Does competition prevail in large size classes of trees in tropical forests? This question is fundamental to our understanding of the demography and dynamics occurring in rain forests. We investigated this question based on an undisturbed late-secondary forest on a 1-ha plot in central Cameroon. Trees were stem-mapped and classified into three size classes: understorey, midstorey and overstorey. The diameter at breast height and yearly biomass increment were determined as measures of plant growth and performance. Spatial statistics such as pair- and mark-correlation functions were used to detect scale-dependent patterns that could be caused by competition within and between the three size classes. The results revealed a random pattern and spatially uncorrelated measures of plant growth of overstorey trees. This suggests that competitive effects are of minor importance in the large size class of overstorey trees. Likewise, only weak evidence for competition between trees was found within the two lower size classes. However, negative distance correlations were found between the different size classes. We suggest that competition within height classes was relatively low due to the diversity of species with their variable niche differentiations and phenotypic plasticity that may compensate for competitive effects.

The point process of vertices of an iteration infinitely divisible or, more specifically, of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation function, as well as the cross-covariance measure and the cross-correlation function of the vertex point process and the random length measure in the general nonstationary regime. We also give special formulae in the stationary and isotropic setting. Exact formulae are given for vertex count variances in compact and convex sampling windows, and asymptotic relations are derived. Our results are then compared with those for a Poisson line tessellation having the same length density parameter. Moreover, a functional central limit theorem for the joint process of suitably rescaled total edge counts and edge lengths is established with the process (ξ, tξ), t > 0, arising in the limit, where ξ is a centered Gaussian variable with explicitly known variance.