Corresponding author: Linton Winder ( lintonwinder@yahoo.co.uk ) Academic editor: Auriel M.V. Fournier
© 2019 Linton Winder, Colin Alexander, Georgianne Griffiths, John Holland, Chris Woolley, Joe Perry.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Winder L, Alexander C, Griffiths G, Holland J, Wooley C, Perry J (2019) Twenty years and counting with SADIE: Spatial Analysis by Distance Indices software and review of its adoption and use. Rethinking Ecology 4: 1-16. https://doi.org/10.3897/rethinkingecology.4.30890
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SADIE (Spatial Analysis by Distance Indices) is designed specifically to quantify patterns in spatially-referenced count-based data. It was developed for dealing with data that can be considered ‘patchy’. Such distributions are commonly found, for example, in insect populations where discrete patches of individuals are often evident. The distributions of such populations have ‘hard edges’, with patches and gaps occurring spatially. In these cases variance of abundance does not vary smoothly, but discontinuously. In this paper we outline the use of SADIE and provide free access to the SADIE software suite, establishing Rethinking Ecology as its permanent home. Finally, we review the use of SADIE and demonstrate its use in a wide variety of sub-disciplines within the general field of ecology.
SADIE, spatial analysis by distance indices, spatially-referenced, count
It is over twenty years since Joe Perry introduced and developed the SADIE (Spatial Analysis by Distance Indices) methodology to study spatial patterns in count-based data where locations are specified (
Traditionally, count-based spatial pattern has been explored using mean-variance relationships (e.g.
In maps a-c, the same 25 counts, with mean, m = 9.08 and variance, s2 = 75.9, are arranged in a 5×5 grid. The variance greatly exceeds the mean, so these counts come from a heterogeneous distribution more highly-skewed than the Poisson distribution. However, the frequency distribution of the counts (07, 33, 53, 6, 8, 9, 209) discards any information regarding the spatial arrangement of the counts. The arrangements clearly differ. In a the counts were deliberately arranged so that the larger counts are relatively far away from other large counts (and the smallest counts are far from other small counts), producing a distribution of the counts that is more regular than random. In b the counts were distributed completely randomly amongst the 25 cells of the grid. In c the larger counts are placed close to one another (as are the smaller counts), to yield a distribution that is highly clustered and spatially aggregated. The SADIE technique exposes these differences in spatial distribution. In a the SADIE index of aggregation Ia was less than unity (Ia = 0.80) indicating regularity, with corresponding probability level P = 0.96 indicating a significantly regular pattern. In b Ia is close to unity (Ia = 0.95, P = 0.57) indicating a randomly allocated pattern. In c Ia greatly exceeds unity (Ia = 1.88, P < 0.0002) indicating a significantly clustered pattern of patches and gaps. In d the value of the local index of clustering is shown for each of the 25 grid units of map c after SADIE analysis. Positive values, shown in red, indicate potential patches and negative values, shown in blue, indicate potential gaps; the larger the value, the greater is the evidence for clustering locally. Significant clustering into a patch in the lower left of the grid, and a gap on its opposite edge is shown where the units lie within the red (patch) or blue (gap) areas. In this example of a red-blue plot both patch (red, Vi=1.9, P<0.001) and gap (blue, Vj=-1.7, P<0.001) clusters are evident (
Geographical Information Systems (GIS) approaches offer, in principle, tools to explore spatial solutions to this problem (
In this section we provide an overview of the key elements of the SADIE system. Full details of methods and key papers that explore approaches to analysing spatially-referenced data are summarised in Table
Key papers that introduce SADIE analytical tools or provide an overview of general methods. A citation count using SCOPUS is also provided.
