Hybrid Multidimensional Scaling Research Articles

Leto: Crowdsourced Radio Map Construction With Learned Topology and a Few Landmarks

Existing crowdsourced indoor positioning systems (CIPSs) usually require prior knowledge about the site and a tedious calibration process. Moreover, they may require a large number of landmarks while ignoring the topology information that may be contained in the crowdsourced data. In this paper, we present Leto, a system that uses <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">le</b> arned <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">to</b> pology information from combined user traces to construct a radio map. Leto relies on crowdsourced WiFi and accelerometer signals only without requiring any prior knowledge about the site. Our key idea is that learned topology information can reduce the required number of landmarks, while available landmarks can transform the topology into a map. We propose a novel framework that efficiently learns the map topology by a hybrid multidimensional scaling (HMDS) algorithm and accurately rectifies the map using only a few anchors by an adaptive force-directed (AFD) algorithm. We also provide a theoretical convergence analysis of the HMDS algorithm. Experimental results on real-world datasets show that Leto can capture useful topology information and achieve significant improvements in radio map construction compared to existing systems.

A Fast Hierarchical Physical Topology Update Scheme for Edge-Cloud Collaborative IoT Systems

The awareness of physical network topology in a large-scale Internet of Things (IoT) system is critical to enable location-based service provisioning and performance optimization. However, due to the dynamics and complexity of IoT networks, it is usually very difficult to discover and update the physical topology of the large-scale IoT systems in real-time. Considering the stringent latency requirements in IoT systems, while the initial processing time for topology discovery can be tolerated, latency due to real-time topology update constitutes an even higher level of challenge. In this paper, a novel fast hierarchical topology update scheme is proposed for the large-scale IoT systems enabled by using the edge-cloud collaborative architecture. Specifically, an event-driven neighbor update algorithm, termed as TriggerOn, is firstly developed to update the local neighbor table of the end devices when device association or disassociation occurs. Based on the updated neighbor tables, the physical topology update of the subnet is conducted at the coordinated edge device, where a hybrid multidimensional scaling (MDS) based 3D localization algorithm is developed to locate the newly associated devices. Simulation results have indicated that as compared to the benchmark methods, the neighbor discovery latency has been reduced dramatically, and the 3D localization accuracy has been improved. Furthermore, the overall latency incurred by the proposed hierarchical physical topology update scheme is significantly lower than the distributed consensus-based update scheme, especially for the large-scale IoT subnets.

A new species of

We investigated the limits of Lepidosperma congestum R.Br. and a putative new species of Lepidosperma Labill. from Victoria and South Australia. Phenetic analyses (flexible UPGMA agglomerative hierarchical fusion and semi-strong hybrid multidimensional scaling) were conducted on a dataset derived from morphological characters scored from herbarium material. The results of our analyses supported the recognition of a new species, which we describe here as Lepidosperma hispidulum G.T.Plunkett, J.J.Bruhl &amp; K.L.Wilson. Our results clarified the differences among L. congestum, L. laeve R.Br. and L. hispidulum, the first two of which have often been misidentified. We also discuss the distribution, habitat and conservation status of L. hispidulum.

A morphometric analysis of the Banksia spinulosa complex (Proteaceae) and its complex taxonomic implications

Specimens of all known taxa and putative entities belonging to the Banksia spinulosa complex were collected from Kuranda in northern Queensland, western to central Queensland and down the eastern coast of Australia to Wilsons Promontory in southern Victoria. These specimens were used to investigate morphological variation in habit, stems, leaves, inflorescences, fruits and seeds in the complex. Phenetic analysis (unweighted pair-group method with arithmetic mean, UPGMA, clustering and semi-strong hybrid multi-dimensional scaling, SSH–MDS, ordination) was performed on the full dataset of 233 entities using 33 characters (18 quantitative, two binary and 13 multistate). To facilitate visualisation of patterns in both clustering and ordination, we also analysed subgroups based on the results of the phenogram from the full dataset. The results showed that the five known and described taxa are phenetically distinct, viz. B. collina sens. str., B. cunninghamii sens. str., B. neoanglica, B. spinulosa and B. vincentia, and provided support for a further 12 morphometrically diagnosable entities, four of which could not be diagnosed with simple combinations of character states and require further investigation. The present study has highlighted that there is much more hidden morphological diversity in the B. spinulosa complex than has previously been recognised in any of the current competing taxonomies.

