Effects, Firstand Second-Order

First-Order Effects

First-order effects are best understood by reference to a pattern of individual point events making up a dot map. First, variations in the receptiveness of the study area may mean that the assumption of equal probability of each area receiving an event made in defining CSR cannot be sustained. For example, if the “events” are trees of a certain species, then almost certainly they will have a preference for patches of particular soil, with the result that there is a clustering of such trees on the favored soils at the expense of the less favored. Similarly, in a study of the geography of a disease, point objects representing the locations of cases naturally will cluster in more densely populated areas. This type of process takes place in space but does not contain within itself any explicit spatial ordering. The results are first-order effects.

First-order properties of point and area processes are thus the expected values that arise when indices associated with the individual points or areas in a study region are calculated. A simple example of such a property is the intensity of a point process, which is the limit as the area over which it is calculated tends to zero of the familiar point density. In other words, it is the spatial density, measured as the “number of points per unit of area.” In GIS, first-order effects are detected by the presence of spatial variation in the density, estimated and visualized using quadrat analysis or kernel density estimation.

Second-Order Effects

It may also be that the second assumption made in defining CSR, that event placements are independent of each other, cannot be sustained. This generates second-order effects. Second-order properties describe the covariance (or correlation): how the intensity of events varies together over space. A simple example of a second-order property is the distance between events in a point pattern.

In general, two such departures from independence are seen. If the existence of an event at one place makes it less likely that other events cluster around it, [Page 123]this gives a tendency toward uniformity of spacing and a pattern that is more regular than random. An example might be the distribution of market towns, each of which for its survival requires access to a population of potential customers spread over some minimum area.

Alternatively, other processes involve aggregation or clustering mechanisms whereby the occurrence of one event at a particular location increases the probability of other events being located nearby. The pattern will be more aggregated/clustered than random. Examples include the distribution of cases of contagious diseases, such as foot-and-mouth disease in cattle or tuberculosis in humans, or the diffusion of an innovation through an agricultural community, where farmers are more likely to adopt new techniques that their neighbors have already used with success. Typically, such a process will have within it a mechanism that causes spatial patterning, such as a distance decay in the interaction between events. It is not simply a process taking place in a heterogeneous space, but a true spatial process that will create a pattern even if the study region is itself homogeneous.

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