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The use of STATICO and COSTATIS, two exploratory three-ways analysis methods: an application to the ecology of aquatic heteroptera in the Medjerda watershed (Tunisia)

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Abstract

This article is intended as a guideline to the use of two exploratory data analysis methods, namely STATICO and COSTATIS. Both techniques have already been used in the field of ecological data analysis, and we present a rapid survey of the ecological literature on three-ways analysis methods. Here, we wish to share some advanced computation and graphical display scripts to help ecologists use these methods. We first recall the main principles of these two methods for the analysis of the relationships between the structures of two series of data tables. In the context of ecology, these two series can be for example (1) a series of species data tables and (2) a series of environmental parameters tables. A detailed, real-size example is presented to show how this strategy can be put in place using the ade4 and adegraphics packages for R. This example relates to the ecology of aquatic Heteroptera in the Medjerda watershed (Tunisia). We show how the outputs of the two methods can be used to interpret the relationships between aquatic Heteroptera species distribution and environmental parameters. Several R scripts to conduct the computations and draw suitable graphical displays are reproduced and explained in the text and in five appendices.

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Acknowledgements

This study was funded by the cooperation program CNRS/DGRST \(\hbox {n}^{\circ }\) 15/R0902 between France and Tunisia. This study was also funded by the Ministry of High Education and Scientific Research of Tunisia. The sampling survey of 2013 was supported by the Laboratory of Hydrobiology of the Faculty of Sciences in Bizerta. We thanks Mr. Abdessalem Ben Hhaj Amara the dean of the Faculty of Sciences in Bizerta, Khalfallah Taoufik, the general secretary, Gharsallah Hafida, director of the financial service, Hamrouni Nizar, Rzeigui Mourad and the members of this service. We also thank Béjaoui Mustapha, Boughdiri Mabrouk for fruitful collaboration. We thank the associate editor and the two reviewers for many useful comments and corrections.

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Authors and Affiliations

  1. Unit of Hydrobiology, Laboratory of Environment Biomonitoring, Faculty of Sciences of Bizerta, University of Carthage, 7021, Jarzouna, Tunisia

    Noura Slimani & Moncef Boumaiza

  2. UMR7179 CNRS/MNHN, Muséum National d’Histoire Naturelle, CP50, 57 rue Cuvier, 75005, Paris, France

    Noura Slimani & Eric Guilbert

  3. Centre International des Technologies de l’Environnement, Boulevard du Leader Yasser Arafat, 1080, Tunis, Tunisia

    Foued El Ayni & Amel Jrad

  4. Université de Lyon, CNRS, UMR 5558, Biométrie et Biologie Evolutive, 69622, Villeurbanne Cedex, France

    Jean Thioulouse

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  1. Noura Slimani
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  2. Eric Guilbert
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  3. Foued El Ayni
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  4. Amel Jrad
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  5. Moncef Boumaiza
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  6. Jean Thioulouse
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Correspondence to Jean Thioulouse.

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Appendices

Appendices

1.1 General plot of the STATICO method (Fig. 3)

This figure can be drawn with the generic plot function, but the version given here is enhanced to add colors and avoid label superimpositions. Note that this figure should be drawn in a square window to keep an appropriate height/width ratio.

figure f

Graph g11 is the correlation circle of the Interstructure (top left). The eigenvalues bar chart g12 of the Interstructure analysis is drawn with the plotEig function and inserted in the correlation circle graph with the insert function to obtain graph g1.

Graph g2 is the factor map of Compromise columns (bottom-left). It is drawn with the s.label function and label color is set to blue. The plabels.optim parameter is set to TRUE, which means that labels are arranged to minimize superimpositions.

Graph g31 is the factor map of Compromise rows (top-right). It is also drawn with the s.label function and label color is set to red. The eigenvalues bar chart g32 of the Compromise analysis is drawn with the plotEig function and inserted in graph 31 with the insert function to obtain graph g3.

Graph g4 is the plot of the “typological value” (squared cosines vs. weights) of the tables. It is drawn with the s.label function.

The four graphs are finally grouped using the ADEgS function to get the final Fig. gtot.

1.2 STATICO Intrastructure for environmental parameters and water bugs (Fig. 4)

This figure uses the facets argument to draw automatically the graphs corresponding to the environmental parameters and species at each date (12 months). The height/width ratio of the window in which this figure is drawn should be set to 1.5 to keep appropriate scales.

figure g

Four graph collections are drawn with the s.label and s.arrow function, using the facets argument: slE (labels) and saE (arrows) for environmental parameters (red labels), and slH (labels) and saH (arrows) for water bugs (blue labels).

Each collection is made of the 12 graphs corresponding to the 12 months with the facets argument and the TL or TC elements of the stat1 object. These elements contain factors defining to which month belongs each environmental parameter or each water bug species.

