Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.defuzzification, fuzzy coding, indicator matrix, measure of fit, multivariate data, multiple correspondence analysis, principal component analysis.

A Geneaology of Correspondence Analysis: Part 2 - The Variants

In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Australian and New Zealand Journal of Statistics. That genealogy consisted of more than 270 key books and articles and focused on an historical development of the correspondence analysis,a statistical tool which provides the analyst with a visual inspection of the association between two or more categorical variables. In this new genealogy, we provide a brief overview of over 30 variants of correspondence analysis that now exist outside of the traditional approaches used to analysethe association between two or more categorical variables. It comprises of a bibliography of a more than 300 books and articles that were not included in the 2012 bibliography and highlights the growth in the development ofcorrespondence analysis across all areas of research

Dynamics of phytoplankton community composition in the western Gulf of Maine

This dissertation is founded on the importance of phytoplankton community composition to marine biogeochemistry and ecosystem processes and motivated by the need to understand their distributions on regional to global scales. The ultimate goal was to predict surface phytoplankton communities using satellite remote sensing by relating marine habitats--defined through a statistical description of environmental properties--to different phytoplankton communities. While phytoplankton community composition is governed by the interplay of abiotic and biotic interactions, the strategy adopted here was to focus on the physical abiotic factors. This allowed for the detection of habitats from ocean satellites based on abiotic factors that were linked to associated phytoplankton communities. The research entailed three studies that addressed different aspects of the main goal using a dataset collected in the western Gulf of Maine over a 3-year period. The first study evaluated a chemotaxonomic method that quantified phytoplankton composition from pigment data. This enabled the characterization of three phytoplankton communities, which were defined by the relative abundance of diatoms and flagellates. The second study examined the cycles of these communities along with environmental variables, and the results revealed that the three phytoplankton communities exhibited an affinity to different hydrographic regimes. The third study focused on the implementation of a classifier that predicted phytoplankton communities from environmental variables. Its ability to differentiate communities dominated by diatoms versus flagellates was shown to be high. However, the increase in data imprecision when using satellite data led to lowered performance and favored an approach that incorporated fuzzy logic. The fuzzy method is well suited to characterize the uncertainties in phytoplankton community prediction, and provides a measure of confidence on predicted communities. The final product of the overall dissertation was a time series of maps generated from satellite observations depicting the likelihood of three phytoplankton communities. This dissertation reached the main goal and, moreover, demonstrated that improvements in the predictive power of the method can be achieved with increased precision and more advanced satellite-derived products. The results of this research can benefit present bio-optical and primary productivity models, and ecosystem-based models of the marine environment

Beyond tandem analysis: Joint dimension reduction and clustering in R

We present the R package clustrd which implements a class of methods that combine dimension reduction and clustering of continuous or categorical data. In particular, for continuous data, the package contains implementations of factorial K-means and reduced K-means; both methods combine principal component analysis with K-means clustering. For categorical data, the package provides MCA K-means, i-FCB and cluster correspondence analysis, which combine multiple correspondence analysis with K-means. Two examples on real data sets are provided to illustrate the usage of the main functions

Climate analogues: A method to assess the potential impact of climate change on Natura 2000 habitat diversity at the regional scale

The need and will to mitigate and adapt to climate change and its threats to biodiversity have risen. Nevertheless, the acting for the conservation of biodiversity remains hampered by knowledge gaps. E.g., for habitat types (in the sense of biotopes) the impact of climate change has been scarcely researched. There are many “species distribution models” (SDMs) that can project species distributions under climate change, but their application to contemporary habitat types poses considerable methodological problems. Here we show the viability of the uncommon method of “climate analogues” to provide data to assess the potential impact of future climate change on habitat types for chosen regions, and the usability of the method compared to SDMs. We assume climate analogues can reflect the potential future habitat data in the study regions when (1) plausibly located future climate analogues are found with relevant climate variables for the studied habitat types, and (2) habitat occurrences relate with their frequency and area to the climate reflected in the climate analogues. We tested the method for three landscapes in Germany using European Natura 2000 habitat data, analyzing five future climate conditions until 2100. Future climate analogues were found southwest of the study regions, primarily in France. They progressed further southwest and from higher to lower elevations with increasing climate change. Ecologically sound habitat types remained stable, increased, and decreased in frequency and area parallel to the magnitude of climate change in the climate analogues. Thus, we regard climate analogues as a viable method to estimate potential climate change induced changes of Natura 2000 habitat types at the regional scale. Nature conservation benefits from climate analogues as they are efficient, data-robust, and promote the implementation of actions, the exchange of conservation experiences, and international collaboration. They are an easy and powerful method to tackle the looming losses of habitat diversity from climate change

MultipleCar: A Graphical User Interface MATLAB Toolbox to Compute Multiple Correspondence Analysis

In this paper we present the toolbox MultipleCar, which is a general program for computing multiple correspondence analysis and which was designed using a graphical user interface. The procedures implemented in MultipleCar are the usual ones that are already available in other applications, plus some additional procedures. MultipleCar makes it possible to compute (1) joint correspondence analysis, and (2) orthogonal and oblique rotation of coordinates. Although MultipleCar was developed in MATLAB, we compiled it as a standalone application for Windows operative systems based on graphical user interfaces. The users can decide whether to use the advanced MATLAB version of MultipleCar, or the standalone version (which does not require any programming skills)

Can a piscicide treatment alter stream ecosystem functioning through trophic cascading effects on benthic invertebrates?