Sedges in the mist: A new species of Lepidosperma (Cyperaceae, Schoeneae) from the mountains of Tasmania

The status of a putative new species of Lepidosperma from the mountains of south-western Tasmania, Australia, was investigated. Phenetic analysis (Flexible UPGMA Agglomerative Hierarchical Fusion and semi-strong hybrid multidimensional scaling) was conducted on a database derived from morphological and anatomical characters scored from herbarium material, culm anatomy slides and scanning electron micrographs of fruit. The results of the analysis support the recognition of a new species, here described as Lepidosperma monticola G.T.Plunkett & J.J.Bruhl. The distribution, habitat and conservation status are discussed.

Modelling niche and neutral dynamics: on the ecological interpretation of variation partitioning results

Many studies have attempted to disentangle the effects of neutral and niche‐mediated processes on community composition using partial Mantel tests and variance partitioning on dissimilarity matrices. Recently, doubts about the reliability of these methods have emerged. Here we explore how the results are affected by three confounding factors that may affect ecological data to different degrees: spatial autocorrelation of the environmental variables, length of the compositional gradient, and sampling noise. We document that the statistical hypotheses tested in these methods may or may not correspond to the ecological hypotheses of interest. A major discrepancy emerges if a large proportion of sampling units in the analysed dataset share no species, in which case compositional dissimilarities saturate to a fixed maximum value although explanatory dissimilarities do not. With increasing dissimilarity saturation, the explanatory power of regression models decrease, which may lead to the erroneous conclusion that the ecological processes represented by the explanatory variables are not operating. A survey of recent literature suggests that there is a general lack of awareness of this problem, although it appears to affect &gt; 10% of relevant studies. Our simulations show that if dissimilarity saturation is due to a long ecological gradient, extended dissimilarities essentially solve the problem for any degree of saturation. Using distances from a hybrid multidimensional scaling alleviates the saturation problem when the degree of saturation is &lt; 60%. However, neither correction method can provide a solution to problems caused by insufficient sampling. How the presence of multiple explanatory gradients in combination with sampling noise affects overall analysis performance remains to be clarified.

Division of labor in colonies of the eusocial wasp, Mischocyttarus consimilis.

The division of labor between castes and the division of labor in workers according to age (temporal polyethism) in social wasps are crucial for maintaining social organization. This study evaluated the division of labor between castes, and the temporal polyethism in workers of Mischocyttarus consimilis Zikán (Hymenoptera: Vespidae). To describe the behavioral repertory of this species, observations were made of 21 colonies, with 100 hours of observations. In order to observe temporal polyethism, each newly emerged wasp was marked with colored dots on the upper area of the thorax. This allowed the observation of behavioral acts performed by each worker from the time of emergence to its death. Through hybrid multidimensional scaling, a clear division between queens and workers could be identified, in which the behaviors of physical dominance and food solicitation characterized the queen caste; while behaviors such as adult—adult trophallaxis, destruction of cells, alarm, foraging for prey, foraging for nectar, and unsuccessful foraging characterized the worker caste. Hybrid multidimensional scaling characterized two groups, with intra—nest activities preferentially accomplished by younger workers, while extra—nest activities such as foraging were executed more frequently by older workers.

Effects of different secondary vegetation types on bat community composition in Central Amazonia, Brazil

AbstractThe process of secondary succession on degraded lands in the Amazon depends on their land‐use histories. In this scenario, little is known about how animal communities respond to different types of secondary vegetation in the region. We examined the effects of abandoned cattle pasture, Vismia‐ and Cecropia‐dominated regrowth on the abundance of bat species and community composition in the Central Amazon, Brazil, based on 11 netting sites and on landscape characteristics. We captured 1444 bats, representing 26 species and two families (Phyllostomidae and Mormoopidae). Among the six most‐captured Phyllostomidae bats, Sturnira lilium and Sturnira tildae had significantly higher capture rates in abandoned pasture, while Rhinophylla pumilio predominated in both Vismia‐ and Cecropia‐dominated regrowth. An hybrid multidimensional scaling ordination revealed significant differences in the bat community among the three types of secondary vegetation. Phyllostominae bats were more common and richer in the less‐disturbed areas of Cecropia‐dominated regrowth, while Stenodermatinae species were more captured in abandoned pastures. Our results suggest that the type of secondary vegetation, together with its land‐use history, affects bat community composition in the Central Amazon. The Phyllostominae subfamily (gleaning animalivores) was habitat selective and disappeared from areas experiencing constant disturbances. On the other hand, Stenodermatinae frugivorous bats often used and foraged in altered areas. We suggest that secondary vegetations in more‐advanced successional stages can be used to augment the total area protected by forest conservation units.

