Multi-trait point pattern reconstruction of plant ecosystems

1. Plants interact locally in many ways and the processes involved (e.g. competition for resources, natural regeneration, mortality or subsequent succession) are complex. These processes give rise to characteristic spatial patterns that vary over time. The corresponding spatial data, that is the locations of individuals and their specific characteristics (e.g. trees of a certain species and their diameters), are known as point patterns, and their statistical analysis can be used to study the underlying processes and their changes due to environmental scenarios. A special application of point pattern analysis is their numerical reconstruction, which is classically used (a) to generate null models that can be contrasted with observed patterns and (b) to evaluate the information contained in observed data using various summary statistics. Sometimes, the reconstructed datasets are also used to initialise individual-based or agent-based plant models with realistic but artificially generated data in order to analyse or forecast the development of plant systems.2. Previous reconstruction methods of point patterns consider only one mark, or they consider several marks but neglect their correlations. We introduce a method that considers individual locations and two marks simultaneously (in our example information on tree species, and diameter at breast height). The method uses different summary statistics of the second-order point pattern analysis, such as the pair correlation function and the mark correlation function. By successively modifying the reconstructed spatial pattern, the distance (also called energy), measured in terms of differences in the summary statistics between the generated pattern and the observed pattern, is minimised and a high statistical similarity is achieved.3. After testing the method on different datasets, the suitability of our method for reconstructing complex spatial forest stands, including the spatial relationships of all considered marks, is shown.4. The presented method is a powerful tool for generating point pattern data. With minor changes, it even enables the reconstruction of forest stands and plant systems larger than those used to collect the inventory data, and although we used two marks only to demonstrate the power of the method, it is easy to include more marks.