were created using chessboard combinations of low and high fertility patches, and had the same overall fertility as the homogeneous medium treatment. Soil patches were designed to be relatively larger (156 cm²) and smaller (39 cm²) than plant root extent. We found plant diversity was significantly lower in the small-scale heterogeneous treatment compared to the homogeneous treatment of the same fertility. Additionally, low fertility patches in the small-scale heterogeneous treatment had lower diversity than patches of the same size in the low fertility treatment. Shoot and root biomass were larger in the small-scale heterogeneous treatment than in the homogeneous treatment of the same fertility. Further, we found that soil resource heterogeneity may reduce diversity indirectly by increasing shoot biomass, thereby enhancing asymmetric competition for light resources. When soil resource heterogeneity occurs at small spatial scales it can lower plant diversity by increasing asymmetric competition belowground, since plants with large root systems can forage among patches and exploit soil resources. Additionally, small-scale soil heterogeneity may lower diversity indirectly, through increasing light competition, when nutrient uptake by competitive species increases shoot biomass production.     

Interactions between neighboring algae and snail grazing in structuring microdistribution patterns of periphyton

The micro-distribution of periphyton (filamentous algae) on homogeneous substrates was examined in experimental tanks with and without the pressure of grazing snails. The growth of periphyton attached to artificial substrate was estimated at a small spatial scale (9.3 mm×9.3 mm cells) by varying the number of grazers (0, 5, or 10 snails per tank), using image processing analysis without removing the periphyton. The results suggest that periphyton growth within a cell was negatively affected by the biomass of periphyton in the cell but was positively affected by the biomass of periphyton in neighboring cells. A semivariogram analysis indicated that spatial heterogeneity increased with increasing grazing pressure. The size of patches was not clearly related to the number of snails, but there was a tendency for relative patch size to increase with snail density. Computer simulations were also conducted to examine factors affecting the degree of spatial heterogeneity. The simulation studies indicated that snails should graze a site that was previously grazed in order to produce the observed spatial heterogeneity of periphyton. The results also indicated that the positive effects of neighboring periphyton on the growth of algae might create patches. The interactions among neighboring algae and snail grazing might be an important factor creating the spatial heterogeneity of periphyton even on homogeneous substrates.     

Environmental heterogeneity,species diversity and co‐existence at different spatial scales

The positive relationship between spatial environmental heterogeneity and species diversity is a widely accepted concept, generally associated with niche limitation. However, niche limitation cannot account for negative heterogeneity–diversity relationships (HDR) revealed in several case studies. Here we explore how HDR varies at different spatial scales and provide novel theories for small‐scale species co‐existence that explain both positive and negative HDR. At large spatial scales of heterogeneity (e.g. landscape level), different communities co‐exist, promoting large regional species pool size and resulting in positive HDR. At smaller scales within communities, species co‐existence can be enhanced by increasing the number of different patches, as predicted by the niche limitation theory, or alternatively, restrained by heterogeneity. We conducted meta‐regressions for experimental and observational HDR studies, and found that negative HDRs are significantly more common at smaller spatial scales. We propose three theories to account for niche limitation at small spatial scales. (1) Microfragmentation theory: with increasing spatial heterogeneity, large homogeneous patches lose area and become isolated, which in turn restrains the establishment of new plant individuals and populations, thus reducing species richness. (2) Heterogeneity confounded by mean: when heterogeneity occurs at spatial scales smaller than the size of individual plants, which forage through the patches, species diversity can be either positively or negatively affected by a change in the mean of an environmental factor. (3) Heterogeneity as a separate niche axis: the ability of species to tolerate heterogeneity at spatial scales smaller than plant size varies, affecting HDR. We conclude that processes other than niche limitation can affect the relationship between heterogeneity and diversity.     