Effects of Degradation and Replacement of Southern Brazilian Coastal Sandy Vegetation on the Dung Beetles (Coleoptera: Scarabaeidae)

ABSTRACTIn this paper we address the effects of anthropogenic disturbance and replacement of Brazilian Coastal sandy vegetation (restingas) on dung beetles communities. We sampled dung beetles in the four main vegetative physiognomies of Guriri Island, Espírito Santo State: forest restinga, restinga Clusia, disturbed restinga (from burning events), and pastures. We placed four sets of two pitfall traps (baited with horse and human dung) in four independent areas of each vegetation type, and collected 14,534 individuals of 13 dung beetle species. Neither log10 of individuals nor log10 of species richness were good predictors of restinga disturbance. However, a significant amount of variation in dung beetle abundance and richness could be explained by bait type. Ordination of these sites using hybrid multidimensional scaling revealed a gradient of habitat disturbance from undisturbed restinga samples to pasture. Dung beetle communities along this gradient demonstrated a complete turnover in species composition, from restinga‐specialists to invasive and generalists species respectively. This complete turnover signals the local extirpation of forest‐adapted species in disturbed and converted areas. Only a single dung beetle species in preserved restingas is protected by Brazilian law (Dichotomius schiffleri). Given the extent of the clearing of restinga habitat, the conservation status of dung beetles associated with restinga forest gives cause for concern.

A hybrid method for multidimensional scaling using city-block distances

The problem of multidimensional scaling with city-block distances in the embedding space is reduced to a two level optimization problem consisting of a combinatorial problem at the upper level and a quadratic programming problem at the lower level. A hybrid method is proposed combining randomized search for the upper level problem with a standard quadratic programming algorithm for the lower level problem. Several algorithms for the combinatorial problem have been tested and an evolutionary global search algorithm has been proved most suitable. An experimental code of the proposed hybrid multidimensional scaling algorithm is developed and tested using several test problems of two- and three-dimensional scaling.

Spatial distribution and habitat of the Anavilhanas Archipelago bird community in the Brazilian Amazon

This study is the first to present a quantitative survey of bird species occurring in the archipelago of Anavilhanas, located in the Rio Negro in the Brazilian Amazon and is part of the Anavilhanas Ecological Station. We asked whether bird community composition is similar among the islands, and between islands and areas dominated by the surrounding upland terra firme forest on the left (east) margin of the Rio Negro. The surveys were conducted in November and December of 1988, using two complementary methods with mist nets and boat transects. A total of 232 bird species was found for Anavilhanas including a survey done in 1998. The families Tyrannidae and Thamnophilidae showed the highest number of species (16.4% and 9.0% of the total respectively). Some species not well known or having limited distributions are relatively frequently encountered in the archipelago, such as Spizastur melanoleucus, Mitu tomentosa, Phaethornis rupurumii, Xiphorhynchus kienerii, Thamnophilus nigrocinereus, Myrmotherula klagesi, Myrmoborus lugubris, Pipra filicauda, and Cephalopterus ornatus. Hybrid Multidimensional Scaling (HMDS) ordination analysis indicated that the bird community composition is similar among islands. However, the bird community composition on the islands was significantly different from that in sites of terra firme forest at Rio Negro margins. Anavilhanas is a unique ecological system in the Amazon and has it own avifauna.

