Spatial analysis of two-species interactions

Summary In this paper, I present and discuss some methods for the analysis of univariate and bivariate spatial point pattern data. Examples of such data in ecology include x-y coordinates of organisms in mapped field plots. I illustrate the methods with analyses of data from mapped field plots on Mount St. Helens, Washington state, USA. The statistical methods I emphasize are graphical methods that rely on analysis of distances between organisms. Hypothesis testing for methods like these is easily done using Monte Carlo methods, which I also discuss. For both univariate and bivariate analyses, I find that second-order methods such as K-function plots are often preferable to first-order methods (i.e., QQ-plots). However, for multivariate analyses, these second-order methods are more sensitive to small sample sizes than first-order analyses.     

Assessing the influence of environmental heterogeneity on bird spacing patterns: a case study with two raptors

Testing for aggregation or regularity in point patterns is difficult in the presence of spatial variation in abundance due to environmental heterogeneity. Using a recently developed method generalizing Ripley's K function for non homogeneous point patterns, we test the aggregation of the nests in two species of birds (little owl and Montagu's harrier) exhibiting heterogeneous distributions in response to landscape structure. We compare the results obtained under different null models accounting for environmental heterogeneity at large and/or small spatial scales.
Whereas both species were initially found to form clusters at some scale, taking spatial heterogeneity into account revealed that 1) territorial little owls showed no clustering of territories when habitat availability was considered; 2) semi-colonial harriers still formed significant clusters, but part of the aggregation in this species could be explained by landscape structure alone. Our results highlight that it is feasible and highly recommended to account for non-stationarity when testing for aggregation. Further, provided that sufficient knowledge of the study system is available, this approach helps to identify behavioural and environmental components of spatial variation in abundance. Additionally, we demonstrate that accounting for large or small-scale heterogeneity affects the perception of spacing behaviours differently, so that both need to be considered.     

基于加权Ripley's K-function的多尺度景观格局分析——以江苏盐城滨海湿地为例

以1987,1992,1997,2002,2007年的遥感影像为例,首次尝试使用加权Ripley's K-function的多尺度格局分析方法,计算了20年来景观异质性在江苏盐城滨海湿地的时间变化和空间分布趋势。通过对研究区的样带划分以及景观类型的点状化处理,建立滨海湿地样带图层和1987—2007年间各类型景观的点格局数据库,从而分析滨海湿地不同类型景观的空间聚集特征变化。基于加权Ripley's K-function的计算表明,在各级空间尺度和时间变化上,各类型湿地的斑块都呈现出空间聚集分布状态,且1987年以来,不同湿地类型的聚集空间特征尺度和空间分布强度均出现了大幅的增减变化,除互花米草滩之外的自然湿地的聚集空间特征尺度和强度都有明显下降甚至少到无法被检测到,而人工湿地却呈现聚集特征尺度和强度的双增长,且该聚集程度有逐渐增强的趋势。分析表明,既考虑样点的空间位置信息又考虑样点分布范围的加权Ripley's K-function方法能很好地表征湿地景观在多尺度上的变异,且与传统空间景观指数等分析方法的结论在一定程度上保持一致。     