Scaling up from local competition to regional coexistence across two scales of spatial heterogeneity: insect larvae in the fruits of <Emphasis Type="Italic">Apeiba membranacea</Emphasis>

Species that live in patchy and ephemeral habitats can compete strongly for resources within patches at a small scale. The ramifications of these interactions for population dynamics and coexistence at regional scales will depend on the intraspecific and interspecific distributions of individuals among patches. Spatial heterogeneity due to independent aggregation of competitors among patchy habitats is an important mechanism maintaining species diversity. I describe regional patterns of aggregation for four species of insect larvae in the fruits of Apeiba membranacea, a Neotropical rainforest tree. This aggregation results from variation in densities at a small scale (among the fruits under a single tree), compounded by significant variation among trees in both mean densities and degrees of aggregation. Both the degrees of aggregation and mean densities are statistically independent within and across species at both spatial scales. I evaluate the regional consequences of these spatial patterns by using maximum likelihood methods to parameterize a model that includes both explicit measures of the strength of competition and spatial variation at both within- and among-tree spatial scales. Despite strong competitive interactions among these species, during 2 years the observed spatial variation at both scales combined was sufficient to explain the coexistence of these species, although other coexistence mechanisms may also operate simultaneously. The observed spatial variation at small spatial scales may not be sufficient for coexistence, indicating the importance of considering multiple sources of spatial heterogeneity when scaling up from experiments that investigate local interactions to regional patterns of coexistence.     

华南海岸英罗港红树植物木榄种群结构的空间异质性

采用位置指数(CE)、分异指数(TC和TH)、Shannon-Wiener多样性指数(D)以及Ripley的K-方程,探讨了华南海岸英罗港树植物木榄种群的分布格局、胸转和树高分异以及冠层结构方面的空间异质性.多数种群呈现随机分布,其个体胸转和树高的分异程度较低;页少数种群呈现集群分布,其个体胸围和树高的分异程度明显.采用地理信息(GIS)对冠层和空隙斑块进行了多种水平垂直尺度的分析,冠层与空隙斑块之间的镶嵌格局因种群而异,这种可基于树冠抽影用Shannon-wiener多样性指数时行定量描述.冠层结构的窨异质性阻碍空间尺度而变化,但这种变化在一定尺度范围内保持相对的稳定.迷一尺度范围可作为木榄红树森更新或生态管理单位的参考尺度.     

华南海岸英罗港红树植物木榄种群结构的空间异质性(英文)

The spatial heterogeneity, including distribution pattern, tree perimeter and height differentiation, and canopy structure heterogeneity, of Bruguiera gymnorrhiza (L.) Lamk populations at Yingtuo Bay, South-China Coast was investigated using the positioning index (CE), differentiation index (TC and TH), Shannon-Wiener diversity index (D), and Ripley‘s K-functions. Most populations showed random distribution and low differentiation in perimeters and heights of individuals, while a few showed clumped distribution and clear differentiation. Canopy and gap patches were analyzed at multiple horizontal and vertical scales using geographic information system (GIS). The mosaic patterns of canopy and gap patches are different among populations, and could be quantitatively described with the Shannon-Wiener diversity index based on crown projection. The spatial heterogeneity of the canopy structure changed with spatial scales, but this kind of change would remain relatively stable over a range of scales. This scale range could be regarded as the referenced scale for a regeneration or ecological management unit for the forest.     

Is fruit size important in the selection of oviposition sites by cranberry fruitworm,Acrobasis vaccinii?

Under laboratory conditions, females of Acrobasis vaccinii (Riley) (Lepidoptera: Pyralidae) oviposit significantly more often on larger than on smaller cranberry fruit. This behaviour ensures that neonate larvae have access to maximum resources and are larger when moving to the next fruit. However, while there is some evidence that on a large spatial scale females may lay eggs in patches of larger fruit, there was no evidence of such an oviposition preference within patches in natural bogs. These results may be explained by the fact that the oviposition period for A. vaccinii begins early in the cranberry season, before fructification is completed, leading to potential competition among females for the first fruit present in the environment. Laying eggs on the first fruit available may be advantageous as this behaviour increases the probability that females select unexploited fruit. This strategy would be particularly effective for maximizing female fitness in grazer frugivorous species (such as the cranberry fruitworm) that live in environments where severe climatic conditions induce limited flowering/fruit formation and where hosts thus are rare.     

