Technical advances in recent decades have made it possible to collect data on the spatial locations of individual animals or plants, and spatially explicit data-sets have become commonly available. This enables us to consider the locations of individuals directly and analyse patterns formed by the locations of individuals in space, so-called spatial point patterns.
The statistical representation of these is a spatial point process, which models the spatial location of individuals or groups of individuals in space, for example to help us understand the spatial distrbution of plants or habitat preferences of a specific animal species. It is, hence, another type of a spatial model
The long equation across the tree trunc is used in the context of point process analyses. It is the likelihood for the Poisson point process model.
For a two-dimensional point process, not only the total number of occurrence (number of points) is random, the location where each point occurred is also a random variable. The spatial arrangement of the set of points can be viewed as a map of locations, referred to as a point pattern. (That is why I decided to paint the tree trunc with a point pattern.) The aim of point pattern analysis is to estimate the intensity function of the point process, from which we can infer the spatial arrangements of points.
Point process models have been widely used for modelling forests (see our page on trees), earthquakes and animal distributions. For example, clustered point process models are used to model animals that tend to appear in groups and marked point process models for rain forest where the height of trees is considered as a mark.
The tree is painted here as a point pattern as different trees in the forest form a point pattern that we study using point process models.
Brown et al. 2013: Multispecies coexistence of trees in tropical forests: spatial signals of topographic niche differentiation increase with environmental heterogeneity. Proceedings of the Royal Society B.Point pattern analysis for blue whales:
Y. Yuan, F. E. Bachl, F. Lindgren, D. L. Brochers, J. B. Illian, S. T. Buckland, H. Rue, T. Gerrodette. Accepted: Point process models for spatio-temporal distance sampling data. Annals of Applied Statistics