An evaluation of the state of spatial point pattern analysis in ecology

Over the last two decades spatial point pattern analysis (SPPA) has become increasingly popular in ecological research. To direct future work in this area we review studies using SPPA techniques in ecology and related disciplines. We first summarize the key elements of SPPA in ecology (i.e. data types, summary statistics and their estimation, null models, comparison of data and models, and consideration of heterogeneity); second, we review how ecologists have used these key elements; and finally, we identify practical difficulties that are still commonly encountered and point to new methods that allow current key questions in ecology to be effectively addressed. Our review of 308 articles published over the period 1992–2012 reveals that a standard canon of SPPA techniques in ecology has been largely identified and that most of the earlier technical issues that occupied ecologists, such as edge correction, have been solved. However, the majority of studies underused the methodological potential offered by modern SPPA. More advanced techniques of SPPA offer the potential to address a variety of highly relevant ecological questions. For example, inhomogeneous summary statistics can quantify the impact of heterogeneous environments, mark correlation functions can include trait and phylogenetic information in the analysis of multivariate spatial patterns, and more refined point process models can be used to realistically characterize the structure of a wide range of patterns. Additionally, recent advances in fitting spatially‐explicit simulation models of community dynamics to point pattern summary statistics hold the promise for solving the longstanding problem of linking pattern to process. All these newer developments allow ecologists to keep up with the increasing availability of spatial data sets provided by newer technologies, which allow point patterns and environmental variables to be mapped over large spatial extents at increasingly higher image resolutions.     

Population dynamics, disturbance, and pattern evolution: identifying the fundamental scales of organization in a model ecosystem

We used auto- and cross-correlation analysis and Ripley's K-function analysis to analyze spatiotemporal pattern evolution in a spatially explicit simulation model of a semiarid shrubland (Karoo, South Africa) and to determine the impact of small-scale disturbances on system dynamics. Without disturnities bance, local dynamics were driven by a pattern of cyclic succession, where 'colonizer' and 'successor' species alternately replaced each other. This results in a strong pattern of negative correlation in the temporal distribution of colonizer and successor species. As disturbance rates were increased, the relationship shifted from being negatively correlated in time to being positively correlated-the dynamics became decoupled from the ecologically driven cyclic succession and were increasingly influenced by abiotic factors (e.g., rainfall events). Further analysis of the spatial relationships among colonizer and successor species showed that, without disturbance, periods of attraction and repulsion between colonizer and successor species alternate cyclically at intermediate spatial scales. This was due to the spatial 'memory' embedded in the system through the process of cyclic succession. With the addition of disturbance, this pattern breaks down, although there is some indication of increasing ecological organization at broader spatial scales. We suggest that many of the insights that can be gained through spatially explicit models will only be obtained through a direct analysis of the spatial patterns produced.     

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.     

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.     

Spatial pattern of the threatened epiphytic bryophyte Neckera pennata at two scales in a fragmented boreal forest

The spatial pattern and occurrence of a threatened bryophyte, Neckera pennata. were studied in relation to the abundance and pattern of suitable substrate trees at two spatial scales: 1) in a 4 x 4 km fraction of fragmented, mostly managed southern boreal forest landscape, and 2) in an old-growth forest stand within this landscape, with abundant occurrence of suitable habitats. To explore in detail the spatial clustering of N. pennata at the forest stand scale, we applied a second order point process analysis based on the Ripley's K-function for binary point patterns, Neckera pennata proved to be a rare species in the studied landscape: it was found only on 31 Populus tremula trees. At the landscape scale, the distribution of the species was highly aggregated: the species occurred only within a 60 ha old-growth forest patch in the whole area. At the forest stand scale, N. pennata proved to be a widespread, randomly distributed species without any tendency towards aggregation. It was found on 19 Populus trees, which was only 1.5% of the total 1253 potential substrate trees within the inventory area. The species showed a statistically significant preference towards large trees. The future of the species in the study area is unclear due to 1) the very low population density and 2) the lack of regeneration of Populus within the protected old-growth forest area hosting the remaining population.     