At-sea distribution and scale-dependent foraging behaviour of petrels and albatrosses: a comparative study

1. In order to study and predict population distribution, it is crucial to identify and understand factors affecting individual movement decisions at different scales. Movements of foraging animals should be adjusted to the hierarchical spatial distribution of resources in the environment and this scale-dependent response to environmental heterogeneity should differ according to the forager's characteristics and exploited habitats. 2. Using First-Passage Time analysis, we studied scales of search effort and habitat used by individuals of seven sympatric Indian Ocean Procellariiform species fitted with satellite transmitters. We characterized their search effort distribution and examined whether species differ in scale-dependent adjustments of their movements according to the marine environment exploited. 3. All species and almost all individuals (91% of 122 individuals) exhibited an Area-Restricted Search (ARS) during foraging. At a regional scale (1000s km), foraging ranges showed a large spatial overlap between species. At a smaller scale (100s km, at which an increase in search effort occurred), a segregation in environmental characteristics of ARS zones (where search effort is high) was found between species. 4. Spatial scales at which individuals increased their search effort differed between species and also between exploited habitats, indicating a similar movement adjustment for predators foraging in the same habitat. ARS zones of the two populations of wandering albatross Diomedea exulans (Crozet and Kerguelen) were similar in their adjustments (i.e. same ARS scale) as well as in their environmental characteristics. These two populations showed a weak spatial overlap in their foraging distribution, with males foraging in more southerly waters than females in both populations. 5. This study demonstrates that predators of several species adjust their foraging behaviour to the heterogeneous environment and these scale-dependent movement adjustments depend on both forager and environment characteristics.     

Why dispersal should be maximized at intermediate scales of heterogeneity

Dispersal is a fundamental biological process that results in the redistribution of organisms due to the interplay between the mode of dispersal, the range of scales over which movement occurs, and the scale of spatial heterogeneity, in which patchiness may occur across a broad range of scales. Despite the diversity of dispersal mechanisms and dispersal length scales in nature, we posit that a fundamental scaling relationship should exist between dispersal and spatial heterogeneity. We present both a conceptual model and mathematical formalization of this expected relationship between the scale of dispersal and the scale of patchiness, which predicts that the magnitude of dispersal (number of individuals) among patches should be maximized when the scale of spatial heterogeneity (defined in terms of patch size and isolation) is neither too fine nor too coarse relative to the gap-crossing abilities of a species. We call this the “dispersal scaling hypothesis” (DSH). We demonstrate congruence in the functional form of this relationship under fundamentally different dispersal assumptions, using well-documented isotropic dispersal kernels and empirically derived dispersal parameters from diverse species, in order to explore the generality of this finding. The DSH generates testable hypotheses as to when and under what landscape scenarios dispersal is most likely to be successful. This provides insights into what management scenarios might be necessary to either restore landscape connectivity, as in certain conservation applications, or disrupt connectivity, as when attempting to manage landscapes to impede the spread of an invasive species, pest, or pathogen.     

Optimal configurations of spatial scale for grid cell firing under noise and uncertainty

We examined the accuracy with which the location of an agent moving within an environment could be decoded from the simulated firing of systems of grid cells. Grid cells were modelled with Poisson spiking dynamics and organized into multiple ‘modules’ of cells, with firing patterns of similar spatial scale within modules and a wide range of spatial scales across modules. The number of grid cells per module, the spatial scaling factor between modules and the size of the environment were varied. Errors in decoded location can take two forms: small errors of precision and larger errors resulting from ambiguity in decoding periodic firing patterns. With enough cells per module (e.g. eight modules of 100 cells each) grid systems are highly robust to ambiguity errors, even over ranges much larger than the largest grid scale (e.g. over a 500 m range when the maximum grid scale is 264 cm). Results did not depend strongly on the precise organization of scales across modules (geometric, co-prime or random). However, independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues.     

