Barriers to Making Order out of Chaos:

General Explanation of the Ordination Graph

This type of graph, called an ordination, is used to graphically show the predominant patterns of variation among individuals of a group. Let me generally explain how they are made. Admittedly, this explanation is over-simplified but is accurate enough to get the idea across. Several characters are measured for each specimen. They must all be continuous variables like size and weight, rather than discrete variables like color, texture, and so forth. Starting with one character, the specimens are spread along the first axis, not on a real graph but in the cyberspace of a computer. A second character is used to spread the data out in a second dimension or along the y axis. The third character spreads these points out along a third dimension. Since this is all happening in mathematical terms, the computer can handle as many dimensions as you like; n-dimensions, so now we have our specimens spread out in n-dimensional space. Imagine it being a cloud of points. The computer then looks through this cloud in various trajectories until it finds the one where the data is most spread out. This trajectory is not the same as the axes which were used to graph the data originally but it represents a combination of these characters. Once the computer finds this first trajectory, or vector, then the computer looks at right-angles to that vector for a second trajectory of maximum spread. The axes on this graph would be those first two vectors, each representing a mixture of characters. Some algorithms for performing ordinations are somewhat different using distance matrices between the points, but the result is basically the same.

That was the hardest concept in this website, so if you got through that we have it made.