Species associations in a heterogeneous Sri Lankan dipterocarp forest

We used point pattern analysis to examine the spatial distribution of 46 common tree species (diameter at breast height >10 cm) in a fully mapped 500x500-m tropical forest plot in Sinharaja, Sri Lanka. We aimed to disentangle the effect of species interactions (second-order effects) and environment (first-order effects) on the species' spatial distributions. To characterize first-order associations (segregation, overlap), we developed a classification scheme based on Ripley's K and nearest-neighbor statistics. We subsequently used heterogeneous Poisson null models, accounting for possible environmental heterogeneity, to reveal significant uni- and bivariate second-order interactions (regularity, aggregation and repulsion, attraction). First-order effects were strong; overall, 53% of all species pairs occupied largely disjoint areas (segregation), 40% showed partial overlap, and 6% overlapped. Only 5% of all species pairs showed significant second-order effects, but about half of the species showed significant intraspecific effects. Significant plant-plant interactions occurred mostly within 2-4 m and disappeared within 15-20 m of the focal plant. While lack of significant species interactions suggests support for the unified neutral theory, species' observed spatial segregation does not support the assumptions of the neutral theory. The strong observed tendency of species to segregate may have supplementary effects on other processes promoting species coexistence.     

A practical approach to the study of spatial structure in simple cases of heterogeneous vegetation

Abstract. Spatial heterogeneity is a characteristic of most natural ecosystems which is difficult to handle analytically, particularly in the absence of knowledge about the exogenous factors responsible for this heterogeneity. While classical methods for analysis of spatial point patterns usually require the hypothesis of homogeneity, we present a practical approach for partitioning heterogeneous vegetation plots into homogeneous subplots in simple cases of heterogeneity without drastically reducing the data. It is based on the detection of endogenous variations of the pattern using local density and second‐order local neighbour density functions that allow delineation of irregularly shaped subplots that could be considered as internally homogeneous. Spatial statistics, such as Ripley's K‐function adapted to analyse plots of irregular shape, can then be computed for each of the homogeneous subplots. Two applications to forest ecological field data demonstrate that the method, addressed to ecologists, can avoid misinterpretations of the spatial structure of heterogeneous vegetation stands.     

Spatial patterns and interspecific associations of three canopy species at different life stages in a subtropical forest, China

Spatial patterns of species at different life stages are an important aspect for understanding causal mechanisms that facilitate species co-existence.Using Ripley's univariate L(t) and bivariate L12(t) functions,we analyzed the spatial patterns and interspecific associations of three canopy species at different life history stages in a 20-ha subtropical forest plot in Dinghushan Nature Reserve.Based on diameter at breast height (DBH),four life stages were distinguished.Castanopsis chinensis and Schima superba showed a unimodal DBH distribution.Engelhardtia roxburghiana showed a bimodal curve.L(t) function analysis showed significantly aggregated distributions of all three species at later life stages and random distribution at early life stages at some scales.From the analysis of L12(t) function,the results showed the positive association was a dominant pattern for most species pairs at most scales but the intensity of association decreases with the increase of life stages.Juveniles of the three species had no negative intra- and interspecific associations with the older life stages.Only premature trees were suppressed by overmature trees at some scales.Considering these results,we found three canopy-dominant species that lacked regeneration.There was no direct competition occurring between understorey individuals.Young trees can grow well under conspecific species with two other species.Longevity and lack of regeneration led to a large number of trees stored in mature and overmature stages,therefore,intra-and inter-competition can be strong at later life stages.     

乌拉山自然保护区白桦种群的年龄结构和点格局分析

白桦群落是乌拉山森林植被的主要类型之一,在高海拔阴坡、半阴坡以纯林形式分布.根据乌拉山自然保护区白桦林不同林龄结构设置3个典型样地,采用种群径级结构代替年龄结构、点格局分析(Ripley's K-Function)方法探讨了乌拉山白桦种群年龄结构、空间分布规律和种群动态.结果表明:(1)乌拉山自然保护区白桦种群径级结构呈典型的“金字塔”型,种群自然更新良好,属增长型种群;(2)由于种内不同个体间为争夺空间和资源,种群在第Ⅲ、Ⅳ径级死亡率较高,自疏作用明显;(3)白桦种群的存活曲线接近于Deevey Ⅰ型曲线;(4)在研究尺度内白桦种群以幼树、中龄树为主时呈聚集分布,而成龄树或老龄树占多数时呈随机分布,即随着种群年龄的增加,其分布格局逐渐由集群分布向随机分布转变.乌拉山白桦种群在小于1.5m的尺度呈聚集分布,即具有2株以上个体“丛生”现象.在环境条件相似的情况下,白桦种群自身的生物、生态学特性是影响其分布格局的最主要因素.     