SPATIAL DYNAMICS OF A HIMANTHALIA ELONGATA (FUCALES, PHAEOPHYTA) POPULATION

In dense monospecific stands of plants intraspecific competition usually results in self-thinning, the concurrent increase in biomass and decrease in density over time. Self-thinning may also result in a change in the spatial pattern of individuals, but so far the spatial dynamics of marine plants has not been investigated. The brown alga Himanthalia elongata ( L.) S. F. Gray forms dense monospecific stands on many northern temperate rocky shores, and various attributes (including its simple form) facilitated the study of the spatial dynamics of this species .
The spatial pattern of settling zygotes was examined in the laboratory. In the absence of water movement, substratum heterogeneity, and a point source, zygotes usually settled in clumps rather than randomly. Within the clumps zygotes appeared to be regularly distributed at a scale similar to the size of the zygotes themselves. Furthermore, the clumps themselves seemed to be regularly distributed. On the shore, well-established stands of "button-stage" Himanthalia populations were examined during a period of extensive growth and self-thinning. Individual plants were initially highly regular in spatial pattern but became less so over time. The pattern of plants dying during self-thinning was also highly regular and probably reflected existing spatial regularity. However, using a hypothesis of mortality as a random event, I found that smaller plants had a less than average survival potential, while larger plants had a greater than average chance. A consideration of the spatial pattern of plants alive at the end of the study revealed regularity at a scale of 2–7 mm but a random spatial pattern at larger scales, which might indicate a small sphere of influence of competing individuals. The best predictor of mean nearest neighbor distances in the populations was mean plant diameter .     

Effects of Spatial Scale of Soil Heterogeneity on the Growth of a Clonal Plant Producing Both Spreading and Clumping Ramets

Soil nutrients are commonly heterogeneously distributed at different spatial scales. Although numerous studies have tested the effects of soil nutrient heterogeneity on growth of clonal plants producing either spreading ramets or clumping ramets, no study has examined the effects on the growth of clonal plants producing both spreading and clumping ramets and how spatial scale affects such effects. To test these effects, clones of Buchloe dactyloides, a stoloniferous clonal plant that produces both clumping and spreading ramets, were grown in six heterogeneous environments with different patch sizes and one homogeneous environment containing the same quantity of nutrients. Total biomass, total number of ramets, number of clumping ramets, number of spreading ramets, spacer length, or root:shoot ratio of the whole plants did not differ significantly among the seven treatments. However, at the patch level there were significant effects of patch size by nutrient level on biomass, number of ramets, number of spreading ramets, and number of clumping ramets, and these four variables were significantly larger in the nutrient-rich patches than in the nutrient-poor patches in the heterogeneous treatment with the largest patch size, but not in the other five heterogeneous treatments with smaller patch sizes. Neither nutrient level nor patch size significantly affected spacer length or root:shoot ratio. Based on our results, we propose that B. dactyloides can efficiently exploit nutrient-rich patches by a plastic response of clumping ramets and spreading ramets at larger spatial scales of soil heterogeneity but not at smaller ones.     

Scaling up from local competition to regional coexistence across two scales of spatial heterogeneity: insect larvae in the fruits of Apeiba membranacea

Species that live in patchy and ephemeral habitats can compete strongly for resources within patches at a small scale. The ramifications of these interactions for population dynamics and coexistence at regional scales will depend on the intraspecific and interspecific distributions of individuals among patches. Spatial heterogeneity due to independent aggregation of competitors among patchy habitats is an important mechanism maintaining species diversity. I describe regional patterns of aggregation for four species of insect larvae in the fruits of Apeiba membranacea, a Neotropical rainforest tree. This aggregation results from variation in densities at a small scale (among the fruits under a single tree), compounded by significant variation among trees in both mean densities and degrees of aggregation. Both the degrees of aggregation and mean densities are statistically independent within and across species at both spatial scales. I evaluate the regional consequences of these spatial patterns by using maximum likelihood methods to parameterize a model that includes both explicit measures of the strength of competition and spatial variation at both within- and among-tree spatial scales. Despite strong competitive interactions among these species, during 2 years the observed spatial variation at both scales combined was sufficient to explain the coexistence of these species, although other coexistence mechanisms may also operate simultaneously. The observed spatial variation at small spatial scales may not be sufficient for coexistence, indicating the importance of considering multiple sources of spatial heterogeneity when scaling up from experiments that investigate local interactions to regional patterns of coexistence.     

