A1 Spreadsheets

Almost all small data sets used to illustrate the functioning of methods eventually passed though Excel, for either data input, simple analyses or data presentation. In spreadsheets, data are usually organized as shown in Figure 2.8; that is, in a single data matrix with releves organized in columns and species and environmental variables in rows. For import and export into other programs I used commas, semicolons or tabulators separating data fields, which are accepted by almost all databases and statistical packages. The tasks I have conducted using spreadsheets are:

• Plotting scatter diagrams (ordinations). Excel offers sufficient formatting options for graphs and all are set automatically. Subsequent manual formatting is needed as ordination axes x and y must be identically scaled and this is achieved only when manually setting the range of the axes and the width and height of the graphs.

• Plotting bubble graphs to display within- and between-group similarities (Figures 4.5 and 11.8), illustrating change of similarity in time series (Figures 9.2) and ordinations of time series exhibiting velocity (Figures 9.16) or acceleration (Figures 9.18). Three vectors are needed for input: x-axis, y-axis and the diameter of the bubbles.

• Numerically integrating differential equations for dynamic modelling. All models presented in Section 10.1 are implemented in Excel. A column is chosen for each state variable; that is, X1, X2, as well as its derivative SX1/St, SX2/St. For time step t = 0 the initial values are written in a row; in the following row the formula for deriving the state at t = 1 is entered. Dragging these cells down by, for example, 100 rows reveals the state of the system at t = 100. Increasing complexity of dynamic models, however, limits the application of spreadsheets.

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