Implications of scale for patterns and processes in stream ecology

Abstract Although the scale-dependence of ecological patterns and processes is recognized by freshwater ecologists, current knowledge of scale effects is rudimentary and non-quantitative. We review issues of spatial and temporal scale in this paper to highlight conceptual problems relating to scale and some potential solutions. We present examples of how the spatial scale of a study influences observed patterns and their interpretation, and discuss how the size of an experimental arena influences the degree to which the dynamics of studied populations are influenced by exchange processes (immigration and emigration). The results of small-scale field experiments in streams will often be strongly influenced by the per capita exchange rates of organisms and differences in exchange rates may explain differences in the perceived effects of stream manipulations across scales. Spatial extent also influences the amount of spatial heterogeneity within a study site or arena, with important consequences for the outcome of predator-prey interactions. We suggest that changes in the availability of prey refuges may help explain why predator manipulations in streams appear to weaken as arena size increases. We also recommend that new techniques for decomposing and quantifying spatial heterogeneity be applied to characterize scale-dependent variation in freshwater systems. Lastly, we discuss the pitfalls of mismatching the temporal scale of experiments and models. Models incorporating spatial heterogeneity and the behaviour of organisms are needed to predict the short-term outcome of perturbations in streams, whereas models predicting long-term dynamics will need to integrate the impacts of episodic disturbance and all life history stages of organisms. In general, we recommend that freshwater ecologists undertake more multi-scale sampling and experimentation to examine patterns and processes at multiple scales, and make greater attempts to match the scales of their observations and experiments to the characteristic scales of the phenomena that they investigate.     

Spatial patterns and competition of tree species in a Douglas-fir chronosequence on Vancouver Island

While the successional dynamics and large-scale structure of Douglas-fir forest in the Pacific Northwest region is well studied, the fine-scale spatial characteristics at the stand level are still poorly understood. Here we investigated the fine-scale spatial structure of forest on Vancouver Island, in order to understand how the three dominant species, Douglas-fir, western hemlock, and western redcedar, coexist and partition space along a chronosequence comprised of immature, mature, and old-growth stands. We quantified the changes in spatial distribution and association of the species along the chronosequence using the scale-dependent point pattern analyses pair-correlation function g(r) and Ripley's L-function. Evidence on intra- and inter-specific competition was also inferred from correlations between nearest-neighbor distances and tree size. Our results show that 1) the aggregation of Douglas-fir in old-growth was primarily caused by variation in local site characteristics, 2) only surviving hemlock were more regular than their pre-mortality patterns, a result consistent with strong intra-specific competition, 3) inter-specific competition declined rapidly with stand age due to spatial resource partitioning, and (4) tree death was spatially randomly distributed among larger overstory trees. The study highlights the importance of spatial heterogeneity for the long-term coexistence of shade-intolerant pioneer Douglas-fir and shade-tolerant western hemlock and western redcedar.     