Diversidade de espécies dos gêneros de Crematogaster, Gnamptogenys e Pachycondyla (Hymenoptera: Formicidae) e complementaridade dos métodos de coleta durante a estação seca numa estação ecológica no estado do Pará, Brasil

As formigas são muito usadas em programas de inventários e monitoramentos, resultando em grande quantidade de material coletado com vários métodos, limitações financeiras e na falta de taxonomos para vários táxons. Para contribuir na elaboração de protocolos alternativos, analisamos a complementaridade de dois métodos de amostragem na detecção da riqueza de espécies. Em seis parcelas de 1 km² distribuídas em 33.000 ha de floresta primária, investigamos a diversidade e a freqüência das espécies de Crematogaster,Gnamptogenys e Pachycondyla, como parte do protocolo de formigas de serapilheira do Projeto TEAM. Em cada parcela, quatro transectos de 100 m foram instalados. Dez sub-amostras foram efetuadas por transecto, usando extrator de Winkler e armadilha de fosso. Registramos 36 espécies, sendo 15 novos registros para o Pará e 29 para a área de estudo. Dezessete espécies foram comuns aos dois métodos, onze foram capturadas com armadilhas de fosso e oito com Winkler. As proporções de espécies representadas por um indivíduo ("singletons") foram altas para ambos os métodos (&gt; 0,4). Dezenove espécies foram coletadas por apenas um método e três foram representadas por apenas um indivíduo em cada método. A análise de ordenação (escalonamento multidimensional semi-híbrido) revelou diferenças na estrutura das comunidades de formigas obtidas pelos dois métodos de amostragem. Houve um efeito de complementaridade entre os dois métodos para a obtenção de um levantamento mais completo da riqueza de espécies, significando que ambos devem ser usados no protocolo. Outros recursos, como a rarefação e/ou diluição das amostras são recursos a serem avaliados em futuras investigações.

The first phenetic analysis of species limits inBertya(Euphorbiaceae)

Morphological and phytogeographical data support the recognition of 41 taxa in Bertya, a genus endemic to Australia with many rare and threatened species. We used 107 morphological characters (69 qualitative, 38 quantitative), including novel characters of leaf basal glands and indumenta, and 166 operational taxonomic units. In three iterations by using cluster analyses and semi-strong hybrid multidimensional scaling ordination, operational taxonomic units were resolved into 41 species (6 new; 5 with very localised distributions). Fifteen (including 3 new) have or merit status as rare, endangered or threatened.

Multidimensional site description of peatlands drained for forestry

Sites (n = 119) on drained mires located in the southern aapa mire zone in Finland were analysed by multivariate techniques. The compositional trends of the understorey vegetation were analysed by means of hybrid multidimensional scaling (HMDS). In addition to field classification, two-way indicator species analysis (TWINSPAN) and flexible unweighted paired group arithmetic average (FUPGMA) classifications were used. The 1st HMDS dimension primarily reflected variation along a gradient from spruce mire influence to hummock-level bog influence. Variation in nutrient status was also connected to this gradient. Factors underlying the 2nd dimension were variation in nutrient status and drainage succession (moisture). Some sample plots representing herb-rich or Molinia-rich types were separated along the 3rd dimension. The variation in understorey vegetation (i.e. the ordination space) showed high maximum correlation with stand volume r = 0.81, mean annual stand volume increment r = 0.76, and post-drainage dominant height r = 0.75. The covariation between the vegetation and peat bulk density in both the 0–10 and 10–20 cm peat layers was also strong: r = 0.55 and r = 0.80. The correlations for Hv.Post were 0.64 and 0.81, respectively. Of the total macronutrient concentrations, phosphorus (r = 0.73, r = 0.75) and nitrogen (r = 0.59, r = 0.64) were the most strongly correlated with species composition. The environmental sample variables were also presented by the vegetation units of numerical classification. Most of the recorded variables, including nutrient amounts (kg ha–1), were examined in site quality (fertility) classes by succession phases as well. Border variants or transitional forms of the site types were common. Additional vegetation criteria (e.g. surface-water influence) more closely defined the ecology of the site. In addition to the site quality classes, a considerable amount of information about the tree stands, vegetation diversity and peat properties was associated with the separation of the succession phases, i.e. in this study transforming (phase II) vs. transformed (final phase III) sites. In conclusion, the actual vegetation appeared to well reflect various aspects of the ecological conditions, even in labile communities of commercial forests on drained peatlands.