Paper | Scope | Citations |
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The pattern of spatial distribution of Dalbergiacearensis saplings and adults were investigated with spatial analysis by distance indices, using the software Sadie Shell, version 8.0. The aggregation index (Ia) was used to explore spatial pattern. | 205 | |
SADIE methodology is discussed in this paper and reviews the method’s advantages over traditional approaches that measure only statistical variance heterogeneity. Two indices and associated tests are considered, one based on the total distance of the sample from a completely regular arrangement, the other from a completely crowded arrangement. A diagnostic plot is presented to aid interpretation. Methods are presented to estimate both ‘typical’ cluster size and inter-cluster distance. | 225 | |
This paper introduces a new index and four new graphical displays, termed ‘red-blue’ plots. The index may be used to detect clusters in the form of patches, comprising several nearby large counts, and in the form of gaps, comprising several nearby small counts. The methods facilitate a comprehensive definition of the size and dimension of a cluster. | 266 | |
Case studies are used to explore the application of spatial methods. The influence of observational scale and the importance of carefully constructing both sampling design and analysis are reviewed. A set of considerations for sampling design to allow useful tests for specific scales of a phenomenon under study are provided. | 432 | |
A method to assess spatial association between two sets of count data is described. This uses a measure of local association for counts, based on comparison of SADIE clustering indexes of the two sets at each sample unit. The mean of the measure is represented by the simple correlation coefficient between the clustering indices of the two sets. Spatial association may be mapped for count data, and clusters of units with positive association or negative dissociation may be identified. | 175 | |
This paper provides guidance to ecologists with limited experience in spatial analysis to help in their choice of techniques. A case-study approach is used to compare analytical approaches. Guidance is provided through a taxonomy of data types, a discussion of the effects of sampling, and consideration of transformations that may be used to convert data. Key spatial analysis techniques developed in plant ecology, animal ecology, landscape ecology, geo-statistics and applied statistics are briefly reviewed. Users are encouraged to initially use simple visualisation techniques, followed by methods appropriate for the data type. | 299 |
(ii) Patch and gap cluster indices (Vi and Vj). These indices are part of the ‘red-blue’ analysis tool and provide a means to measure the presence of spatial pattern by identifying neighbourhoods of consistently high counts (patches) or low counts (gaps) respectively. In the raw data, each location has its designated x,y coordinate and a corresponding count (c). SADIE assigns each location an index of clustering using the mean count m; either a positive νi index for patch units with ci>m, or a negative νj index for gap units with cj<m. These cluster indices are then used to calculate overall cluster indices Vi and Vj for patches and gaps, respectively, with associated significance values. The indices indicate whether the dataset is characterised by the presence of measurable patches, gaps, or both (Figure
(iii) Red-blue plots. Red-blue plots provide a visual representation of the degree of clustering (Figure
(iv) Association index X. Two populations may be spatially positively associated, negatively dissociated, or not be associated at all. The SADIE suite of tools includes a measure of local spatial association, represented by the local index χk. This index is based on the similarity between the clustering indices of the two populations, measured locally at each location (Figure
Spatial association and dissociation is illustrated by map a where there are ten red and ten green individuals, and map b where the ten green individuals are in exactly the same positions, and there are ten blue individuals. In fact, when viewed as single populations, the blues have a similar spatial pattern to the reds, their positions being merely a rotation and reflection of the reds. If counts were taken of the individuals in 25 cells using the dashed lines, then all three populations, red, green and blue, would each have identical frequency distributions: one count of 4, one of 3, one of 2, one of 1, and 21 zeroes. Furthermore, for both maps, only in the central cell do any of the non-zero counts coincide. For both the red-green counts and the blue-green counts, there are sixteen (0,0) pairs, one (2,0), one (0,2), one (3,0), one (0,3), one (4,0), one (0,4) and one (1,1) pair. The non-spatial correlation coefficient between the counts of the reds and greens, and between the blues and greens, is the relatively small value of -0.115, indicating no difference between the maps and neither strong similarity or dissimilarity. However, in a the ten red and the ten green individuals occur in similar areas and appear positively spatially associated and, by contrast, in b right-hand map, the ten green individuals occupy different areas and appear negatively spatially dissociated from the ten blue individuals. SADIE analysis gives the following values of Ia (with corresponding probability levels, Pa) for the green individuals: 1.45 (0.0079); for the reds: 1.18 (0.13); for the blues: 1.03 (0.36). Using the correlation between the clustering indices of each individual population, the SADIE index of association X (with corresponding probability level P) was, for the red and green populations in map (a): 0.578 (0.01); for the blue and green populations in map (b): -0.117 (0.66). The SADIE association index is capable of distinguishing the strong positive association in map (a) from the (albeit somewhat weaker) negative dissociation in map (b). In a similar fashion to red-blue plots, which give a visual representation of the degree and location of the clustering indices arranged into patches and gaps, SADIE association analysis allows the construction of plots that show areas of strong association and dissociation. For example the plot in map (c) is constructed from the association analysis of the clustering indices from the blue and red populations of map (b); it shows areas of significant positive association in plum and of dissociation in green.
Additionally,
SADIE is available to users as a series of Windows-based programs that were developed by Kelvin Conrad and originally made available on his ‘SADIE Re-heated website’. These programs have Help Files that provide both background on methods and instructions for use. Count-based data files (x, y, count) are required in simple text format. SADIE allows pairwise comparisons of distributions when association is being investigated. Other variables (e.g. continuous environmental variables) can also be incorporated into analyses, contingent on these data being spatially referenced. Continuous variables need to be integerized prior to analysis. In addition,
SADIEShell Version 2.0. Calculates the aggregation index Ia and red-blue indices Vi and Vj, with associated probabilities. Also generates the file “cluster.dat” which is required for association analysis;
N_AShell Version 1.0. Calculates the association index X with associated probability for a pair of datasets;
AssocBatchSetup01. Designed to perform all pairwise associations when there are more than two datasets; it operates on a list of SADIE spatial pattern results files. The resulting output comprises the association analysis results for the complete matrix (between any two sets) or a triangular matrix of comparisons, with each analysis held in a separate results folder.
AssocExtractor060 Version 0.6. This program extracts the section of the file containing the local association indices. This is the equivalent of the cluster.dat file from SadieShell.
ClusterShell Version 1.0. A program to measure characteristics of patch and gap clusters created by a SADIE red-blue analysis. Its purpose is to identify all patch and gap clusters by assigning each unit either to a cluster or to a non-clustered area. The program also identifies units that are on the boundaries of a grid, defines cluster centroids and examines the minimum distances between the cluster centroids and between the edges of clusters.
