Water depth history
An individual species can not live everywhere: it is constrained by its physical environment. We see this every day in our own lives - cattails are limited to the water's edge, while oaks are restricted to drier land. The same is true in the marine realm, and has been true throughout geologic time.
We can see the effects of this in the geologic record. Species are not found randomly, but in groups we call communities, defined by paleontologists by the most common and dominant species found in the group. Once several samples of a community have been collected, the paleontologist can pretty well predict what species will be present from a cursory examination of the rocks, and these predictions are usually borne out with further examination.
A basic question in the study of both ancient and modern communities is whether they respond to the environment as a community, or if each species responds as an individual. There are reasons to believe both, but much evidence supports the individualistic philosophy.
If species reflect the environment, then the abundance of the species should be a measure of the environment. There is a set of mathematical techniques called "ordination methods", which attempt to do just that. The gradients could be many things - temperature, salinity, turbidity, depth, etc. When the techniques are applied, the data reveal clear patterns in time and space.
One of the most powerful of these ordination techniques is reciprocal averaging, or correspondence analysis. The data from the Mohawk River Valley has been analyzed with this technique (actually, a subtle variant of the technique, called detrended correspondence analysis). The gradient illustrated here is the most prominent. The color panels on the lower part of the screen indicate the range of scores, from low (shallow) on the left, to high (deep) on the right.
The trend in ordination scores parallel what one would expect for water depth in the deposits, and can be used as precise measure of water depths. The paleocurrent indicators support this interpretation.