SELECTIVE LOGGING EFFECTS ON ABUNDANCE, DIVERSITY, AND COMPOSITION OF TROPICAL UNDERSTORY HERBS

Little is known about the impacts of selective logging on herbaceous plants of tropical forests. If logging impacts on nontimber species are low and little time is required for recovery, logged forests could be compatible with conservation of some elements of the understory flora. As many nontimber species may have commercial value, knowledge about the impacts of different logging intensities is necessary to determine levels of timber extraction compatible with multiple use of forests. In this study, we examined the effects of logging intensity, time after logging, and skidder tracks, on the composition and diversity of the ground-level herb community of a terra-firme forest in central Amazonia. Logging was carried out at varying intensities in eight 4-ha experimental plots in 1987, three plots in 1993, and five plots were controls. Herb community composition, analyzed with hybrid multidimensional scaling (HMDS), was not significantly affected by logging intensity, but was significantly related to the are...

Vegetation Responses following Wildfire on Grazed and Ungrazed Sagebrush Semi-Desert

A 20-year set of cover data on sagebrush semi-desert plant communities responding to wildfire and livestock grazing near Mills in central Utah provided an opportunity to compare the assumptions and adaptability of classical and state-and-transition models for describing secondary succession. Cover data were organized and analyzed by plant species, growth forms, and other ground cover classes. Graphical analysis, ordination (employing semi-strong hybrid multi-dimensional scaling), regression, and analysis-of-variance were used to determine whether the patterns observed were best described as community change (tightly linked species) or individualistic change (each species acting independently). Distinct differences in total plant cover, growth form, and species composition were found between burned (both grazed and ungrazed) and the unburned and grazed treatments. Conventional graphical and statistical analyses of burned and ungrazed plots showed greater and earlier expansion of perennial grasses and then relatively less cover-weighted compositional change in recent years compared to the other treatments. Vegetation on none of the treatments appears to have stabilized toward either the pre-burn sagebrush semi-desert, a new state or the potential natural community for the site involved. Pathways of change reflected in the ordinations have been complex in all treatments. The only obvious trends in responses of individual species were to fire and the inverse relationship of cheatgrass to total perennial vegetational cover. All this evidence points to few tight linkages between species or growth form groups and thus favors viewing these patterns individualistically. While the state-and-transition model allows greater flexibility than the classical model in the depiction of plant community/individual species changes consequent to any management action, it doesn't apply readily everywhere, as exemplified by this case study. DOI:10.2458/azu_jrm_v55i2_west

Vegetation responses following wildfire on grazed and ungrazed sagebrush semi-desert

A 20-year set of cover data on sagebrush semi-desert plant communities responding to wildfire and livestock grazing near Mills in central Utah provided an opportunity to compare the assumptions and adaptability of classical and state-and-transition models for describing secondary succession. Cover data were organized and analyzed by plant species, growth forms, and other ground cover classes. Graphical analysis, ordination (employing semi-strong hybrid multi-dimensional scaling), regression, and analysis-of-variance were used to determine whether the patterns observed were best described as community change (tightly linked species) or individualistic change (each species acting independently). Distinct differences in total plant cover, growth form, and species composition were found between burned (both grazed and ungrazed) and the unburned and grazed treatments. Conventional graphical and statistical analyses of burned and ungrazed plots showed greater and earlier expansion of perennial grasses and then relatively less cover-weighted compositional change in recent years compared to the other treatments. Vegetation on none of the treatments appears to have stabilized toward either the pre-burn sagebrush semi-desert, a new state or the potential natural community for the site involved. Pathways of change reflected in the ordinations have been complex in all treatments. The only obvious trends in responses of individual species were to fire and the inverse relationship of cheatgrass to total perennial vegetational cover. All this evidence points to few tight linkages between species or growth form groups and thus favors viewing these patterns individualistically. While the state-and-transition model allows greater flexibility than the classical model in the depiction of plant community/individual species changes consequent to any management action, it doesn't apply readily everywhere, as exemplified by this case study.

Floristic description and environmental relationships of Tasmanian Sphagnum communities and their conservation management

A floristic data set spanning 15 years was compiled from vegetation surveys of Sphagnum peatlands across Tasmania. The data were ordinated by hybrid multi-dimensional scaling and a three-dimensional solution was most satisfactory. The strongest floristic gradient corresponded to changes in altitude and moisture. Original data were included from Sphagnum peatlands outside their commonly recorded altitudinal, geologic and geographic ranges. Several new types of Sphagnum peatland are described. While many of Tasmania’s subalpine and alpine Sphagnum peatlands are protected within reserves, this is not the case for montane and lowland Sphagnum peatlands. During the past decade, the pressure on Sphagnum peatlands outside the Tasmanian reserve system has continued to increase. Threats such as Sphagnum-moss harvesting, peat mining, burning, grazing and forestry operations have an impact on both the number and condition of Sphagnum peatlands.