The collections of labels and arrows graphs are superimposed with the superpose function. They are then split in two (months January to June, and months July to December), and the positions of the elementary graphs corresponding to the 6 months are rearranged to place side by side the environmental parameters graph and the water bugs graph of each pair.

This rearrangement of elementary graph positions is done with the layout2position function. It allows an easier comparison of species and environmental parameters graphs month by month.

Both collections of graphs are grouped again using the ADEgS function and plotted side by side.

1.3 STATICO Intrastructure for the sampling sites (Fig. 5)

This figure also uses the facets argument to draw automatically the graphs corresponding to the sampling sites of the environmental parameters table and of the species data table at each date (12 months). The height/width ratio of the window in which this figure is drawn should be set to 1.5 to keep appropriate scales.

figure h

Intrastructure plot of the STATICO method for the sampling sites of the environmental parameters (top, red labels) and water bugs (bottom, blue labels).

In this figure, the facets argument of the s.traject and s.label functions is used to draw automatically collections of graphs. In these collections, each elementary graph corresponds to one table (i.e., one month). The selection of the rows that go into each graph is done with the stat1$supTI factor that is built during analysis computations.

The first collection of graphs (st1) is trajectory lines that links the 12 sites of the environmental parameters tables in the upstream-downstream order. The second collection (sla1) draws the site labels (1–12, in red). Both collections are superimposed with the superpose function, resulting in graph s1.

The same procedure is used for the 12 sites of the water bugs tables (with blue labels), resulting in graph s2. Graphs s1 and s2 are placed one under the other and plotted with function ADEgS.

1.4 General plot of the COSTATIS method (Fig. 6)

This figure can be drawn with the generic plot function, but the version given here is enhanced to add colors and avoid label superimpositions. This figure should be drawn in a square window to keep an appropriate height/width ratio.

figure i

There are six elementary graphs that correspond to several elements of the COSTATIS analysis numerical outputs.

The two correlation circles on the left of the figure show the projection of unconstrained axes in the Co-inertia factor map. They correspond here to the axes of the two separate PTA. They are drawn with the s.corcircle function and stored in objects g1 and g2. The eigenvalues bar chart is drawn with the plotEig function, giving object g3.

The main graph is graph g4. It is a special graph, drawn with the s.match function. This function takes two sets of coordinates for the same series of points and draws an arrow between each pair of coordinates. Here, the two series of coordinates are cost1$mX, the coordinates of the sites in the environmental parameters tables and cost1$mY, the coordinates of sites in the species tables. The twelve arrows are numbered 1–12 and correspond to the 12 sites (green labels).

The two graphs in the lower part of the figure are the graphs of water bugs and of environmental parameters. Each one is drawn with the s.arrow and s.label function resulting in objects g51 and g52 (water bug species, blue labels) and g61 and g62 (environmental parameters, red labels). The two graphs of each pair are superimposed with the + operator.

The final figure gtot is obtained by joining the six elementary graphs with the ADEgS function and a fixed layout that allocates more space to the main graph g4.

1.5 COSTATIS Intrastructure plot (Fig. 7)

This is a synthetic figure, showing the superimposition of the rows (sampling sites: 1–12) and columns (environmental parameters: red labels and water bugs: blue labels) of both series of tables. The height/width ratio of the window in which this figure is drawn should be set to 0.5 to keep appropriate scales.

figure j

This figure is composed of two graphs: the environmental parameters graph (left) and the water bugs graph (right). The limits of the four (scaled) coordinate vectors, cost1$supIX, cost1$c1, cost1$supIY and cost1$l1 are first computed to set the same limits for all the graphs.

The environmental parameters graph is the superimposition of three elementary graphs: sl1 (s.label function, red labels), sa1 (s.arrow function) for parameters, and sc1 (s.class function, green labels grouped by site) for sampling sites. These three graphs are superimposed with the superpose function to get the first part of the Fig. (ss1).

The water bugs graph is also the superimposition of three elementary graphs: sl2 (s.label function, blue labels), sa2 (s.arrow function) for Heteroptera species, and sc2 (s.class function, green labels grouped by site) for sampling sites. These three graphs are superimposed with the superpose function, leading to the second graph ss2.

Graphs ss1 and ss2 are grouped side by side with the ADEgS function to get the complete Fig. st1.

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Slimani, N., Guilbert, E., Ayni, F.E. et al. The use of STATICO and COSTATIS, two exploratory three-ways analysis methods: an application to the ecology of aquatic heteroptera in the Medjerda watershed (Tunisia). Environ Ecol Stat 24, 269–295 (2017). https://doi.org/10.1007/s10651-017-0370-6

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  • DOI: https://doi.org/10.1007/s10651-017-0370-6

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