Strategies for Modeling Regeneration Density in Relation to Distance from Adult Trees

Research Highlights: We proposed new methodologies for the spatial analysis of regeneration processes and compared with existing approaches. Background and Objectives: Identifying the spatial relationship between adult trees and new cohorts is fundamental to understanding the dynamics of regeneration and therefore helps us to optimize the stand density and natural regeneration when undertaking regeneration fellings. Most of the statistical approaches analyzing the spatial dependence between adult trees and new individuals (seedlings or saplings) require a complete census and mapping of all individuals. However, approaches considering individuals grouped into sampling points or subplots (i.e., density data) are limited. In this study, we reviewed and compared approaches (intertype point pattern analyses and a generalized additive model) to describe the spatial relationship between adult trees and density regeneration in a Pinus sylvestris L. monospecific stand in Spain. We also proposed a new approach (intertype mark variance function) to disentangle the effect of the tree-size on sapling density and the effect of the spatial pattern. Materials and Methods: To this end, we used a half-hectare plot in which all the individuals of P. sylvestris have been mapped and measured. Results: Our results indicated that sapling distribution was related to distance from the adult trees, thus displaying distance-dependence patterns, but it was not related to the size of the adult trees. The intertype mark correlation function was an useful tool to distinguish the effect of the marks (sapling density and tree size) from the effect of the spatial pattern of the classes (trees cohorts in our case). Conclusions: The largest number of saplings was found with increased distance between adult trees (>11 m), and the generalized additive model may be useful to explain spatial relationships between adult trees and regenerating cohorts when other measured biotic variables (e.g., soil stoniness, etc.) and repeated measurements are available.