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.