Joint assessment of density correlations and fluctuations for analysing spatial tree patterns

Abstract

Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of tropical rainforests, as demonstrated, e.g. in the 50 ha tropical forest plot on Barro Colorado Island, Panama. These kinds of plots have been crucial to shed light on diverse qualitative features, emerging both at the single-species or the community level, like the spatial aggregation or clustering at short scales. Here, we build on the progress made in the study of the density correlation functions applied to biological systems, focusing on the importance of accurately defining the borders of the set of trees, and removing the induced biases. We also pinpoint the importance of combining the study of correlations with the scale dependence of fluctuations in density, which are linked to the well-known empirical Taylor’s power law. Density correlations and fluctuations, in conjunction, provide a unique opportunity to interpret the behaviours and, possibly, to allow comparisons between data and models. We also study such quantities in models of spatial patterns and, in particular, we find that a spatially explicit neutral model generates patterns with many qualitative features in common with the empirical ones.

Emergent spatial patterns of coexistence in species-rich plant communities

“…We found high clustering levels at short scales only at the scale-invariant regime, together with anomalous density fluctuations and fully compatible rank abundance distributions of species. Both quantities' joint assessment justifies the non-trivial emergent correlations among species and suggests the qualitative agreement of BCI data with the scale-invariant regime [20].…”

“…Some works have recently highlighted the ability of SENM to produce single-species patterns characterized by spatial density correlations and fluctuations in qualitative agreement with field data in the 50 ha tropical forest plot on Barro Colorado Island (BCI) [15,20,21]. In particular, the prevalence of tree clumping at smallscales together with anomalous spatial density fluctuations [20,22,23]. Nevertheless, the role of dispersion and immigration in maintaining the biodiversity richness and their effects in the emergent spatial point patterns remains an open question.…”

“…From a global perspective, we have made progress in developing a theoretical framework connecting spatial neutral models (subject to demographic fluctuations), ecological networks, and critical transitions, a pivotal challenge to understand the crucial interplay between ecological dynamics and species interactions [8,9]. In particular, we showed that SENMs are susceptible to reproduce most of the main features observed experimentally in natural rainforests: (i) The rank abundance distribution, (ii) high level of clustering at short scales [22], (iii) non-trivial spatial density fluctuations for local dispersal kernels [20], (iv) a modular-like Pearson's correlation matrix between species in the scale-invariant regime, (v) the emergence of scale-free distribution of clusters previously reported in Kalahari vegetation or tree-canopy gaps in BCI [26,27] and, (vi) to generate the specific spatial patterns leading to the coexistence mechanism of multiple species also existing in real forests [3].…”

“…Additional analyses of our theory have been done to test the replication ability of diverse empirical facts in Barro Colorado. In particular, we computed the pair correlation function, g(r), and the spatial density fluctuations, δ r n, along with its associated rank abundance curves (see SI4 and [20] for further explanations). We found high clustering levels at short scales only at the scale-invariant regime, together with anomalous density fluctuations and fully compatible rank abundance distributions of species.…”

Characterizing spatial point processes by percolation transitions

“…One of the main concerns to study the macroscopic properties of spatial point process requires to deal adequately with borders [62,63]. This issue usually involves two particular problems: knowing the boundaries, how to reduce the biases, and, more subtle, how to correctly identify the not convex borders of a set of points [42,64]. For instance, establishing proper boundaries is essential to avoid spurious behaviors from the pair correlation function and different spatial density-based measures [42].…”