Fundamentals: Maps as Outcomes of Processes

Spatial analysis investigates the patterns that arise as a result of spatial processes, but we have not yet defined either of these key terms.

Here, the rather circular definition, "A spatial process is a description of how a spatial pattern might be generated" is offered. This emphasizes how closely interrelated the concepts of pattern and process are in spatial analysis. In spatial analysis, you don't get patterns without processes. This is not as odd a definition as it may sound. In fact, it's a fairly normal reaction when we see a pattern of some sort, to guess at the process that produced it.

A process can be equally well described in words or encapsulated in a computer simulation. The important point is that many processes have associated with them very distinct types of pattern. In classical spatial analysis, we make use of the connection between processes and patterns to ask the statistical question, "Could the observed (map) pattern have been generated by some hypothesized process (some process we are interested in)?"

Measuring event intensity and distance methods (section 8.3) and statistical tests of point patterns (section 8.4)

These sections are intended to show you that for at least one very simple process (a completely random process), it is possible to make some precise mathematical statements about the patterns we would expect to observe. This is especially important because human beings tend to have a predisposition to see non-random patterns, even if there is no pattern.

Don’t get bogged down with the mathematics involved. It is more important to grasp the general point here than the particulars of the mathematics. We postulate a general process, develop a mathematical description for it, and then use some probability theory to make predictions about the patterns that would be generated by that process.

In practice, we often use simulation models to ask whether a particular point pattern could have been generated by a random process. The independent random process (IRP), also described as complete spatial randomness (CSR), has two requirements:

• an event must have an equal likelihood of occurring in any location; and
• there must be no interactions between events.

The discussion of first- and second-order effects in patterns is straightforward. Perhaps not so obvious is this: complete spatial randomness (i.e., the independent random process) is a process that exhibits no first- or second-order effects. In terms of the point processes discussed above, there is no reason to expect any overall spatial trend in the density of point events (a first-order effect), nor is there any reason to expect local clustering of point events (a second-order effect). This follows directly from the definition of the process: events occur with equal probability anywhere (no trend), and they have no effect on one another (no interaction).

Stochastic processes in lines, areas, and fields

The basic concept of a random spatial process can be applied to other types of spatial object than points. In every case, the idea is the same. Lines (or areas or field values) are randomly generated with equal probability of occurring anywhere, and with no effect on one another. Importantly, the mathematics become much more complex as we consider lines and areas, simply because lines and areas are more complex things than points!