Change in spatial distribution patterns of a biennial plant between growth stages and generations in a patchy habitat

BACKGROUND AND AIMS: The aim of the study was to evaluate factors causing change in spatial distribution patterns of plants between growth stages and generations for a monocarpic biennial plant, Lysimachia rubida. It was assumed that habitat heterogeneity was a primary factor determining spatial patterns of plants, and a randomization procedure was developed for testing the null hypothesis that only spatial association with ground surface conditions determined spatial patterns of plants. METHODS: A 5-year demographic census was conducted on an open dry habitat that was heterogeneous with regard to the ground surface conditions. KEY RESULTS: There was significant habitat association in that plants at vegetative and reproductive stages were denser in areas with smaller gravel than with larger gravel. Point process analyses rejected the null hypothesis of the spatial association with ground surface conditions. CONCLUSIONS: The results suggest that other factors, such as patchy seed dispersal, secondary dispersal of the seeds and life-history variation at various spatial scales, also affected spatial patterns of individuals in a population of L. rubida. Spatial structures and dynamics of a local population in a patchy habitat represent various performances of plants within patches and seed dispersal within a patch and beyond the patch.     

Extrinsically and intrinsically generated spatial patterns of algal abundance in an experimental stream

Spatial heterogeneity in species abundance arises from both extrinsic (largely abiotic) and intrinsic (largely biotic) processes. The relative importance of these two types of processes can vary across ecological systems and across temporal and spatial scales. Numerous empirical studies have explored spatial patterns resulting from extrinsic and intrinsic processes, however the interaction of these two types of processes can result in complex patterns that are difficult to test. We used a unique model system consisting of periphytic algae grown on agar in an experimental stream to manipulate an extrinsic and an intrinsic process. We manipulated an extrinsic process by varying the spatial arrangement of nutrients creating both heterogeneous and homogeneous environments for the algae. We manipulated an intrinsic process by introducing a snail herbivore to the system. The resulting spatial algal patterns showed that both types of processes were important in producing spatial abundance patterns and that the patterns occurred at two distinct spatial scales in our system. At the scale of the imposed nutrient heterogeneity, algae “tracked” the differences in nutrient supply rates. The snail herbivores both reduced and promoted spatial patterns in algal abundance at different spatial scales reflecting their species-specific foraging behavior. An ability to detect differences in algal abundance allowed the snails to reduce the power of patterns at the scale of the imposed nutrient heterogeneity; however below a spatial scale of approximately 30 mm the snails could no longer detect differences in algal abundance and so foraged randomly. At this spatial scale the spatial heterogeneity in algal abundance increased and the resulting algal patterns were relatively spatially fixed through time. We suggest that this relative constancy may arise in part from a detected weak Allee effect in algal growth rates.     

Scales of aboveground and below-ground competition in a semi-arid woodland detected from spatial pattern

Abstract. Semi-arid woodlands are two-phase mosaics of canopy and inter-canopy patches. We hypothesized that both aboveground competition (within canopy patches), and below-ground competition (between canopy patches), would be important structuring processes in these communities. We investigated the spatial pattern of trees in a Pinus edulis-Juniperus monosperma woodland in New Mexico using Ripley's K-function. We found strong aggregation of trees at scales of 2 to 4 m, which indicates the scale of canopy patches. Canopy patches were composed of individuals of both species. Crown centers of both species were always less aggregated than stem centers at scales less than canopy patch size, indicating morphological plasticity of competing crowns. In the smallest size classes of both species, aggregation was most intense, and occurred over a larger range of scales; aggregation decreased with increasing size as is consistent with density-dependent mortality from intraspecific competition. Within canopy patches, younger trees were associated with older trees of the other species. At scales larger than canopy patches, younger trees showed repulsion from older conspecifics, indicating below-ground competition. Hence, intraspecific competition was stronger than interspecific competition, probably because the species differ in rooting depth. Woodland dynamics depend on the scale and composition of canopy patches, aggregated seed deposition and facilitation, above- and below-ground competition, and temporal changes in the spatial scale of interactions. This woodland is intermediate in a grassland-forest continuum (a gradient of increasing woody canopy cover) and hence we expected, and were able to detect, the effects of both above- and below-ground competition.     