Ecoregions and benthic macroinvertebrate assemblages of Swedish streams

A total of 694 streams was sampled for benthic macroinvertebrates in the autumn of 1995 as part of the Swedish national stream survey. After removal of sites considered to be impacted, 428 streams were available to test a geographical classification of benthic macroinvertebrates using ecoregions. Cluster analysis, semi-strong hybrid multidimensional scaling, and a permutation test procedure were used to investigate if the 6 main ecoregions of Sweden could be a useful tool to partition the species variance of benthic assemblages. Taxon richness, abundance, and diversity differed between ecoregions, with the main difference occurring in the northern part of the country where the arctic–alpine region had lower taxon richness, number of individuals, and Shannon–Wiener diversity than the southern parts of the country. The permutation test of assemblage composition and the comparison of the flexible β unweighted pair-group method using arithmetic averages (UPGMA) cluster groups with the ecoregion classification also showed significant differences between the arctic–alpine and the boreal, boreonemoral, and nemoral regions. Despite this result, the benefit of an ecoregion classification for biomonitoring of streams using macroinvertebrates is not convincing because there is a gradual change in macroinvertebrate assemblage composition from north to south. Benthic macroinvertebrate stream assemblages are structured both by large-scale factors (i.e., on a geographical scale), and by small-scale factors (i.e., on a local scale). Ecoregion classifications alone, therefore, may not sufficiently partition variance in assemblage composition, and a nested approach, including other factors such as altitude, stream size, and catchment characteristics, is probably needed to improve ecoregion classifications and biological assessments that use stream benthic macroinvertebrates.

Classification of macroinvertebrate communities across drainage basins in Victoria, Australia: consequences of sampling on a broad spatial scale for predictive modelling

Summary1. Spatial scale may influence the interpretation of environmental gradients that underlie classification and ordination analyses of lotic macroinvertebrate communities. This could have important consequences for the spatial scale over which predictive models derived from these multivariate analyses can be applied.2. Macroinvertebrate community data (identified to genus or species) from edge and main‐channel habitats were obtained for sites on rivers from 25 of the 29 drainage basins in Victoria. Trends in community similarity were analysed by carrying out separate multivariate analyses on data from the edge habitats (199 sites) and the main‐channel habitats (163 sites).3. Hierarchical classification (UPGMA) showed that the edge data could be placed into 11 site groups and the main‐channel data into 12 site groups.4. Ordination analysis (hybrid multidimensional scaling) showed no sharp disjunctions between site groups in either habitat; overlap was frequent. Correlation of the ordination patterns with environmental variables showed that edge communities varied longitudinally within a drainage basin and from the east to the west of Victoria. These two trends were superimposed on one another to form a single gradient on the ordination. The taxon richness of edge communities was also related to the species richness of macrophytes at a site. Main‐channel communities also displayed a longitudinal and a geographic gradient, but these two gradients were uncorrelated on the ordination.5. Community similarity only weakly reflected geographic proximity in either habitat. A preliminary subdivision of Victoria into a series of biogeographic regions did not match the pattern of distribution of site groups for the edge habitat, illustrating the difficulties of applying to lotic communities a priori regionalizations based on terrestrial features of the landscape.6. The longitudinal gradients in the two data sets were commonly observed in data gathered at smaller spatial scales in Victoria. The other gradients (geographic, macrophyte), however, were either not consistently repeated or not evident at smaller spatial scales. At small spatial scales (i.e. within a single drainage basin) gradients were related to variables that varied over restricted ranges, e.g. mean particle size of the substratum.7. Species richness was very variable when plotted against river slope or distance of site from source; both of these are measures of position on the longitudinal gradients. In contrast to suggestions in the literature, species richness did not show a unimodal trend on these gradients, or any other trend.8. Environmental gradients (apart from longitudinal gradients) that underlie predictive models of macroinvertebrate distribution are reflections of the spatial scale on which the model has been constructed and cannot be extrapolated to different scales. Models must be suited to the spatial scale over which predictions are required.