Red-Blue Batch Runner Version 1.0. This program is specifically designed to perform a large set of spatial analyses. The resultant output is placed in the designated input folders and many analyses can be performed sequentially without additional user intervention. It has stringent requirements for data file names and folder storage. If only a few SADIE analyses are required, then SADIEShell is easier to use.
Results Collector Version 0.61. This program extracts the section of the file containing the summary statistics and confidence intervals.
We surveyed papers that included the phrase ‘spatial analysis by distance indices’ in the title or abstract using the SCOPUS database of peer-reviewed literature (www.scopus.com, accessed July 2018). This allowed us to identify studies that applied SADIE directly for analytical purposes, and provided a snapshot of the range of disciplines using the technique. In total, 130 papers were evaluated (Figure
Cumulative number of papers published that use the phrase ‘spatial analysis by distance indices’ explicitly in the title or abstract. Data generated from searching the SCOPUS database for the period 1995–2017.
Snapshot of papers using the SADIE technique identified by interrogating the SCOPUS database using the search term ‘spatial analysis by distance indices’ within the abstract or title. Data presented as research field with short description and number of papers utilising the technique.
Research field | Description | Number of papers |
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Acarology | Mites as pests in agricultural systems | 1 |
Agricultural Botany | Weed ecology | 1 |
Animal Ecology | Ecology of animals in natural systems | 5 |
Arachnology | Spiders as natural enemies in agricultural systems | 2 |
Bacteriology | Pathology of bacterial diseases in agriculture | 2 |
Biocontrol Plants | Biocontrol in natural (estuarine) ecosystems | 1 |
Disease Ecology | Insect vectors of human diseases | 2 |
Oligochaetology | Earthworm ecology in agricultural and natural systems | 3 |
Entomology | Insect pests and their insect natural enemies | 44 |
Fungal Ecology | Wood-decaying fungi in forest ecosystems | 1 |
Marine Biology | Coral reef ecology | 1 |
Methods | Extension of SADIE or allied methods | 6 |
Mycology | Pathology of fungal diseases in agriculture | 18 |
Landscape Ecology | Landscape-scale studies | 4 |
Nematology | Nematode pests in agriculture | 5 |
Oomycetes | Diseases in agricultural systems | 2 |
Plant Ecology | General studies related to ecological theory or non-agricultural habitats | 18 |
Pollution Ecology | Distribution of soil invertebrates | 1 |
Limacology | Slugs as pests in agricultural systems | 1 |
Stored Product Pests | Insect pests of stored products | 2 |
Vertebrate Pests | Pests in agricultural systems | 1 |
Virology | Pathology of viral diseases in agriculture | 9 |
We also reviewed papers that were ‘highly cited’; arbitrarily set at fifty SCOPUS citations excluding SADIE methodology papers (Table
Turechek and Madden (1999) studied the spatial pattern of strawberry leaf blight in perennial production systems. The study adopted an intensive sampling approach that evaluated infection at the level of leaflet, leaf, plant and field. Overall, results showed that the incidence of leaf blight was characterised mainly by small, loosely aggregated clusters of diseased leaflets.
Highly cited papers from the SCOPUS database (arbitrarily set at more than 50) utilising SADIE as an analytical tool.
Authors | Title | Research Field | Cited |
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Modelling the dynamic spatio-temporal response of predators to transient prey patches in the field | Entomology | 140 |
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Small-scale environmental heterogeneity and spatiotemporal dynamics of seedling establishment in a semiarid degraded ecosystem | Plant Ecology | 139 |
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Aggregation and temporal stability of carabid beetle distributions in field and hedgerow habitats | Entomology | 126 |
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Isolating the components of activity-density for the carabid beetle Pterostichusmelanarius in farmland | Entomology | 119 |
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Spatial patterns of surface soil properties and vegetation in a Mediterranean semi-arid steppe | Plant Ecology | 110 |
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Spatiotemporal patterns and dispersal of stink bugs (Heteroptera: Pentatomidae) in peanut-cotton farmscapes | Entomology | 74 |
Turechek and Madden 1999 | Spatial pattern analysis of strawberry leaf blight in perennial production systems | Mycology | 69 |
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Spatial distribution of pest insects in oilseed rape: Implications for integrated pest management | Entomology | 61 |
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Predatory activity and spatial pattern: The response of generalist carabids to their aphid prey | Entomology | 61 |
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The spatial and temporal distribution of the grain aphid Sitobionavenae in winter wheat | Entomology | 57 |
The four key SADIE methods papers (
Designed and wrote the manuscript: LW, CA, GG, JH, CW, JP. Prepared the figures: JP, LW.
Authors | Contribution | ACI |
---|---|---|
LW | 0.20 | 1.250 |
CA | 0.15 | 0.882 |
GG | 0.15 | 0.882 |
JH | 0.15 | 0.882 |
CW | 0.15 | 0.882 |
JP | 0.20 | 1.250 |
This paper is dedicated to the memory of our friend and colleague Dr Kelvin Conrad, whose love of science was an inspiration to us all. The UK’s Biotechnology and Biological Sciences Research Council supported the development of SADIE.