Processing of detritus is an important ecosystem function in freshwaters. In rivers and streams, the activity of shredding invertebrates play an important role in processing of coarse-particulate organic matter such as leaf litter. In stream food webs, fish may act as top predators and control activity of consumers such as shredders top down. This top-down effect may be of a directly consumptive nature, or indirect and mediated by species traits. Most studies on trophically cascading effects in stream ecosystems are done in small scale, either in small laboratory setups, or in in-stream experimental units such as cages or flow through channels. These setups are very useful in exploring specific effects and relationships, but might not be adequate to document effects on whole stream or catchment scale. I utilized a management-imposed rotenone treatment of the sub-arctic watercourse Skibotn catchment in Troms, northern Norway, as a setup for a large scale field experiment. Using pairs of coarse- and fine-meshed plastic litter bags filled with dry birch ( Betula pubescens ) leaf litter, I measured decomposition rates ( kd − 1 ), and collected and identified leaf litter colonizing invertebrates in riffle habitats in the autumn one year before (2014), and one year after (2017) the treatment. Nordkjos catchment, an untreated catchment in the adjacent area, was studied simultaneously. Shredding invertebrates contributed to litter decomposition in both years in all but one stream, but I found no significant change in invertebrate-mediated decomposition between the two years on catchment scale. There was no marked change in density or diversity of invertebrates in the litter bags between the two years, while fish had a diverse diet dominated by Baetid mayflies. However, young of the year salmonids were present already in a few sites after the treatment. Results of this field experiment indicate that fish did not have a strong top-down effect on shredding invertebrates in Skibotn catchment. The most likely explanation is that fish densities were low and their diets were not dominated by the most important shredder species. The studied streams are heterogenic environments and subject to natural stochasticity that might outweigh any small ecological effects, emphasizing the importance of good background data when performing before- after- impact control studies

Differences in biological traits composition of benthic assemblages between unimpacted habitats

There is an implicit requirement under contemporary policy drivers to understand the characteristics of benthic communities under anthropogenically-unimpacted scenarios. We used a trait-based approach on a large dataset from across the European shelf to determine how functional characteristics of unimpacted benthic assemblages vary between different sedimentary habitats. Assemblages in deep, muddy environments unaffected by anthropogenic disturbance show increased proportions of downward conveyors and surface deposit-feeders, while burrowing, diffusive mixing, scavenging and predation traits assume greater numerical proportions in shallower habitats. Deep, coarser sediments are numerically more dominated by sessile, upward conveyors and suspension feeders. In contrast, unimpacted assemblages of coarse sediments in shallower regions are proportionally dominated by the diffusive mixers, burrowers, scavengers and predators. Finally, assemblages of gravelly sediments exhibit a relatively greater numerical dominance of non-bioturbators and asexual reproducers. These findings may be used to form the basis of ranking habitats along a functional sensitivity gradient

A methodology for landscape characterisation based on GIS and spatially constrained multivariate analysis

Landscape is about the relationship between people and place and in 2000 was defined by the European Landscape Commission (ELC) as "an area as perceived by people whose character is the result of natural and human actions and interactions”. In the 70s the reason for studying the landscape was because of the necessity of attributing a value to it. Nowadays the motivations behind managing, conserving and enhancing the landscape is because the landscape is the place where people belong to and, consciously or not, recognise themselves. In addition, people identify different landscapes on the basis of the particular combinations of the elements in the landscape. As a consequence a landscape can be distinguished from another on the basis of its character which, according to the Landscape Character Assessment (LCA) guidance for England and Scotland (C. Swanwick and Land Use Consultant, 2002), is defined as “a distinct, recognisable and consistent pattern of elements in the landscape that makes one landscape different from the other rather than better or worse”. This definition was the starting point of a PhD research project aimed at developing and implementing a methodology able to identify and quantify the character of the Scottish landscape through the application of GIS and statistics. The reason for doing this research was to provide the landscape architects and practitioners with a tool that could help them to define the landscape character types in a more consistent, objective, and scientifically robust way. One of the objectives of the research was to identify the spatial patterns formed by the landscape elements by taking into account the influence of the spatial location. The first law of geography, which states that "everything is related to everything else but near things are more related than distant ones" (W Tobler, 1970), was transposed in the assumption of the presence of spatial autocorrelation amongst the data which contributes to form spatial patterns within the data. Since landscape comprises of many elements, data were also multivariate, thus the analysis required a method of calculation able to deal simultaneously with multivariate and spatial autocorrelation issues. MULTISPATI-PCA, a spatially constrained Principal Component Analysis, was the statistical technique applied for the analysis of the data whose results showed that it was possible to detect the spatial structure of the data and that each spatial pattern corresponded to a distinct landscape. Despite their importance in forming the character of the landscape, aesthetic and perceptual aspects were not inlcuded in MULTISPATI-PCA analysis. It was preferred to test the technique only on data that were quantifiable in a more objective way. Perhaps taking into account the human perception of the landscape can be the starting point for future investigation