空间幅度变化对景观格局分析的影响

景观格局指数是量化描述景观格局特征的主要方法之一,各种格局指数的尺度依赖性使比较分析景观格局特征和尺度推绎复杂化,分析不同指数随空间幅度变化的一般行为有助于景观格局分析结果的解释和降低空间尺度推绎的复杂性。研究以2种真实景观和27种模拟景观为分析对象,考查了16种常用的景观水平格局指数随空间幅度变化行为。根据这些指数因幅度变化行为可预测性把它们分为两类：第1类随幅度变化可预测性强,指数与幅度之间的关系可用简单的函数关系来表达;这类指数包括缀块数、边界总长、景观形状指数和缀块丰度密度;前两者随幅度增加呈幂函数形式增加,而缀块丰度密度随幅度增加呈幂函数下降,景观形状指数随幅度增加呈直线增加。第2类指数随幅度变化的可预测性较差,指数随幅度的变化存在多种可能(不同形式的增加、减小或保持不变),不可用一种或多种简单的函数关系来描述所有的情况。这类指数包括缀块丰度、缀块密度、边界密度、最大缀块指数、平均缀块面积、缀块面积标准差、缀块面积变异系数、平均缀块形状指数、面积加权平均缀块形状指数、双对数回归分维数、聚集度指数与Shannon多样性指数。第2类指数随幅度的变化行为受景观格局特征和指数本身算法的影响。总体上来说,第2类格局指数随幅度变化呈折线增加或减小;但当景观的缀块类型较多、各类型优势度比较均等、空间分布格局比较随机时,它们随幅度变化形为的可预测性增加,随幅度增加的函数关系主要有3种：幂函数减小、对数函数增加或直线增加,因指数和格局特征不同而异。研究的结果在揭示了常用景观指数随幅度变化的一般关系外,也启示我们在进行景观格局的比较分析,比较景观的幅度应相同或采用尺度效应图(scalograms)更有效。     

Ecological application of wavelet analysis in the scaling of spatial distribution patterns of Ceratoides ewersmanniana

Ecological experiments are usually conducted on small scales, but the ecological and environmental issues are usually on large scales. Hence, there is a clear need of scaling. Namely, when we deal with patterns and processes on larger scales, a special connection needs to be established on the small scales that we are familiar with. Here we presented a wavelet analysis method that could build relationships between spatial distribution patterns on different scales. With this method, we also studied how spatial heterogeneity and distribution patterns changed with the scale. We investigated the distribution and the habitat of C. ewersmanniana in two plots (200 m × 200 m; the distance between these two plots is 15 km) at Mosuowan desert. The results demonstrated that spatial heterogeneity and distribution patterns were incorporated into larger scales when the wavelet scale varied from one (5 m) to four (20 m). However, if the wavelet scale was above five (25 m), the spatial distribution patterns varied placidly, the oscillation frequency of landforms stabilized at 110 m, and the dynamic quantity period of C. ewersmanniana stabilized at 115–125 m. We also identified signal mutation points with wavelet analysis and verified the heterogeneity degree of local space with position variance. We found that position variance decomposed the distribution patterns on large scales into small sampling plots, and the position with the largest variance also had the strongest heterogeneity. In a word, the wavelet analysis method could scale-up spatial distribution patterns and habitat heterogeneity. With this method and other methods derived from this one, such as wavelet scale, wavelet variance, position variance and extremely direct-viewing graphs, wavelet analysis could be widely applied in solving the scaling problem in ecological and environmental studies.