基于网络K函数的西双版纳人工林空间格局及动态

区域植被格局的分布特征受诸多要素影响,但其空间格局和动态具有一定规律或自相关性,道路网络作为景观中显著的人工线性要素,在很大程度上影响着区域的植被格局特征,特别是人工植被的分布特征.运用网络K函数,分析了道路网络和人工林空间格局分布的相互关系,并且用二元网络K函数研究了人工林扩展对针叶林和阔叶林的影响.结果表明:人工林在1970-2000年间种群分布格局有非常明显的变化,特别是从1990到2000年,种群面积不断扩大,主要从北部地区扩展到西北和东南地区.1970-1990年人工林扩展主要集中在低海拔的道路网络附近,沿道路网络呈现明显的集聚分布,公路效应明显.但后期逐渐向距公路较远、海拔较高的地区扩展,到2000年在大尺度下人工林斑块呈显著随机分布.同时,人工林面积的增长对针叶林影响显著,对阔叶林有影响但是并不显著.二元网络K函数表明,在1970到1990年人工林与针叶林沿道路网络在小尺度为负关联,在局部地区存在着竞争,但在大尺度上对环境条件的要求具有一致性为正关联.到2000年,在大尺度上人工林与针叶林的种群分布格局呈显著负相关,人工林面积的不断扩展导致了针叶林面积的下降.     

Spatial aggregation and association in different resource-patch distributions: experimental analysis with Drosophila

1. Laboratory experiments using homogeneous resources were conducted to examine intra- and interspecific spatial egg distribution of D. simulans, D. auraria and D. immigrans in three different resource-patch distribution patterns: patchy, even and clustered. 2. Individuals of each species were introduced separately or simultaneously into the cage, into which artificial substrates were placed and allowed to oviposit for 24 h. Spatial analyses were performed with indices of intraspecific aggregation (J), interspecific association (C) and L-function based on Ripley's K-function. 3. Eggs were always spatially aggregated irrespective of species and the resource-patch distribution patterns. Spatial egg aggregation was influenced significantly by the resource-patch distribution pattern and tended to be weaker in the clustered resource-patch distribution than in the patchy or even resource-patch distribution. 4. Spatial extent of egg aggregation was always beyond the single resource patch scale, indicating aggregation of ovipositing females. 5. Interspecific association of egg distribution was absent or very weak. Thus, these results present experimental evidence of independent egg aggregation among drosophilids.     

The measurement of marine species diversity, with an application to the benthic fauna of the Norwegian continental shelf

Species diversity includes two aspects, the number of species (species richness) and the proportional abundances of the species (heterogeneity diversity). Species richness and heterogeneity diversity can be measured over different scales; a single point, samples, large scales, biogeographical provinces and in assemblages and habitats. In the literature, the terminology of these scales is confused. Here, scales are given a uniform notation. Scales of species richness and heterogeneity diversity are distinguished from turnover (beta) diversity, which is the degree of change in species composition along a gradient. Methods of measurement of the scales of species richness, heterogeneity diversity, turnover diversity and for estimating total species richness are reviewed. Two methods for measuring heterogeneity diversity are recommended Exp H′ (where H′ is the Shannon-Wiener index) and 1/Simpson’s index, together with an equitability index J′. The reviewed methods are then applied to a data set from the Norwegian continental shelf to illustrate the advantages of the recommended methods. Finally, the application of the methods to assessment of effects of disturbance, to studies of gradients of species richness and to conservation issues are discussed.     

Spatial patterns of plant association in grazed and ungrazed shrublands in the semi‐arid Karoo,South Africa

Abstract. The investigation of vegetation pattern and plant association by spatial statistics has become increasingly popular among plant ecologists. Recently, Individual‐centered analysis (ICA) has been introduced as a new tool for analysis of multi‐species co‐occurrence patterns. We tested this new technique by applying it to spatial data from grazed and ungrazed shrub communities in the semi‐arid Great Karoo, South Africa. There were substantial but complex and scale‐dependent differences in pattern between grazed and ungrazed vegetation. Unpalatable species that increase in abundance in grazed vegetation possibly play a key role in the change of vegetation pattern. At small scales we found indications of aggregation (< 30 cm) at the ungrazed, but of repulsion (30 – 40 cm) at the grazed site. An additional non‐random pattern at 60 – 170 cm at the grazed site was probably due to the clumped distributions of some species on broader scales. We show that the interpretability of ICA results is improved when the actual observed and expected frequencies of species combinations are added to the program output. The main strength of ICA is that it has the potential to detect association patterns that involve more than two species.