Figure 1.12 Lakes interconnected by a river network (left) can be binary-coded as shown on the right.
Numbers are assigned in an arbitrary order to the edges (arrows) of the network. There is no use in representing the "root" of the network (arrow 0); all lakes would be coded '1' for that arrow.
arrow matrix, a value '1' is assigned to each arrow found downstream from the lake, meaning that the corresponding river segment is available for fish to reach that lake. All other arrows are coded '0' for the lake. The resulting matrix is a complete numerical coding of the hydrographic network information: knowing the coding procedure, one could reconstruct the picture from the matrix entries.
The coding method may be tailored to the ecological problem at hand. For a dispersion phenomenon going downstream, arrows could point the other way around; in this case, a lake would be coded '1' in the table for arrows arriving in that lake from upstream. The pattern of interconnections does not even need to be a tree-like structure; it may form a more general type of directed network, but note that no cycle is allowed. Coding the information allows the use of this type of geographical information in different types of numerical models, like multiple regression (Chapter 10) or canonical analysis (Chapter 11). In many of these methods, zeros and ones are interchangeable.
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